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Capacitors September 2000 — Greenwood SC Harmonics and Capacitors — Dynamic Overvoltages KILOVAR BRIEFS Issue 3 of the Kilovar Briefs discussed steady state sources of harmonics. These included arc furnaces, solid state energy conversion equipment, rotating machinery and transformers. During steady state operation of an AC power system, harmonics in the transformer magnetizing current are a small percentage of the load current. Energizing a transformer results in substantial amounts of harmonic current in the transformer inrush current. This is a transient event lasting up to a few seconds. If the transformer is switched with capacitors, it is possible that a resonant condition may exist that results in dynamic overvoltage caused by an interaction of the inrush current and capacitors. Dynamic overvoltages are defined as long-term resonant overvoltages lasting many cycles and even seconds that can result in damage to capacitors, transformers, surge arresters and/or solid state power conversion equipment. In this issue of the Kilovar Briefs, we will examine the mechanism of creating dynamic overvoltages and the means to prevent them from occurring when switching capacitors. Consider the basic circuit shown in Figure 1, which includes a supply transformer feeding an industrial load, a switch used to energize the load and a load transformer. Often, these types of systems are energized with no load applied to the transformer. Figure 2 shows a typical inrush current wave form following transformer energization. This is a non-sinusoidal wave that exponentially decays to a steady state magnetizing current level. Typically, inrush current is rich in second, third, fourth, and fifth harmonics. A Fourier analysis of the harmonic components of this wave form is tabulated in Table 1. The exact shape and magnitude of the inrush current depends on the transformer characteristics and the initial condition of the residual transformer flux. Substantial low order harmonic currents momentarily exist in the transformer inrush current. Figure 3 shows the bus voltage on the load side of the switch. Despite the harmonic content of the current, the voltage is not noticeably distorted. 6 Figure 1. Typical Industrial Load Transformer. A M P S 0.00 TIME 400 MSEC Figure 2. Typical Inrush Current Wave Form Following Transformer Energization. 2.00 PU -2.00 0 TIME 400 MSEC Figure 3. Bus Voltage Following Switching in Figure 1. TABLE 1 Harmonic Components of Inrush Current in Transformer Energization Harmonic % of Fundamental Amps 0 64.70 275.0 1 100.00 425.0 2 25.40 108.0 3 8.49 36.1 4 5.46 23.2 5 3.32 14.1 September 2000 • Supersedes 11/85 Printed in USA 1 Harmonics and Capacitors — Applying Capacitors in the Harmonic Environment In Issue 5 of the Kilovar Briefs, a filter design was discussed as a measure for preventing steady state harmonic resonance caused by the fifth harmonic content of the steady state load current. The equivalent circuit and the impedance diagram is shown in Figure 6. The presence of the filter reduces the system parallel resonant frequency from 310 hertz to 211 hertz (3.5 x the fundamental frequency). A filter always forces the parallel resonant frequency to a level below that of the filter tuning frequency. Since the transformer inrush current is richer in the lower order harmonics, applying a filter circuit can actually make the switching problem more severe. Figure 7 shows the dynamic overvoltage in this case is more onerous than without the filter. We, therefore, have the situation where capacitors can be applied successfully in a steady state harmonic environment, possibly requiring the use of a filter reactor to detune the circuit. However, the design may not be adequate for the transient harmonic environment; caused by switching the capacitor and transformers together. Z (n) S I (n) S I (n) I (n) F Z (n) H F Figure 4a. Equivalent Circuit for Power Factor Connector Capacitor. 12 Parallel Resonant Frequency 8 Impedance (Ohms) In Issue 4 of the Kilovar Briefs, we discussed this same circuit. A shunt capacitor was applied on the converter bus to correct the system power factor from 75% to 98%. The equivalent circuit is shown in Figure 4 along with its impedance spectrum. This circuit is resonant at 310.2 hertz. This means that any fifth harmonic current present in the circuit will be substantially amplified, resulting in a resonant overvoltage. The inrush current shown in Figure 2, whose harmonic components are shown in Table 1, is the current injected into the circuit from the transient current source. The fifth harmonic content of the inrush current results in a resonant dynamic overvoltage. An example of the dynamic overvoltage is shown in Figure 5. This overvoltage condition is a direct result of injecting a harmonic current into a tuned tank circuit, which amplifies harmonic currents at the timed frequency, resulting in the high overvoltage. If the capacitor had tuned the circuit to the 4th harmonic, the overvoltage would have been more severe. ZS(n) 4 0 -4 -ZS(n) ZF(n) -8 -12 1 2 3 4 5 6 7 8 Harmonic Number Figure 4b. Impedance Spectrum. 1.50 PU -1.50 0 TIME 400 MSEC Figure 5. Dynamic Overvoltage across Capacitors Following Transformer Energization. 2 KILOVAR BRIEFS Z (n) 6 A S I (n) S I (n) I (n) F Z (n) H B L Figure 6a. Equivalent Circuit for Tuned Filter. Figure 8. Typical Industrial Load with Capacitor Filter. 8 There is a simple solution to this problem — switch the capacitor and/or the filter circuit separately from switching the transformer. The network configuration for this solution is shown in Figure 8. For energizing the circuit, switch A should be closed to energize the load transformer, followed by closing switch B some seconds or minutes afterward to energize the capacitors and/or the filter network. By following this simple switching scheme, the capacitors are never in the circuit during the time that the inrush current is present. As a result, the circuit is not tuned to a frequency present in the transformer inrush current and, therefore, there is no chance of a dynamic overvoltage occurring! Impedance (n’s) 4 ZS(n) 0 -ZS(n) -4 ZF(n) -8 Parallel Resonant Frequency -12 1 2 3 4 5 Harmonic Number 6 The distribution engineer reading this discussion may wonder if reclosing a distribution feeder with its capacitors and transformers could also result in dynamic overvoltages. The resonant frequency of the circuit is analyzed in a manner similar to that already described. With the capacitors in service, it is likely that the system resonant frequency is 300–500 hertz. Fortunately, there is normally adequate load on the distribution feeder and this load acts as damping, preventing dynamic overvoltages from occurring. The combination of switching an unloaded transformer and a capacitor bank is most susceptible to dynamic overvoltages. The lower the system natural frequency is, the more likely is the chance of dynamic overvoltages occurring following switching. Figure 6b. Impedance Spectrum. 2.00 PU -2.00 0 TIME 400 MSEC Figure 7. Dynamic Overvoltage across the Capacitor Bank following Switching of the Filter and Load Transformer Together. 3 P.O. Box 1640 Waukesha, WI 53187 http://www.cooperpower.com ©2000 Cooper Industries, Inc. Printed on Recycled Paper