Applied Harmonics 263 Isp (5.5) = 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 4.5 5 5.5 6 6.5 0 2 4 6 8 10 12 14 0246810 Harmonic number h 12 14 16 18 20 Harmonic current allowed to flow in Xs Isp (5.5) = 0.1 Isp (5.5) = 0.3 Isp (5.5) = 0.5 Isp (5.5) = 0.5 Isp (5.5) = 0.3 Figure 6.23 An example of a C filter where the maximum harmonic current allowed to flow in the system is 10, 30, and 50 percent at the tuned harmonic order of 5.5. Lm Ca Cm R C filter with a 3.0-Mvar notch filter L notch C notch C filter 0 2 4 6 8 10 12 14 16 18 20 Harmonic number h 0 1 2 3 4 5 6 7 8 9 Harmonic current allowed to flow in Xs Figure 6.24 A C filter with and without a notch filter. Applied Harmonics Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. ters can work independently of the system impedance characteristics. Thus, they can be used in very difficult circumstances where passive filters cannot operate successfully because of parallel resonance prob- lems. They can also address more than one harmonic at a time and combat other power quality problems such as flicker. They are particu- larly useful for large, distorting loads fed from relatively weak points on the power system. The basic idea is to replace the portion of the sine wave that is miss- ing in the current in a nonlinear load. Figure 6.25 illustrates the con- cept. An electronic control monitors the line voltage and/or current, switching the power electronics very precisely to track the load current or voltage and force it to be sinusoidal. As shown, there are two funda- mental approaches: one that uses an inductor to store current to be injected into the system at the appropriate instant and one that uses a capacitor. Therefore, while the load current is distorted to the extent demanded by the nonlinear load, the current seen by the system is much more sinusoidal. Active filters can typically be programmed to correct for the power factor as well as harmonics. 6.6 Harmonic Filter Design: A Case Study This section illustrates a procedure for designing harmonic filters for industrial applications. This procedure can also be used to convert an existing power factor correction capacitor into a harmonic filter. As described in Sec. 4.1.2, power factor correction capacitors are used widely in industrial facilities to lower losses and utility bills by improv- ing power factor. On the other hand, power factor correction capacitors may produce harmonic resonance and magnify utility capacitor-switch- ing transients. Therefore, it is often desirable to implement one or more capacitor banks in a facility as a harmonic filter. 264 Chapter Six OR NONLINEAR LOAD Figure 6.25 Application of an active filter at a load. Applied Harmonics Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Filter design procedures are detailed in the steps shown below. The best way to illustrate the design procedures is through an example. A single-tuned notch filter will be designed for an industrial facility and applied at a 480-V bus. The load where the filter will be installed is approximately 1200 kVA with a relatively poor displacement power factor of 0.75 lagging. The total harmonic current produced by this load is approximately 30 percent of the fundamental current, with a maxi- mum of 25 percent fifth harmonic. The facility is supplied by a 1500- kVA transformer with 6.0 percent of impedance. The fifth-harmonic background voltage distortion on the utility side of the transformer is 1.0 percent of the fundamental when there is no load. Figure 6.7 shown earlier depicts the industrial facility where the filter will be applied. The harmonic design procedures are provided in the following steps. 1. Select a tuned frequency for the filter. The tuned frequency is selected based on the harmonic characteristics of the loads involved. Because of the nature of a single-tuned filter, the filtering should start at the low- est harmonic frequency generated by the load. In this case, that will be the fifth harmonic. The filter will be tuned slightly below the harmonic frequency of concern to allow for tolerances in the filter components and variations in system impedance. This prevents the filter from act- ing as a direct short circuit for the offending harmonic current, reduc- ing duty on the filter components. It also minimizes the possibility of dangerous harmonic resonance should the system parameters change and cause the tuning frequency to shift. In this example, the filter is designed to be tuned to the 4.7th. This is a common choice of notch frequency since the resulting parallel res- onant frequency will be located around the fourth harmonic, a har- monic frequency that is not produced by most nonlinear loads. The notch filter is illustrated in Fig. 6.26. 2. Compute capacitor bank size and the resonant frequency. As a general rule, the filter size is based on the load reactive power requirement for power factor correction. When an existing power factor correction capacitor is converted to a harmonic filter, the capacitor size is given. The reactor size is then selected to tune the capacitor to the desired fre- quency. However, depending on the tuned frequency, the voltage rating of the capacitor bank may have to be higher than the system voltage to allow for the voltage rise across the reactor. Therefore, one may have to change out the capacitor anyway. This example assumes that no capacitor is installed and that the desired power factor is 96 percent. Thus, the net reactive power from the filter required to correct from 75 to 96 percent power factor can be computed as follows: Applied Harmonics 265 Applied Harmonics Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. ■ Reactive power demand for a 75 percent power factor would be 1200 ϫ sin [arccos (0.75) ] ϭ 794.73 kvar ■ Reactive power demand for a 96 percent power factor would be 1200 ϫ sin [arccos (0.96) ] ϭ 336.0 kvar ■ Required compensation from the filter: 794.73 Ϫ 336.0 ϭ 457.73 kvar For a nominal 480-V system, the net wye-equivalent filter reactance (capacitive) X Filt is determined by X Filt ϭϭ ϭ0.5034 ⍀ X Filt is the difference between the capacitive reactance and the induc- tive reactance at fundamental frequency: X Filt ϭ X Cap Ϫ X L For tuning at the 4.7th harmonic, X Cap ϭ h 2 X L ϭ 4.7 2 X L 0.48 2 (1000) ᎏᎏ 457.73 kV 2 (1000) ᎏᎏ kvar 266 Chapter Six Filter Reactor Power Factor Correction Capacitor 480-Volt Bus Figure 6.26 Example low-voltage filter configuration. Applied Harmonics Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Thus, the desired capacitive reactance can be determined by X Cap ϭϭ ϭ0.5272 ⍀ At this point, it is not known whether the filter capacitor can be rated at 480 V, the same as the system, or will have to be rated one step higher at 600 V. To achieve this reactance at a 480-V rating, the capac- itor would have to be rated kvar ϭϭ ϭ437 kvar Similarly, at 600 V, the capacitor would have to be rated 682 kvar. For now, the filter will be designed using a 480-V capacitor rated 450 kvar, which is a commonly available size near the desired value. For this capacitor rating, X Cap ϭ 0.5120 ⍀ 3. Compute filter reactor size. The filter reactor size can now be selected to tune the capacitor to the desired frequency. From step 1, the desired frequency is at the 4.7th harmonic or 282 Hz. The filter reactor size is computed from the wye-equivalent capacitive reactance, determined in step 2, as follows: X L (fund) ϭϭϭ0.02318 ⍀ or L ϭϭ0.06148 mH Alternatively, the reactor size can be computed by solving for L in the following equation: f h ϭ where f h ϭ 4.7 ϫ 60 ϭ 282 Hz. The next step is to evaluate the duty requirements for the capacitor and reactor. 1 ᎏᎏ 2 ͙LC (wy ෆ e) ෆ X L (fund) ᎏ 2ϫ60 0.5120 ᎏ 4.7 2 X Cap (wye) ᎏ h 2 0.48 2 (1000) ᎏᎏ 0.5272 kV 2 (1000) ᎏᎏ X Cap 0.5034 (4.7 2 ) ᎏᎏ 4.7 2 Ϫ 1 X Filt h 2 ᎏ h 2 Ϫ 1 Applied Harmonics 267 Applied Harmonics Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 4. Evaluate filter duty requirements. Evaluation of filter duty require- ments typically involves capacitor bank duties. These duties include peak voltage, current, kvar produced, and rms voltage. IEEE Standard 18-1992, IEEE Standard for Shunt Power Capacitors, is used as the limiting standard to evaluate these duties. Computations of the duties are fairly lengthy; therefore, they are divided into three steps, i.e., com- putation for fundamental duties, harmonic duties, and rms current and peak voltage duties. 5. Computation of fundamental duty requirements. In this step, a funda- mental frequency operating voltage across the capacitor bank is deter- mined. The computation is as follows: a. The apparent reactance of the combined capacitor and reactor at the fundamental frequency is X fund ϭ |X L Ϫ X Cap (wye) | ϭ |0.02318 Ϫ 0.5120| ϭ 0.489 ⍀ b. The fundamental frequency filter current is I fund ϭϭϭ567 A c. The fundamental frequency operating voltage across the capacitor bank is V L Ϫ L,Cap (fund) ϭ ͙3 ෆ ϫ I fund ϫ X Cap (wye) ϭ 502.8 V This is the nominal fundamental voltage across the capacitor. It should be adjusted for any contingency conditions (maximum system voltage), and it should be less than 110 percent of the capacitor rated voltage. d. Because of the fact that the filter draws more fundamental cur- rent than the capacitor alone, the actual reactive power produced is larger than the capacitor rating: kvar fund ϭ ͙3 ෆ ϫ I fund ϫ kV actual ϭ 471 kvar 6. Computation of harmonic duty requirements. In this step, the maxi- mum harmonic current expected in the filter is computed. This current has two components: the harmonic current produced by the nonlinear load (computed in step a) and the harmonic current from the utility side (computed in step b). 480/͙3 ෆ ᎏ 0.489 kV actual /͙3 ෆ ᎏᎏ X fund 268 Chapter Six Applied Harmonics Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. a. Since the nonlinear load produces 25 percent fifth harmonic of the fundamental current, the harmonic current in amperes produced by the load would be I h (amps) ϭ I h (pu) ϭ 0.25 ϭ 360.8 A b. Harmonic current contributed to the filter from the source side is estimated as follows. It will be assumed that the 1 percent fifth-har- monic voltage distortion present on the utility system will be limited only by the impedances of the service transformer and the filter; the utility impedance will be neglected. ■ Fundamental frequency impedance of the service transformer: X T (fund) ϭ Z T (%) ϭ 0.06 ϭ 0.0092 ⍀ ■ The fifth-harmonic impedance of the service transformer (the trans- former is inductive): X T (harm) ϭ hX T (fund) ϭ 5 ϫ 0.0092 ϭ 0.0461 ⍀ ■ The harmonic impedance of the capacitor bank is X Cap (wye), harm ϭϭϭ0.1024 ⍀ ■ The harmonic impedance of the reactor is X L (harm) ϭ hX L (fund) ϭ 5 ϫ 0.02318 ϭ 0.1159 ⍀ ■ Given that the voltage distortion on the utility system is 0.01 pu, the estimated amount of fifth-harmonic current contributed to the filter from the source side would be I h (utility) ϭ ϭϭ46.5 A 0.01 ϫ 480 ᎏᎏᎏᎏ ͙3 ෆ ϫ 0.0461 Ϫ 0.1024 ϩ 0.1159 V h (utility) (pu) ϫ kV actual ᎏᎏᎏᎏ ͙3 ෆ ϫ X T (harm) Ϫ X Cap (wye),harm ϩ X L (harm) 0.512 ᎏ 5 X Cap (wye) ᎏ h 0.48 2 ᎏ 1.5 kV 2 actual ᎏ MVA Xfmr 1200 ᎏᎏ ͙3 ෆ ϫ 0.48 kVA ᎏᎏ ͙3 ෆ ϫ kV actual Applied Harmonics 269 Applied Harmonics Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. c. The maximum harmonic current is the sum of the harmonic cur- rent produced by the load and that contributed from the utility side: I h (total) ϭ 360.8 ϩ 46.5 ϭ 407 A d. The harmonic voltage across the capacitor can be computed as fol- lows: V Cap (L-L,rms-harm) ϭ ͙3 ෆ I h (total) ϭ ͙3 ෆ ϫ 407 ϫϭ72.2 V 7. Evaluate total rms current and peak voltage requirements. These two quantities are computed as follows: a. Total rms current passing through the filter: I rms,total ϭ ͙I 2 fund ϩ ෆ I h 2 (utili ෆ ty) ෆ ϭ ͙567 2 ϩ ෆ 407 2 ෆ ϭ 698 A This is the total rms current rating required for the filter reactor. b. Assuming the harmonic and fundamental components add together, the maximum peak voltage across the capacitor is V L-L,Cap (max,Peak) ϭ V L-L,Cap (fund) ϩ V Cap (L-L,rms-harm) ϭ 502.8 ϩ 72.2 ϭ 575 V c. The rms voltage across the capacitor is V L-L,Cap (rms,total) ϭ ͙V 2 L-L,C ෆ ap (fund) ෆ ϩ V 2 ෆ Cap (L-L, ෆ rms-harm ෆ ) ෆ ϭ ͙502.8 ෆ 2 ϩ 72 ෆ .2 2 ෆ ϭ 508 V d. The total kvar seen by the capacitor is kvar Cap (wye),total ϭ ͙3 ෆ I rms,total ϫ kV L-L,Cap (rms,total) ϭ ͙3 ෆ ϫ 698 ϫ 0.508 ϭ 614 kvar 8. Evaluate capacitor rating limits. The duties (peak voltage, rms volt- age and current, and kvar produced) for the proposed filter capacitor are compared to the various IEEE standard limits in Table 6.4. This would be a very marginal application because the capacitor duties are 0.512 ᎏ 5 X Cap (wye) ᎏ h 270 Chapter Six Applied Harmonics Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. essentially at the maximum limits. There is no tolerance for any devi- ation in assumptions or increases in service voltage. A 480-V capacitor will likely have a short life in this application. When this happens, a capacitor rated for higher voltage must be used. At 600 V, the equivalent capacitor rating would be 450 ϫϭ703 kvar A nominal rating of 700 kvar with the reactor values computed in step 3 would provide essentially the same filter within normal manufactur- ing tolerances. The 600-V capacitor would be well within its rating in this application. 9. Evaluate filter frequency response. The filter frequency response is now evaluated to make sure that the filter does not create a new reso- nance at a frequency that could cause additional problems. The har- monic at which the parallel resonance below the notch frequency will occur is computed as follows: h 0 ϭ Ί ϭ Ί ϭ 3.97 This assumes the service transformer reactance dominates the source impedance. Including the utility system impedance will lower the fre- quency. This filter results in a resonance very near the fourth harmonic, which is an interesting case. Normally, there are very few significant sources of an even harmonic during steady-state operation and this fil- ter would work acceptably. However, there are significant fourth-har- 0.512 ᎏᎏᎏ 0.0092 ϩ 0.02318 X Cap (wye) ᎏᎏ X T (fund) ϩ X L (fund) 600 2 ᎏ 480 2 Applied Harmonics 271 TABLE 6.4 Comparison Table for Evaluating Filter Duty Limit Duty Definition Limit, % Actual values Actual values, % Peak voltage 120 119 RMS voltage 110 106 RMS current 180 129 kvar 135 136 614 kvar ᎏᎏ 450 kvar kvar Cap(wye),total ᎏᎏ kvar rated 698 A ᎏ 541 A I rms,total ᎏᎏ I Cap(rated) 508 V ᎏ 480 V V L-L,Cap(rms,total) ᎏᎏᎏ kV rated 575 V ᎏ 480 V V L-L,Cap(max,Peak) ᎏᎏᎏ kV rated Applied Harmonics Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. monic currents during events such as transformer energization. If the filter is in service when a large transformer is energized and there is very little load to dampen the resonance, there can be overvoltages that persist well past the usual inrush transient period. In this case, the designer should first include the utility system impedance in the cal- culation. To gain additional margin from the fourth, the basic filter size would have to be increased. 10. Evaluate the effect of filter parameter variations within specified toler- ance. Filter designers generally assume capacitors are designed with a tolerance of ϩ15 percent of the nominal capacitance value. Reactors are assumed to have a tolerance of ±5 percent of the nominal inductance. These tolerances can significantly affect the filter performance should the frequency response over this range create a harmful resonance. Therefore, the final step is to check the filter design for the various extremes. This is automatically done in some filter design software. Steps 1 through 10 illustrate a typical single-tuned filter design. Multiple single-tuned filters might be necessary when a single-tuned filter does not control harmonics to acceptable levels. For example, 5th, 7th-, and 11th-harmonic filters may be needed for some large six-pulse loads. The general procedure is the same except that the reactive power requirement is first divided between the filter stages. Evaluating the effect of component tolerance is particularly important since there are multiple filters involved. The tuning characteristic of the filter is described by its quality fac- tor Q. Q is a measure of the sharpness of tuning and, for series filter resistance, is defined as Q ϭ where R ϭ series resistance of filter elements n ϭ tuning harmonic X L ϭ reactance of filter reactor at fundamental frequency Typically, the value of R consists of only the resistance of the inductor. This usually results in a very large value of Q and a very sharp filter- ing action. This is normally satisfactory for the typical single-filter application and results in a filter that is very economical to operate (small energy consumption). However, sometimes it is desirable to introduce some intentional losses to help dampen the response of the system. Aresistor is commonly added in parallel with the reactor to cre- ate a high-pass filter. In this case, Q is defined as the inverse of the above series case so that large numbers reflect sharp tuning. High-pass nX L ᎏ R 272 Chapter Six Applied Harmonics Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. [...]... behaved erratically TABLE 6. 5 Computation for Transformer Derating Harmonic Current, % Frequency, Hz Current, pu I2 I2h2 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 100.00 65 .70 37.70 12.70 4.40 5.30 2.50 1.90 1.80 1.10 0 .60 0.80 0.40 0.20 0.20 0.20 60 180 300 420 540 66 0 780 900 1020 1140 1 260 1380 1500 162 0 1740 1 860 1.000 0 .65 7 0.377 0.127 0.044 0.053 0.025 0.019 0.018 0.011 0.0 06 0.008 0.004 0.002 0.002... Currents in Low-Voltage Power Supply Systems for Equipment with Rated Current Greater Than 16 A ■ IEC 61 000-3 -6 (19 96) : Electromagnetic Compatibility (EMC) Part 3: Limits Section 6: Assessment of Emission Limits for Distorting Loads in MV and HV Power Systems Basic EMC publication Prior to 1997, these standards were designated by a 1000 series numbering scheme For example, IEC 61 000-2-2 was known as... Community (CENELEC); thus, they are also designated with the EN 61 000 series For example, IEC 61 000-3-2 is also known as EN 61 000-3-2 6. 8.3 IEC 61 000-2-2 IEC 61 000-2-2 defines compatibility levels for low-frequency conducted disturbances and signaling in public low-voltage power supply systems such as 50- or 60 -Hz single- and three-phase systems with nominal voltage up 240 and 415 V, respectively Compatibility... and P < 60 0 W No Yes Portable tool? No Class D Yes Class D Figure 6. 35 Flowchart for classifying equipment according to IEC 61 000-3-2 to IEC 61 000-3-2 are shown in Tables 6. 8 through 6. 10 Note that harmonic current limits for class D equipment are specified in absolute numbers and in values relative to active power The limits only apply to equipment operating at input power up to 60 0 W IEC 61 000-3-4... LV systems is less than 1 kV, while the nominal voltage for MV systems ranges between 1 and 44 kV NRS 048 has not established limits for harmonic voltages for HV systems yet However, it adopts IEC 61 000-3 -6 planning levels for harmonic voltages for HV and EHV systems (shown in Table 6. 14) as its recommended planning limits for HV systems (the nominal voltage is between 200 and 400 kV) 6. 8.7 EN 50 160 ... and MV systems, except for the absence of higher-order harmonic limits in EN 50 160 6. 9 References 1 M F McGranaghan, “Overview of the Guide for Applying Harmonic Limits on Power Systems IEEE P519A,” Eighth International Conference on Harmonics and Quality of Power, ICHQP 1998, Athens, Greece, pp 462 – 469 2 IEEE 519-1992, Recommended Practices and Requirements for Harmonic Control in Electric Power Systems. .. Transactions on Power Apparatus and Systems, Vol 101, No 3, March 1981 7 M F McGranaghan, E W Gunther, “Design of a PC-Based Harmonic Simulation Program,” Second International Conference on Harmonics in Power Systems, Winnipeg, Manitoba, October 19 86 8 D Xia, G T Heydt, “Harmonic Power Flow Studies Part I—Formulation and Solution,” IEEE Transactions on Power Apparatus and Systems, June 1982, pp 1257–1 265 9 W... Current (A) 1000 500 0 –500 –1000 0 10 Harm Fund 3rd 5th 7th 9th 11th 13th 15th % 100.0 65 .7 37.7 12.7 4.4 5.3 2.5 1.9 20 30 Phase –37 –97 – 166 113 – 46 –158 92 –51 40 Time (ms) 50 60 70 Harm 17th 19th 21st 23rd 25th 27th 29th 31st % 1.8 1.1 0 .6 0.8 0.4 0.2 0.2 0.2 80 Phase –151 84 –41 –148 64 –25 –122 102 Figure 6. 27 Phase current and its harmonic characteristics Fundamental amps: 285.5 A Phase angles... Guide for Applying Harmonic Limits on Power Systems 4 R C Dugan, “Simulation of Arc Furnace Power Systems, ” IEEE Transactions on Industry Applications, November/December 1980, pp 813–818 5 M F McGranaghan, J H Shaw, R E Owen, “Measuring Voltage and Current Harmonics on Distribution Systems, ” IEEE Transactions on Power Apparatus and Systems, Vol 101, No 7, July 1981 6 M F McGranaghan, R C Dugan, and W... individual harmonic voltages in the low-voltage network are shown in Table 6. 7 They are given in percentage of the fundamental voltage 6. 8.4 IEC 61 000-3-2 and IEC 61 000-3-4 Both IEC 61 000-3-2 and 61 000-3-4 define limits for harmonic current emission from equipment drawing input current of up to and including 16 A per phase and larger than 16 A per phase, respectively These standards are aimed at limiting harmonic . Applied Harmonics 263 Isp (5.5) = 0.1 0 0.1 0.2 0.3 0.4 0.5 0 .6 0.7 4.5 5 5.5 6 6.5 0 2 4 6 8 10 12 14 02 468 10 Harmonic number h 12 14 16 18 20 Harmonic current allowed to flow. website. ■ Reactive power demand for a 75 percent power factor would be 1200 ϫ sin [arccos (0.75) ] ϭ 794.73 kvar ■ Reactive power demand for a 96 percent power factor would be 1200 ϫ sin [arccos (0. 96) ] ϭ 3 36. 0. governing harmonic limits, includ- ing IEEE 519-1992, IEC 61 000-2-2, IEC 61 000-3-2, IEC 61 000-3-4, IEC 61 000-3 -6, NRS 048-2, 13 and EN50 160 . 14 6. 8.1 IEEE Standard 519-1992 The limits on harmonic voltage