Published by

- Miss Panaya Sudta, Customer Relation Division, Provincial Electricity Authority, Email: nica_pny@hotmail.com
- Prof. Weerakorn Ongsakul, Energy Field of Study (FoS) of SERD, Asian Institute of Technology, Email: ongsakul@gmail.com
- Mr.Patiphan Thupphae, Energy Field of Study (FoS) of SERD, Asian Institute of Technology, Email: sunpatiparn@gmail.com
- Mr. Wichian Khumwong, Customer Relation Division, Provincial Electricity Authority, Email: wichian.k@gmail.comcom

*Published in PEACON & INNOVATION 2018 “PEA4.0 : Road to Digital Utility” 24 ^{th}-25^{th} September, 2018. Centra Government Complex Hotel & Convention Centre Chaeng Watthana Chaeng Watthana, Bangkok*

**Abstract**

Nowadays the rapid evolution of power systems leads electricity system transfer from centralized fossil fuel to decentralized distributed generation (DG). The distributed generation based on single phase wind turbine generator placement and sizing problem is formulated as a nonlinear integer optimization problem. Single phase wind turbine installation in distribution systems is beneficial and requires optimal placement and sizing of this DER. However, the addition of single phase wind turbine can cause power quality problems such as over voltage levels and increasing of harmonic waveform. Hence, single phase wind turbine should be optimally located and rated taking the presence of power into account.

The goal is to minimize the overall cost of total real power losses and maintain voltage level and power quality. The optimal single-phase wind turbine placement and sizing problem is tackled by H-particle swarm optimization (HPSO). To include the presence of real power, the developed HPSO is integrated with power distribution system. The modified IEEE 13-bus three phase unbalanced radial network is used to validate effectiveness. This case study is implemented on MATLAB. The results present the necessity of including harmonics in optimal single-phase wind turbine placement and sizing to avoid any possible problems that occur with power quality issue.

Key words: *Single-phase wind turbine, microgenerator, HPSO, optimization tools*

**1. Introduction**

In epochal years, the infrastructure of a distribution systems is extensively expanding that facing the pressure to integrate the distributed generation (DER) based such as solar rooftop PV, electric vehicle (EV), and single-phase wind generation, which are commonly penetrated in distribution systems in order to support governments policies. Consideration in the term of utility power system these penetration of DER helps reduce real power losses, release system capacity, and improve voltage profile. The achieving such benefits among other benefits depends on the most appropriate method to manage these the installation of DER, which in this paper focus on single-phase wind turbine generator.

In addition, along with voltage drops and real power loss, the growing of electricity demand requires upgrading the distribution system infrastructure, when electric loads are increasing, the voltage profile tends to decrease with the dispersion feeder being below the acceptable operating limit. The installation of distributed generation based on single-phase wind generators can help to enhance performance of utility electric power distribution systems.

However, the use of harmonic devices on the controller part of this type of DER in the widespread distribution system create the unexpected harmonic distortion throughout the system. Harmonics causes overheating due to excessive wear and and tear of electrical equipment. The integration of single-phase wind generator without considering harmonic sources in the system may lead to an increase in the total harmonic distortion because of the reflection between the control devices and the components in the system. Distorted radial distribution systems are inherently unbalance in several reason. Firstly, distribution supply both single and three phase loads through distribution transformers. Secondly, phases of transmission lines are unequally loaded. Lastly, overhead lines in distribution systems are not transposed not the same as transmission systems.

From the previous experimental the developed heuristic models, varying according to local search engine ranking of the best global single-phase wind generator, which makes the cost of losing all power to the actual performance of the DG decreases [1]. The purpose is to reduce the actual cost of power loss and the efficiency of the evaporator capacitor while observing the practical limitations. The result shows that the neglect of the presence of a harmonic source may Carpinelli et al. Correct the position of the capacitor and scale the problem in such a way that the overall cost decreases. [2].

In this paper use the same method of the problem of scaling solar rooftop PV, which is best defined as an integer programming problem is not linear, with no limitation as limitation is the rms. The voltage of the bus and the deviation of the total harmonics. One source speculated that the station utility. The heuristic algorithm, based on local variability, offers to overcome the prohibitive computational time associated with considering every potential capacitor size in a given repetition. Yan contributes to Harmonic loading in distribution systems [3].

Hybrid dynamic evolution algorithms have been developed to determine the position and the capacitance in the distorted delivery system well. Sensitivity tests were conducted prior to the optimization process to monitor the buses for reactive energy compensation. Costs related to the cost of actual power loss, spinning capacitors, and harmonic distortion. Use the estimated energy flow method and the linear harmonic flow method to calculate the cost functions at fundamental and harmonic frequencies.

Therefore, to study the effects of single-phase wind generator location and size on the increasing number of harmonic distortions, a harmonic power flow algorithm was integrated with the particle swarm optimization algorithm to calculate the harmonic related terms. These terms were the harmonic bus voltages, harmonic real power losses, and total harmonic distortions. The total real power loss and the cost of the real power loss and shunt capacitor installation were considered as objectives of the optimal DG based on single-phase wind generator locational and sizing problem.

The findings of this research indicate that the inclusion of single-phase wind generator in power distribution systems without harmonics consideration may cause a serious harmonic distortion problem, where the objective functions were subject to inequality and equality constraints. The inequality constraints were those associated with limits on bus voltages, total harmonic distortions (THD), and the total number and size of single-phase wind generator to be installed and thus, the equality constraints were the nonlinear electric power flow equations.

**2. Problem Formulation**

**2.1 Optimal placement and sizing formulation**

The main purpose of installing the capacitors in an electrical distribution system is to reduce the total power loss and also improve the voltage level in a system. The formulation of total power losses utilized in this study as the constraint parameters for the optimization solution is given in equation (1).

where, m and N_{l} is the feeder number and total number of feeder, respectively. In the market, the size of the single-phase wind generators is given in fixed size. In this study, a complete size of single-phase wind turbine is designed based on the combination of several generators with smallest size of rated power. Single-phase wind turbine installation cost is chosen proportional to the size of the generators. The size of the generators to be installed at the selected destination is limited to the maximum size of rated power load [4]. Where the available generator size given in Table 1. The most optimal placement and the size of the installed are referred to the cost of total power loss as expressed in equation (2).

**Table 1. ***Available discrete single-phase wind turbine generator sizes*

Model | Rated Power (kW) | Swept area sq. m | Rotor Radius |
---|---|---|---|

CF20 | 20 | 135 | 6.55 |

Gaia-Wind 133-11kW | 11 | 133 | 6.5 |

CF15 | 15 | 92 | 5.4 |

Westwind 20 kW | 20 | 82 | 5.2 |

Evoco 10 | 9.55 | 74 | 4.85 |

Aircon 10s | 9.8 | 45 | 3.8 |

Xzeres 442SR | 10 | 41 | 3.6 |

Bergey Excel 10 | 10 | 38 | 3.5 |

where, K_{s }is the cost coefficient for power losses ($/kW) and j is the number of selected buses required for the single-phase wind generators installation. The objective function from equation (2) is bounded by a number of constraints which are the allowable minimum and maximum voltage limit and limitation of generator size specified at each bus.

Thus, the inequality constraints considered in this study can be described as follows.

where:

- V
_{lower}bound of bus voltage limits; - V
_{max }upper bound of bus voltage limits; - |V
_{i}| rms value of the bus voltage and defined by

However, the minimum constraint of inductive reactive power for this study is set to zero to provide wide selection of generators sizing. The PSO technique developed for this case study will execute equations (3), (4), (5), and (6) at every computational iteration. The global best solution will not be update unless the objective function, is improved or reduced and this condition is described in equation (7).

where, k is the number of computational iteration.

**2.2 Particle Swarm Optimization Technique**

Particle Swarm Optimization was introduced by R. Eberhart and J, Kennedy, inspired by social behavior of bird flocking or fish schooling. It is a part of modern heuristic optimization algorithm, it work on population or group in which individuals called particles move to reach the optimal solution in the multidimensional search space. It works with direct real valued numbers, which eliminates the need to do binary conversion of a classical canonical genetic algorithm. The number of particles in the group is Np. The initial population of a PSO algorithm is randomly generated within the control variables bounds. Each particle adjusts its position through its present velocity, previous positions and the positions of its neighbors. Each particle updates its position based upon its own best position, global best position among particles and its previous velocity vector according to the following equations:

where:

- v
_{i}^{k+1}velocity of i^{th}particle at (k +1)^{th}iteration - w inertia weight of the particle
- v
_{i}^{k}the velocity of i^{th}particle at k^{th}iteration - c
_{1}, c_{2}acceleration constants. - r
_{1}, r_{2}randomly generated number between [0, 1] - p
_{best i }the best position of the i_{th}particle obtained based upon its own experience - g
_{best}global best position of the particle in the population - x
_{i}^{k+1}position of i^{th}particle at (k +1)^{th}iteration - x
_{i}^{k}the position of i^{th}particle at k^{th }iteration - X constriction factor. It may help insure convergence. Suitable selection of inertia weight provides good balance between global and local explorations.

**3. Methodology **

**3.1 Construction of distribution system simulation**

In this study, circuitry-based commercial software has been chosen to develop IEEE 13-bus three-phase unbalanced radial distribution system. The model was designed by taking into account several important electrical components such as the three-phase load, distribution line, buses, incoming source and measurement blocks. The load flow simulation is performed which will provide the measurement in a time domain response at a steady state condition.

In Figure 1, the IEEE 13-bus three-phase unbalanced distribution system is embodied with the total real and reactive power of 3676.50 kW and 2560.90kVar, respectively. The system is considered to be unbalanced since there are several buses connected with only single or two-phase load. The sampling time of simulation is set as 50μs and 50 Hz is set for the frequency. The system is operating at the nominal voltage of 4.16 kV accept at bus 634 where the voltage is step down to 480 V.

**3.2 OPF single-phase wind generator with HPS**

**Figure 1. ***IEEE 13-Bus Three Phase Unbalanced Distribution System*

To consider harmonics, the total harmonic distortion (THD) limit at each bus is included as the optimization constraints to ensure that the harmonic distortion levels at all bus are within the allowable limits. Results of the harmonic power flow (HPF) subroutine is integrated with the PSO algorithm to determine the harmonic real power losses, and total harmonic distortions. The PSO-HPF based algorithm that incorporate HPF with HPSO algorithm show as the flow chart in Figure 2.

**Figure 2.** *Optimal single-phase wind generator placement and sizing using HPSO technique*

The procedure of PSO algorithm implemented in this study to obtain the optimal value of the objective function is discussed as follows:

- Perform a three-phase unbalanced load flow solution for the original system (without the single-phase wind generator placement) to obtain the total power loss and other required data.
- Start the developed PSO algorithm by generating a swarm of the particles randomly in the feasible region of the search space. As previously mentioned in section, each particle is associated with two vectors, the position vector and velocity vector.
- The position vector of each particle represents a potential solution to the problem at hand. The feasible swarm is passed to the RDPF subroutine as initial guess to minimize power mismatch equations.
- Each particle recalls its best position associated with the best fitness value (e.g. the real power loss). Each particle records the best position achieved by the entire swarm.
- Update process of particles’ positions results in continuous values of particles’ positions and made discretization of particles’ position vectors.
- Feasible check the particles to ensure that no particle flies outside the feasible region.

**4. Results and Discussion**

The algorithm of PSO technique and a case study of IEEE 13 bus three-phase unbalanced distribution model were developed in MATLAB. The HPSO is executed for 10 times with 100 iterations of optimization process is specified for each time.

With the presence of harmonics, two different cases investigate the impact of single-phase wind generators installation on the voltage profiles, total harmonic distortions, total real power losses, and total cost are considered.

- Case 1 represents the system without total harmonics consideration after single-phase generator installation.
- Case 2 represents the system with harmonics consideration after single-phase generator installation.

**Table 2. ***Available discrete single-phase wind turbine generator sizes*

The maximum number of iterations was taken as 100 for the tuning process of each parameter. It was found that the PSO algorithm was less sensitive to its parameters when the problem dimension was small (the problem dimension was single-phase wind generators). However, the larger the problem dimension is, the more sensitive the PSO algorithm becomes. The solution of the optimal solar rooftop PV placement and sizing problem using developed PSObased algorithm was able to find optimal locations and that overall cost was minimized. The simulation results for initial case, cases 1, and 2 is reported in Table I. Based on Tables II execution gives the best solution with respect to the best total cost considered as its objective function.

The convergence characteristics of the developed PSO-HPF-based approach for cases 1 and 2 in the optimal placement and sizing of solar rooftop PV problem with the total cost being the objective with HPSO consideration is depicted in Figure 3.

**Figure 3.**

**4. Conclusion**

In this paper, the single-phase wind generator placement and sizing problem was formulated as a constrained nonlinear integer programming problem with both locations and ratings of single-phase wind generator is discrete. The constraints considered were of two types: equality and inequality. The equality constraints were the nonlinear power flow

equations. The developed PSO-HPF-based algorithm was tested on an unbalanced 13-bus test system to calculate the optimal locations and sizes of single-phase wind generator taking harmonics into account.

**Reference**

[1] Y. Baghzouz and S. Ertem, “Shunt capacitor sizing for radial distribution feeders with distorted substation voltages,” IEEE Trans. Power Del., vol. 5, pp. 650–657, Apr. 1990.

[2] “Systems with harmonic distortion,” in Proc. IASTED Int. Conf. Power and Energy Systems, May 13–15, 2002, pp. 352-353.

[3] G. Carpinelli, P. Varilone,“Capacitor placement in three-phase distribution systems with nonlinear and unbalanced loads,” Proc. Inst. Elect. Eng., Gen., Transm. Distrib., vol. 152, pp.47–52, 2005.

[4] A. Eajal, S. Member, and L. Fellow, “Unbalanced Distribution Systems with Harmonics considered Using PSO,” vol. 25, pp. 1734–1741, 2010.

[5] P. Sudta “Optimal DG Based on Solar Rooftop PV Placement and Sizing in Unbalanced Distribution Systems with Harmonics Consider Using PSO” PEACON2017