Practical Experiences and Mitigation Methods of Harmonics in Wind Power Plants

Published by Babak Badrzadeh, Senior Member, IEEE, and Manoj Gupta
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 49, NO. 5, SEPTEMBER/OCTOBER 2013

Abstract—This paper discusses practical experiences and mitigation methods of harmonics in wind power plants. Traces obtained from harmonic measurements of actual wind turbines are presented for the type 3 and type 4 turbines, and the harmonic performances of these wind turbines are elaborated on. Simulation case studies obtained from the harmonic analysis of various practical wind power plants are presented. The case studies presented include both resonance and nonresonance conditions. Finally, practical harmonic mitigation techniques including harmonic filtering and harmonic compensation are discussed.

Index Terms—Harmonic emission, harmonic mitigation, harmonic modeling and simulation, harmonic resonance, harmonic susceptibility, power system harmonics, wind power plants.

I. INTRODUCTION

This paper discusses practical experiences and mitigation methods of harmonics in wind power plants (WPPs). The modeling methodology for the wind turbine and balance of plant components and the required analysis techniques for the WPPs have been discussed in [1].

Harmonics generated by voltage source converter (VSC)- based wind turbine generators (WTGs) do not remain constant but vary according to the converter control and the switching scheme. The harmonic signature of these devices cannot therefore be predicted by mathematical equations such as the Fourier analysis. It is therefore necessary to investigate the harmonic profiles obtained from field measurements thoroughly such that some commonalities can be drawn for various turbine types and various operating conditions. Results obtained from field measurements of harmonic in WPPs have been discussed in a number of technical literatures [2]–[9]. All these papers, however, report the aggregate harmonic signature of the WPP. This will include the combined effect of the WTG and all other balance of plant components, which does not therefore provide any insight on the precise harmonic performance of the WTG.

The accompanying paper has proposed the methodology for conducting power system harmonic studies for WPPs and the required models for individual components. With this achieved, it would be essential to conduct a number of power system harmonic studies using integrated network models compiled from those individual component models. This allows investigating the harmonic performance at the plant level and validating the simulation results against the field measurements. Both nonresonance and resonance conditions are discussed, and pertinent mitigation measures are discussed where necessary.

Harmonics generated by the WTGs are generally insignificant from a harmonic distortion standpoint. They, however, have the potential to excite an internal or external resonance points or destabilize the system operation. While passive harmonic filters can be useful in some certain applications, they may not necessarily be the most efficient or cost-effective solution for other applications. Different harmonic mitigation techniques applied to practical WTGs and WPPs are also discussed in this paper.

Fig.1. Schematic diagram of the system used for harmonic measurements and corresponding measurement points.

II. PRACTICAL EXPERIENCES OF HARMONIC SIGNATURE OF WIND TURBINES

For a better appreciation of the points related to the harmonic signature of type 3 and type 4 WTGs that were discussed in the accompanying paper, measurements obtained at the HV side of the turbine transformer for the type 3 and type 4 turbines are discussed in this section. Measurements were conducted according to the existing version of the IEC 61400-21 standard [10]. The schematic diagram of the system used for the measurements and corresponding measurement point is shown in Fig. 1. The measurements were carried out on a single wind turbine. For both type 3 and type 4 turbines under consideration, the turbine transformer HV side is rated at 10.5 kV, whereas the transformer low voltage side voltage is 690 and 650 V for the type 3 and type 4 wind turbines, respectively. For different cases, wind turbines are connected to different power systems with different nominal voltages. The grid transformer voltage levels are not therefore shown in the figure. The short-circuit apparent power at the HV side of the grid transformer varies between 75 and 115 MVA for different grid conditions.

Fig.2. Most significant integer harmonic currents up to the 50th order for type 3 and type 4 turbines.

Fig.3. Most significant high-frequency harmonic currents between 2.1 and 8.9 kHz for type 3 and type 4 turbines.

Fig.4. Most significant interharmonic currents for type 3 and type 4 turbines.

Fig.5. Harmonic current distortion of a type 4 turbine under two different test conditions.

Fig.6. Harmonic current distortion for two type 3 turbines of the same design but different ratings.

Fig.7. Variation of the most significant harmonic currents for type 4 turbines as function of turbine loading.

Figs. 2–7 show the harmonic current spectrum of type 3 and type 4 turbines for different frequency ranges of interest. A pessimistic assumption is taken here where the largest individual harmonics for different turbine loading conditions are stated in the same figure. In reality, all the largest individual harmonic currents cannot occur simultaneously. The total harmonic distortion measured in practice is therefore generally lower than that calculated from these figures unless a resonance condition occurs.

Common traits observed from the inspection of these figures are as follows.

1) Dominant low order noncharacteristic harmonics as shown in Fig. 2. For the type 3 turbine, the 5th and 7th harmonics have the largest magnitude, whereas the 2nd, 11th, and 13th are the largest for the type 4 turbine. These harmonics are noncharacteristic because they are not generated by the pulse width modulation (PWM) switching mechanism but introduced due to the interaction of WTG with the source power system. The presence of these low order harmonics depends on the background harmonics of the source power system and the application of harmonic cancellation techniques which will be discussed later in this paper.

2) High order harmonics associated with the PWM switching and its multiples. For the type 3 turbine, the most significant components include the 49th and 51st orders. The 39th and 41st orders are the largest for the type 4 turbine. Note that these harmonic are dependent on the converter switching frequency which may vary from one turbine type to another or even between two different turbines of the same type. No generic or general conclusions can therefore be made with respect to the largest high frequency harmonic current components. It is, however, understood that the most dominant switching harmonics are in the range of 2–10 kHz.

3) Zero-sequence triplen harmonics including the 3rd, 9th, and 15th could appear due to an asymmetry in the voltage of the medium voltage (MV) grid. For the type 3 and type 4 turbines discussed in Figs. 2–4, the zero-sequence triplen harmonics are within the acceptable range. Significantly high level of harmonic currents could occur if the WTG is connected to a weak and unbalanced source power system with some level of background triplen harmonic voltage. Note that this excessive harmonic distortion is not generated by theWTG, but it is the contribution of the grid which is measured at the WTG terminals. An example is shown in Fig. 5 for the type 4 turbine. In the figure system, conditions A and B indicate connection to a highly unbalanced and a relatively balanced source power system, respectively. Such high level of low order harmonic currents can be mitigated by various harmonic mitigation methods that will be explained later in this paper. Note that WTGs are generally connected to the MV grid via a star–delta connected transformer. The use of delta winding at the high side avoids the transfer of zero-sequence triplen components at the high side under balanced operating conditions. The zero-sequence components can, however, flow in the star winding unless the neutral point is not connected to the earth.

4) Inspection of Fig. 4 which depicts the dominant interharmonic current components reveals that, at certain cases, the magnitude of interharmonic currents can be larger than that of the integer harmonic currents. The interharmonics shown are arranged in subgroups, each covering a 50-Hz window from 75 to 375 Hz. For both type 3 and type 4 turbines, the largest interharmonic current is the 75-Hz subgroup which has a comparable magnitude to the most significant integer harmonic current components as shown in Fig. 2. In VSCs, interharmonic current components are generally produced when operating the two converters of a back-to-back system at different frequencies [11] or when connected to an unbalanced system [12]. In general, VSCs exhibit lower level of interharmonic currents compared to the line- or load-commutated converters due to the presence of an intermediate dc-link capacitor. Compared to a dc-link inductor, the capacitor acts as a filter for interharmonic components that tends to transfer from one converter to another. For a WTG, the operating frequency of the rotor-side converter is not generally constant but varies as a function of wind speed. During wind pattern changes, WTGs can therefore be a source of interharmonic currents.

5) As demonstrated in Figs. 5 and 6, the harmonic currents measured at the WTG terminals cannot be assumed constant. Fig. 5 shows the harmonic currents of a type 4 turbine when connected to two different source power systems, e.g., systems A and B. Fig. 5 shows the harmonic current injection of two type 3 turbines with similar control strategy but different ratings when connected to two different source power systems, e.g., systems C and D. These figures indicate the need for conducting harmonic measurements for each particular wind power plant. In the absence of such measurements, the largest values of individual harmonic currents can be taken, but this can give rise to the unnecessary design of harmonic filters at some circumstances. As will be demonstrated by practical case studies in Section III, this does not often give rise to a problem. This is because, in most cases, the individual and total harmonic components of the WPPs are well within the statutory limits except during resonance conditions.

Fig.8. Variation of the most significant harmonic currents for type 3 turbines as function of turbine loading.

6) Figs. 7 and 8 illustrate the variation of harmonic current distortion as a function of wind turbine loading. No obvious trend can be deduced from these figures with respect to the variation of individual harmonics or the variation of the ratio of two individual components. This is because the variation of the harmonic currents as a function of turbine loading is stochastic. Despite this stochastic behavior, the variation of harmonic currents with respect to the turbine loading is marginal except for the 2nd harmonic component for the type 4 wind turbine. If harmonic measurements are carried out on-site for a range of turbine loading, the resulting harmonic current injection can be entered in a harmonic power flow simulation tool. In the absence of such data, this stochastic behavior can be neglected with constant harmonic current injection applied in all cases.

As shown in Figs. 7 and 8, several harmonic orders are larger when operating a type 3 or type 4 WTG at partial power. This does not, however, imply that a partial power operation is considered as more onerous from the grid harmonic distortion standpoint. This is because the values provided here are in percentage; a low power production will give rise to a lower distortion in ampere in many cases compared to the full power operation.

Another conclusion that can be drawn from these figures is that, in all cases except for the 2nd harmonic variations for the type 4 turbines, the harmonic distortion remains practically constant when operating at 60% loading and above. More distinct variations can be observed at light load operation.

Inspection of Figs. 2–6 indicates similar harmonic performance for type 3 and type 4 wind turbines. This is because both turbine types use PWM switched back-to-back VSCs with comparable switching frequencies. The main differentiator between the harmonic performance of type 3 and type 4 wind turbines arises from the way that the electrical generator is connected to the grid. With type 3 turbines, the electrical machine is not fully decoupled from the grid. Low order harmonics generated by the machine such as slip harmonics and slot harmonics are therefore reflected at the wind turbine terminals. Such harmonics are not relevant for type 4 wind turbines due to the full decoupling of the machine side and grid side and the fact that, with type 4 turbines, the machine slip is zero.

Fig.9. Harmonic distortion spectrum at PCC bus with MSC in service.

Fig.10. Harmonic impedance scan at the WPP collector grid and PCC with MSC in service.

III. CASE STUDIES

This section discusses the harmonic performance of type 3 and type 4 turbines for both resonance and nonresonance conditions. Depending on the location of the installation, either IEC or IEEE standards are used. Power system studies reported in this section were carried out with DIgSILENT Power Factory simulation tool which allows the user to enter the magnitude and phase angle of the measured harmonic and interharmonic current components. Both balanced and unbalanced scenarios can be investigated. Additionally, the phase cancellation of corresponding harmonic components is accounted for using the IEC second summation law [13].

A. Nonresonance Conditions

This case study discusses a typical situation which usually occurs in WPPs where the harmonic distortion at various bus bars is within the statutory limits without the need for harmonic filters. This WPP uses type 3 turbines. Fig. 9 shows that the simulated voltage harmonic distortion reduces at the point of common coupling (PCC) as more capacitor banks are energized.

Fig.11. Harmonic distortion spectrum at the WPP with MSC in service.

Fig.12. Total harmonic distortion at PCC bus versus WPP power output.

Fig.13. Variation of the total harmonic voltage distortion as function of the capacitor size (horizontal axis is time in seconds).

Fig.14. Harmonic impedance scan for different operating conditions.

Fig.15. Harmonic penetration results for different operating conditions.

The total harmonic voltage distortion is well below the maximum limit for all cases. Distortion at the 46th harmonic is marginally higher than the IEC limit due to a grid resonance point around the 43rd harmonic as shown in Fig. 10. This is not, however, expected to cause any equipment malfunctioning, and no harmonic mitigation method is necessary in this case for the following reasons.

1) The long-term thermal effect of harmonics is evaluated for the sum of all harmonic components. Any potential thermal impact that can be caused by one harmonic component exceeding the permissible level will be compensated by the fact that all other harmonics and the total harmonic distortion are well within the statutory limits.

2) The only case where the planning levels of IEC 61400- 3-6 are exceeded is for operation at zero reactive power which is a very occasional operating point given the reactive power requirements of the particular wind power plant.

3) The likelihood of other system components injecting the 46th harmonic component is very low. System wide impact of the 46th harmonic is therefore negligible.

In this practical example, the WPP is therefore allowed to have a higher harmonic allocation for the 46th harmonic so long as it does not cause the network operator to breach its obligations in terms of harmonic management.

Fig. 11 shows the variation of the harmonic voltage distortion as a function of the level of the reactive power compensation. This figure indicates that the calculated harmonic voltage distortion for the 6th order harmonic marginally exceeds the IEC limit for higher level of reactive power compensation. These levels are unlikely to cause any equipment malfunctioning on the WPP itself and will have negligible effect on the PCC. They can be readily reduced by tuning the reactive power compensation capacitors; however, it is not necessary in this particular case for the following reasons.

1) Although the level of the 6th harmonic exceeds the planning level of IEC 61400-3-6, it is within the compatibility level of this standard which is 0.5%.

2) The long-term thermal effect of harmonics is evaluated for the sum of all harmonic components. Any potential thermal impact that can be caused by one harmonic component exceeding the permissible level will be compensated by the fact that all other harmonics and the total harmonic distortion are well within the statutory limits.

3) The harmonic compliance is assessed at the PCC rather than the collector grid.

Fig. 12 shows the changes in total harmonic distortion at the PCC as a function of the WPP’s active power variation. In this case, the IEC specified limit of 3% is not shown as it lies off the top edge of the plot. This plot shows that the worst case total harmonic distortion at the PCC will be around 0.5% which is significantly lower than the IEC limit.

B. Resonance Caused by Grid Capacitor Bank With Type 3 Turbine

As discussed earlier, the harmonic signature of VSC-based wind turbines is generally insignificant. When a harmonic frequency coincides with one of the network resonance frequencies, a harmonic resonance can occur. This results in the amplification of the harmonic currents and voltages. A low harmonic current injection from the WTG can therefore be seen as a high harmonic voltage distortion at the PCC. Harmonic currents tend to flow from the harmonic generating sources to the lowest impedance seen. The lowest impedance is normally provided by the reactive power compensation capacitors. The installation of capacitors will shift the resonance point to lower frequencies. When coinciding with one of the dominant harmonics, a parallel resonance can occur. A practical example of harmonic resonance due to the use of plain mechanically switched capacitor (MSC) banks at the collector grid of the WPP with type 3 turbines is discussed here. The trace of the total harmonic voltage distortion as measured in practice is shown in Fig. 13. Results obtained from field measurements during the actual operation of this wind power plant indicate five distinct operating conditions as given in the following:

1) from 0 to 1000 s: no MSC;
2) from 1000 to 1500 s: one MSC;
3) from 1500 to 2000 s: two MSCs;
4) from 2000 to 2100 s: one MSC;
5) from 2100 to 3000 s: no MSC.

Results obtained from harmonic impedance scan and harmonic penetration studies are shown in Figs. 14 and 15, respectively. The harmonic impedance scan reveals a high impedance at around the 11th harmonic when one MSC is installed. As the 11th harmonic is also generated by the WTGs, the 11th harmonic and the total harmonic distortion can be as high as 12% as shown in Fig. 15. With two MSCs in service or without any MSC at all, the peak resonance point lies approximately around the 8th and the 18th harmonic order, respectively. These operating points will give rise to an acceptable level of harmonic distortion as confirmed by Fig. 15. This is because the WTG does not produce any appreciable level of the 8th and 18th harmonics. The mitigation method applied in practice to resolve the high total harmonic distortion (THD) problems is discussed in the next section.

TABLE I – VARIOUS WPP OPERATING MODES CONSIDERED

.
Fig.16. Impedance scan at the PCC for the WPP.

Fig.17. Voltage harmonic distortion at the PCC.

Fig.18. Voltage harmonic distortion at the PCC (lower order zoomed).

C. Resonance Caused by Grid Capacitor Bank With Type 4 Turbine

This case study discusses the possibility of harmonic resonance in a WPP utilizing type 4 turbines and proposes appropriate operating modes to avoid such a resonance. The operating modes investigated in terms of the WPP active and reactive powers are summarized in Table I where the size of each capacitor bank is 2.7 Mvar. The impedance scan and harmonic penetration studies for all cases looking at the PCC are shown in Figs. 16 and 17. From the impedance scan, two dominant peaks are visible: one at the lower order frequencies (3rd–7th order harmonics) and the other at higher frequencies (37th–44th order harmonics). The impedance scan for the lower order has a more pronounced impact as WTGs generate relatively higher harmonic current for those harmonics. The total harmonic voltage distortion at the PCC is primarily due to the 3rd–7th order harmonics. A closer inspection of the voltage harmonic distortion for the lower order harmonics is shown in Fig. 18.

Fig. 18 indicates that the total harmonic voltage distortion at the PCC exceeds the IEEE 519 standard voltage harmonic limits when there are no or six capacitor banks in service. Pertinent mitigation methods would be necessary to maintain the harmonic within the IEEE 519 standard limit. With four and eight capacitor banks, the voltage harmonic distortion is within the limits due to a shift in the resonance frequency away from the 4th and 5th harmonics. The WTG injects these harmonic currents, and if a resonance point is close to these harmonic frequencies, a harmonic voltage amplification will occur.

The three case studies presented in this section have demonstrated that a low harmonic current at the wind turbine terminals can give rise to a low or high harmonic voltage profile at the grid. A direct relationship cannot therefore be established between the harmonic currents at the wind turbine terminals and harmonic voltage at the collector grid or at the point of common coupling. The main factors determining the harmonic voltage profile are the network impedance and the presence of background harmonic voltages at the grid.

IV. HARMONIC MITIGATION

In general, the harmonic distortion of WPPs can be managed by the use of active and passive harmonic filters, the use of multilevel converters in wind turbines instead of the commonly used two-level converters, the use of selective harmonic elimination (SHE) modulation strategy, the use of converter control for harmonic compensation, and third harmonic current injection [14]. The most common methods applied to modern wind turbines are classified into the turbine- and system-level mitigation methods as discussed in this section. One important consideration in designing passive harmonic filters is that, while they are effective in the mitigation of the certain harmonic order(s), they could give rise to the amplification of some other harmonics if not carefully deigned.

Fig.19. Schematic representation of the harmonic filters typically installed at a type 3 WTG.

Fig.20. Example of the harmonic filter branches for the grid-inverter-side filter.

Fig.21. Example of the harmonic filter branches for the stator-side filter.

A. Harmonic Filtering

1) Turbine Level Filtering: Most commercial wind turbines utilize VSCs at both the grid- and rotor-side converters for both type 3 and type 4 turbines. The modulation of these converters gives rise to the generation of harmonics at both the gridand rotor-side converters. The resulting harmonics are therefore generally dealt with by the installation of the harmonic filters at both the grid- and rotor-side converters. The schematic diagram of the required filter for a type 3 wind turbine is shown in Fig. 19. Note that the high-frequency electromagnetic compatibility choke and dv/dt filters are also utilized as the machine terminals to deal with the zero-sequence common mode voltage and currents which practically eliminate the shaft bearing currents. These filters are not explicitly discussed from a harmonic study standpoint as they are not effective for the frequency range of harmonic studies.

An example demonstrating the constituting components of the grid-inverter-side harmonic filter is shown in Fig. 20. This figure shows that the filter comprises the following two branches:

1) a tuned LC circuit for damping resonance with the transformer and the grid inductance; 2) a base filter for damping of the switching frequency and its multiples;

Fig.22. Schematic representation of a type 3 turbine without active front-end converter.

Fig.23. Schematic diagram of the default capacitor bank.

As shown in Fig. 21, the stator-side filter consists of the three following branches:

1) a tuned LC circuit for damping the switching frequency;
2) a tuned LC circuit for damping twice the switching frequency;
3) a base filter for multiples of the switching frequency.

Note that a variation of the conventional type 3 turbines sometimes implemented in practice does not include any active PWM converter as shown in Fig. 22. For this design of type 3 turbine, a stator-side harmonic filter is not therefore necessary.

2) System Level Filtering: The system level mitigation techniques generally deal with the harmonic resonance aspect rather than the harmonic emission aspect. These methods generally aim to avoid any harmonic resonance issue which can cause a dangerously high level of harmonics even for an acceptable level of harmonic injection from the WTGs. A simple way to avoid the harmonic resonance issues is to tune the resistive and the inductive part of the capacitor. For the system discussed in Section III-B, this can be achieved by converting the existing capacitor banks to the 11th and 5th harmonic filter banks. Each branch of such a filter is schematically shown in Fig. 23. The methodology to derive the R, L, and C parameters is discussed in detail in [15].

Simulation results obtained from the harmonic penetration studies indicate that, with an 11th harmonic filter bank, the THD reduces to 2% from the 12%, mainly due to the filtering of the 11th harmonic. With the 11th and 5th harmonic filter banks, the THD reduced further to 0.9% due to the filtering of the 5th harmonic. As shown in Fig. 24, with the use of tuned filters, the harmonic distortion limits during operation with one or two capacitor banks are maintained within the limit specified by the IEEE Std 519 for the voltage levels between 69 and 161 kV. Alternatively, a C-type harmonic filter can be employed. In a C-type filter, an auxiliary capacitor is connected in series with the reactor as shown in Fig. 25. The auxiliary capacitor is smaller than the main capacitor. The reactor and auxiliary capacitor are chosen to form a series resonance at the fundamental frequency. The impedance of the branch comprising the reactor and auxiliary capacitor is therefore zero. The damping resistor is practically short-circuited at the fundamental frequency, and a C-type filter produces negligible fundamental frequency losses. The reactive power rating of the filter is determined by the main capacitor only.

Fig.24. Harmonic penetration results for different operating conditions in the presence of tuned harmonic filters.

Fig.25. Schematic diagram of the C-type filter.

B. Harmonic Compensation

Passive harmonic filters are generally effective in mitigating harmonic current emissions emanated from the WTGs. They are not, however, effective in dealing with systems with appreciable levels of background harmonic voltages. For these conditions, a harmonic compensation method can be adopted. In a harmonic compensation method, no actual damping resistance is used, but the energy is stored in the dc-link capacitance of the back-to-back converter. The energy dissipation is therefore significantly lower than that with a passive damping resistor. The main objective of the harmonic compensation is to reduce the harmonic currents generated by the generator due to the stator and rotor windings and to mitigate the background harmonic voltage. Nonlinearities in the stator and rotor windings results in harmonics in the stator currents. As shown in Fig. 2 for a type 3 turbine, the 5th and 7th harmonics are the most significant orders. For a type 3 turbine, the harmonic content in the rotor voltage gives rise to slip-harmonic frequencies in the stator currents. A grid harmonic compensation reduces the amplitude of the harmonic content in the line currents by using the grid converter to make harmonic currents in opposite phase angle to the harmonic currents on the stator. Note that slip harmonics generally fall in the category of the interharmonic for which more stringent limits are imposed. The grid harmonic compensation can be superimposed on the grid current controller using a summation junction. The overall design should be such that the grid current control performance remains unchanged with and without the grid harmonic compensation. Considering that the most significant harmonics for a type 3 turbine are the 5th and 7th orders, the harmonic frequencies can be calculated by (1) and (2)

.

where
n = 1, 2, 3, . . .;
m = 1, 2, 3, . . .;
fh hth harmonic frequency;
fsh hth slip-harmonic frequency.

Considering the first slip harmonic, this is simplified to

.

where generator speed; ng,sync synchronous generator speed.

The effectiveness of the harmonic compensation using the grid harmonic damping is illustrated in Fig. 26 for a type 3 turbine. In the figure, the upper and lower graphs correspond to those with and without harmonic compensation, respectively.

The harmonic compensation method described earlier can be used independently or along with a SHE modulation strategy which also aims at mitigating the low order harmonics. The discussion provided in this section has mainly focused on the type 3 turbine. The same principles hold true for a type 4 turbine except that no compensation is required for the slip harmonics.

Fig.26. Impact of harmonic compensation technique to reduce the magnitude of low order harmonics in a type 3 turbine (upper and lower graphs are those with and without the harmonic compensation, respectively).

V. CONCLUSION

This paper discussed practical experiences and mitigation methods of harmonics in wind power plants. The harmonic signature of practical type 3 and type 4 turbines was first presented. It was shown that VSC-based WTG can generate an appreciable level of low order harmonics and interharmonics in addition to the high order switching harmonics. As these low order harmonics are to a large extent generated by the interaction with the source power system, results obtained from different measurements can reveal different levels of harmonic currents and voltages. The impact of turbine loading condition was observed, but it was perceived to be marginal.

Simulation results obtained from conducting power system harmonic studies on practical WPPs are presented. For the nonresonant conditions, the magnitude of harmonics is significantly lower than the statutory limits. Resonances excited by the grid capacitor bank for WPPs using type 3 and type 4 turbines were investigated, and pertinent mitigation methods applied in practice were highlighted.

Different mitigation methods applied in practical WPPs were discussed. This includes turbine- and system-level mitigation techniques. In general, passive filters at the system level and/or the turbine level are employed. The use of harmonic compensation at the turbine level provides an active mechanism to deal with the low order harmonics and interharmonics, therefore avoiding the risk of resonances internally at the turbine or externally with the interconnected network.

REFERENCES

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Authors: Babak Badrzadeh (S’03–M’07–SM’12) received the B.Sc. and M.Sc. degrees from Iran University of Science and Technology, Tehran, Iran, in 1999 and 2002, respectively, and the Ph.D. degree in the area of electrical power engineering from Robert Gordon University, Aberdeen, U.K., in 2007. After spending a short period as an Assistant Professor at the Technical University of Denmark, Lyngby, Denmark, he joined Mott MacDonald, Transmission and Distribution Division, U.K., as a System Analysis and Network Planning Engineer. From March 2010 to March 2012, he was with Plant Power Systems, Vestas Technology R&D, Aarhus, Denmark, where he acted as a Lead Engineer in the area of advanced wind power plant simulation and analysis. Since May 2012, he has been with the Australian Energy Market Operator, Melbourne, Australia, as a Network Models Specialist. His areas of interest include power system electromechanical and electromagnetic transients, application of power electronics in power systems, wind power plants, and modeling and simulation.

Manoj Gupta received the M.Tech. degree in power systems from the Indian Institute of Technology, Kanpur, India, in 1996. He has over 15 years of experience in power system analysis and modeling. He has worked with ABB in India and Germany and Mott MacDonald in the U.K. He is currently working with Vestas in Singapore, where he leads a team for wind power plant interconnection and grid code compliance studies. His areas of interest are power system analysis and modeling for renewable, oil, and gas, industrial plants, protection, and distribution network planning.

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Intelligent Redundant Measuring Circuit with Primary Circuit Error Detection

Published by Bartosz DOMINIKOWSKI, Politechnika Łódzka, Instytut Systemów Inżynierii Elektrycznej. ORCID: 1. 0000-0002-4762-2005

Abstract. Differential amplifiers in measuring systems are often exposed to external factors, which may lead to disturbance of their proper operation. Due to the capabilities of microprocessor systems, the intelligent algorithms work well in systems for diagnosing circuit errors such as a short circuit or a circuit break. A group of switches is connected to the primary circuit which are designed to check the condition of the measurement system branches. If an error is detected, the measurement of voltage is switched to the additional system.

Streszczenie. Wzmacniacze różnicowe w układach pomiarowych często narażone są na czynniki zewnętrzne, które mogą doprowadzić do zaburzenia ich prawidłowej pracy. Ze względu na możliwości układów mikroprocesorowych algorytmy inteligentne sprawdzają się systemach diagnostyki błędów obwodowych takich jak zwarcie lub przerwa obwodu. Do obwodu podstawowego dołączono grupę przełączników, które mają za cel sprawdzić stan gałęzi systemu pomiarowego. W przypadku wykrycia błędu pomiar przełączany jest na tor dodatkowy. (Inteligentny nadmiarowy tor pomiarowy z wykrywaniem błędów toru podstawowego).

Słowa kluczowe: detekcja błędów, wzmacniacz, algorytm inteligentny.
Keywords: error detection, amplifier, intelligent algorithm.

Introduction

The development of electronic components makes more and more demands on measuring systems regarding their static, dynamic and quality properties. Diagnostics of analog circuits includes fault detection, which consists in verifying whether the measuring system functions in accordance with the design assumptions. In the event of a failure, the diagnostic system indicates the location of the damaged elements along with identification of the type of failure. Identification of the damaged element provides the measuring system the important information during its operation. Many fault diagnostic methods have been discussed in the references [1-3]. The mathematical analysis of analog systems, due to the tolerance of individual elements of the measurement system, is a problem of failure testing (data error). Analog measurement systems have a great advantage over digital converters of the measured value due to the possibility of selecting parameters such as the range and speed of the processed signal by selecting the appropriate component. Such systems with parameters matched to the measurement appear in industrial applications. Analogue measurement technique often uses special differential operational amplifiers to process the voltage signal from a measure and converter (e.g. a low Ohm resistance shunt). This circuit amplifies the signal and provide a high impedance to the signal source. These systems allow to the measurement of the voltage difference between the given measuring points. Such an electronic circuit is often used in traction batteries to measure the voltage on a single cell. Many integrated amplifier circuits can be found in industrial electronics. Often their measurement error is minimal. These systems cannot be easily monitored for additional fault monitoring circuit. Therefore, in systems with high measurement reliability, circuits composed of individual elements (outside the integrated structure) should be designed. All the resistance elements of the amplifier circuit exposed on the outside of the integrated circuit are able to monitor of their operation. Additional fault monitoring circuits in the differential amplifier are connected to its nodes. Amplifiers are often internal protected. Which means that the circuits connected to it are most often damaged. An example of protection for amplifier circuits is given in [4]. The loss of measurement information due to an open or short circuit in the measurement system can lead to failure of the entire monitored measurement circuit. In measuring systems in electric vehicles, this is a significant problem due to the energy transmission between the energy storage. Incorrect measurement information can damage the electric energy storage system in vehicle’s electrical.

Damage of electrical systems is often divided into repairable and non-repairable. The stream of damage in the differential amplifier circuit may change its structure, which leads to the malfunction of the entire system. Some configurations of the differential amplifier obtained as a result of a failure cannot be distinguished from its correct operation based only on signals measured at the its input and output. In such a situation, the only possibility of maintaining the measurement of the input signal is appropriate damage detection and the use of an additional measurement system.

Often the voltage signal is measured in the dangerous conditions such as: flammable gases, dust, vibroacoustic, high or low temperature and high humidity. Such environmental parameters may have influence on the failure of the measurement system. Failure of the measuring system operating in such an environment may consist in: short-circuit or breakage of a branch of the electrical circuit, change in the resistance of the resistors operating in it or damage the amplifier. The external factors that can cause a fault consisting in shorting the resistor is silver migration. Accidental galvanic connection of circuits operating close to each other may short-circuit the branches. The break in the circuit with the resistor may be caused by a sulfur containing atmosphere (which results in the production of silver sulfide) or corrosion. Other causes of a circuit break with a resistor are high mechanical stress, which causes solder cracks or connecting the measuring system to too high voltage (electrical breakdown of the element) and electrical overloads. Elements working in the measuring system are related to the aging process and change of their nominal parameters. The above-mentioned problems are the reason for equipping the measuring circuit with an additional circuit. Many fault of resistors have been discussed in the references [5, 6].

Materials and Methods

Due to the complex problem of electrical device failure detection, the mathematical description or circuit analysis of the failure do not give good results. The author of the article designed a system for detecting unrepairable errors. In the analyzed measuring system of the differential amplifier, all voltage nodes are available for measurements. To check the functionality of the measuring circuit, the author of the article used additional switchable circuits activated with a given time interval.

A given section of the electrical circuit can:

• conduct electricity (branch operational),
• do not conduct electricity (the same voltage operate at its ends) – (state without failure),
• be open or shorted (branch failure).

The diagnostic system of the branch circuit of the differential amplifier is shown in Figure 1. This system consists of two resistors (amplifier resistor: R1,…, R4 and measuring RM1,…, RM4) and a DC voltage source Vcc. During the measurement of the correctness of the operation the branch differential amplifier the input signal source (V1, V2) and the output should be disconnected. In this aim the switch A11, A31, A22 should be opened. At the same time, the voltage measurement is switched to the additional (redundant) measuring system. The values of the resistors RM1, …, RM4 are selected so that the measurement of the signal from them should be not a problem for systems measuring the voltage from them. The measured value from RM1, …, RM4 are sent to the input of the intelligent algorithm. The test circuit works is divided into parts:

• Disconnecting the electric branches (l1, l2, l3, l4– Figure 1) from the amplifier (OA– Figure 1) by switches (marked in Figure 1 with the symbol A);

• Connected to branches ends the DC voltage source (Vcc – Figure 1) with a resistor (RM1, …, RM4 – Figure 1) by switches (marked in Figure 1 with the symbol B) for the duration of measurement test time.

During the circuit test, a resistive voltage divider is created which is supplied by the voltage Vcc. The values of the individual elements are equal: all RM=10kΩ, R1=R2=R3=R4=25kΩ.

Fig. 1. Diagram of the basic circuit of a differential amplifier with fault diagnosis circuits of its branches

The analog circuits operating in the proposed system for monitoring the parameters of a branch of the differential amplifier should have a large frequency band. This is important because failures can change quickly. Measurement errors can occur in the test circuit of the differential amplifier. For this reason, the author of the article corrected the obtained data by a program. As a result, the voltage values during diagnostics on the measuring resistors RM1,…, RM4 can only have three values: 0V, 1,42V, 5V depending on the conductivity state of the electric branch. The voltage supplying the circuit with measuring resistors RM1,…, RM4 is Vcc = 5V and comes from the power supply of the amplifier. The operational amplifier working in a differential system was chosen as zero-drift, zero-crossover. The operational amplifier is supply by voltage stabilized. The maximum current for testing the correct operation of the differential amplifier circuits is 2mA. To measure the voltage from measuring resistors (RM1,…, RM4), the author of the article used integrated amplifiers with high input impedance. These amplifiers implement a gain factor of 1 V/V and are available two in one integrated circuit. These systems are also powered from the same voltage stabilizer with the output voltage parameter Vcc.

The proposed solution, with the diagram shown in Figure 1, guarantees detection of a circuit failure in a measurement system using a differential amplifier. Reliability of detection of errors in the operation of the differential amplifier depends on the installation the additional test circuit. The most accurate results are obtained by connecting the monitoring circuit between the start and the end of point the amplifier branch.

Data from the series resistor (RM1,…, RM4– Figure 1) are transferred to the microprocessor, which are analyzed by the Fuzzy Neural Network implemented in it. The selection number of input signals of the intelligent algorithm is related with the optimization of the diagnostic system operation. Information about a failure in the differential amplifier circuit is important for the monitored circuit. The above data may indicate problems which could damage the main circuit. An example is the short-circuit of a certain part of the main circuit through the measuring system by a differential amplifier. This situation can change the configuration of the main circuit connection.

The author of the article selected 66 failure states of the differential amplifier circuit branch and entered them into a table which is used for learning Fuzzy Neural Network. Above-mentioned table contains 4 columns and 67 rows filled with values for three operating states of the individual electric branches of the differential amplifier and is storage in the file. Depending on the operating status of the branch, there may be three different voltage values in the system: working properly (1,42V), open (0V) or shorted (5V) circuit. A Fuzzy Neural Network (FNN) was used to create a database of faults in the differential amplifier circuits. The advantages of using neural fuzzy systems are their mathematical ability to represent linguistic rules. This allows them to be used for: estimation, identification and classification tasks.

Fuzzy rules contain membership functions composed of many parameters. Often their exact values are unknown. System ANFIS (Adaptive Network Fuzzy Inference System) – allows to build a fuzzy model with parameters selected by the neural network. Fuzzy Neural Networks can provide high efficiency in solving the problem of failure detection of a differential amplifier circuit. The author of the article used a model of Takagi-Sugeno Kang (TSK) fuzzy neural network in the differential amplifier damage detection system. In the TSK model, the premises of the fuzzy rule are fuzzy, while the conclusion uses functional dependencies. The purpose of the Fuzzy Neural Network in the measurement system is to indicate only the place and type of failure (hidden in one number), so the polynomial characterizing the conclusion of the rule is zero order (constant number). Such a simplified model of intelligent network layer allows for minimizes the calculations performed by the microprocessor. Because the above-mentioned the intelligent network is designed for faults monitor of four branch circuits of the differential amplifier, the fuzzy rule can be written as follows: R(i): IF (VRm1 is A1) AND (VRm2 is A1) AND (VRm3 is A1) AND (VRm4 is A1), THEN y=c. Signals in the premises of the rule (VRm1, VRm2, VRm3, VRm4) are the voltage drops across resistors in additional fault detection circuits of the differential amplifier circuits. The value of this voltage drop indicates the type of damage (break, short circuit) or its absence in a electric branch. The intelligent network is implemented in structure with a multi-input (input vector – IN) and one output. The output of this intelligent algorithm is a value varying from 0 to 66 which related with a given fault in the differential amplifier circuit. For example: the failure of the circuit l1 (see Figure 1) consisting in a break, the system measures the values of voltage drops on individual measuring resistors (RM1,…, RM4) and writes the obtained values to the input network vector IN = [0 1,42 1,42 1,42]T (IN=[VRm1 VRm2 VRm3 VRm4]T , where: T– vector transposition). The intelligent network generates an output signal equal 11. In time of the test circuit the measurement of input voltage (V1-V2) is switch on the additional measurement circuit and the error report is generated for the system user. A fragment of the failure states of the circuit the differential amplifier branch is shown in Table 1.

Table 1. Table of failure states in the differential amplifier circuit

.

Line 2 (n = 1) in Table 1 corresponds to failure-free (input1=1,42V, input2=1,42V, input3=1,42V, input4=1,42V, IN=[1,42 1,42 1,42 1,42]T ) of operation the differential amplifier branch with an output of intelligent network equal 0. Each other line in Table 1 indicates failure operation of a branch of the differential amplifier and is coded by number in the sixth column.

Transformed into a neural network the fuzzy model diagnosing circuit errors of the differential amplifier system consists of several layers of neurons:

• input – the input values of the network coming from the circuits testing the operation of the differential amplifier branch which are written to the vector IN;

• the first hidden layer – responsible for fuzzification the input values of the IN vector in the linguistic values of the fuzzy rules. Elements of this layer intelligent network contain functions of membership of the input vector IN according to µA(VRm1), µA((VRm2), µA((VRm3), µA((VRm4);

• second hidden layer – the activation level of the fuzzy rule is compute. Neurons from this layer perform the function of the t-norm in the form of an algebraic product (π) for the kth rule which is determined by the relationship [7]:

.

where: i– iteration, N– number of input variables, k– kth rule of inference, A – fuzzy set;

• defuzzification – sharpening of the output variable from network which representing fault of the differential amplifier is defined by the relationship [7]:

.

where: y(x) – the output value of the neural fuzzy network, ck– constant value in fuzzy rule conclusion, M– number of inference rules, k– kth rule of inference.

The fuzzy neural network is built in Matlab program by using the Fuzzy Logic Toolbox. This network has four input variables and one output variable. To build fuzzy rules, Gauss membership functions were used by the following relationship [8]:

.

where: x-input variable, σ– width (responsible for the shape of the function), c– fuzzy set center.

Information about the Fuzzy Neural Network is presented in [9-11]. Figure 2 shows the functions of belonging to the input space of the intelligent algorithm after the learning process.

Fig. 2. Membership functions of the signal VRM1 from the circuit monitoring circuit l1 of the differential amplifier

The circuits testing the operation of individual branches of the differential amplifier are identical with the values of the resistors working in the amplifier (R1, .., R4, RM1, …, RM4) and the value of the supply voltage Vcc. The membership function parameters for each input variable of the neural fuzzy network are parameters identical. Appropriate data are required for the learning and testing process of the fuzzy neural network. This values has been defined in the file in the form of a table. The number of intelligent network input variables cannot be too large because the model of the differential amplifier diagnostic system becomes very complex in time and computation. Complicated models are not suitable for operate on the microprocessor system. If the same number of membership functions N is assigned to each input variable x (voltage values from the resistors Rm1, …, Rm4 – Figure 1) of the fuzzy network model, then the maximum number of rules of the proposed system is obtained on the basis of the dependence NX . In the case of the proposed neural fuzzy system, for each input variable x = 4 (four branches of the differential amplifier) three membership functions were given, which gives 81 rules. With an increase of the size of the input vector, the number of rules of the neural fuzzy system increases exponentially. The advantages of the fuzzy neural network are:

• its elements are connected in a legible manner,

• use of the measurement data (all failures of the differential amplifier circuits) to teach it,

• the possibility of interpreting the network as a fuzzy model by using the rules in the expert notation: “if the input is – then the output is”. Such a fuzzy rule indicates exactly the type of failure and its place of occurrence.

Results

The proposed system of redundant circuit with failure detection of the differential amplifier was designed and tested in the Matlab/Simulink simulation program. For its verification, the author of the article used rectangular input functions presented in Figure 3 a), b), c) and d).

Fig.3. a), b), c), d) Input and e) output signals of the algorithm detecting incorrect operation of the differential amplifier circuits

These functions (Figure 3 a), b), c), d)), were generated by forced failure states in a given branch of the differential amplifier (see Figure 1). Respectively for a given time interval, the operation of the diagnostic system is as follows:

• time interval from t=0 to 0,1s (see waveform Figure 3 a), b), c), d)), input vector IN=[1,42 1,42 1,42 1,42]T , answer of the intelligent system y=0 (see waveform Figure 3 e)). This information means that all branches of the differential amplifier are working properly. The data is listed in Table 1 (row number 2, n=1);

• time interval from t=0,1 to 0,2s (see waveform Figure 3 a), b), c), d)) the input vector IN= [5 5 5 5]T system response y=1 (see waveform Figure 3 e)). This information means that there is a fault in the circuits of the differential amplifier consisting in shorting the all resistors (R1,.., R4). The data is listed in Table 1 (row number 3, n=2);

• time interval from t=0,2 to 0,3s (see waveform Figure 3 a), b), c), d)) the input vector IN= [0 0 0 0]T system response y=2 (see waveform Figure 3 e)). This information means that there is a failure in the circuits of the differential amplifier consisting in opening the all resistors (R1,.., R4). The data is listed in Table 1 (row number 4, n=3);

• time interval from t=0,3 to 0,4s (see waveform Figure 3 a), b), c), d)) the input vector IN= [1,42 0 0 0]T system response y=3 (see waveform Figure 3 e)). This information means that the branch l1 of the amplifier is working correctly, while the rest of the branch of the differential amplifier has a break in the circuits. The data is presented in table 1 (row number 5, n=4);

• time interval from t=0,4 to 0,5s (see waveform Figure 3 a), b), c), d)) the input vector IN= [1,42 0 0 5]T system response y=4 (see waveform Figure 3 e)). This information means that the amplifier branch l1 is working properly. The error appeared in branch: l2 and l3 (break) and a short circuit in l4. The data is listed in Table 1 (row number 6, n=5);

• time interval from t=0,5 to 0,6s (see waveform Figure 3 a), b), c), d)) the input vector IN=[1,42 0 5 0]T system response y=5 (see waveform Figure 3 e)). This information means that the branch l1 is working correctly. The error appeared in branch: l2 and l4 (break), and short circuit in l3. The data are listed in table 1 (row number 7, n=6).

The intelligent algorithm was checked by computer testing by forcing all failure states. The obtained data confirmed the effectiveness of the proposed algorithm.

Discussion

Redundant systems are used in dangerous measurements or industrial conditions. Such systems create reliable measurement systems. Systems based on intelligent techniques better map the shape of the assumed system characteristics. The proposed algorithm correctly diagnoses circuit faults of the differential amplifier. Due to the external environmental conditions, the use of monitoring systems for the correct operation of the measurement system is metrologically important.

REFERENCES

[1] Gizopoulos D., Advances in Electronic Testing: Challenges and Methodologies; Springer: Dordrecht, The Netherlands, (2006)
[2] Kabisatpathy P., Barua, A., Sinha S., Fault Diagnosis of Analog Integrated Circuits; Springer: Dordrecht, The Netherlands, (2005)
[3] Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance, Springer, (2006)
[4] Daniel Miller, Nick Scandy, Op Amp ESD Protection Structures, Texas Instruments Incorporated, (2020)
[5] Michael Reid Maurice N. Collins Eric Dalton Jeff Punch David A. Tanner, Testing method for measuring corrosion resistance of surface mount chip resistors, Microelectronics Reliability, Volume 52, Issue 7, July (2012), 1420-1427
[6] Michael Reid, Jeff Punch, Claire Ryan, John Franey, Gustav E. Derkits, Jr., William D. Reents, Jr., Luis F. Garfias The Corrosion of Electronic Resistors, IEEE Transactions on Components and Packaging Technologies, VOL. 30, NO. 4, DECEMBER 2007
[7] Stanisław Osowski, Sieci neuronowe do przetwarzania informacji, Oficyna Wydawnicza Politechniki Warszawskiej, (2006)
[8] Andrzej Piegat, Fuzzy Modeling and Control, Springer, (2001)
[9] Maria Mrówczyńska, Approximation abilities of neuro-fuzzy networks, Geodesy And Cartography, Vol. 59, No 1, (2010), 13-27
[10] Mrówczyńska, M., Gil, J. System neuronowo-rozmyty w zastosowaniu do badań deformacji konstrukcji Mrówczyńska, Czasopismo Techniczne. Środowisko (2008), R. 105, z. 2-Ś, 215-221
[11] Dudek G. Neuro-fuzzy approach to the next day load curve forecasting, Przegląd Elektrotechniczny, R. 87 NR 2, (2011) 61-64

Autorzy: dr inż. Bartosz Dominikowski, Politechnika Łódzka, Instytut Systemów Inżynierii Elektrycznej, ul. Stefanowskiego 18, 90-537 Łódź, E-mail: bartosz.dominikowski@p.lodz.pl.

Source & Publisher Item Identifier: PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 98 NR 12/2022. doi:10.15199/48.2022.12.53

Analysis of Interactions in the Circuit of the Power System with Nonlinear Load and LC Passive Filter

Published by Mirosław WCIŚLIK, Paweł STRZĄBAŁA,
Kielce University of Technology, Department of Electric Engineering, Automatic Control and Computer Science

Abstract. The paper deals with an AC circuit containing the nonlinear load and a LC passive filter. Nonlinear load voltage at the power terminals proportional to the signum function of current is considered. The current-voltage characteristic of such load is unambiguous (without hysteresis). A quality analysis of the circuit voltages and currents was carried out. Distribution of active and reactive power for fundamental and higher harmonics in the circuit were also performed.

Streszczenie. W pracy analizowany jest obwód prądu przemiennego z przykładowym obciążeniem nieliniowym i filtrem biernym LC. Przyjęto obciążenie nieliniowe, którego napięcie na zaciskach zasilania jest proporcjonalne do funkcji signum prądu. Charakterystyka napięciowo – prądowa obciążenia jest jednoznaczna (bez histerezy). Przeprowadzono analizę jakościową przebiegów napięć i prądów obwodu. Wykonano analizy rozkładu mocy czynnej i biernej dla harmonicznej podstawowej i wyższych harmonicznych w obwodzie. Analiza oddziaływań w obwodzie systemu elektroenergetycznego z obciążeniem nieliniowym i filtrem biernym LC.

Keywords: nonlinear load, higher harmonics, reactive power compensation, interaction analysis.
Słowa kluczowe: obciążenie nieliniowe, wyższe harmoniczne, kompensacja mocy biernej, analiza oddziaływań.

Introduction

In order to improve energy efficiency and electricity savings, it is necessary to reduce the interaction between the power system and nonlinear receivers. For this purpose, LC passive filters are commonly used. These filters compensate the reactive power in the circuit and may reduce the flow of higher harmonics of current into the power system. Nonlinear loads, that most often disturb the quality of power supply voltage are arc furnaces and rectifiers [1]. In [2] it has been shown that nonlinear load with unambiguous current-voltage characteristics has a total reactive power equal to zero, and the reactive power of the first harmonic of this load is converted into the reactive power of the higher harmonics and fully transferred to the equivalent reactance of the supply circuit. This property is also characteristic for rectifiers. The phenomenon of power conversion in circuits with nonlinear loads and LC passive filters has not been analysed in the literature so far. Usually the nonlinear load is replaced by a simplified model of a current source. There is assumed that the nonlinear receiver is a generator of higher harmonics of current [3],[4],[5],[6]. In order to take into account the conversion phenomena, the AC circuit with LC passive filter and nonlinear load is considered. There was assumed that the voltage at terminals of nonlinear load is proportional to the current signum function. It is a model of the electric arc and a bridge rectifier.

Model of analyzed circuit

The analysed AC circuit is shown in Fig.1. The circuit contains bridge rectifier supplied by a sinusoidal voltage source with the amplitude Es and the angular frequency ω. The inductance Ls and resistance Rs represent the impedance of the supply system. The LC passive filter is connected to the PCC point, and represented by: inductance Lf, capacity Cf and resistance Rf. The impedance of the load supply system is represented by the inductance L1 and the resistance R1. It is assumed that the inductance Ls is much smaller than the inductance L1. Including a capacitor Cp makes it easier to solve the modelled circuit in Simulink. The algebraic loop problem occurs in the model if the capacitor Cp is not included. Applying a very small value of the capacitor resolves this problem. The value of capacitance Cp was assumed much smaller than capacitor Cf. For such relation, the impact of capacity Cp on circuit operation is insignificant. If the ripple output voltage Uc are very small, it may be assumed that the current-voltage characteristics Ub(I1) is unambiguous (without hysteresis). This characteristic may be described as the signum function of current I1: Ub(I1)=(Uo+2Ud)·sign(I1), where: Uo – is the constant component in the output voltage of rectifier, Ud – is the diode voltage of bridge rectifier.

Fig.1. AC circuit model with nonlinear load and LC passive filter

To simplify and reduce number of parameters the analysis was carried out using dimensionless variables. For this purpose reference variables in the form of reactance ωL1 and supply voltage amplitude Es were used. Additional the time scaling τ=ωt was introduced. Therefore, the circuit equations may be written following:

.

where dimensionless variables are written:

.

where: k – denote circuit part and parameter index.

The MATLAB/Simulink system was used to analyse the circuit under consideration in Fig.1. An operational diagram of circuit was created in Simulink on the basis (1)-(4).

Analysis of interactions in circuit

In this section the power factor PF and total harmonic distortion THD of voltages and currents in circuit were analysed. These quantities are defined following [7]:

.

where: P,S – respectively active and apparent power; U1, I1 – rms value of fundamental component voltage and current; Un, In – rms value of nth harmonic component voltage and current; n – harmonic order (n = 1,2,3,…,max).

The continuous operation mode of the rectifier was analyzed. Parameters of simulation were following: uo = 0.5, rs = r1 = rf = 0.01 and xf = 0. The obtained results refers to case when the value of the variable xf is equal to zero. It is common case occurring in the power system circuits with nonlinear loads and reactive power compensation systems [5]. For above assumptions the power factor PF of the sinusoidal voltage source (VS) as function xs and cf is shown in Fig.2. The maximum value of PF occurs for cf equal to approx. 0.5, but only for small values xs. An increase in the inductance of the power supply system may significantly reduce the power factor. The influence of the stiffness of supply network is particularly visible at xs > 0.05 i.e. when the inductance of the power supply system Ls is greater than 5% of the inductance L1.

Fig.2. The power factor PF of supply voltage source in function xs and cf : a) 3D plot and b) contour plot

The largest distortion of the voltages and currents in the circuit are particularly visible when the power system becomes less rigid. As a result of these interactions, the power factor of the circuit may be much lower than expected.

For non-rigid power supply system capacitor bank to reactive power compensation causes an increase of currents and voltages distortion in the circuit. These distortion may be much greater than ones before compensation. This is due to the resonances occurring in the circuit [5]. For example, total harmonic distortion THD of current is and voltage up are shown respectively in Fig.3 and Fig.4. The peaks are characteristic. For current is maximum value of THD may be greater than 200%. Whereas for cf and xs equal to zero, it is only 12%.

Fig.3. Total harmonic distortion of supply source current is in function xs and cf : a) 3D plot and b) contour plot
Fig.4. Total harmonic distortion of voltage up in function xs and cf

These distortion are observed also in current i1. Total harmonic distortion THD of current i1 is presented in Fig.5. The values of this coefficient are much smaller than for current is (Fig.3), and its value may only reach approx. 35%. The THD fluctuation for voltage ub may be equal to approx. 20%, whereas without power compensation THD of voltage ub is constant and equal to 47%.

Fig.5. Total harmonic distortion of current i1 in function xs and cf

Analysis of example currents and voltages waveforms in circuit

The total harmonic distortion THD of voltages and currents waveforms may be reduced if inductance Lf is connected in series with a capacitor Cf. Depending on the resonant frequency of such LC circuit higher harmonics are reduced [5].

Fig.6. The voltages and currents waveforms for: uo = 0.5, xs = 0.1, cf = 0.5 and different value xf : a) xf = 0 and b) xf = 0.2378

The example waveforms obtained for parameters: cf = 0.5, xs = 0.1, rs = r1 = rf =0.01 and uo = 0.5 are shown in Fig.6a and Fig.6b, respectively for xf = 0 (i.e. without inductance Lf) and xf = 0.2378 (with inductance Lf). Parameter xf was calculated for resonant frequency order nr equal to 2.9. Significantly smaller distortions for waveforms in Fig.6b are observed. Whereas the transients after switching on the supply voltage become longer than for xf = 0. Therefore, obtained waveforms are shown only in steady state, achieved after approx. 13 cycles. The period for the adopted time scale τ is equal to 2π.

The values of THD for analysed waveforms are presented in Table 1. For xf = 0.2378 the THD of current is decreased about ten times compared to xf = 0, whereas for current if approximately four times. The distortion of the voltage up is also much smaller than for xf = 0. The THD of current i1 and voltage ub are practically unchanged.

Table 1. Total harmonic distortion for currents and voltages waveforms in circuit

.

After taking into account the parameter xf, the power factor PF is also improved at specific points of the analyzed circuit. The values of power factor PF and power factor of fundamental harmonics PF1 are shown in Table 2. These were measured at the voltage source terminals (PFin, PF1in), the PCC point (PFPCC, PF1PCC) and the input terminals of nonlinear load (PFload, PF1load). The power factor PF significant increased for xf = 0.2378 in voltage source VS and PCC point. The power factor of nonlinear load PFload increases slightly. After taking into account parameter xf the power factor of the fundamental components don’t change significantly.

Table 2. The power factor PF and power factor for fundamental components PF1 in different part of circuit

.

The obtained power factor results are close to unity for the voltage source VS and PCC point. The value of this coefficient for nonlinear load remains practically constant, both when inductance Lf in a circuit occurs or not.

Power distribution in circuit

The distribution of active and reactive power in analysed circuit was carried out in MATLAB/Simulink system. The total active and reactive power were calculated following:

.

The reactive power was defined as the product of voltage and current time derivative dI/dt and averaged over the period T [2]. The powers (7) may be written as sum of the power of first harmonic component and power of higher harmonics components:

.

where: Ph1, Qh1 – respectively the active and reactive power of the fundamental component; Phh, Qhh – respectively the active and reactive power of the sum of higher harmonics.

The power distribution in circuit was analysed for total power, first harmonic power and higher harmonics power. Calculating the total powers (P,Q) and the powers of the first harmonics (Ph1,Qh1), the powers of the higher harmonics (Phh,Qhh) may be determined from (8). The power components were referenced to E2s/ꙍL1 and analysed using dimensionless variables. The analyse was carried out for the same parameters as previous section.

Figure 1a shows the distribution of reactive power in circuit for xf = 0. The total reactive power and the power of first harmonic of the voltage source VS are close to zero. This is due to the reactive power compensation in circuit. The total reactive power of nonlinear load NL is also close to zero, whereas the reactive power of the first harmonic and the reactive power of the higher harmonics of this load have similar values, but opposite signs. The reactive power conversion of first harmonic into the reactive power of higher harmonics is observed. Next, the reactive power of higher harmonics of nonlinear load NL is fully transferred to the equivalent reactance of the supply circuit.

Fig.7. Distribution of reactive power in circuit for: a) xf = 0 and b) xf = 0.2378

For xf = 0.238 (Fig.7b) the reactive power of higher harmonics at the PCC point, inductance Ls and LC filter decreased. The reactive power of higher harmonics in nonlinear load does not change significantly in compare to xf = 0. Its value is comparable to the reactive power of first harmonic of load and reactive power of higher harmonics of the inductance L1.

The parameter xf has not a significant influence on active power in circuit. For xf = 0.238 very small changes of active power are observed in compare to xf = 0. Therefore, the distribution of active power shown in Fig.8 concerns only to the case if xf = 0.238. The active power of the higher harmonics on all elements is close to zero. In effect the total active power and the active power of the fundamental harmonic are comparable.

When a capacitor to reactive power compensation is used, the reactive power of higher harmonics increases in the circuit. The reactive power of higher harmonics is dissipated in all parts of circuit, excluding the voltage source, that is sinusoidal. After taking into account inductance Lf, this power is reduced to zero in selected elements and points of circuit. The power of higher harmonics of nonlinear load and inductance L1 remained practically unchanged, even if inductance Lf is used.

Fig.8. Distribution of active power in circuit for xf = 0.2378

Conclusion

The model of circuit with nonlinear load and LC passive filter enabled quantitative analysis of power conversion phenomena and harmonics propagation. The analyses confirm influence of the mains inductance on increase of currents and voltages distortion in circuit.

The analyses indicate need to take into account the additional series inductance for capacitor banks in analysis of power factor and total harmonic distortion in circuit. The inductance of LC passive filter selected for 2.9th harmonic frequency order (in close to 3rd harmonic) allowed to significantly reduce power conversion phenomena occurring in the circuit. This inductance should be also taken into account in the analysis of other higher harmonics.

REFERENCES

[1] Singh B., Chandra A.: Power Quality – Problems and Mitigations Techniques, John Wiley & Sons Ltd, 2015
[2] M. Wciślik: Powers Balances in AC Electric Circuit with Nonlinear Load, IEEE 2010
[3] R. Klempka: Designing a group of single-branch filters taking into account their mutual influence, Archives of electrical engineering, 2014, s. 81 – 91
[4] M. Włas: Engineering design of passive filter structures, Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej Nr 28, s. 143-148, 2010
[5] A. Lange and M. Pasko: Selected methods of improving electrical energy quality with LC systems, Gliwice: Wydawnictwo Politechniki Śląskiej, 2015
[6] C. S. Mboving, Z. Hanzelka and R. Klempka: Different approaches for designing the passive power filters, Przegląd Elektrotechniczny, 11 2015, s. 102-108
[7] IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems, IEEE Std 519-1992, 15/2004

Authors: Professor Mirosław Wciślik, Kielce University of Technology, Department of Electric Engineering, Automatic Control and Computer Science, al. Tysiąclecia Państwa Polskiego 7, 25- 314 Kielce, E-mail: wcislik@tu.kielce.pl; MSc Paweł Strząbała, Kielce University of Technology, Department of Electric Engineering, Automatic Control and Computer Science, al. Tysiąclecia Państwa Polskiego 7, 25-314 Kielce, E-mail: pstrzabala@tu.kielce.pl

Source & Publisher Item Identifier: PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 96 NR 3/2020. doi:10.15199/48.2020.03.14

Analysis of Selected Power Quality Indicators at Non-Measured Distribution Network Points Based on Measurements at Other Points

Published by Andrzej FIRLIT, Bogusław ŚWIĄTEK, Zbigniew HANZELKA, Krzysztof PIĄTEK, Mateusz DUTKA, Tomasz SIOSTRZONEK, AGH University of Science and Technology, Krakow, Poland

Abstract. The article presents a method enabling estimation of the selected power quality indicators at a given point of a power network, on the basis of the power quality indicators recorded at the nearest vicinity points. For needs of the estimations, artificial neural network algorithms were applied. The result is a neural model that defines the relationship between the power quality indicators of the same type, at adjacent points. The paper presents results of analyses and tests under real operating conditions of the distribution system.

Streszczenie. W artykule przedstawiono metodę umożliwiającą estymację wybranych wskaźników jakości energii elektrycznej w zadanym punkcie sieci elektroenergetycznej na podstawie wskaźników jakości energii elektrycznej zarejestrowanych w punktach leżących w najbliższym otoczeniu. Do estymacji wykorzystano algorytmy sztucznych sieci neuronowych. W rezultacie uzyskano neuronowy model określający relację pomiędzy wskaźnikami jakości energii elektrycznej tego samego typu w sąsiadujących ze sobą punktach. W artkule przedstawiono wyniki analiz i testów dla rzeczywistych warunków pracy sieci dystrybucyjnej. (Analiza wybranych wskaźników jakości energii elektrycznej w nieopomiarowanych punktach sieci dystrybucyjnej wyznaczonych na podstawie pomiarów w innych punktach).

Keywords: power quality indicators, estimation of power quality indicators, artificial neural networks, statistical analysis of power quality indicators.
Słowa kluczowe: jakość energii elektrycznej, estymacja wskaźników jakości energii elektrycznej, sieci neuronowe, analiza statystyczna wskaźników jakości energii elektrycznej.

Introduction

Works related to measurements and long-term recording of the power quality indicators (PQ) have become almost a daily practice of distribution system operators (DSOs). They are mainly related to the complaints reported by the (electric energy) recipients, but more and more frequently they result from the knowledge about the levels of the PQ indicators in a power supply system. This data is a valuable source of information on the technical condition of a particular part of the network and it can be used to take preventive, modernization and investment measures. Apart from portable analytic units, used for ad-hoc metering works, operators are also equipped with continuous monitoring systems based on stationary units. Such analyzers are usually placed in crucial points of a system. Additional data sources are successively installed smart meters and advanced metering infrastructure (AMI). More and more frequently the AMI meters enable measurement and recording of selected PQ indicators. Certain models have been equipped with algorithms enabling a user to calculate aggregated PQ indicators in accordance with the recommendation of the Energy Regulatory Office (in Polish: Urząd Regulacji Energetyki) [1].

Due to a very complex structure of the distribution system it is not possible to place an instrument at every point of the system. This approach is not justified, primarily from the economic point of view. Therefore, there comes a question whether this problem could be solved by various approximation methods and already carried out measurements and records [4, 5, 6, 7].

Estimation of PQ indicators

A goal of the PQ estimation is to determine the 10-minute value of a selected PQ indicator at a selected point of the power grids, where a suitable meter, e.g. PQ analyzer, has not been installed. The estimation is carried out on the basis of the indicator value from one or higher number of points at the nearest vicinity, where the analyzers are permanently installed or long-term measurements and records have already been completed.

The analysis was carried out for the following PQ indicators: voltage RMS U, short-term Pst and long-term Plt flicker severity indicators and (measure of voltage fluctuations), total harmonic distortion THDU, content of higher voltage harmonics and K2U voltage asymmetry coefficient. In every case a linear relationship was assumed between the estimated coefficient and the determined coefficients at the nearest vicinity points.

.

where: pwy(k) value of the indicator at the tested point of the network, pwe(k,i) – value of the indicator at the point located in the nearest vicinity of the tested point, k – 10- minute-value/sample number, lwe – number of inputs, i – point index, wi, b – fixed factors.

Application of the artificial neural network method

For the above mentioned PQ indicators, the relation (1) was implemented by means of the artificial neural networks (ANNs). The result is a neural model comprising a single linear neuron with one or more inputs. The relation (1) describes such a neuron. The coefficients wi, b are the weights of the neuron. However, the model requires access to the measurement data of pwy(k), i.e. historical data of the indicator to be estimated in the future. Hence, there comes the following procedure of the model construction:

– take or measure and record values of the indicators at the point, where the indicator is to be estimated, and at points in the nearest vicinity,

– teach the neuron,

– verify the model. If the verification is negative, add another point – it might happen that the disturbance comes from a point not taken into account.

Quality of the model operation was assessed by summing the PQ coefficient values determined by the ANN model, staying within ±5%, ±10% and ±20% of the current real value, expressed as a percentage of the total number of samples – estimation accuracy (validity) coefficient. Due to such a model it is possible to estimate the value of the indicator on the basis of the values of indicators acquired from measuring points in the nearest vicinity.

Model teaching process

Determination of the coefficients wi and b is carried out by the minimizing, by the method of the quickest quality drop of the Q indicator, expressed by the relation (2):

.

where: N – number of values (samples).

This indicator has one minimum, which ensures finding a global solution. The values of the coefficients wi and b are calculated by means of the iterative method, according to the relations (3) and (4):

.

where: iter – iteration no., η – teaching speed factor, e(k) – teaching error.

Due to the relations (1)÷(5) an estimation algorithm based on ANN (EA-ANN) was developed.

Analysis of the results of estimation for selected indicators, for real conditions of the distribution network operation

The tests were carried out in two different test networks (parts of the DSO network): in a network with a high power load reception, strongly affecting the operator’s system (the test network no. 1) and in a network, where there were no PQ problems (the test network no. 2).

Fig.1. Test network no. 1 – a schematic diagram of the considered part of the power grid with marked measuring points: P1 to P6

Evaluation of values calculated by the developed EAANN was carried out on the basis of the estimation accuracy coefficient and by comparing statistic numerical measures laid down in the regulation [2] and the standard [3] for selected PQ indicators respectively (percentile 5% and 95%, marked as CP05 and CP95). Statistical measurements were calculated for real values of selected PQ indicators and for values returned by EA-ANN at the power grid points without a measuring instrument (target).

Test network no. 1

The case under consideration concerns the power supply system of a large industrial customer supplied from the 110 kV level, having an internal MV distribution network with varied voltage levels. In the recipient’s power supply system there is a large disturbing load affecting the operator’s system heavily. Figure 1 presents a simplified diagram of a part of the considered power supply system with marked points, where the analyzers are connected – P1 to P6.

Class A PQ analyzers were installed at six points of the power supply system under. Measurements and recordings lasted six weeks. Verification of the values estimated by the EA-ANN, for the case without a measurement at a particular point, is the final result of the algorithm. The following figures show the results obtained, for:

– the factor Pst,P2 at a point P2 – 20 kV on the grounds of the point P1 – 110 kV – Pst,P2 = f(Pst,P1) – Fig.2,

– the factor Pst,P3 at a point P3 – 30 kV on the grounds of the point P1 – 110 kV – Pst,P3 = f(Pst,P1) – Fig.3,

– the factor K2U,P3 at a point P3 – 30 kV on the grounds of the point P1 – 110 kV – K2U,P3 = f(K2U,P1) – Fig.4,

Fig.2. Verification of the estimation model Pst,P2 in P2 – 20 kV on the grounds of P1 – 110 kV – Pst,P2 = f(Pst,P1) – zoom in [7]
Fig.3. Verification of the estimation model Pst,P3 in P3 – 30 kV on the grounds of P1 – 110 kV – Pst,P3 = f(Pst,P1) – total time frames [7]
Fig.4. Verification of the estimation model K2U in P3 – 30 kV on the grounds P1 – 110 kV – K2U,P3 = f(K2U,P1) [7]

In figures 2, 3, 4, the measured values are presented in blue and the estimated values in red (this also applies to figures 6, 7, 8). The values of the validity coefficient, CP95 and a relative error calculated for actual and estimated runs are shown in table 1.

Table 1. Overview of the validity coefficient values, CP95 and the relative error – test network no. 1

.

The relative error for CP95 is between 1.12% and 3.84%. Therefore, the CP95 values calculated on the basis of the estimated values do not deviate significantly from the CP95 values determined on the grounds of the measured values.

Fig.5. Test network no. 2 – a schematic diagram of the considered part of the power grid with the following points marked: point A – point with the analyzer, point L – point with the meter, E1, E2, E3 – points for which values are estimated

Test network no. 2

The case under consideration concerns a part of MV – 20 kV distribution network (one outlet from the main power supply point, approx. 6.5 km long). No significant disturbance sources were found in this system. Figure 5 shows a simplified diagram of the network under consideration. There is marked location of the stationary PQ analyzer (point A) and the electric energy meter (point L) at 20 kV level, and E1, E2 and E3 points at 400 volts level, for which the values are estimated. Measurements and recordings were carried out 4-5 weeks. Estimation was made of the value for:

– voltage rms UnN,E1 at point E1 400 V, on the grounds of the point A 20 kV – UnN,E1 = f(USN,A),

– voltage rms UnN,E2 at point E2 400 V on the grounds of the point L 20 kV – UnN,E2 = f(USN,L) – Fig. 6,

– THDU-nN,E1 at point E1 400 V on the grounds of the point A 20 kV – THDU-nN,E1 = f(THDU-SN,A) – Fig. 7,3

– Pst-nN,E3 at point E3 400 V on the grounds of the point A 20 kV – Pst-nN,E3 = f(Pst-SN,A) – Fig. 8,

– 7. harmonic HU7-nN,E3 at point E3 400 V on the grounds of the point A 20 kV – HU7-nN,E3 = f(HU7-SN,A) – Fig.9.

Figures 6, 7, 8 show a comparison of the real values (measured, blue) and the estimated values. The values of the validity coefficient, CP95 and CP05 and the relative error calculated for real and estimated runs are presented in the Table 2. The relative error for CP95/CP05 for voltages does not exceed 0.03%, which is low. The relative error for CP95 for other PQ indicators does not exceed 8.33%. Larger error values apply to a percentile CP05 (not presented in Table 2). They result from low levels of indicator values.

Fig.6. Verification of estimation model UnN,E2 in E2 – 400 V on the grounds of L – 20 kV – UnN,E2 = f(USN,L) [7]
Fig.7. Verification of estimation model THDU-nN,E2 in E2 – 400 V on the grounds of L – 20 kV – THDU-nN,E2 = f(THDU-SN,L) [7]
Fig.8. Verification of estimation model Pst-nN,E3 w E3 – 400 V on the grounds of A – 20 kV – Pst-nN,E3 = f(Pst-SN,A) [7]
Fig.9. Verification of estimation model HU7-nN,E3 w E3 – 400 V on the grounds of A – 20 kV – HU7-nN,E3 = f(HU7-SN,A)

Table 2. Summary of values: validity coefficient, CP95 and CP05 and the relative error – test network no. 2

.
Conclusions

Analysis of the results acquired from the developed algorithm of estimation of PQ coefficient values using the concept of artificial neural networks enables their positive evaluation. The absolute errors of the estimated statistical values of CP95 and CP05 statistical measures range from 0.0% to 8.33%. After exclusion of the case for the low level of Plt,CP95 = 0.12 coefficient (in practical terms it is a very low value), for which the limit value is 1.0, the relative error interval goes down to 4.86%. The proposed approach may be an alternative or supplementation to the results acquired from the simulation of a power grid model that needs to be built earlier in a selected programming environment.

REFERENCES

[1] Technical Specification for tender procedures for the supply of metering infrastructure for AMI systems in the Polish market – Annex 1 – power quality indicators (in Polish), Urząd Regulacji Energetyki URE, (2015)
[2] Regulation of the Minister of Economy dated 4 May 2007 on detailed conditions for the operation of the power supply system (in Polish), (2007)
[3] PN-EN 50160 – Voltage supply parameters in public power supply networks
[4] Gała M., Application of artificial neural networks to assess the impact of non-linear receivers on the electric energy quality (in Polish), Przegląd Elektrotechniczny, 87 (2011), No. 6, 40-46
[5] Gała M., Application of neural method of voltage estimation to evaluation of influence of nonlinear loads on electric energy quality, 10th International Conference on Electrical Power Quality and Utilisation EPQU 2009, IEEE Conference Proceeding, (2009), 1-6
[6] Eremia M. (Editor), Liu Ch., Edris A., Advanced Solutions in Power Systems: HVDC, FACTS, and Artificial Intelligence, IEEE Press, Wiley, (2016)
[7] Firlit A., Świątek B., Piątek P., Dutka M., Siostrzonek T., Estimation of selected power quality indicators at unmetered distribution network points (in Polish), Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej, 67 (2019), 17-20

Authors: dr inż. Andrzej Firlit, e-mail: afirlit@agh.edu.pl; dr inż. Bogusłąw Świątek, e-mail: boswiate@agh.edu.pl; prof. dr hab. inż. Zbigniew Hanzelka, e-mail: hanzel@agh.edu.pl; dr inż. Krzysztof Piątek, e-mail: kpiatek@agh.edu.pl; mgr inż. Mateusz Dutka, email: mdutka@agh.edu.pl; dr inż. Tomasz Siostrzonek, e-mail: tsios@agh.edu.pl; AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland.

Source & Publisher Item Identifier: PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 96 NR 5/2020. doi:10.15199/48.2020.05.07

Siting Hydropower Plant by Rough Set and Combinative Distance-Based Assessment

Published by Ahmed M. Agwa1,2, Shaaban M. Shaaban1,3,
Northern Border University (1), Al-Azhar University (2), Menoufia University (3), Egypt

Abstract. Each power plant (PP) is solo entity whose construction site is determined by different criteria in accordance with some physical rules. Latterly, great importance is provided to siting PP in inexact surroundings. Multiple-criteria decision-making for the proper location of the PP construction is relevant. The objective of this research is to create a model for decision-makers to rank available sites for installing hydropower plant (HPP) in accordance with multiple-criteria attributes e.g. accessibility to electrical grid, power potential, economical respects, environmental influence, topography, and natural hazards. In this research, a novel application of a hybrid approach that employs rough set theory (RST) and combinative distance-based assessment (CODAS) method is proposed to prioritize available locations for installing HPP. Firstly, the strength of RST is adopted to get minimal attributes reduction set. Secondly, the relative weights of minimal attributes are determined using RST. Finally, CODAS technique is utilized to calculate the rank of alternatives. The comparison between the proposed method-based results and the results without attributes reduct, proves that the proposed method saves the time and energy.

Streszczenie. Zaproponowano nowatorskie zastosowanie podejścia hybrydowego, które wykorzystuje teorię zbiorów przybliżonych (RST) i metodę oceny kombinowanej opartej na odległości (CODAS) w celu ustalenia priorytetów dostępnych lokalizacji do zainstalowania elektrowni wodnej (HPP) zgodnie z atrybutami wielokryterialnymi, np. dostępność do sieci elektrycznej, potencjał energetyczny, aspekty ekonomiczne, wpływ środowiska, topografia i zagrożenia naturalne. (Planowanie usytuowania elektrowni wodnej metodą wstępną i kombinowanąocena na podstawie odległości).

Keywords: Hydropower plant, site selection, multiple-criteria decision-making, rough set, combinative distance-based assessment
Słowa kluczowe: Elektrownia wodna, wybór miejsca, podejmowanie decyzji według wielu kryteriów, zgrubny zestaw, kombinowana ocena oparta na odległości

Introduction

Global warming has caused by the increase in industrial activities and unrestrained usage of fossil fuels. Consequently, the climate of several places is unforeseeable nowadays and has turned into unusual. Therefore, the hydropower importance arises as one from the best sources of renewable energy which is distinguished as environmentally friendly, safe, sustainable, and economical [1, 2].

Selecting the best site for installing hydropower plant (HPP) is a tremendously complex procedure as various and contradictory criteria need to be studied in detail. In general, the dependence of the feasibility of installing a power plant (PP) on location, results in a multiple-criteria decision making (MCDM) problem. During the procedure of siting PP, there are quantifiable and epistemic uncertain criteria. The uncertain criteria associated can be modeled correctly by means of an algorithm which imitates natural intelligence.

Throughout installing industrial locations like PPs, numerous hurtful elements that are dangerous to environment and living organisms will augment due to reducing the area of large forests in erection stage and pollutants. Moreover, hurtful gases may be emitted owing to the combustion of fuel in the thermal PPs. Our already highly polluted environment will deteriorate by irresponsibly and improperly siting the PP construction. Consequently, environment influence evaluation (EIE) is habitually executed after determining possible site for installing an industrial plant. EIE procedures act as a strict requirement in siting for long time and have presently attracted researchers’ interests.

Criteria e.g. accessibility to electrical grid and economical respects also act significant roles in siting PPs. During siting HPP, water flow rate and watery head are important criteria since the output power of HPP is directly proportional to them.

Numerous researchers have aimed to prioritize available locations for installing PPs by means of several approaches. Particularly, geographical information system (GIS) [3-9], ordered weighted averaging accompanied by linear weighted averaging [10], artificial neural networks learned by genetic algorithm [11], neuro-fuzzy structure [12], technicality of ordering preference using similarities to ideal solution (TOPSIS) accompanied by vlše kriterijumska optimizacija kompromisno rešenje (VIKOR) (which can be translated from Bosnian to English, better criterion optimization compromise solution) [13], and analytic hierarchy process (AHP) [14].

Other approaches like fuzzy logic (FL) [15,16], FL accompanied by TOPSIS [17-19], FL accompanied by both of AHP and TOPSIS [20, 21], expert system [22], and linear programming [23], were applied to rank available sites for installing PPs.

In addition to the above approaches there are others have been utilized to grade available locations for installing PPs such as graph theory accompanied by matrix method [24], multi-attribute choquet integral [25], hierarchical decision model [26], resources spatial and temporal conjunction [27], and rough set theory (RST) accompanied by multi-objective programming [28].

With reference to the above brief survey, it is still a room for ranking available sites for installing HPP. In this regard, the research will address RST and combinative distance based assessment (CODAS), which was designed in 2016 [29], in order to grade available locations for installing HPP since published results of RST and CODAS are hopeful and verify their preference over other methods.

RST

RST can be utilized to draw out knowledge from a scope in a brief manner while preserving the content of the information [30]. In RST, distinguishing two objects acts a critical role for choosing a feature [31].

Knowledge Systems

Assume an information system (OB, ATT, VAL, f), where OB – a non-empty group of objects and ATT – a nonempty group of limited attributes, VAL – a group of values of attributes, f – a mapping which from OB to VAL, and fa(x) means the value of attribute a of object x.

Indistinguishability Relation

In RST, an equivalence relation RA is the base of sorting procedure and it can be stated w.r.t. to A (where A ⊆ ATT) as stated in (1).

.

If (x, y) ∈ RA, then it is said that x and y are indistinguishable using attributes from A. Equivalence classes created by equivalence relation RA are called as categorization [x]A.

Approximations of Sets

Upper and lower approximations of X ⊆ OB, are stated as below:

.

Rough set is the ordered pair (RA ↓ X, RA ↑ X).

Dependency of Attributes

An evaluation of dependency of two attributes sets A, B ⊆ ATT is presented in RST. The evaluation is called a degree of dependence of A on B (γB(A)) and stated in (4).

.

where card – the set cardinality and POSB(A) – a positive zone of categorization [x]A (or shortly a positive zone of A) for B. The set POSB(A) includes the objects of OB that perhaps be categorized as pertaining to one equivalence class of RA, utilizing attributes from B. The parameter γB(A) determines ratio of the objects that can be correctly categorized. It can be said that A relies on B to degree γB(A). The value of γB(A) ranges from 0 to 1.

Importance of Attributes

The parameter γ is utilized to identify a vital conception for investigations about importance of an attribute as revealed in (6).

.

where σBa– the importance of an attribute a, a ∈ B, B ⊆ ATT, which indicates how significant the attribute a is in B, concerning categorization [x]A. Removal of attribute a is tested and its importance is determined by the resultant change in categorization [x]A.

The described importance relies on both set A and B so it is relative value. Thus, an attribute perhaps owns different importance for different categorizations and in different sets (set B in (6)). To identify an absolute importance of an attribute in (7), the entire set of attributes ATT is taken as the sets A and B in the description A = B = ATT.

.

And taking in consideration that γATT (ATT) = 1, then:

.
Attributes Reduct and Core Attributes

Suppose an attribute a, a ∈ B, B ⊆ ATT, if POSB([x]A) = POSB−{a}([x]A), then a is redundant to B, concerning [x]A, otherwise a is indispensable.

If RB = RATT and POSB([x]A) ≠ POSB−{a}([x]A), then B is named a reduct subset for information system and symbolized as RED(ATT); the intersection of these reduct subsets is called core and symbolized as CORE = ⋂RED(ATT).

Weights of Attributes

When each attribute importance is normalized, each attribute weight (wti) can be obtained as stated in (9).

.
CODAS

CODAS is a modern method utilized efficiently in MCDM. In this technique, the desirability of all obtainable alternates is measured based on two criteria, first of them, the Euclidean spacing (l2 -norm) measurement between every alternate and the worst solution. The second criterion is the corresponding measurement of Taxicab spacing (l-norm) [32]. It’s obvious that the alternate that owns larger spacing from the worst solution is more desired. In this technique, if two alternates are incomparable in accordance with the Euclidean spacing, the Taxicab spacing will be utilized as secondary measurement [33]. Assume that there are m alternates and k criteria. The steps of CODAS for MCDM are as following:

1st Step
The decision-making matrix (X), is constructed as below:

.

where xij (xij > 0) – the value of performance of alternate i on criterion j (i ∈ {1, 2…, m} and j ∈ {1, 2…, k}).

2nd Step
The matrix of normalized values (nij) of performance, is computed using linear normalization as following:

.

where Nc,Nb – the groups of cost and benefit criteria, consecutively

3rd Step
The matrix of the weighted normalized values (rij) of performance, is computed as follows:

rij = wtjnij

where wtj – the weight of criterion j, which is computed using (9) and subjected to the two following conditions:

.

4th Step
The worst solution (ws) is the minimum value of the weighted normalized values of performance as calculated below:

.

5th Step
The Euclidean spacing (Ei) and Taxicab spacing (Ti) between alternates and the worst solution, are computed as below:

.

6th Step
The relative assessment matrix (RE) is constructed, as following.

.

where n ∈ {1, 2…, m} and δ – a threshold function for determining whether two alternates own equal Euclidean distances or not, and is stated as below:

.

where β – the threshold parameter which the decisionmakers had defined. The value of β is between 0.01 and 0.05.

Two alternates will be compared using the Taxicab distance as an additional value if the variance between their Euclidean distances is less than β. In this paper, β = 0.02 is utilized for the computations.

7th Step
The assessment score for every alternate, is calculated as following:

.

8th Step
The alternates are ranked in descending order in accordance with the assessment scores values.

The flowchart in Fig. 1 displays the steps of the suggested approach including RST and CODAS for siting HPP.

Results, Validations, and Discussions

In this section, a case study located in northern Iran is tested to legalize the performance and the effectiveness of the suggested approach in MCDM for sitig HPP.

Knowledge System of Siting HPP

Table 1 includes the required information system for RST about available locations of HPP. Twenty-two available locations (Loc1, Loc2…, Loc22) and twelve conditional attributes (ca1, ca2…, ca12) with their values are displayed in Table 1. Decision attribute (DA) indicates the level of suitability (0 for low appropriateness, 1 for medium appropriateness, 2 for high appropriateness). Interpretations of conditional attributes (ca1, ca2…, ca12) and their values (1, 2, 3) are revealed in Table 2.

Categorization and attributes dependency, which are computed using (1) to (5), are not mentioned to avoid boring lengthy article to the readers but their values are utilized to calculate the reduct and importance of attributes.

Attributes Reduct by RST

The consistency of appropriateness level with twelve conditional attributes is tested during this stage. For extracting reduct using RST, redundant attributes need to be defined and a decision table is required to be created free of inconsistencies. To find the redundant attributes of assessments, removal of attributes one by one is tested, and the categorization is checked each time to insure no inconsistency has arisen. The results reveal that a2, a6, a7, a9, a10, a11, a12 are redundant attributes and a1, a3, a4, a5, a8 are indispensable attributes. That is to say, accessibility to electrical grid, water flow rate, watery head, economical respects, and topography are the core for appropriateness level for siting HPP and the other indices can be omitted because they are unnecessary information for siting HPP. Consequently, Table 3 is gotten by removing the redundant attributes from Table 1.

Fig.1. Flowchart of siting HPP by RST and CODAS

Determination of Importance and Weights of Attributes by RST

The importance of the core attributes ca1, ca3, ca4, ca5, ca8 is calculated using (8) and the results are 0.091, 0.227, 0.227, 0.136, 0.091 respectively. The attributes weight of ca1, ca3, ca4, ca5, ca8 is calculated by normalization of attribute importance using (9) as revealed in (23) to (27).

.

Table 1. Information system of siting HPP

.

Table 2. Conditional attributes and their values

.

Table 3. Core attributes

.
Ranking the Available Locations of HPP by CODAS

After determination of the criteria weights by RST, the rank of HPP sites is obtained using CODAS. In CODAS, firstly decision-making matrix is constructed in Table 4.

In siting HPP problem, ca1, ca3, ca4, ca5, ca8 criteria are cost criteria because they are desired to be minimized. The matrix of normalized values of performance is computed in Table 5 using (11).

The weighted normalized performance values and the worst solution are computed in Table 6 using (12) and (16), consecutively.

The Euclidean and Taxicab distances between alternatives and the worst solution are computed in Table 7 using (17) and (18), consecutively. The relative assessment matrix is computed using (20). The assessment scores (Η) of alternatives are computed using (22) and the locations are ranked in descending order in accordance with H values as revealed in Table 7.

Table 4. Decision-making matrix

.

Table 5. The matrix of normalized values of performance

.

Table 6. The matrix of the weighted normalized values of performance and the worst solution

.

Table 7. Rank of alternatives

.
Results without Attributes Reduct

In the previous subsection, the alternatives order for siting HPP is gotten by CODAS after using RST with attributes reduct. In this section, the same case study is tested without attributes reduct to prove usefulness and effectiveness of the proposed method in MCDM for siting HPP. All the criteria in Table 1 are going to be utilized to make a decision. Table 8 displays the criteria weights when utilizing all criteria. Therefore, the rank of all locations is revealed in Table 9.

Obviously, the same rank is obtained and the most desirable choice in two different situations is identical. Consequently, the proposed approach is proved to be useful and effective tool in siting HPP. Furthermore, the proposed approach saves much time and energy due to attributes reduct by RST and avoids human perceptions and judgments using information entropy weight which is dependent on the real data.

Table 8. The attributes weights without attributes reduct

.

Table 9. Rank of alternatives without attributes reduct

.
Conclusions

Rank of the available locations for installing HPP can be considered as MCDM problem. Hybrid approach of RST and CODAS has been presented for this purpose. RST is utilized for attributes reduct and attributes weights calculation. CODAS is utilized for locations rank determination. The obtainable sites for installing HPP are ranked by the proposed approach for a case study placed in northern Iran. The same case study is tested without attributes reduct. Sameness of the gotten results in two states verifies that the proposed approach is characterized by good performance, efficacy and saving in the required time and energy. Hence, the proposed approach can be recommended as MCDM tool for siting PPs other than HPP.

REFERENCES

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[5] Romanelli J.P., Silva L.G.M., Horta A., Picoli R.A., Site selection for hydropower development: a GIS-based framework to improve planning in Brazil, Journal of Environmental Engineering, 144 (2018), No. 7, 1-10.
[6] Sanchez-Lozano J.M., García-Cascales M.S., Lamata M.T., Identification and selection of potential sites for onshore wind farms development in Region of Murcia, Spain, Energy, 73 (2014), 311-324.
[7] Larentis D.G., Collischonn W., Olivera F., Tucci C.E.M., Gisbased procedures for hydropower potential spotting, Energy, 35 (2010), 4237-4243.
[8] Lakshmi S.V., Sarvani G.R., Selection of suitable sites for small hydropower plants using Geo-Spatial technology, International Journal of Pure and Applied Mathematics, 119 (2018), No. 17, 217-240.
[9] Kaliraj S., Malar V.K., Geospatial analysis to assess the potential site for coal based thermal power station in Gujarat, India, Advances in Applied Science Research, 3 (2012), No. 3, 1554-1562.
[10] Temel P., Evaluation of potential run-of river hydropower plant sites using multi-criteria decision making in terms of environmental and social aspects, MSc thesis, Middle East Technical University, (2015).
[11] Shimray B.A., Singh K.M., Khelchandra T., Mehta R.K., Ranking of sites for installation of hydropower plant using MLP neural network trained with GA: a MADM approach, Computational Intelligence and Neuroscience, 2017 (2017), 1-8.
[12] Shimray B.A., Singh K.M., Khelchandra T., Mehta R.K., A new MLP–GA–Fuzzy decision support system for hydro power plant site selection, Arabian Journal for Science and Engineering, 43 (2018), 6823-6835.
[13] Adhikary P., Roy P.K., Mazumdar A., Selection of small hydropower project site: a multi-criteria optimization technique approach, ARPN Journal of Engineering and Applied Sciences, 10 (2015), No. 8, 3280-3285.
[14] Silva H., Blengini A., Mota L., Pezzuto C., Lavorato M., Carvalho M., Multi-criteria analysis of Brazilian wind farms, International Journal of Renewable Energy Research, 10 (2020), No. 2, 1042-1053.
[15] Erol İ., Sencer S., Özmen A., Searcy C., Fuzzy MCDM framework for locating a nuclear power plant in Turkey, Energy Policy. 67 (2014), 186-197.
[16] Deveci M., Cali U., Kucuksari S., Erdogan N., Interval type-2 fuzzy sets based multi-criteria decision-making model for offshore wind farm development in Ireland, Energy, 198 (2020), 117317.
[17] Wang C.N., Su C.C., Nguyen V.T., Nuclear power plant location selection in Vietnam under fuzzy environment conditions, Symmetry, 10 (2018), 548.
[18] Kurt Ü., The fuzzy TOPSIS and generalized Choquet fuzzy integral algorithm for nuclear power plant site selection – a case study from Turkey, Journal of Nuclear Science and Technology, 51 (2014), No. 10, 1241-1255.
[19] Erdebilli B., Yildizbasi A., Arikan Ü.Z.B., Using intuitionistic fuzzy TOPSIS in site selection of wind power plants in Turkey, Advances in Fuzzy Systems, 2018 (2018), 6703798.
[20] Locatelli G., Mancini M., A framework for the selection of the right nuclear power plant, International Journal of Production Research, 50 (2012), no. 17, 4753-4766.
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Authors: Ahmed Mahmoud Agwa, Electrical Engineering Department, Faculty of Engineering, Northern Border University, Arar 1321, Saudi Arabia & Electrical Engineering Department, Faculty of Engineering, Al-Azhar University, Cairo 11651, Egypt, Email: ah1582009@yahoo.com; Shaaban Mohamed Shaaban, Electrical Engineering Department, Faculty of Engineering, Northern Border University, Arar 1321, Saudi Arabia & Department of Engineering Basic Science, Faculty of Engineerin, Menoufia University, Shebin El-Kom 32511, Egypt, E-mail: shabaan27@gmail.com

Source & Publisher Item Identifier: PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 97 NR 3/2021. doi:10.15199/48.2021.03.03

Particle Swarm Optimization Algorithm for Solar PV System under Partial Shading

Published by Fawaz S. Abdulla1, Ali N. Hamoodi2, Abdulaziz M. Kheder3, Northern Technical University, Engineering Technical College of Mosul, Mosul, Iraq. ORCID. 1. 0000-0002-6888-0580, 2. /000-0003-0991-3538, 3. 0000-0003-2606-4697

Abstract. Conventional maximum power point tracking (MPPT) has several demits such as steady-state oscillation and the inability to distinguish between multipacks generated under partial shading conditions (PSC). This paper studies the compression between the conventional Perturb and Observe (P&O) algorithm and the Particle Swarm Optimization ( PSO) algorithm to track global peak (GP) . Matlab Simulink carried out under PSC, the result shows that the PSO algorithm is successful to capture GP with 98.6% efficiency and the P&O algorithm is failed to capture the GP.

Streszczenie. Konwencjonalne śledzenie punktu maksymalnej mocy (MPPT) ma kilka wad, takich jak oscylacja stanu ustalonego i niemożność rozróżnienia opakowań zbiorczych generowanych w warunkach częściowego zacienienia (PSC). Ten artykuł bada kompresję pomiędzy konwencjonalnym algorytmem Perturb and Observe (P&O) a algorytmem Particle Swarm Optimization (PSO) w celu śledzenia globalnego piku (GP). Matlab Simulink przeprowadzony w ramach PSC, wynik pokazuje, że algorytm PSO z powodzeniem wychwytuje GP z wydajnością 98,6%, a algorytm P&O nie jest w stanie wychwycić GP. (Algorytm optymalizacji roju cząstek dla systemu fotowoltaicznego w warunkach częściowego zacienienia)

Keywords: particle swarm optimization (PSO), maximum power point (MPPT), photovoltaic (PV), partial shading condition (PSC).
Słowa kluczowe: algorytm rojowy, system fotowoltaiczny,

Introduction

Renewable energy represents the energy of future, especially with use advance control system. solar energy system considered as very important option for electricity generation[1, 2]. Furthermore, World energy consumption rises nearly 50% by 2050 [3]. Besides the fossil fuel depletion and increases pollution, all these challenges tend to focus on alternate energy resources. Solar energy is the most interesting option to fill this gap between generation and demand. It is a freely abundant, sustainable and clean energy source without environmentally negative effects. The power harvested from the PV module is non-linear and has a unique maximum power point (MPP), which is depends on the solar irradiance and ambient temperature. This state will be more complex when a PV power system operate under PSC. In such case a PV modules received non-uniform irradiance. Hence the P-V characteristic curve has multiple peaks. Several local peaks(LP) and one of them is the GP. The conventional MPPTs especially P&O algorithm and Incremental conductance algorithm are unable to distinguish between them and fail to capture GP.

Recently, numerous MPPT algorithms were carried out to track GP regardless of environmental condition changes such as particle swarm optimization (PSO), anti-colony, bee colony, and gray wolf optimization. Because the PV power losses under PSC may be greater than 70% of the generated power [4].

1. PV equivalent circuit

PV cells represent the main component of the PV power system, which is made by two or more wafers of doping Silicon. One cell is generated a small amount of power, about one watt[5], this value insufficient to load requirement. A group of solar cells are blocked together in parallel and series via grid collector busbar to get desired power value and this block is called a PV module. Also, a number of PV modules are arranged in series to constitute a string and increase the voltage to the desired level. A group of strings connected in parallel to form an array and enhance the output current. In the night, the solar cell is not active and act as a P-N junction diode[6]. Depending on the Shockley diode equation, the single diode model represents the simplest and more common PV model [7]. The model is used to describe the output characteristics curves. Fig.(1) represent the single diode modelling of PV cell, which consists of parallel connection between diode and current source with shunt, and series resistors. The diode represents the effect of the P-N junction of the PV cell. The series resistance is used to describe the internal losses of one PV cell and adjacent PV cells connected to it and shunt resistance to show the effect of ground leakage current.

.

where: Ipv – Photovoltaic output current of a module, Iph – photo generated current, Io – saturation current, ID – Diode current, Q –Electron charge (1.6×10-19 C), Vpv – Output voltage of PV module, Rs – Series resistance, Rsh – Shunt resistance, n – Ideality factor, K – Boltzmann’s constant (13.8×10-23 J/k).

Fig.1. The equivalent circuit of PV cell

2. Characteristics of PV module

The output curves of 350W half-cut PV module are obtained under standard test conditions (STC) (G=1000 W/m2, T=25oC, AM=1.5) where: G – solar irradiance, T – ambient temperature, AM – Air mass Fig.2 represents the (I-V) and (P-V) characteristic curves of PV module The characteristic curves have three important points used to explain the electrical behave of the PV module.

The first is short circuit points, which are obtained when the output terminals of the PV module are shorted and the output current is called Ish. The second is the open circuit point if output terminals of the PV module are opened and the terminal voltage called Voc. The third point is MPP, the maximum operating point of the PV module. At this point, the output current is called IMPP and the voltage is VMPP. The PV module should be operated at MPP to extract maximum from the PV module – where: Ish – Short circuit current of PV module, Voc – open circuit voltage of PV module, IMPP – PV module current at MPP, VMPP – PV module voltage at MPP.

Fig.2. (I-V) and (P-V) characteristic curves of PV module

3. The effect of partial shading

Normally, the PV power system outdoor installed, this means it is exhibited to external circumstances. PSC is one of the challenging effects on PV system performance. In this case, the PV power system is composed of four PV modules arranged in series; each one of them received a different irradiance level due to cloud movements, trees, buildings, or manufacturing mismatch. The shaded PV cells act as a load more than an energy source and the current of adjacent cells pass through it, lead to generating the hot spot on shaded cells. To protect PV cells from a hot spot, a group of PV cells connected to bypass diodes in parallel. Under uniform irradiance the bypass diode inactive, but under PSC the bypass diode active and allow to the current passing through it. Half-cut PV module technology is used to reduce PSC power losses via cutting PV modules into two parts: upper and lower. Each module has double numbers of cells. If one part is shaded, the bypass diode of an affected part will act, but the not shaded part still generates electrical power. The PV module can save about 50% power in the case of PSC [8]. The parameters of KDP350 PV module are given in table1.

Fig.3. PV modules under PSC
Fig.4. (P-V) curve under PSC

Fig.3. represents the simulation of PV modules under PSC. Local and global peaks under PSC are shown in Fig.4.

Table 1. KD-P350 PV module parameters

.
4. Boost converter

The MPPT circuit consists of a boost converter connected between PV array and load to regulate the DC voltage and current to the optimal value. Because low energy conversion of a PV system, the adoption of MPPT becomes more necessary for maintain the operation point at MPPT. A circuit diagram of boost converter illustrated in fig.5 which is contains an IGBT, diode, passive inductance and capacitance, and resistive load. The operation of the boost converter can be described into two modes. The first mode starts when the IGBT switched-on for period Ton. The input inductor current rises from L1 to L2 [9]. At the same time, the boost capacitor discharged and provide output current to the load. The second mode starts when the IGBT switched-off and the inductor stored energy in the previous mode are discharged through the diode.

Fig.5. Boost convert

The converter parameters illustrated in table 2.

Table 2. The boost converter parameters

.
Fig.6. Flowchart of P&O algorithm

5. Perturb and observe algorithm

Most commonly used in PV systems to drive DC/DC converter with certain duty cycle for maintaining the operation point at MPP. The advantages of this method that simple, easy to implement, and low cost. The basic concept of P&O is that perturb the output voltage by a small magnitude and observes the change of output power after each amount. If ΔP is positive, still raise the output voltage of DC-DC converter in the same direction and get more convergence to MPP. Else if, ΔP is negative we are going in the divergence of MPP and should decrease the value of output voltage. The main drawbacks of this method are oscillation around MPP and inaccurate tracking under PSC. Fig.6 illustrates the algorithm of P&O method – where: ΔP – the MPPT output power change

Fig.7 Flowchart of PSO algorithm
Fig.8 PV array with PSO and P&O MPPTs

6. Particle swarm optimization

PSO is a Meta-heuristic algorithm introduced by (James Kenndy and Russell Eberhart in 1995) to optimize nonlinear and multidimensional problems [10]. This method was inspired by simulating the community behaves of fishes schooling and birds flocking [10]. The basic strategy of PSO is that each particle moves in search space to find the optimum solution. PSO optimization depends on two main equations of velocity and position.

.

where: xik – previous position of particle, x(k+1) – updated position after each iteration, vik – previous velocity of particle, vi(k+1) – updated velocity after each iteration, xibest – personal experience of each particle, Xgbest – social experience of whole swarm, w – the inertia weight, C1 and C2 – acceleration coefficients, r1 and r2 – random numbers between [0 ,1]

7. Modeling the circuit diagram

The circuit diagram consists of four PV modules connected as the string to raise the output voltage at the desired value. Each PV module in the string received a different irradiance level, the incident irradiance on the first PV module is 500W/m2, the second one received 800W/m2, the third and fourth PV modules received the same value of solar irradiance which is equal 1000W/m2. For obtained maximum energy from the sun, the PV module connected to the MPPT to capture MPP and extract the maximum power available under PSC. Fig.8 illustrate the circuit design with two algorithms, PSO and P&O.

8. Simulation results

In this PV system two MPPTs, PSO and P&O are examined under PSC. The PV array is four 350W polycrystalline half-cut PV modules connected in series for reached output voltage and power to the desired value. VMPP and IMPP of PV array under STC are (154.4V, 8.94A) sequentially. Under PSC (P-V) curve have three peaks, one of them is GP located between two LPs. As mentioned in fig.4, the power at GP is equal to 890W, the first LP is 680W and the second LP is 790W. The prime goal of PSO based MPPT is to distinguish between multi-peaks generated under PSC and maintain the operation point at GP.

8.1 P&O algorithm

Fig.9 represents the relationship between the voltages before and after boosting with respect to time.

Fig.10 represents the relationship between the currents before and after boosting with respect to time. Fig.11 represents the relationship between the output power of P&O MPPT with time.

8.2 PSO algorithm

Fig.12 Represent the relationship between the voltages before and after boosting with respect to time. Fig.13 represents the relationship between the input and output current of PSO MPPT. There is an oscillation in the input current due to PSC effect and the boost circuit regulate it. Fig.14 represents the relationship between the PSO MPPT output power after boosting with time.

Table 2. Represents the obtained results for two algorithms ( PSO and P&O).

Fig.9. P&O MPPT input and output voltage vs. Time
Fig.10. P&O MPPT input and output current vs. Time
Fig.11. P&O MPPT output power vs. Time
Fig.12. PSO MPPT input and output Voltage vs. Time
Fig.13. PSO MPPT input and output current vs. Time
Fig.14. PSO MPPT output power vs. time

Table 3. obtained resultant

.
9. Conclusions

The influence of PSC on PV staring performance is examined and analyzed via two MPPTs under the same circumstances. The Simulink results indicated above, which are show the output power extracted from PV string, when using P&O MPPT is equal to 650W. But when we use PSO MPPT the output extracted power is 877.9W. The PSO algorithm is stable, accurate, and provides constant maximum output power with high efficiency whatever conditions change. On the other hand, the P&O MPPT has high steady-state fluctuation around MPP and poor performance under PSC.

REFERENCES

[1] ashif Ishaque, et al., A Direct Control Based Maximum Power Point Tracking Method for Photovoltaic System Under partial Shading Conditions using Particle Swarm Optimization algorithm, Applied Energy 99 (2012): 414-422.
[2] Ali M. Eltamaly, et al., Photovoltaic Maximum Power Point Tracking Under Dynamic Partial Shading Changes by Novel Adaptive Particle Swarm Optimization Strategy, Transactions of the Institute of Measurement and Control 42.1 (2020): 104-115.
[3] Outlook, Annual Energy. , U.S. Energy information administration, Department of Energy (2020).
[4] Eltamaly, Ali M., and Almoataz Y. Abdelaziz, eds, Modern Maximum Power Point Tracking Techniques for Photovoltaic Energy Systems. Springer, 2019.
[5] Teo, Kenneth Tze Kin, et al., Maximum Power Point Tracking of Partially Shaded Photovoltaic Arrays using Particle Swarm Optimization, 2014 4th International Conference on Artificial Intelligence with Applications in Engineering and Technology. IEEE, 2014.
[6] Mahdi, A. J., et al., Improvement of a MPPT Algorithm for PV Systems and its Experimental Validation, International Conference on Renewable Energies and Power Quality. Vol.25. 2010.
[7] González-Longatt, Francisco M. ,Model of Photovoltaic Module in Matlab, i Cibelec 2005 (2005): 1-5.
[8] Joshi, Arati, Afrah Khan, and S. P. Afra., Comparison of Half Cut Solar Cells with Standard Solar Cells, 2019 Advances in Science and Engineering Technology International Conferences (ASET). IEEE, 2019.
[9] Abouelela, Mohamed, Power Electronics for Practical Implementation of PV MPPT, Modern Maximum Power Point Tracking Techniques for Photovoltaic Energy Systems, Springer, Cham, 2020. 65-105.
[10] Kennedy, James, and Russell Eberhart. Particle Swarm Optimization, Proceedings of ICNN’95-international conference on neural networks. Vol. 4. IEEE, 1995.

Source & Publisher Item Identifier: PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 97 NR 10/2021. doi:10.15199/48.2021.10.17

Inrush Current Impact Limitation in Smart Building Applications

Published by 1. Mariusz STOSUR1, 2. Kacper SOWA2, 3. Piotr ORAMUS1, 4. Adam RUSZCZYK2, 5. Pawel ALOSZKO3,
ABB E-mobility, Krakow, Poland (1), ABB Technology Center, Krakow, Poland (2), ABB Corporate Technology Center, Krakow, Poland (3)
ORCID. 1. 0000-0002-1522-3405, 2. 0000-0001-8246-2337, 3. 0000-0002-4810-3936, 4. 0000-0001-7477-8139, 5. 0000-0002-1668-6292

Abstract: This paper presents a hybrid switches based on semiconductors and mechanical switches. Devices are dedicated to limitation of adverse effect of capacitive type loads start-up especially in domestic applications, during which high value of inrush current is generated. Two different approaches are studied in the paper, both of them using energy harvesting to operate. The proposed solution combine together several advantages switches, such as: increased lifetime of the mechanical part, small on-state losses, smaller dimensions in comparison to mechanical switches, increased durability on overcurrent states, arc-less switching, or limited switching transients. In presented case solution is adopted as rocker switch of LED light sources.

Streszczenie. W artykule przedstawiono łączniki hybrydowe oparte na półprzewodnikach i łącznikach mechanicznych. Urządzenia przeznaczone są do ograniczania niekorzystnych skutków załączania obciążeń typu pojemnościowego, zwłaszcza w zastosowaniach domowych, podczas których generowana jest duża wartość krótkotrwałego prądu załączania. W artykule przeanalizowano dwa różne podejścia, z których oba wykorzystują do działania pozyskiwanie energii. Zaproponowane rozwiązanie łączy w sobie kilka zalet wyłączników, takich jak: zwiększona żywotność części mechanicznej, małe straty w stanie załączenia, mniejsze wymiary w porównaniu do wyłączników mechanicznych, zwiększona trwałość w stanach nadprądowych, czy ograniczenie łączeniowych stanów przejściowych. W prezentowanym przypadku przyjęto rozwiązanie jako łącznik kołyskowy źródeł światła LED. (Ograniczenie wpływu krótkotrwałego prądu załączania w zastosowaniach inteligentnych budynków).

Keywords: inrush current, transient state, arcing, mechanical contacts, hybrid switches
Słowa kluczowe: krótkotrwały prąd załączania, stany przejściowe, łuk elektryczny, zestyki, łączniki hybrydowe

Introduction

Traditional and mechanical switches find an application in electric circuits which are used in many branch of an industry and in residential installations [1-2]. The proper functioning of mechanical switching apparatus depends on surface conditions of electrical contacts. It should be also emphasized that, the electrical contacts are a part of an electrical switch, which is the most responsible for its proper functioning.

Moreover, the design of the electrical contacts must be resistant for phenomena such as: a mechanical abrasion, an oxidation and a corrosion, contact welding, heating and a temperature rise. The electric arc erosion of the contacts also happens due to inrush current during switching operation – especially during turning on LED light lamps, which are perfect example of capacitive type of the loads.

For these reasons, limiting arc erosion is important issue. The limitation of the electric arc erosion maintains the surface of electrical contacts in good conditions for longer time which, as a consequence, causes an increase of lifespan of entire switch. Hence, the limitation of the electric energy and the electric arc erosion is an important issue to provide a high reliability of electricity transmission in electrical circuits [3-4].

One of the most effective method proposed in this note for limiting electric arc energy is application of hybrid switch. Basically, hybrid switches connect many advantages of mechanical and semiconductor switches, such as: increased lifetime of the switch, small on-state losses, smaller dimensions in comparison to mechanical switches, increased durability on overcurrent states, arc-less switching, or limited switching transients. Idea presented in this document helps to limit arc erosion during light switching-on operations [5-7].

Despite that hybrid constructions being combination of mechanical and semiconductor switches are devices known from many years, the proposed idea includes new method for control of semiconductor part. Thanks to this, a design and overall complexity of entire hybrid switch is significantly simplified.

Modern LED sources of light are typical capacitive type of loads, connected to the mains through single-phase rectifier (Graetz bridge). Electrical diagram of LED bulb driver is illustrated in Fig. 1a.

In such a circuit an inrush current will always occur, when capacitor will be fully discharged and switching instance occurred in non-zero crossing of line voltage, in accordance with formula (1):

.

where: C – the value of capacitance; uline – instantaneous value of line voltage; uc0 – value of capacitor voltage.

According to formula (1) the highest value of the current will occur when: uline = max and uc0 = 0 V (turning on in maximum of line voltage when capacitor is fully discharged). Such a case (current recorded during turning on LED lamps) is illustrated in Fig. 1b. Initial value of the current for 8 bulbs (8 × 11 W) can even exceed 90 A.

This paper presents two different methods of inrush current limitation. The first one based on triac semiconductor switch connected with two mechanical switches working in defined sequence during switching operation and the second one based on MOSFET semiconductor switch connected into the operated switch.

.
Fig.1. An example of LED light (bulb): a) – electrical schematic and appearance; b) – inrush current transients during LED lights turning on in maximum line voltage

Application of hybrid switching allows to achieve almost completely arc-less and limiting inrush current through application of synchronized switching (the current starts to flow in circuit at voltage zero-crossing). This approach significantly increases reliability of the switch in comparison to traditional mechanical switch. Development of low voltage hybrid switch (using triac semiconductor elements) with increased lifetime could be interesting for household and industry applications.

Principle of operation of proposed hybrid switches

Currently, LED lights may cause a welding of a conventional light switch contacts and their erosion (inrush current effect during switching operation), which introduce accelerated aging and reduction of switch lifetime and reliability (Fig. 2). The presented idea increases lifetime of light switches by means of application of semiconductor components. During switching operation, current starts to flow at voltage zero-crossing, and almost entire current commutates into semiconductor branch, which significantly helps to keep mechanical contacts of the switch in good conditions for long time. Basic principle of operation for Zero Voltage Switching (ZVS) switch is presented in Fig. 3.

Fig.2. Mechanical switch and welding/corrosion of contact after several hundred cycles of “open-close” operation

1. Triac solution

This solution comprises double mechanical contact switch with coupled drives in defined way (connected together through dedicated cam). Proposed solution provides defined time delay (≥ 10 ms) between closing both switch contacts (called further “slow” and “fast” contact). According to Fig. 3. The semiconductor branch is connected in series with fast switch and in parallel with the main switch (slow contact), which provides galvanic insulation of interrupting circuit.

Fig.3. ZVS LED light switch with inrush current elimination – basic principle of operation

Switching sequence of proposed device is as following:

(I) Drive of the switch is pushed by pressing it, which first resulting in closing of fast switch. As a result, energy from energized circuit is harvested by triac gate-driver (GD), which is composed of single-phase rectifier with capacitor (detailed electrical diagram is depicted in Fig. 6a). The capacitor is fully charged within 5 ms, which allows to prepare triac for starting conduct current. Current patch during sequence is illustrated in Fig. 4.

Fig.4. First (I) switching sequence of the device

(II) When the level of the energy stored in capacitor is sufficient and the nearest zero voltage crossing occurred, triac is ignited by optotriac module. This leads to significant limitation of inrush current value. The level of the energy stored in capacitor provides triac ignition for several periods of line voltage. Current patch during this sequence is illustrated in Fig. 5.

Fig.5. Second (II) switching sequence of the device

(III) In the final step branch witch thyristors is bypassed by slow contact, hence current commutated to branch with lower loses and triac is turned off as illustrated in Fig. 6. Time between closing of slow and fast contacts is above 10 ms.

Fig.6. Third (III) switching sequence of the device

Diagram of the circuit and designed in Autodesk Eagle PCB integrated with light switch are presented in Fig. 7. The size of the PCB allows direct integration with existing solutions of the switches.

Experimental verification has been carried out in circuit depicted in Fig. 8a with several types of LED bulbs (different manufacturers). Voltage across switch and two currents have been recorded. A description of the oscillograms depicted in Fig. 8b is in accordance with switching sequence. Initial value of current has been significantly reduced – from 90 A (Fig. 1b) to 8 A (Fig. 8b), that is more than 11 times.

Fig.7. ZVS LED light switch with inrush current elimination: a) schematic diagram; b) ÷ e) practical implementation

2. MOSFET solution

The second of proposed ideas is based on mechanical rocket switch which is bypassed by semiconductor switches (e.g. MOSFET’s), as illustrated in Fig. 9.

The mechanical contacts of the switch are normally opened and electric circuit is off (LED light is off). After mechanical contacts closing operation, di/dt (inrush current) is generated, due to LED light capacitance charging.

High di/dt is caused by voltage induction in primary winding of current transformer in accordance with formula (2):

.
Fig.8. Experimental verification of elaborated circuit operation:na) view of laboratory stand; b) measured oscillograms

Fig.9. Hybrid LED light switch – mechanical switch with bypassed by semiconductor switch

Hence, di/dt impulse is responsible for generation of energy pulse which triggers the MOSFET’s, that bypass the mechanical contacts during closing or opening operation (in other words the MOSFET elements are bypassing current from mechanical contacts during “closing/opening operation”. Diagram of the circuit and designed PCB integrated with light switch are illustrated in Fig. 10.

Experimental verification has been also carried out in circuit depicted in Fig. 8b with several types of LED bulbs. Two currents have been recorded as illustrated in Fig. 11, MOSFET branch current and main switch current.

3. Measured and calculated waveforms

In this section, measured waveforms are presented for three different cases:

• circuit was energized by standalone mechanical switch,
• circuit was energized by hybrid switch based on MOSFET,
• circuit was energized by hybrid switch based on triac.

Fig.10. LED light switch with inrush current impact limitation: a) schematic diagram; b)÷d) practical implementation
Fig.11. Experimental verification of developed circuit operation

The magnitudes were measured according to simplified circuit diagram with marked measurement points in Fig. 12: the waveforms of currents (current of entire switch A1, current of semiconductor branch A2, current of mechanical contacts A3) and voltage across the switch during energization V. The waveforms are presented in sections 1- 3 for three considered cases.

Fig.12. Simplified circuit diagram with marked measurement points

Based on measured voltage and currents, the following magnitudes were calculated: the power of LED energized by semiconductor branch, power of LED energized by mechanical contacts, amount of energy dissipated at semiconductor branch and amount of energy dissipated at mechanical contacts. The power and energy during energization process were calculated according to formulas (3) and (4).

.

Calculated waveforms are also presented in points 1÷3.

1. Standalone switch

Measured waveform of voltage across the standalone mechanical switch is presented in Fig. 13.

Fig. 13. Measured voltage waveforms – standalone mechanical switch

Measured current waveforms of mechanical contacts of standalone switch are presented in Fig. 14.

Fig.14. Measured current waveforms/inrush current – standalone mechanical switch

Calculated waveform of power led by mechanical contacts of standalone switch is presented in Fig. 15.

Fig.15. Calculated power waveforms – standalone mechanical switch

Calculated waveform of energy dissipated at mechanical contacts of standalone switch is presented in Fig. 16.

Fig.16. Calculated waveform of energy dissipated at contacts

2. MOSFET solution

Measured waveform of voltage across the mechanical contacts in hybrid switch with MOSFET is presented in Fig. 17.

Fig.17. Measured voltage waveforms – MOSFET solution

Waveform of voltage across the mechanical contacts in hybrid switch with MOSFET is presented in Fig. 18.

Fig.18. Measured voltage waveforms – MOSFET solution

Measured current waveforms of entire hybrid switch with MOSFET component are presented in Fig. 19.

Fig.19. Measured current waveforms of entire switch – MOSFET solution

Measured current waveform of MOSFET component is presented in Fig. 20.

Fig.20. Measured current of semiconductor branch – MOSFET solution

Measured current waveform of mechanical contacts in hybrid switch with MOSFET component is presented in Fig. 21.

Fig.21. Measured current of mechanical contacts – MOSFET solution

Calculated power waveforms led by MOSFET component and mechanical contacts are presented in Fig. 22.

Fig.22. Calculated power waveforms: a) power at mechanical contacts; b) power at semiconductor branch – MOSFET solution

Calculated energy waveforms dissipated at MOSFET component and mechanical contacts are presented in Fig. 23.

Fig.23. Calculated energy waveforms: a) energy dissipated at mechanical contacts; b) power dissipated at semiconductor branch – MOSFET solution

3. Triac solution

Measured waveform of voltage across the mechanical contacts in hybrid switch with triac component is presented in Fig. 24.

Fig.24. Measured voltage waveforms – Triac solution
Fig.25. Zoomed measured voltage waveforms – Triac solution
Fig.26. Measured current waveforms of entire switch – Triac solution

Zoomed waveform of voltage across the fast mechanical contacts in hybrid switch when triac component conducts is presented in Fig. 25.

Measured current waveforms of entire hybrid switch with triac component are presented in Fig. 26.

Measured current waveform of triac component is presented in Fig. 27.

Fig.27. Measured current of semiconductor branch – Triac solution

Measured current waveform of slow mechanical contacts in hybrid switch with triac component is presented in Fig. 28.

Fig.28. Measured current of mechanical contacts – Triac solution

Calculated power waveforms led by triac component and mechanical contacts are presented in Fig. 29.

Fig.29. Calculated power waveforms: a) power at mechanical contacts; b) power at semiconductor branch – Triac solution

Calculated energy waveforms dissipated at triac component and mechanical contacts are presented in Fig. 30.

.
Fig.30. Calculated energy waveforms: a) energy dissipated at mechanical contacts; b) power dissipated at semiconductor branch – Triac solution

Analysis of obtained results

This part of paper contains comprehensive descriptions of two solid state solutions of inrush current limiting devices, dedicated for integration with LED light switches (rockers type). The principle of operation in both cases are completely different. Triac solution significantly reduces peak value of inrush current during LED’s turning-on, while MOSFET solution limits only energy dissipation during contact bouncing. In both cases, the energy dissipated at contacts is reduced, hence both lifespan of mechanical contacts as well as lifespan of entire mechanical switch are increased.

Table 1. Comparison of main features of developed solutions is presented in Tab. 1

.

Both solutions do not need auxiliary power supply and can be connected into existing mechanical switch as extended module. The main function of the proposed solutions is to limit energy dissipated on mechanical contacts during inrush transients to eliminate undesired phenomena, such as arc erosion and contact welding that could lead to permanent damage of the mechanical switches.

Application of Triac solution requires modification of mechanical switch in comparison to MOSFET solution. However, MOSFET solution is more complex due to self-triggering principle of operation (based on di/dt detection).

The biggest advantage of the triac solution is significantly higher the efficiency for limitation of inrush current in energizing circuit.

Comparison of main features of developed solutions is presented in Tab. 1.

Detailed comparison of energy dissipation on mechanical contact, and inrush current limitation are depicted in Fig. 31 and 32.

Fig.31. Comparison of calculated energy values for considered cases
Fig.32. Comparison of inrush peak current for considered cases

As shown in Fig. 31, the energy losses dissipated at semiconductors branches are higher than on mechanical contacts due to characteristics of semiconductor elements (on-state resistance), however during normal operation, semiconductors are bypassed by mechanical contact.

The MOSFET solution does not limit the peak value of inrush current in comparison to the base case (Fig. 32). It results from its principle of operation – where part of the energy from initial di/dt impulse is harvested and used to ignition of the MOSFET, during mechanical contacts bouncing.

In case of Triac solution, the value of inrush current is 95% reduced in comparison to base case – what summarized in Table 2.

Table 2. Comparison of inrush peak current and calculated energies for considered cases

.
Conclusions

Hybrid LED light switch (mechanical switch with bypassing semiconductor circuit) may find an application in electric circuits which are being used in each branch of an industry and in residential installations, however the proper functioning of such switching apparatus strongly depends on surface conditions of electrical contacts and electrical conditions within power network. The novel circuits presented in the paper utilizes:

• triac device switched on in zero voltage which provide elimination of inrush current generated by capacitive type of the loads, as modern LED lights,

• MOSFET device absorbing significant part of the inrush current during LED lights turning on.

Compact size and simplicity of developed PCBs allows their easy integration with existing solutions. The proposed hybrid LED light switch (mechanical switch bypassed by semiconductor switch) during switching operation enables to achieve:

• arc-less switching operation,
• mitigation of switching transients,
• increased lifespan / decreased aging of contacts and the whole switch in comparison to existing mechanical switches,
• increased durability on overcurrent states in comparison to semiconductor switch,
• limited on state losses in comparison to semiconductor component.

Further development of proposed solution may provide further facilities, such as: sizing and cost optimization. Proposed solutions may be also developed for issue related to switching off circuit, which may provide complex limitation of electric arc energy both during switching-on and switching-off electrical circuits.

REFERENCES

[1] Holroyd F. W. and Temple V. A. K., Power semiconductor devices for hybrid breakers, IEEE Trans. Power Eng. Rev., vol. PER-2, no. 7, (1982), 48-49
[2] Steurer M., Frohlich K., Holaus W., Kaltenegger K., A novel hybrid current-limiting circuit breaker for medium voltage: Principle and test results,” IEEE Trans. Power Del., vol. 18, no. 2 (2003), 460-467
[3] Oramus P., Florkowski M., Rybak A., Sroka J., Investigation into Limitation of Arc Erosion in LV Switches Through Application of Hybrid Switching, IEEE Transactions on Plasma Science, vol. 45, 2017, p. 446-453
[4] Oramus P., Florkowski M., Limitation of Electric Arc Energy in LV Switches During Inductive Current Interruption, IEEE Transactions on Power Delivery, vol. 32, 2017, p. 1946-1953
[5] Van Gelder P., Ferreira J. A., Zero volt switching hybrid DC circuit breakers,” Proc. IEEE Ind. Appl. Conf., vol. 5, (2000), 2923-2927
[6] Jungblut R., Sittig R., Hybrid high-speed DC circuit breaker using charge-storage diode, Proc. IEEE Ind. Comm. Power Syst. Tech. Conf., (1998), 95-99
[7] Asplund G., Lescale V., Solver C. E., Direct-current breaker for high power for connection into a direct-current carrying highvoltage line, U.S. Patent 5 517 378, (1996)

Authors: dr inż. Mariusz Stosur, ABB E-mobility, ul. Starowislna 13A, 31-038 Krakow, Poland, E-mail: mariusz.stosur@pl.abb.com; dr inż. Kacper Sowa, ABB Electrification, ul. Starowislna 13A, 31-038 Krakow, Poland, E-mail: kacper.sowa@pl.abb.com; dr inż. Piotr Oramus ABB E-mobility, ul. Starowislna 13A, 31-038 Krakow, Poland, E-mail: piotr.oramus@pl.abb.com; dr inż. Adam Ruszczyk, ABB Electrification, ul. Starowislna 13A, 31-038 Krakow, Poland, E-mail: adam.ruszczyk@pl.abb.com; mgr inż. Pawel Aloszko, ABB Corporate Technology Center, ul. Starowislna 13A, 31-038 Krakow, Poland, E-mail: pawel.aloszko@pl.abb.com.

Source & Publisher Item Identifier: PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 98 NR 7/2022. doi:10.15199/48.2022.07.20

Analysis of Changes in Electrical Parameters of Photovoltaic Roof Tiles Depending on the Place of Shading and Connection Configuration

Published by Dariusz KURZ1, Ryszard NAWROWSKI2, Szczepan KAŁUŻA3, Politechnika Poznańska, Instytut Elektrotechniki i Elektroniki Przemysłowej (1)
ORCID: 1. 0000-0002-6737-0052; 2.0000-0003-0974-2935

Abstract. The paper presents the research on the influence of the connection configuration and the location of the PV cells shading on the output parameters of photovoltaic roof tiles. The problem of shading occurs in all photovoltaic installations, but in the case of solar tiles it can cause much greater power losses than in the case of traditional panels. The series, parallel and series-parallel configurations of photovoltaic roof tiles with different shading locations were tested. The values of roof tiles output parameters, current-voltage and power characteristics of the analyzed systems were presented.

Streszczenie. W pracy przedstawiono badania wpływu konfiguracji połączeń oraz lokalizacji zacienienia ogniw PV na parametry wyjściowe dachówek fotowoltaicznych. Problem zacienienia występuje we wszystkich instalacjach z fotowoltaicznymi, jednak w przypadku dachówek solarnych może on powodować znacznie większe straty mocy niż w przypadku tradycyjnych paneli. Przebadano konfiguracje szeregową, równoległą oraz szeregowo-równoległą dachówek fotowoltaicznym z różnymi miejscami wystąpienia zacienień. Przedstawiono wartości parametrów wyjściowych dachówek, charakterystyki prądowo-napięciowe oraz mocowe analizowanych układów. (Analiza zamiany parametrów elektrycznych dachówek fotowoltaicznych w zależności od miejsca zacienienia i konfiguracji połączeń).

Słowa kluczowe: dachówka fotowoltaiczna, zacienienie, punkt mocy maksymalnej, konfiguracja połączeń dachówek solarnych.
Keywords: photovoltaic roof tile, shading, maximum power point, configuration of photovoltaic roof tiles connection.

Introduction

Photovoltaic installations in Poland have been gaining popularity over the last few years. Types of photovoltaic cells (PV) used in panels change – in practice, polycrystalline cells have already been driven out of the market and replaced by monocrystalline cells with a higher photovoltaic conversion efficiency. Furthermore, also half-cell protected by three bypass diodes have become a standard nowadays. In addition to this, new technologies related to building-integrated photovoltaics (BIPV) have been gaining more and more popularity. These include photovoltaic roof tiles, skylights, windows, etc. During many years of operation of a photovoltaic installation, its output parameters change, however, there can also be temporary situations, which affect reductions in the value of generated power, such as, for instance, shadings of PV cells. The causes of PV cell shading on PV generators may be constant and periodical (as, e.g. structural elements of a building or landscape) or random (dirt, leaves, animals, birds and their droppings, etc.) The constant elements should be taken into account when designing installations and eliminated, however, the random shadings are unpredictable, therefore, various procedures which will minimise the related losses must be applied. In the case of traditional PV panels, the problem of shadings is widely described, analysed and studied in the literature. There are many publications regarding experimental studies [1-5], or mathematical and simulation analyses [6-9] discussing this problem.

In the case of BIPV elements, this problem may be more noticeable in view of their smaller area, lower values of electrical parameters and necessity of ensuring series-parallel connections in chains connected to a single inverter tracker input (MPPT).

In classic photovoltaic installations (especially prosumer ones), where traditional PV panels are used, a series connection to the input of the MPPT inverter is provided. The output parameters of the serial chain of panels match the input parameters of the inverter. The current generated by the panels is approx. 10-12 A, the inverter current protection is about 16 A at most. The PV chain voltage may be up to approx. 900 V, which is also within the range of operating voltages of the inverters. PV roof tiles analysed in this paper are characterised by lower values of currents and voltages, which necessitates the use of series-parallel connections in input chains to the inverters. The presence of PV cell shadings in mixed chains will cause different energy effects than in the case of serial chains, and this is not yet sufficiently explored in the literature and confirmed in experimental studies.

This publication presents results of tests of solar roof tiles operating in real conditions, connected in various configurations, with analysis of output electrical parameters caused by local shadings, located in different roof tile areas.

Subject of study

The study was performed using photovoltaic roof tiles of a Polish manufacturer, a company operating under the name Fotton. The view of the tile is presented in fig. 1 and its technical data is given in table 1.

Fig.1. Fotton FTDS52 solar tile [10]

Table 1. Technical data of FOTTON FTDS52 solar tile under STC conditions [10]

.

In order build an exemplary and most popular prosumer installation in Poland with a power of about 4.5 kW, it would be necessary to use 10 traditional PV panels with a power of 450 W, each connected into a single serial chain, whose output parameters would be about Im = 11 A and Um = 410 V. For the analysed solar roof tile, 86 tiles and two chains consisting of a row of 43 roof tiles would need to be used. Owing to this, a PV generator chain with approximate parameters of Im = 10.6 A and Um = 421 V would be obtained, that is, close to those of the panels. The inverter in both cases would operated with the same efficiency, and the other protective elements of the installation would be the same in both cases. The roof area covered with PV roof tiles would approx. be 34 m2 , and in the case of panels, just about 22 m2.

In order to check the impact of the configuration of connections and the locations of the PV roof tile shading, many measurements in different variants, on the test stand presented in figure 2a were carried out in accordance with the measurement diagram from figure 2b. During the measurements, environmental conditions were very stable, therefore, the accurate observation of relationships and the drawing of correct conclusions were possible.

Fig.2. Test stand: a) view of the stand; b) electrical diagram

Study of the impact of configuration of connections of unshaded PV roof tiles

The study of the impact of configuration of connections on electrical parameters of photovoltaic roof tiles was conducted within one day in July 2021. The value of radiation power density osciliated within 980 – 988 W/m2 during the measuring tests. The study covered a single PV roof tile and the connection of three roof tiles in a series, parallel and mixed configuration (one roof tile connected in series with tiles connected in parallel). Based on the obtained measuring data, current-voltage characteristics presented in figure 3 were plotted.

Fig.3. Comparison of characteristics of a single PV roof tile with characteristics of three PV roof tiles in different configurations of connections

When analysing the comparison of characteristics I = f(U) in different configurations of connections (fig. 3), it is possible to notice that the weather conditions were stable and the characteristics do not deviate from the norm. The compatibility of existing relationships – the sums of currents and voltages depending on the configuration – were confirmed. Visible “stepped” shape of the curve for the mixed configuration is caused by the uneven number of roof tiles. The values of currents from two roof tiles connected in parallel were aggregated and the voltages from the first roof tile and the group of parallel roof tiles were also aggregated. The output parameters of PV roof tile configurations were determined in accordance with the following equations [8,11]:

.

where: Pm – maximum power [W], Im – current at maximum power point [A], Isc – short-circuit current of a circuit [A], Um – voltage at maximum power point [V], Um – open circuit voltage [V], FF – fill factor [-], η – photovoltaic conversion efficiency [%], E – irradiance [W/m2], S – active surface of the PV roof tile [m2].

The value of the power generated by a single roof tile was 38 W, while the series, parallel and mixed configuration generated 109 W, 98 W and 81 W of electrical power respectively. It is possible to draw a conclusion that the type of configuration (series or parallel) had no significant effect on the value of generated power, which will, however, look completely different when the shading of PV cells of roof tiles occurs. The mixed configuration is characterised by a double increase in power in comparison with a single roof tile (instead of the triple increase), in view of the uneven number of (three) tiles. If this system consisted of two roof tiles in a parallel configuration and two in a series configuration, the value of generated power would be four times one. The detailed explanation of this situation was described when analysing the diagram from figure 10 and the characteristics plotted in figure 11.

Shading of a single PV roof tile

When investigating the impact of the shading on the operation of a single PV roof tile, one row (9 cells horizontally) and 4 columns of cells (4 columns vertically in 2 rows of cells) were obscured, as shown in figure 4. Measurements for these shading methods were performed, and then compared with the unshaded roof tile (fig. 5).

Fig.4. Configuration of the shading of a single photocell: a) with an obscured column, b) with obscured rows
Fig.5. Current-voltage characteristics of a single PV roof tile for different shading variants at E = 591 W/m2

When comparing graphs I = f(U) of a single PV roof tile for different cases of shading from figure 5, it is possible to observe a very high decrease in short-circuit current Isc for panel variants both with shaded columns (0.02 A) and in the obscured row of cells (0.05 A). The roof tile practically does not produce current (and thus also power). For a case with shaded columns (fig. 4b) the open circuit voltage Uoc is lower in comparison to the situation with the shaded row (fig. 4a) and amounts to 6.7 V and 9.4 V respectively. On the other hand, the unshaded roof tile generated open circuit voltage equal to 10.7 V and short-circuit current equal to 1.79 A at irradiance of E = 591 W/m2 , which results in the generation of power equal to 15.02 W.

Shading in the series connection

Other tests were carried out using a chain of three PV roof tiles connected in series with one whole shaded PV generator (fig. 6a) and with shaded halves of all roof tiles (fig. 6b). The obtained characteristics I = f(U) were compared with the characteristics of unshaded PV roof tiles (fig.7).

Fig.6. Configuration of the shading of three PV roof tiles connected in series: a) with one completely obscured generator, b) with obscured halves of all roof tiles

Fig.7. Current-voltage characteristics of three PV roof tiles connected in series for different shading variants at E = 981 W/m2

It is possible to notice that in the first case where one complete PV panel was shaded, the total voltage of the chain is the sum of voltages generated by two other PV generators (Uoc = 19.3 V instead of 30.3 V). The shaded roof tile does not generate current and was bypassed by a by-pass diode, owing to which the current in the configuration with the shading was 5.37 A, and in the case of the chain without the shading – 5.64 A. For all the three half-shaded PV roof tiles, it is possible to observe the lack of current generation (0.05 A) and the voltage is the sum of voltages of three shaded roof tiles (18.4 V), which is a confirmation of the data presented in fig. 5, where one roof tile generated voltage of 6.7 V. For a system with the obscured roof tile, the system generates the power of 68.78 W, while in the other case, only 0.1 W.

Shadings in the parallel connection

Similar forms of shading of PV roof tiles were used for their parallel connection (fig. 8) and the same comparison was plotted for current-voltage curves (fig. 9).

Fig.8. Configuration of the shading of three PV roof tiles in a parallel connection: a) with a single panel obscured completely, b) with obscured halves of all roof tiles

Fig.9. Current voltage characteristics of three PV roof tiles in a parallel connection for different shading variants at E = 981 W/m2

When analysing the graphs I = f(U) (fig. 9) of three PV roof tiles connected in parallel for different cases of shading, it is possible to observe a similar situation for the serial connection. When the panel is shaded completely (fig. 8a), the short-circuit current is obtained as the sum of currents generated by two other unshaded roof tiles, (10.48 A instead of 15.54 A) and the voltage of the open circuit equal to 9.65 V, which was reduced from 9.96 V by the shaded panel. A decrease in voltage on the bypass diode may range between 0.2 – 0.7 V, which was confirmed. With the shading of halves of all PV roof tiles, the open circuit voltage is equal to 6.78 V (just like in the case with figure 5) and the short-circuit current is 0.05 A. In the presented configurations, when the whole roof tile is obscured, the generated power is equal to 58.45 W, and when halves of roof tiles are shaded, it is 0.8 W.

Shadings in the series-parallel connection

In order to investigate the impact of the shading location on output parameters of a series-parallel chain of PV roof tiles, measurements were carried out for the configuration without shadings as in figure 10, owing to which base current-voltage characteristics were obtained for the purpose of further analysis (fig. 11). Respective currents and voltages in the series and parallel chain of the configuration were subject to measurements for the purpose of accurate representation of the propagation of currents and voltages in the respective parts of the circuit.

Fig.10. Schematic diagram of the measurement system to study the effect of shading on the performance of three PV roof tiles in a series-parallel connection

Fig.11. Current-voltage characteristics of three unshaded PV roof tiles in series-parallel connection at E = 961 W/m2

When analysing graphs I = f(U) of three unshaded PV roof tiles in a series-parallel connection, presented in figure 11, it is possible to notice that currents I_PV3 and I_PV2 are almost equal to each other, which means that the uniform propagation of current I takes place in the parallel chain. These roof tiles generate maximum short-circuit current at the given irradiance, which means that the resultant short-circuit current is equal to 10.14 A and flows through the PV1 roof tile connected in series. As the PV1 tile cannot operate at such a value of current (higher than the maximum current generated by it) a characteristic “curve” is noticeable as the voltage increases and its value is determined at the level of the short-circuit current of a single roof tile (about 5 A). This means that at the maximum power point, the PV1 tile determines the value of the current flowing in the circuit, dissipated to the two tiles from the parallel configuration (PV2 and PV3), which will be limited to about 50% of their power. Since there is no shading and all the tiles are uniformly illuminated, the voltages U_PV1 and U_PV2 are equal to each other (10.49 V and 10.67 V, respectively) and the total system voltage is their sum (21.15 V). The value of power generated at the maximum power point is equal to 81.55 W.

The following locations of shadings in the tested system were analysed:

• on half of two PV roof tiles in the parallel chain (fig. 12),
• on the whole roof tile from the parallel chain (fig. 14),
• on the entire roof tile connected in series to the group of two parallel ones (fig. 16),
• one row of cells of the roof tile from the parallel part of the connection (fig. 18),
• 4 columns from two rows of roof tiles, from the parallel part of the connection (fig. 20).

The following figures 12, 14, 16, 18 and 20 only present the variable fragment of the circuit from figure 10, also showing the place of occurrence of shadings for its accurate location. The remaining load-measuring part remained unchanged in each case.

The first shading case considered is the half-obscuration of the two PV roof tiles of the parallel chain (fig. 12).

Fig.12. Configuration of shading of three PV roof tiles in series-parallel connection with obscured halves of the parallel branch

Fig.13. Current-voltage characteristics of three PV roof tiles in series-parallel connection with obscured halves of roof tiles at E = 957 W/m2

When analysing characteristics of the three PV roof tiles in a series-parallel connection for the variant in which halves of roof tiles in the parallel chain from figure 13 are shaded, it is possible to observe that the parameters of the circuit are determined only by the PV1 roof tile from the series (current, voltage and I-U characteristics are similar to a single roof tile, and are described in fig. 3). PV2 and PV3 tiles generate 2.53 A and 2.75 A respectively when short-circuited, but they are disconnected from the circuit (bypassed) by the by-pass diodes, so they do not introduce any changes in the circuit. Maximum generated power is 28.61 W.

Next, the case for complete obscuration of one PV panel from the parallel branch was investigated (as shown in fig. 14).

Fig.14. Configuration of the shading of three PV roof tiles in a series-parallel connection with one panel in the parallel branch completely obscured

Fig.15. Current-voltage characteristic is of three PV roof tiles in series-parallel connection with a obscured roof tile of the parallel branch at E = 948 W/m2

When analysing the characteristics of three PV tiles in a series-parallel connection, for the case of complete obscuration of one roof tile in the parallel chain from figure 15, it can be noted that:

• the PV3 roof tile does not work because of the complete obscuration – it practically does not generate any current (0.29 A) and is omitted by the by-pass diode,

• the PV1 and PV2 roof tiles may function normally and generate higher values of currents and voltages, as they are not limited by PV3,

• the resultant voltage is the sum of voltages from the PV1 and PV2 tiles.

The above-mentioned situation is more advantageous than that related to the system presented in fig. 12, as the system generates more than twice the power (66.61 W), even though the shade area is identical, but located in a different way. The shade located on the entire single roof tile (and not on two halves) caused its disconnection from the circuit, without affecting the others in a negative way, which may work with the nominal power under the given conditions.

The shading variant analysed next is the complete obscuration of one PV generator connected in series to a parallel group of roof tiles (fig. 16). When analysing I-U characteristics of the presented system (fig. 17) it can be noted that the value of short-circuit current Isc of the system is the sum of currents generated by PV2 and PV3 tiles. The obscured PV1 roof tile was bypassed by a by-pass diode, owing to which the roof tiles from the parallel system may generate maximum values of currents and are not limited at 50%, as was the case in the system from figure 10. However, the bypassed series roof tile does not generate voltage in practice (only the by-pass diode voltage is visible), so the total voltage of the system is the sum of voltages of parallel roof tiles and voltage on the by-pass diode of the PV1 tile. In the circuit, the maximum value of power generated is 67.55 W.

Fig.16. Configuration of the shading of three PV roof tiles in a series-parallel connection, with a roof tile obscured in series

Fig.17. Current-voltage characteristics of three PV roof tiles in a series-parallel connection with a roof tile obscured in series at E = 964 W/m2

Then, the case of horizontal shading of the row of cells of a PV roof tile located in the parallel branch (fig. 18) was investigated.

Fig.18. Configuration of the shading of three PV roof tiles in a series-parallel connection with an obscured row of cells

Fig.19. Current-voltage characteristics of three PV roof tiles in a series-parallel connection with an obscured column of cells at E = 917 W/m2

When analysing the characteristics from figure 19, it is possible to notice a similar situation as that described in the configuration from figure 14. The shaded PV2 roof tile, in view of its obscuration was bypassed by a by-pass diode, so it does not limit the operation of the PV3 roof tile. Owing to this, the PV1 and PV2 may work with their maximum powers, and the output parameters of the system are: short circuit current – 5.54 A, open circuit voltage – 20 V and generated power – 73.87 W.

The last shading variant is the obscuration of a half of a PV roof tile from the parallel branch (4 columns in two rows, as presented in figure 20).

Fig.20. Configuration of the shading of three PV roof tiles in a series-parallel connection with obscured rows of cells

Fig.21. Current-voltage characteristics of three PV roof tiles in a series-parallel connection with obscured rows at E = 914 W/m2

When analysing the characteristics of the studied system, presented in figure 21, it is again possible to observe a similar situation to the one described previously. The shaded PV2 roof tile is bypassed by a by-pass diode, therefore, it does constitute not a load for the remaining part of the system. The output parameters are: short-circuit current – 5.52 A, open circuit voltage – 20.28 V, power – 68.66 W.

Summary

The studies allowed for the gaining of knowledge concerning the influence of the shading location on the output parameters of the installation composed of photovoltaic roof tiles. Based on the measurement data, the values of parameters characterising the process of energy generation from the system of PV tiles were determined, and the obtained results were presented in Table 2. The table header contains the numbers of figures of systems for which the studies were performed.

During the testing of the impact of the shading on the operation of three PV roof tiles in a series-parallel connection, also power-voltage characteristics were determined for different shading variants. When analysing the comparison of the characteristics P = f(U) from figure 22, it can be seen that the highest value of the generated maximum power Pm was achieved for the system in which no shading was present (for the system in figure 10, the obtained power was 81.54 W). On the other hand, the lowest value of generated power Pm = 28.61 W was obtained for the system in fig. 12, in which the halves of two PV roof tiles in the chain, where the generated power was reduced by as much as 65% were obscured. The reason for such a large decrease in the value of maximum power Pm can be observed along the characteristic curve I = f(U) from figure 13, where there was a simultaneous decrease in the value of the generated current and voltage of the system during the obscuration of the halves of the photovoltaic tiles, which were excluded from operation by the bypass diodes.

Table 2. List of values of parameters investigated in the analysed measuring systems

.
Fig.22. Comparison of characteristics P = f(U) of three PV roof tiles in a series-parallel connection, in different shading configurations

In the variants related to obscuration of the PV cell row or column, as well as to the total shading of the PV roof tile in the parallel branch, similar reductions in the maximum power Pm were observed in relation to the unshaded system. The output parameters of the systems presented in figures 14, 18 and 20 and the current-voltage characteristics (fig. 15, 19 and 21) carried out for them are very similar to each other, which is the best of the analysed situations, with the shading of the PV cells. The value of the generated power, in comparison with the system without shadings, was lower by about 9-17%. When analysing characteristics I = f(U) of individual cases from figures 15, 19 and 21, we can only observe a reduction in the value of short-circuit current Isc, at invariable open circuit voltage Uoc, in each of these cases, which is a good situation from the point of view of operation of a photovoltaic inverter. The value of power generated in these systems is similar to the one generated in the configuration from figure 16, however, a change in the value of currents and voltages is observed. This system is characterised by about twice the value of current and half the value of voltage in view of the operation of the parallel part of the system only, at complete shading, and thus, disconnection of the PV1 roof tile by the by-pass diode. The shading situation which causes the smallest losses of generated power is presented in fig. 16, when the horizontal row of PV cells was subject to obscuration. It was then that the open circuit voltage generated by the obscured roof tile was higher than in the case of obscuration of the columns. This translated into power losses in comparison with the system without shading by only 9%, and generation efficiency that was most similar to the operation of the system under unshaded conditions. The obtained fill factor FF of the unshaded system had a very low value, due to the odd number of roof tiles in the series part of the system.

To sum up, investors who decide to install the photovoltaic installation composed of solar roof tiles instead of traditional PV panels must reckon with a significant change in electrical parameters of the input chain to the inverter, as well as a change in conditions of its operation during the occurrence of local shading of PV cells. The apparent creation of a shadow with a given area on PV roof tiles may cause different losses of generated power due to its location (within one or more roof tiles) compared to photovoltaic panels.

REFERENCES

[1] Cardinale-Villalobos L., Meza C., Méndez-Porras A., MurilloSoto L.D., Quantitative Comparison of Infrared Thermography, Visual Inspection, and Electrical Analysis Techniques on Photovoltaic Modules: A Case Study, Energies 15 (2022), 1841. https://doi.org/10.3390/en15051841
[2] Al Mamun M.A., Hasanuzzaman M., Selvaraj J., Experimental investigation of the effect of partial shading on photovoltaic performance, IET Renew. Power Gener. 11 (2017), No. 7, 912-921, https://doi.org/10.1049/iet-rpg.2016.0902.
[3] Deline Ch., Meydbray J., Donovan M., Forrest J., Partial shade evaluation of distributed power electronics for photovoltaic systems, in: 38th IEEE Photovoltaic Specialists Conference (IEEE PVSC), 2012, Austin, Texas, 3-8.06.2012, 1627-1632, https://doi.org/10.1109/PVSC.2012.6317908
[4] Hamdi S., Saigaa D., Drif M., Modeling and simulation of photovoltaic array with different interconnection configurations under partial shading conditions for fill factor evaluation. International Renewable and Sustainable Energy Conference (IRSEC), 2014, 17-19 Oct. 2014, Ouarzazate, Morocco https://doi.org/10.1109/IRSEC.2014.7059896
[5] Jansson P.M., Whitten K., Schmalzel J.L., Photovoltaic module shading: smart grid impacts, in: Sensors Applications Symposium (SAS IEEE), 2011, San Antonio, Texas, 22- 24.02.2011, 323-328, https://doi.org/10.1109/SAS.2011.5739826
[6] Abdulkadir M., Yatim A.H.M., Yusuf S.T., An improved PSObased MPPT control Strategy for photovoltaic systems, Int. J. Photoenergy, 11 (2014), https://doi.org/10.1155/2014/818232.
[7] Nasiruddin I., Khatoon S., Jalil M.F., Bansal R.C., Shade diffusion of partial shaded PV array by using odd-even structure, Solar Energy, 181 (2019), 519-529, https://doi.org/10.1016/j.solener.2019.01.076
[8] Trzmiel G., Głuchy D., Kurz D., The impact of shading on the exploitation of photovoltaic installations, Renewable Energy, 153 (2020), 480-498, https://doi.org/10.1016/j.renene.2020.02.010
[9] Liqun L., Zhiyi S., Chunxia L., Wyjściowa charakterystyka matrycy fotowoltaicznej w warunkach częściowego zacienienia – zasada superpozycji napięć DC z wykorzystaniem pakietu Matlab, Przegląd Elektrotechniczny, 12a (2012), 284
[10] https://www.fotton.pl/produkt/dachowka-solarna-fotton/, access: 02.03.2022
[11] Szczerbowski R.: Instalacje fotowoltaiczne – aspekty techniczno-ekonomiczne, Przegląd Elektrotechniczny, 10 (2014), s. 31-36, https://doi:10.12915/pe.2014.10.08

Autorzy: dr inż. Dariusz Kurz, Politechnika Poznańska, Instytut Elektrotechniki i Elektroniki Przemysłowej, ul. Piotrowo 3a, 60-965 Poznań, E-mail: Dariusz.Kurz@put.poznan.pl; prof. dr hab. inż. Ryszard Nawrowski, Politechnika Poznańska, Instytut Elektrotechniki i Elektroniki Przemysłowej, ul. Piotrowo 3a, 60-965 Poznań, E-mail: Ryszard.Nawrowski@put.poznan.pl; inż. Szczepan Kałuża, Politechnika Poznańska, Instytut Elektrotechniki i Elektroniki Przemysłowej, ul. Piotrowo 3a, 60-965 Poznań, E-mail: Szczepan.Kaluza99@gmail.com.

Source & Publisher Item Identifier: PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 98 NR 7/2022. doi:10.15199/48.2022.07.21

Optimization of the Reliability of Power Electric Distribution Grids MV with the use of Heuristic Algorithms

Published by Wojciech NITA1, Sylwester FILIPIAK2, PGE Dystrybucja S.A. Oddział Skarżysko-Kamienna (1), Politechnika Świętokrzyska (2)

Abstract — The article aims to present the application of selected heuristic algorithms to improve the reliability indices of MV distribution grids. Improving the reliability and efficiency of power distribution grids is currently a topical and important issue. The paper includes analyses of selected algorithms, in particular algorithms utilising heuristic methods for multicriteria optimisation of the scope of activities improving the reliability and efficiency of power electric distribution grids. Evolutionary algorithms were also used to determine the fronts of the Pareto optimal solutions sets.

Streszczenie. Celem artykułu jest przedstawienie zastosowania wybranych heurystycznych algorytmów populacyjnych do optymalizacji wskaźników niezawodności sieci dystrybucyjnych SN. Poprawa niezawodności i efektywności systemów dystrybucyjnych energii elektrycznej jest ważnym i aktualnym zagadnieniem. W artykule zastosowano wybrane algorytmy do wielokryterialnej optymalizacji zakresu przedsięwzięć poprawiających niezawodność i efektywność systemów dystrybucyjnych energii na przykładzie wybranej terenowej sieci elektroenergetycznej SN. Zastosowano również algorytmy ewolucyjne w celu wyznaczania frontów zbiorów rozwiązań Pareto – optymalnych (Optymalizacja niezawodności elektroenergetycznych sieci dystrybucyjnych SN z wykorzystaniem populacyjnych algorytmów heurystycznych).

Słowa kluczowe: optymalizacja, sieci elektroenergetyczne, metody ewolucyjne.
Keywords: optimization, power grids, evolutionary methods.

Introduction

The article is an extension of the analyzes presented in [15], which concerned optimization models for power distribution networks. Below is an extension of the methodology presented in [15, 16] with the possibility of including in the distribution network optimization models an extended range of measures to improve the reliability of power electric distribution networks.

The present paper presents the results of analyses aimed at determining efficient methods of optimising the projects implemented to improve the reliability and efficiency of power distribution grids, using as an example an MV power distribution grid. In particular, the purpose of the calculations is to determine which power line sections and power grid devices should be subjected to modernisation works. The problem of the location of devices and selected measures to improve the grid’s reliability was also analysed. Alternative plans for grid modernisation were determined for selected power line sections and power grid devices [14].

The alternative modernisation plans include changing the reliability parameters of specific devices and switching station bays resulting from taking into account the impact of modernisation of grid devices on the analysed MV distribution grid reliability indices. For this purpose, heuristic methods proved useful in solving computationally complex problems were adopted.

The measures and activities that increase the reliability of power grids include [2, 3, 9, 10]:

• installation of radio-controlled switches,
• use of sheathed conductors or change to cable lines,
• increasing the share of live-line operations,
• modernisation of the main power supply station (conversion to the H-5 system),
• shortening MV line sections,
• construction of new connections between the main lines,
• installation of FDIR (Fault Detection, Isolation and load Restoration) automatic systems and short-circuit current flow indicators with edition in the SCADA system,
• installation of an LV fuse burnout control system in MV/LV substations,

Modern technologies and power equipment make it possible to quickly restore the operation of power lines after failure. For this purpose, among others, short-circuit current flow indicators are used to detect the point where the earth fault or phase-to-phase fault occurs. The analysed variant modernisations of the grid selected measures to improve reliability were included [18].

In the analyzed possible variants of modernization of power distribution networks, actual data on the failure frequency of power network devices were taken into account.

The computational methodology used

Heuristic iterative search methods were used to analyse the problem because [1, 4, 11]:

• most of the practical tasks are NP-hard and conventional algorithms cannot be used to solve them,
• these methods do not process the decision variables directly, but their coded forms,
• these methods are gradient less methods – the value of the objective function derivative is not used, but the information about the value of the objective function is used,
• processing of the coded solutions is executed with the use of random procedures, although the entire process remains a deterministic process,
• the primary goal of the algorithm is to improve the current solution, and the optimal solution is the result of such correction.

As far as the heuristic methods are concerned, algorithms were developed based on the observation of nature and physical phenomena.

Such methods include inter alia [17, 19, 20, 21]:

• Simulated Annealing,
• Genetic Algorithm,
• Gases Brownian Motion Optimisation Algorithm,
• Artificial Swarm Intelligence.

The above-mentioned algorithms enable solving complex, multidimensional, discrete or not fully defined problems [1, 2]. Heuristic methods can be classified as local search methods and population search methods. In the second group, the entire population of solutions is processed. Examples of such algorithms are evolution and swarm algorithms. Population algorithms include inter alia [7, 12]:

• Genetic Algorithms,
• Evolutionary Strategies,
• Particle Swarm Optimisation,
• Moth-Flame Optimization

Based on the properties of these methods, it can be concluded that swarm optimisation algorithms, as well as genetic and evolutionary algorithms, can be useful in solving the problem analysed in the present paper. The issue discussed uses decision variables from discrete sets (selection of new devices localisation and modernisation of the existing devices) and continuous sets (modernisation of MV line sections along a selected line length). The analysed problem was considered using the approach that aggregates the criteria functions and a set of Pareto optimal solutions was determined.

The efficiency of the evolution algorithms based on the Pareto concept was confirmed for problems with three goals [6, 8]. As the number of goals increases, using these methods becomes less effective. The following problems can be distinguished when more than three goals are considered [7, 8]:

• the selection pressure based on Pareto dominance towards the Pareto front decreases as the number of goals increases. Almost all solutions in the population are not dominated when the number of goals is large,

• in order to bring the Pareto front closer, an exponential increase in the number of solutions is required.

In the algorithms based on the Pareto concept, new dominance relations are searched for to maintain the required selection pressure. This group of methods includes the NSGA-II, NSGA-III ( Nondominated Sorting Genetic Algorithm), SPEA2, evMOGA, MOGA/D and many other algorithms [6, 13].

The NSGA-III multi-criteria evolution algorithm that is in line with the NSGA-II structure is based on the reference benchmarks consideration [6]. This algorithm promotes population elements that are not dominated but are close to a set of benchmarks. The ev-MOGA algorithm is also very efficient. It is an elite, multitasking algorithm [13]. The above-mentioned algorithms were used to analyse the problem under consideration.

Computational models

The calculations take into account the values of power grid equipment reliability indices resulting from the modernisation measures implemented to MV distribution grids. The scope of the modernisation works included, inter alia, installation of better equipment, taking into account the radio-controlled switches and reclosers installed on the power lines systems.

The reliability indices that are crucial for the distribution grid are inter alia:

• expected number of disturbances (power outages),
• the average duration of a single disturbance,
• the expected value of disconnected power or undelivered electric energy.

One of the methods used in assessing the reliability of power grids is the partial intensity of disturbances method. This method is based on the knowledge of the disturbance intensity and the average disturbance time of the analysed structure elements [5 ,18].

For the system consisting of m number of elements connected in parallel, the following dependency can be used:

.

where: N – the average intensity of disturbances, taw – average duration of a single disturbance,

The MV power grid model that was modelled in the Matlab program and presented in Figures 1 and 2 was analysed.

Fig.1. Model diagram of the analysed MV grid

Fig.2. Model diagram of the main power supply station

There are several indices used in the world to assess the reliability (continuity) of the power supply. The most frequently used are [5, 12]:

• SAIFI (System Average Interruption Frequency Index) – a system index of the average number of power outages per end-user, defined as the ratio of all unplanned power outages during the year to the number of endusers connected to the grid. SAIFI does not include short power outages of less than 3 minutes [pcs/enduser].

• SAIDI (System Average Interruption Duration Index) – a system index of the average annual total time of power outages, determined as the annual total time of all power outages divided by the total number of end-users connected to the grid [minutes/end-user].

• MAIFI (Momentary Average Interruption Frequency Index) – an index of the average number of temporary power outages for the end-users, determined as the average annual number of power outages shorter than 3 minutes or shorter than 1 minute that the end-user can expect. It is calculated as the quotient of the number of all short outages during the year to the number of endusers connected to the grid.

The tables below contain the values of reliability indices for the MV line sections before and after the analysed distribution grid MV modernisation. SAIFI, SAIDI, MAIFI reliability indices for grid devices were calculated taking into account the value of failure duration, failure intensity and other indices.

Table 1. Reliability indexes of the MV line section before and after modernisation

.

The following optimisation criteria were taken into account in the developed models of the analysed grid:

• reduction of the resultant SAIFI index (alternatively MAIFI),
• reduction of the resultant SAIDI index,
• reduction of expenditure on modernisation of the MV grid,
• reduction of grid technical losses,
• reduction of the MV grids operating costs.

For the analysed problem, the implementation of calculations with the use of an aggregating approach was adopted, as well as the methodology of multi-criteria calculations with the use of evolutionary algorithms, allowing to find sets of Pareto optimal solutions.

The solutions were sought taking into account the fulfilment of technical conditions regarding load capacity, throughput, voltage conditions and short-circuit parameters. The decision variables in the analysed task are the values of the decision variables (between 0.0 and 1.0) that determine the scope of modernisation of selected grid devices and the selection of grid elements to be modernised.

For the proposed coding method, operators changing the values of decision variables were used, keeping their values within the designated range to ensure the correctness of the solutions. The following vector objective function was adopted for the calculations:

.

f1(x) – minimisation of the resultant SAIFI index:

.

where: ni – number of unplanned outages at end-users in a given location, Li – number of end-users,

f2(x) – reduction of the resultant SAIDI index:

.

where: Ti – time of end-users power outage in the given location,

f3(x) – reduction of the resultant MAIFI index:

.

f4(x) – determines the energy effect of reducing energy loss in the lines of the analysed MV grid (longitudinal power losses in grid components were taken into account):

.

with: τi – duration of the largest load losses in the ith MV line, Rmi – resistance of the ith section of the line after modernisation,

For the analysed grid, the values of SAIFI, SAIDI and MAIFI reliability indices were determined for individual MV line sections. In these calculations, the values of failure intensity and failure duration were assumed, taking into account the length of the MV line section to be modernised and the technologies to be used for the modernisation [5,6].

Calculation example

During the calculation, an aggregated approach was used and the objective function taking into account the four adopted criteria.

The calculation procedure for determining solutions had the following stages of calculations:

• loading the technical and reliability data collected for the analysed grid system,

• decoding variants of solutions in which decision variables are taken from discrete sets (choice of location or modernisation of devices) continuous decision variables (modernisation of MV line sections along a selected line length).

• calculation of power flow in the analysed MV grid,

• calculation of the resultant reliability indices for the analysed MV grid,

• calculating the value of the aggregate objective function (or separately criterion functions for determining the set of Pareto optimal solutions).

The results of the calculations using the genetic algorithm are presented in Charts 3 and 4, while Charts 5 and 6 show the course of calculations using the swarm algorithm.

Fig.3. The course of calculations with the genetic algorithm

Fig.4. The second example of calculations using the genetic algorithm

Calculated solution describes of MV grid system with marked components of the analysed grid selected for modernisation and with marked locations of devices improving the failure rates of the analysed MV distribution grid.

Fig.5. The course of calculations with the use of the swarm algorithm

The performed analyses confirmed the usefulness of the algorithms used to optimise the scope of projects increasing the efficiency of MV distribution systems. The results of solutions with the use of selected heuristic algorithms include information on the selection of grid equipment to be modernised and the scope of the modernisation.

Tables 2 and 3 contain the calculated values of the criterion functions for the obtained solutions and the calculated values of the reliability indexes of the individual line sections of the analysed MV distribution grid.

Fig.6. The second example of calculations using the swarm algorithm

Table 2. Values of reliability indexes of MV line sections after modernisation

.

Table 3. Values of criterion functions for the obtained solutions

.

A graphic presentation of the designated solution is shown in Figure 7, which shows a diagram of the considered MV grid system with marked components of the analysed grid selected for modernisation and with marked locations of devices improving the failure rates of the analysed MV distribution grid.

As a result of the calculations, it was determined measures implemented to improve the reliability indices of the MV distribution grid. Among others, they include optimal locations for measures to improve grid efficiency in the form of, for example locations of radio-controlled switches. In table 4 contains a description of measures designated for the modernisation of individual MV lines.

Table 4. Description of measures designated for the modernisation

.
Fig.7. Model diagram of the power distribution network with marked possible sections of the line for modernization (rectangles symbolize the modernization of selected sections of the line MV, circles symbolize the location switch disconnectors of radio-controlled)

In this table, the calculated measures and devices to improve the grid reliability were determined for successive MV line sections in the form of appropriate switchgear and distribution equipment, or the conversion of lines using different technology. For the scope of the considered grid modernisation projects defined using discrete variables (location of new devices and modernisation of the existing ones) and continuous variables (modernisation of MV line sections along a selected length), criterion functions were calculated using the formulas given above.

An important part of these calculations are the dependencies and definitions used to calculate the reliability indices (including reliability coefficients, failure intensity and duration of failures and power outages) for individual analysed power line sections and the entire analysed fragment of the grid. Following the described definitions, SAIFI, SAIDI and MAIFI indices for individual MV line sections and the entire fragment of the distribution grid were then calculated.

In the further part of the paper, the problem with the use of selected multi-criteria evolution algorithms is analysed. NSGA II and III, SPEA2 and ev-MOGA algorithms were used for the calculations [2, 6]. These algorithms allow determining sets of Pareto optimal solutions. The chart below presents the Pareto optimal solutions fronts found using these algorithms.

In global optimisation, the quality of the algorithm can be evaluated based on the global optimum found, and e.g. through the number of objective function calls. In multicriteria optimisation, two categories of algorithm evaluation are distinguished [13]:

• performance related to the number of iterations, the number of objective function calls,
• efficiency, including the accuracy and convergence of the solutions found.

When assessing the effectiveness of the algorithm, one should evaluate how the found solution front is close to the real (or known) front and how the solutions are distributed along the front. In the analysed case, it was stated that the fronts of solutions that have been found using three different evolutionary algorithms coincide, which proves the convergence of the results obtained with different methods. In the following graphs (8 and 9), the calculated values of the criterion functions are described in relative units. A chart with the identified Pareto fronts and dotted solutions, obtained according to the aggregated approach is presented in Figure 9.

Fig.8. Identified Pareto optimal solutions fronts

After the analysis, it was discovered that the individual solutions found through the aggregated methodology were arranged along the identified front of solutions. It serves as a confirmation that the convergence of the results obtained with various methods, including the criteria aggregating methods and the independent adoption of individual criteria (when searching the Pareto optimal sets).

Fig.9. Chart with fronts and individual points resulting from the application of the aggregate approach
Fig.10. Set of Pareto optimal solutions (NSGA II algorithm)

Calculations were also made to determine a set of Pareto optimal solutions with the use of the NSGA II algorithm for three criteria: reduction of grid failure rates, reduction of technical losses and reduction of capital expenditure. The result of the calculations is shown in Figure 10.

As a result of further analyses, sets of solutions for those three criteria were obtained using three algorithms, NSGAII, SPEA2 and evMOGA, as shown in Figure 11.

Fig.11. A set of solutions for three criteria, obtained with three algorithms: NSGA-II, SPEA2 and evMOGA

Figure 12 shows the set of solutions obtained using the NSGA II algorithm for the three selected criteria. Whereas Charts 12 and 14 presents, apart from the information in Figure 12, individual points are marked representing solutions obtained using the aggregated approach.

Fig.12. The obtained set of Pareto optimal solutions – obtained using the NSGA II algorithm

Fig.13. The obtained set of Pareto optimal solution and the point (red colour) found using the aggregated approach

Fig.14. The obtained set of Pareto optimal solution and the point (red colour) found using the aggregated approach – additional view

The charts show a comparison of the obtained results. The performed analyses prove the reasonableness of using heuristic algorithms, including evolutionary algorithms, to determine measures to be implemented to increase the distribution grids reliability.

Conclusions

The article contains the results and conclusions of the analyses carried out in the field of optimisation calculations with selected algorithms for the analysed problem of determining the scope of modernisation projects for the selected power electric distribution grids. The application of selected evolutionary algorithms for the determination of Pareto optimal solutions and the determination of Pareto fronts for the optimisation problem of a selected MV power distribution grid was also analysed.

In addition, the proposed methodology of evolutionary calculations can be used in practice for optimisation and preparation of complex distribution grids modernisation schedules, including the grids with a very large number of elements. The obtained sets of Pareto optimal solutions contain alternative sets of solutions distributed along the obtained Pareto front, which allows for a detailed analysis of the most interesting range of solutions for the decisionmakers.

The calculations were performed using various heuristic methods and the calculations show a high level of convergence, allowing to review possible solutions for the analysed problem.

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Autorzy: dr inż. Wojciech Nita, PGE Dystrybucja S.A. Oddział Skarżysko-Kamienna, dr hab. inż. Sylwester Filipiak prof. PŚk, Politechnika Świętokrzyska w Kielcach, Katedra Elektrotechniki Przemysłowej i Automatyki, E-mail: filipiak@tu.kielce.pl

Source & Publisher Item Identifier: PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 98 NR 6/2022. doi:10.15199/48.2022.06.09

Statistical Analysis and Modeling of the Reliability of Overhead Low Voltage Lines

Published by Łukasz GRĄKOWSKI, Andrzej Ł. CHOJNACKI, Katarzyna GĘBCZYK, Kornelia BANASIK Kielce University of Technology, Faculty of Electrical Engineering, Automatic Control and Computer Science

Abstract: The paper present a thorough analysis of seasonality and causes of failures of low voltage overhead lines. Such lines are mainly characteristic of rural areas. An average duration of failures, average duration of emergency shutdown and average duration of power supply interruptions were determined. Based on empirical data, probability density functions for the above-mentioned times were also determined.

Streszczenie: W artykule przedstawiona została wnikliwa analiza sezonowości oraz przyczyn awarii linii napowietrznych niskiego napięcia. Linie takie są charakterystyczne przede wszystkim dla terenów wiejskich. Wyznaczono średni czas trwania awarii, średni czas trwania wyłączenia awaryjnego oraz średni czas trwania przerw w zasilaniu odbiorców. Na podstawie danych empirycznych wyznaczono również funkcje gęstości prawdopodobieństwa dla ww. czasów. (Analiza statystyczna oraz modelowanie niezawodności linii elektroenergetycznych niskiego napięcia).

Keywords: overhead LV lines, reliability, power industry
Słowa kluczowe: linie napowietrzne nN, niezawodność, energetyka

Introduction

Modern electricity customers have very high demands regarding the quality and continuity of electricity supply. The total length of overhead LV lines and the number of customers connected to them is systematically increasing. Such a situation increases the risk of restrictions in the supply of electricity to customers in the event of a failure of the transmission system. This results in significant material damage and, in extreme cases, can lead to a risk to human health or life.

Over the last few years, in connection with, among others, Poland’s accession to the European Union, the interest in the problem of reliability of power systems has increased. The reason for this is the fact that even the shortest interruption results in dissatisfaction of electricity consumers and material losses. High reliability of operation of LV lines allows to reduce the time of interruptions in power supply to customers, and thus to minimize the costs of losses resulting from the lack of power supply to customers [5].

Low-voltage networks consist mainly of overhead lines, cable lines, cable and overhead connections, as well as all kinds of connectors. Overhead lines are used primarily in field networks, while cable lines are mostly used in urban networks. Overhead LV networks are usually built as radial systems, while cable networks are built as loop systems with partitions in the cable joint.

Low-voltage overhead lines are built in many different variants. In domestic distribution companies, aluminium wires are commonly used for the construction of overhead LV lines; copper wires are very rarely used and steel-aluminium wires are used in exceptional cases. Currently, mainly single-metal wires with cross-sections from 16 mm2 to even 120 mm2 are used.

In low-voltage overhead lines, insulated wires in the form of twisted pair solid wires or multiconductor insulated wires are increasingly used. The disadvantage of insulated wires is their high price. On the other hand, when using insulated wires, purchasing such components as insulators or crossbars is unnecessary. In such case, the total cost of construction is only slightly higher than the cost of construction of a line with bare conductors, with significant reduction in the amount of interferences (especially transient ones) during operation [1].

Insulators are used to separate (isolate) live line conductors from the supporting structures and from each other. LV lines mainly use single- or double-groove standing insulators. For dead-end and corner poles with significant tension forces, spool insulators are used. The material used for the construction of LV insulators is mainly porcelain [2].

The supporting structures of low-voltage lines are power poles. Depending on the function performed, the following types of poles are distinguished: straight-line poles, corner poles, resistance poles, corner resistance poles, dead-end poles and branch poles. Currently, reinforced concrete structures are used as the basic type of poles.

Class A surge arresters are instruments designed to protect devices installed in low-voltage overhead lines. They are adapted to be installed outside the protected building (pole connections).

The basic components of LV overhead line accessories include hooks, holders, connectors, clamps and ties [3, 7].

In his paper, the author presented the results of reliability tests of LV overhead lines operated in domestic distribution companies. The research concerned the causes of failures and seasonal variability in the frequency of defects. The author also conducted an analysis of the duration of failures, duration of emergency shutdowns and duration of interruptions in power supply to consumers. All the analyses were carried out at the level of significance α=0.05 [6, 8, 9, 10].

Analysis of seasonality and causes of failures

The monitoring of the failure rate of LV overhead lines covers a period of 10 years. During that time a total of 10458 failures occurred. The number of failures of individual groups of devices is presented in Table 1. Table 2 shows the failures of LV overhead lines in individual months. Figure 1 shows a histogram of the empirical frequency of failures in the subsequent months of the year and the approximation function.

Table. 1. Failures observed on LV overhead lines over 10 years of observation

.
Fig.1. Empirical values and approximation function of seasonal variability of failure frequency of LV overhead lines

The greatest number of failures was observed in summer months (May – August) and winter months (January – December). During the summer period, 4135 failures occurred, which makes up for 39.5% of all damages. During winter months, 1742 failures occurred, which makes up for 16.7% of all damages. In the remaining months, the failure rate of overhead LV lines is below the average damage intensity of 8.33%.

The seasonal variability in the frequency of failures over a year can be described by means of an approximation function in the following form:

(1) f(i) = a·i4 + b·i3 + c·i2 + d·i + e

where: i – consecutive month number, a, b, c, d, e – approximation function coefficients.

The coefficients of approximation function of seasonal variability of failure frequency of LV overhead lines are: a = 0.0103, b = – 0.2815, c = 2.5181, d = – 8.0493, e = 14.968. The correlation coefficient between empirical values and the approximation function is r = 0.92.

The percentage share of LV overhead lines failure causes is given in Table 3 and graphically presented in Figure 2. The percentage share of individual causes of failures in the total number of failures is shown in Figure 3.

Table. 2. Summary of the number of failures in each month

.

Table. 3. Causes of defects of LV overhead lines in each month

.
Fig.2. Causes of LV overhead line failures

The most frequent cause of LV overhead line failures are ageing processes, which caused about 22.83% of all damages. Other causes were trees/branches and wind, which caused 11.64% and 11.45% of all damages, respectively. Seasonal causes, but with a significant impact on the failure rate of LV overhead lines, are lightnings and ice/rime ice. They caused 10.95% and 6.70% of all damages, respectively.

Fig.3. Percentage share of causes of LV overhead line failures

Duration of failure

Duration of failure ta determines the transition of the device from failure state back to usability state. It is a very important parameter used to determine the extent of the failure, as well as its economic and business consequences [3, 4, 11, 13].

Statistics on the duration of LV overhead line failures include 10458 cases. On the basis of empirical data, a hypothesis on log-normal distribution of duration of failures was assumed. The empirical and theoretical course of LV overhead line failure duration is shown in Figure 4. The determined values of distribution parameters are as follows:

m = 1.88 and σ = 1.14. Parametric verification was also carried out. Obtained parameter values: t̄a = 11.30 h, s = 13.29 h and confidence interval for an average value of 11.05 h < t̄a < 11.56 h.

The average failure rate parameters of LV overhead lines obtained from the research are as follows: ¯λa = 62.3614 1/a·100km and qa = 74.45·10-3 1/100km.

Fig.4. Empirical and theoretical course of failure duration ta of LV overhead lines Duration of emergency shutdown

Duration of emergency shutdown

Duration of emergency shutdown twa is the time counted from the moment the object is shut down as a result of its damage to the moment the object is switched on after its repair [3]. Statistics on the duration of emergency shutdowns of LV overhead lines include 10344 cases. On the basis of empirical data, a hypothesis on log-normal distribution of duration of emergency shutdowns was assumed. The empirical and theoretical course of duration of emergency shutdowns of LV overhead lines is shown in Figure 5. The determined values of distribution parameters are as follows:

m = 1.73 and σ = 1.15. Parametric verification was also carried out. Obtained parameter values: t̄wa = 9.68 h, s = 10.98 h and confidence interval for an average value of 9.47 h < twa < 9.90 h.

The average failure rate parameters of LV overhead lines obtained from the research are as follows: ¯λwa= 61.6816 1/a·100km and qwa = 63.81·10-3 1/100km.

Fig.5. Empirical and theoretical course of emergency shutdown duration twa of LV overhead lines

Duration of interruptions in power supply to consumers

The time of interruption in power supply to consumers tp is the time counted from the moment of the failure to the moment of restoring power supply to the consumer [12]. Therefore, it is the time when consumers have no access to electricity. Statistics on the duration of interruptions in power supply to consumers include 9983 cases. On the basis of empirical data, a hypothesis on log-normal distribution of the duration of interruptions in power supply was assumed.

The empirical and theoretical course of the duration of power supply interruptions is shown in Figure 6. The determined values of distribution parameters are as follows:

m = 0.95 and σ = 1.61. Parametric verification was also carried out. Obtained parameter values: t̄p = 5.34 h, s = 7.54 h and confidence interval for an average value of 5.19 h < tp < 5.49 h.

The average failure rate parameters of LV overhead lines obtained from the research are as follows: ¯λp = 59.5289 1/a·100km and qp = 35.02·10-3 1/100km.

Fig.6. Empirical and theoretical course of the duration of power supply interruptions tp

Summary

LV overhead lines are the final element of the power distribution system (mainly in rural areas). Modern electricity customers (including rural ones) have very high demands regarding the quality and continuity of electricity supply. The reason for this is the fact that even the shortest interruption results in dissatisfaction of electricity consumers and material losses. High reliability of operation of LV overhead lines allows to reduce the time of interruptions in power supply to customers, and thus to minimize the costs of losses resulting from the lack of power supply to customers.

Due to their low energy consumption, rural networks have been treated for many years as distribution systems of minor importance. As a result of this, practically no research was conducted on the problem of the quality and reliability of electricity supply to consumers in rural areas. A significant increase in load in recent years has resulted in an increase in the number of failures in field LV networks. Therefore, it was necessary to conduct comprehensive reliability tests of these power systems in order to determine the methods of their operation.

Due to the limited size of this paper, only a fragment of the analysis concerning the durations of failures, durations of emergency shutdowns and durations of interruptions in power supply to consumers, as well as seasonality and causes of failures was presented. The determined values of the reliability parameters are as follows:

t̄a = 11.30 h, ¯λa = 62.3614 1/a·100km, qa = 74.45·10-3 1/100km, t̄wa = 9.68 h, ¯λwa= 61.6816 1/a·100km, qwa = 63.81·10-3 1/100km, t̄p = 5.34 h, ¯λp = 59.5289 1/a·100km, qp = 35.02·10-3 1/100km.

The probability density functions of durations of failures, durations of emergency shutdowns and durations of interruptions in power supply to consumers were determined. The proposed probability distributions are log-normal distributions. An analysis of seasonality and causes of failures was performed. On its basis it can be concluded that inspections, repairs and measurements of LV overhead lines should be carried out in March, April and November, as the intensity of failure is the lowest in these months. The period of increased intensity of damage are the spring and summer months. The most common causes of failure were ageing processes, trees and branches, wind and lightnings. While we have no influence on the weather conditions, we can significantly improve the reliability of power grids by increasing the frequency of inspections and repairs.

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Authors: M.Sc. Eng. Łukasz Grąkowski, PhD Eng. Andrzej Ł. Chojnacki, M.Sc. Eng. Katarzyna Gębczyk, M.Sc. Eng. Kornelia Banasik, Department of Energy Basics, Kielce University of Technology, Faculty of Electrical Engineering, Automatic Control and Computer Science Poland, lgrakowski@tu.kielce.pl, a.chojnacki@tu.kielce.pl, kgebczyk@tu.kielce.pl, k.banasik@tu.kielce.pl

Source & Publisher Item Identifier: PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 95 NR 12/2019. doi:10.15199/48.2019.12.59