Electrical Power Systems Quality, Second Edition phần 6

Applied Harmonics Applied Harmonics 263 14 12 10 8 0.7 0.6 0.5 Isp (5.5) = 0.5 0.4 0.3 Isp (5.5) = 0.3 0.2 0.1 Isp (5.5) = 0.1 0 4.5 5 5.5 6 6.5 6 Isp (5.5) = 0.1 Isp (5.5) = 0.3 4 Isp (5.5) = 0.5 2 00 2 4 6 8 10 12 14 16 18 20 Harmonic number h 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. 9 8 C filter with a 3.0-Mvar notch filter 7 Lnotch 6 Lm R 5 Ca Cnotch 4 Cm 3 2 1 C filter 00 2 4 6 8 10 12 14 16 18 20 Harmonic number h Figure 6.24 A C filter with and without a notch filter. 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. Applied Harmonics 264 Chapter Six 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. OR NONLINEAR LOAD Figure 6.25 Application of an active filter at a load. 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. Applied Harmonics Applied Harmonics 265 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: 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. Applied Harmonics 266 Chapter Six 480-Volt Bus Filter Reactor Power Factor Correction Capacitor Figure 6.26 Example low-voltage filter configuration. Reactive power demand for a 75 percent power factor would be 1200 sin [arccos (0.75) ] 794.73 kvar Reactive power demand for a 96 percent power factor would be 1200 sin [arccos (0.96) ] 336.0 kvar Required compensation from the filter: 794.73 336.0 457.73 kvar For a nominal 480-V system, the net wye-equivalent filter reactance (capacitive) XFilt is determined by XFilt kVk(1000) 0.482 (1000) 0.5034 XFilt is the difference between the capacitive reactance and the induc-tive reactance at fundamental frequency: XFilt XCap XL For tuning at the 4.7th harmonic, XCap h2XL 4.72XL 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. Applied Harmonics Applied Harmonics 267 Thus, the desired capacitive reactance can be determined by 2 2 XCap 0.5272 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 kV2 (1000) 0.485(1000) 437 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, XCap 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: XL (fund) 0.02318 or L 2 L (fund) 0.06148 mH Alternatively, the reactor size can be computed by solving for L in the following equation: 1 h 2 LC where fh 4.7 60 282 Hz. The next step is to evaluate the duty requirements for the capacitor and reactor. 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. ... - tailieumienphi.vn