Electrical Power Systems Quality, Second Edition phần 5

Fundamentals of Harmonics 210 Chapter Five range of power system equipment, most notably capacitors, transform-ers, and motors, causing additional losses, overheating, and overload-ing. These harmonic currents can also cause interference with telecommunication lines and errors in power metering. Sections 5.10.1 through 5.10.5 discuss impacts of harmonic distortion on various power system components. 5.10.1 Impact on capacitors Problems involving harmonics often show up at capacitor banks first. As discussed in Secs. 5.9.3 and 5.9.4, a capacitor bank experiences high voltage distortion during resonance. The current flowing in the capac-itor bank is also significantly large and rich in a monotonic harmonic. Figure 5.32 shows a current waveform of a capacitor bank in resonance with the system at the 11th harmonic. The harmonic current shows up distinctly, resulting in a waveform that is essentially the 11th har-monic riding on top of the fundamental frequency. This current wave-form typically indicates that the system is in resonance and a capacitor bank is involved. In such a resonance condition, the rms current is typ-ically higher than the capacitor rms current rating. IEEE Standard for Shunt Power Capacitors (IEEE Standard 18-1992) specifies the following continuous capacitor ratings: 135 percent of nameplate kvar 110 percent of rated rms voltage (including harmonics but excluding transients) 180 percent of rated rms current (including fundamental and har-monic current) 120 percent of peak voltage (including harmonics) Table 5.1 summarizes an example capacitor evaluation using a com-puter spreadsheet that is designed to help evaluate the various capac-itor duties against the standards. The fundamental full-load current for the 1200-kvar capacitor bank is determined from I 1200 50.2 A LL 3 13.8 The capacitor is subjected principally to two harmonics: the fifth and the seventh. The voltage distortion consists of 4 percent fifth and 3 per-cent seventh. This results in 20 percent fifth harmonic current and 21 percent seventh harmonic current. The resultant values all come out 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. Fundamentals of Harmonics Fundamentals of Harmonics 211 200 150 100 50 0 –50 –100 –150 –200 0 10 20 30 Time (ms) Figure 5.32 Typical capacitor current from a system in 11th-harmonic resonance. well below standard limits in this case, as shown in the box at the bot-tom of Table 5.1. 5.10.2 Impact on transformers Transformers are designed to deliver the required power to the con-nected loads with minimum losses at fundamental frequency. Harmonic distortion of the current, in particular, as well as of the volt-age will contribute significantly to additional heating. To design a transformer to accommodate higher frequencies, designers make dif-ferent design choices such as using continuously transposed cable instead of solid conductor and putting in more cooling ducts. As a gen-eral rule, a transformer in which the current distortion exceeds 5 per-cent is a candidate for derating for harmonics. There are three effects that result in increased transformer heating when the load current includes harmonic components: 1. RMS current. If the transformer is sized only for the kVA require-ments of the load, harmonic currents may result in the transformer rms current being higher than its capacity. The increased total rms current results in increased conductor losses. 2. Eddy current losses. These are induced currents in a transformer caused by the magnetic fluxes. These induced currents flow in the windings, in the core, and in other conducting bodies subjected to the magnetic field of the transformer and cause additional heating. This component of the transformer losses increases with the square of the frequency of the current causing the eddy currents. Therefore, 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. Fundamentals of Harmonics 212 Chapter Five TABLE 5.1 Example Capacitor Evaluation Recommended Practice for Establishing Capacitor Capabilities When Supplied by Nonsinusoidal Voltages IEEE Std 18-1980 Capacitor Bank Data: Bank Rating: Voltage Rating: Operating Voltage: Supplied Compensation: Fundamental Current Rating: Fundamental Frequency: Capacitive Reactance: 1200 kVAr 13800 V (L-L) 13800 V (L-L) 1200 kVAr 50.2 Amps 60 Hz 158.700 Ω Harmonic Distribution of Bus Voltage: Harmonic Frequency Volt Mag V Volt Mag V Line Current I Number (Hertz) (% of Fund.) (Volts) (% of Fund.) 1 60 100.00 7967.4 100.00 3 180 0.00 0.0 0.00 5 300 4.00 318.7 20.00 7 420 3.00 239.0 21.00 11 660 0.00 0.0 0.00 13 780 0.00 0.0 0.00 17 1020 0.00 0.0 0.00 19 1140 0.00 0.0 0.00 21 1260 0.00 0.0 0.00 23 1380 0.0 0.00 25 1500 0.00 0.0 0.00 Voltage Distortion (THD): 5.00 % RMS Capacitor Voltage: 7977.39 Volts Capacitor Current Distortion: 29.00 % RMS Capacitor Current: 52.27 Amps Capacitor Bank Limits: Calculated Peak Voltage: 107.0% RMS Voltage: 100.1% RMS Current: 104.1% Limit Exceeds Limit 120% No 110% No 180% No kVAr: 104.3% 135% No this becomes a very important component of transformer losses for harmonic heating. 3. Core losses. The increase in core losses in the presence of harmon-ics will be dependent on the effect of the harmonics on the applied voltage and the design of the transformer core. Increasing the volt-age distortion may increase the eddy currents in the core lamina-tions. The net impact that this will have depends on the thickness of 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. Fundamentals of Harmonics Fundamentals of Harmonics 213 the core laminations and the quality of the core steel. The increase in these losses due to harmonics is generally not as critical as the previous two. Guidelines for transformer derating are detailed in ANSI/IEEE Standard C57.110-1998, Recommended Practice for Establishing Transformer Capability When Supplying Nonsinusoidal Load Currents. The common K factor used in the power quality field for transformer derating is also included in Table 5.2.2 The analysis represented in Table 5.2 can be summarized as follows. The load loss PLL can be considered to have two components: I2R loss and eddy current loss PEC: LL I2R P CW (5.27) The I2R loss is directly proportional to the rms value of the current. However, the eddy current is proportional to the square of the current and frequency, which is defined by EC KEC I2 h2 (5.28) where KEC is the proportionality constant. The per-unit full-load loss under harmonic current conditions is given by LL å Ih2 (å Ih2 h2 ) P C R (5.29) where PEC R is the eddy current loss factor under rated conditions. The K factor3 commonly found in power quality literature concerning transformer derating can be defined solely in terms of the harmonic currents as follows: TABLE 5.2 Typical Values of PEC R Type Dry Oil-filled MVA Voltage 1 — 1.5 5 kV HV 1.5 15 kV HV 2.5 480 V LV 2.5–5 480 V LV 5 480 V LV PEC R, % 3–8 12–20 9–15 1 1–5 9–15 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. Fundamentals of Harmonics 214 Chapter Five K å (Ih2 h2) (5.30) h Then, in terms of the K factor, the rms of the distorted current is derived to be 1 PEC R Ih 1 K P C R (pu) (5.31) where PEC R eddy current loss factor h harmonic number Ih harmonic current Thus, the transformer derating can be estimated by knowing the per-unit eddy current loss factor. This factor can be determined by 1. Obtaining the factor from the transformer designer 2. Using transformer test data and the procedure in ANSI/IEEE Standard C57.110 3. Typical values based on transformer type and size (see Table 5.2) Exceptions. There are often cases with transformers that do not appear to have a harmonics problem from the criteria given in Table 5.2, yet are running hot or failing due to what appears to be overload. One common case found with grounded-wye transformers is that the line currents contain about 8 percent third harmonic, which is relatively low, and the transformer is overheating at less than rated load. Why would this transformer pass the heat run test in the factory, and, perhaps, an over-load test also, and fail to perform as expected in practice? Discounting mechanical cooling problems, chances are good that there is some con-ducting element in the magnetic field that is being affected by the har-monic fluxes. Three of several possibilities are as follows: Zero-sequence fluxes will “escape” the core on three-legged core designs (the most popular design for utility distribution substation transformers). This is illustrated in Fig. 5.33. The 3d, 9th, 15th, etc., harmonics are predominantly zero-sequence. Therefore, if the winding connections are proper to allow zero-sequence current flow, these har-monic fluxes can cause additional heating in the tanks, core clamps, etc., that would not necessarily be found under balanced three-phase or single-phase tests. The 8 percent line current previously mentioned 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