Published by Electrotek Concepts, Inc., PQSoft Case Study: *Industrial Harmonic Filter Design*, Document ID: PQS0504, Date: June 30, 2005.

**Abstract: **The industrial harmonic problem can be solved using a comprehensive approach including site surveys, harmonic measurements, and computer simulations.

Simple calculations are used to determine the system resonant frequencies and then the preliminary model development is completed. Initial estimates of voltage distortion levels are made based on the level of harmonic current injection and the frequency response characteristic.

This case study presents the configuration of low voltage power factor correction capacitors as harmonic filters to improve poor power factor and reduce excessive voltage distortion levels.

##### PROBLEM STATEMENT

The plastics manufacturer (refer to power factor correction case) is now experiencing equipment problems, such as several capacitor bank fuses blowing, and a capacitor can failure. The plant engineer believes that the problem may be related to harmonics. He measures the following bus voltage waveform (Figure 1):

##### Harmonic Evaluations

The industrial harmonic problem can be solved using a comprehensive approach including site surveys, harmonic measurements, and computer simulations. One general procedure used for a harmonic analysis study consists of the following steps:

− Preliminary analysis / model development

− Harmonic measurements

− Perform computer simulations

− Determine impact on equipment

− Evaluate harmonics with respect to limits

− Develop solutions (including filter design)

Simple calculations are used to determine the system resonant frequencies and then the preliminary model development is completed. Initial estimates of voltage distortion levels are made based on the level of harmonic current injection and the frequency response characteristic.

**Model Development and Drive Characteristic**

A simplified model, as illustrated in Figure 2, can be developed for the initial analysis. Harmonic measurements of the ASD indicated the following characteristic:

Drive rating: 500 HP

Drive voltage: 480 V

Fundamental Current: 600 A

Harmonic Number | % of Fundamental | Amps |
---|---|---|

5 | 28 | 168 |

7 | 12 | 72 |

11 | 7 | 42 |

13 | 4 | 24 |

THD: | 31.5% |

**Voltage Distortion and Harmonic Resonance Calculation**

Hand calculations can be used to determine the voltage distortion level without capacitors. This value is then compared with measured quantity to determine the accuracy of the preliminary model.

The transformer impedance can be determined from:

X_{tx }= (kV^{2} * Z_{pu})/ MVA = (0.480^{2} * 0.06) / 1.5 = 0.0092Ω

**Table 1 – Voltage Distortion Calculation**

h | I_{h} | X_{h}=h*X_{t} | h=I_{h}*X_{h} |
---|---|---|---|

5 | 168 | 0.046 | 7.73 |

7 | 72 | 0.064 | 4.64 |

11 | 42 | 0.101 | 4.25 |

13 | 24 | 0.119 | 2.87 |

The total harmonic voltage distortion (V_{THD}) is determined by:

V_{THD} = **√**(7.73^{2} + 4.64^{2} + 4.25^{2} +2.87^{2}) / 2.77^{2} = 3.74%

The customer has added 500kVAr of power factor correction at the 480 volt bus. The addition of a capacitor bank creates a parallel resonance condition. The parallel resonance occurs at the frequency where the shunt capacitive reactance is equal to the inductive source reactance and can be expressed in terms of the 60 Hz values as follows:

h = 1 /(2π**√**(L_{s}C)) = **√**(X_{c}/X_{s}) ≈ **√**(100*kVA_{tx})/(kVAr_{cap} * Z_{tx(%)})

where:

h = parallel resonance frequency (x 60 Hz)

X_{c }= shunt capacitive reactance (C – capacitance) (ohms)

X_{sc }= short circuit reactance (L_{s} – inductance) (ohms)

kVA_{tx} = step-down transformer rating (kVA)

Z_{tx} = step-down transformer impedance (percent)

kVAr_{cap} = capacitor bank rating (kVAr)

This simple relationship provides an excellent first check to see whether or not harmonics are likely to be a problem. Almost all harmonic distortion problems occur when this parallel resonance moves close to the 5^{th} or 7^{th} harmonic, since these are the largest harmonic current components in loads like ASDs. However, the 11^{th} and 13^{th} harmonics can also be a problem when ASDs (PWM type) are a large percentage of the total load.

For the 500 kVAr power factor correction capacitor bank installation, the harmonic resonance is very near the 7^{th} harmonic.

h ≈ √(100*kVA_{tx})/(kVAr_{cap} * Z_{tx(%)}) = **√**(100*1500)/(500*6.0) = 7.08

assuming:

kVA_{tx}: step-down transformer rating (1500 kVA)

Z_{tx}: step-down transformer impedance (6%)

kVAr_{cap} : capacitor bank rating (500 kVAr)

The frequency response characteristic, determined from computer simulation, is illustrated in Figure 3.

The addition of the 500kVAr power factor correction capacitor increases the voltage distortion to 11.5% (determined from computer simulation).

The initial solution to the problem would appear to be the installation of a 7^{th} harmonic filter. This would create a low impedance condition and reduce the 7^{th} harmonic voltage distortion. However, the installation of the 7^{th} harmonic filter create a new parallel resonance very near the 5^{th} harmonic. Recalling the current spectrum for the ASD, the 5^{th} harmonic component was higher than the 7^{th} (168A vs. 72A), therefore the voltage distortion will actually increase. Figure 4 illustrates the simulated frequency response characteristic for this condition.

The installation of the 7^{th} harmonic filter increased the voltage distortion to 16.2% (determined by simulation). The proper solution to the problem is the addition of a 5^{th} harmonic filter. Configuration of the power factor correction capacitor as a 5^{th }harmonic filter reduced the voltage distortion to 3.2% (determined by simulation). In general, it is best to apply harmonic filters at the lowest generated harmonic frequency. The filter configuration for this case is illustrates in Figure 5.

**Filter Design Methodology**

The harmonic filter, illustrated in Figure 5, provides a low impedance path for harmonic currents, thereby minimizing harmonic voltage distortion problems. The filter is tuned slightly below the harmonic frequency of concern. This method allows for tolerances in the filter components and prevents the filter from acting as a short circuit for the offending harmonic current. This allows the filter to perform its function of providing low impedance at the harmonic frequency while helping to reduce the duty on the filter components.

The general method for applying filters is as follows:

− Apply one single-tuned shunt filter first, and design it for the lowest generated frequency.

− Determine the voltage distortion level at the low voltage bus. The commonly applied limit of 5% was introduced in IEEE Std 519-1992.

− Vary the filter elements according to the specified tolerances and check its effectiveness.

− Check the frequency response characteristic to verify that the newly created parallel resonance is not close to a harmonic frequency.

− If necessary, investigate the need for several filters, such as 5^{th }and 7^{th}.

##### SUMMARY

The industrial harmonic problem can be solved using a comprehensive approach including site surveys, harmonic measurements, and computer simulations.

Simple calculations are used to determine the system resonant frequencies and then the preliminary model development is completed. Initial estimates of voltage distortion levels are made based on the level of harmonic current injection and the frequency response characteristic.

A harmonic filter provides a low impedance path for harmonic currents, thereby minimizing harmonic voltage distortion problems.

REFERENCES

IEEE Recommended Practice for Electric Power Distribution for Industrial Plants (IEEE Red Book, Std 141-1986), October 1986, IEEE, ISBN: 0471856878

IEEE Recommended Practice for Industrial and Commercial Power Systems Analysis (IEEE Brown Book, Std 399-1990), December 1990, IEEE, ISBN: 1559370440

IEEE Recommended Practice for Protection and Coordination of Industrial and Commercial Power Systems, March 1988, IEEE, ISBN: 0471853925

**RELATED STANDARDS**IEEE Std. 519-1992

IEEE Std. 1036-1992

**GLOSSARY AND ACRONYMS**ASD: Adjustable-Speed Drive

CF: Crest Factor

DPF: Displacement Power Factor

PF: Power Factor

PWM: Pulse Width Modulation

THD: Total Harmonic Distortion

TPF: True Power Factor