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passive power filter
Electric Power Systems Research 73 (2005) 9–18
A PWM controlled variable damping resistor for protecting the power capacitor/passive power filter Jinn-Chang Wua , Hurng-Liahng Joub,∗ , Kuen-Der Wub b
a Department of Electrical Engineering, Kun Shan University of Technology, Tainan Hsien 710, Taiwan, ROC Department of Electrical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 80782, Taiwan, ROC
Received 31 October 2003; received in revised form 13 June 2004; accepted 13 June 2004 Available online 8 September 2004
Abstract A protection device for the power capacitor/passive power filter has been proposed. This device includes a control circuit, a conventional switch, a PWM switch and a resistor. The PWM switch is connected in parallel with a resistor to form a variable damper, serially connected to the power capacitor/passive power filter, in order to avoid the resonant amplification phenomenon. A conventional switch is used to switch on/off the power capacitor/passive power filter to the power distribution system. The control circuit calculates the voltage and the current of the power capacitor/passive power filter and compared to their upper tolerance values. The compared results are adapted to determine the duty ratio of PWM switch and the operation of conventional switch in order to protect the power capacitor/passive power filter circuit from the damage of over-voltage/over-current. Besides, this protection device can also improve the inrush current problem of the power capacitor/passive power filter at the instant of turning on. The performance of the proposed protection device has been verified by computer simulation. The simulation results show that the proposed PWM controlled variable damping resistor has the expected performance. © 2004 Elsevier B.V. All rights reserved. Keywords: PWM; Capacitor; Passive power filter; Damper
1. Introduction Most loads in the electric power system have the characteristic of inductance. The phase of inductive load current lags with the utility voltage. As a result, the current in the transmission or distribution power system contains not only the active current but also the reactive current. Therefore, it reduces the power transmission efficiency in the transmission or distribution power system and degrades the voltage regulation at the load terminal. In order to solve those problems, utilities or electric power users install a capacitor set or an automatic power factor regulator (APFR) in the power feeder to improve the power factor. The capacity of power capacitor set used in a power system is about 25–35% of the total capacity of power system. The capacity even reaches to 50% ∗ Corresponding author. Tel.: +886 7 3814526x5519; fax: +886 7 3921073. E-mail address: [email protected] (H.-L. Jou).
0378-7796/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2004.06.003
in some power systems [1]. Evidently, the power capacitor is widely used in the power system. With the development of power electronics, the power electronic facilities, such as uninterruptible power supply (UPS), motor driver and battery charger, have been used for power conversion application to improve the energy efficiency and the operation performance. The input characteristic of power electronic facilities is nonlinear, and its input current has the characteristics of high harmonic current and poor power factor. The voltage waveform of the power system is distorted due to the harmonic current, and the distorted waveform results in the degradation of power quality [2]. Because of low hardware and maintenance cost of the passive power filters, this problem has been solved conventionally by using passive power filters that consist of inductors and capacitors [3,4]. However, the power capacitor/passive power filter may result in the problem of power resonance. Although some active power facilities have been developed to solve the problems
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of harmonic pollution and power factor improvement [5–7], the high cost limits the wide spread use of these facilities. The power capacitor/passive power facilities are still widely used in the industrial power system due to the low cost. The resonance phenomenon occurs in the power capacitor for reactive power compensation or in the passive power filter for harmonic suppression. The resonance phenomenon between the impedance of a power distribution system and the power capacitor/passive power filter occurs frequently due to serious harmonic pollution in the modern industrial power system. The resonance phenomenon results in the over-voltage/over-current of power capacitor/passive power filter [8–11]. When the power distribution system contains the harmonic whose frequency is near to the resonant frequency, the amplitude of the harmonic voltage/current may be amplified more than 10 times producing over-voltage/overcurrent causing the damage of the power capacitor/passive power filter. However, the voltage/current rating of power capacitor/passive power filter is selected based on its normal operation value. Hence, the damage of power capacitor/passive power filter caused by the harmonic resonance includes over-voltage resulting in insulation damage, or overcurrent resulting in overheating damage. The investigation of harmonic events in Japan shows that the inductor damage is 65% and the capacitor damage is 26% in the power system [12]. Obviously, the damage of power inductor/capacitor due to harmonics is a very serious problem. In order to prevent the power capacitor/passive power filter from over-voltage/over-current caused by the harmonic resonance, the voltage/current rating of the power capacitor is increased conventionally. This solution not only increases the overall cost but also fails to protect the power capacitor/passive power filter from damage due to harmonic resonance. If the current rating of the inductor does not increase simultaneously, the inductor will be damaged due to overcurrent caused by the resonance phenomenon. This may be the reason behind the fact that the inductor damage is more (about 65%) when compared to the capacitor damage (26%). Consequently, the conventional solution is ineffective. A protection method for power capacitor/passive power filter, based on controlling the effective value of an inserting damping resistor by a PWM switch and a resistor, is proposed in this paper. This method can protect the power capacitor/passive power filter from over-voltage/over-current and the inrush current at the instant of turn-on by inserting a PWM controlled variable damping resistor. Finally, computer simulation is made to verify its performance.
2. Basic theory 2.1. The over-voltage and over-current protection Fig. 1(a) shows a simplified industrial power system with power capacitor/passive power filter. The load in the industrial power system is a nonlinear load, which is named as the
Fig. 1. The simplified industrial system with power capacitor/passive power filter: (a) the circuit diagram and (b) the equivalent circuit.
un-compensated nonlinear load. The neighboring power facilities may also contain nonlinear loads, which names as the un-compensated neighboring nonlinear load. Hence, Fig. 1(a) may contain two harmonic sources, an un-compensated nonlinear load and an un-compensated neighboring nonlinear load. To simplify the analysis, both nonlinear loads are simplified as the harmonic current sources (ILh , Inh ). Fig. 1(b) shows the harmonic equivalent circuit of Fig. 1(a). As seen in Fig. 1(b), the harmonic current injected into the power capacitor/passive power filter (Ich ) can be derived as Ich =
Zsh (ILh + Inh ) Zch + Zsh
(1)
where h is the index for representing the harmonic order. The power resonance occurs when the denominator of Eq. (1) approaches to zero. It will result in a large harmonic current injecting into the power capacitor. The amplitude of the injected harmonic current may be several times larger than the amplitude of harmonic current source. In the same time, the harmonic voltage across the capacitor will also be amplified. Hence, the power resonance may result in overvoltage/over-current and cause damage to the power capacitor/passive power filter. From Eq. (1), it can be found that the power capacitor/passive power filter cannot distinguish the harmonic currents generated by the un-compensated nonlinear load or the un-compensated neighboring nonlinear load. It means that the power capacitor/passive power filter supplies a low impedance path of harmonic current not only for the uncompensated nonlinear load but also for the un-compensated neighboring nonlinear load. In the industrial distribution system, the harmonic current of the un-compensated neighboring nonlinear loads will flow into the power capacitor/passive power filter and result in over-current. Hence, the investigation of harmonic sources is necessary before designing power
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Fig. 2. The frequency response of the passive power filter current to the load harmonic current under different damping resistors.
capacitor/passive power filter. Otherwise, the installation of power capacitor/passive power filter may further degrade the distortion of the utility current leading to its damage. The harmonic damage of power capacitor/passive power filter is mainly due to the resonance with the power system impedance and the excessive injection of harmonic current from the un-compensated neighboring nonlinear load. Based on the basic circuit theory of resonance, it can be found that the resonance will be suppressed by inserting a damping resistor in series with the power capacitor/passive power filter. If a damping resistor (R) is inserted in series with the power capacitor/passive power filter, Eq. (1) can be rewritten as Ich =
Zsh (ILh + Inh ) Zch + Zsh + R
(2)
From Eq. (2), it can be found that a term R is added in the denominator. Hence, the value of denominator is enlarged at the resonant frequency, and the resonance can be effectively suppressed. Fig. 2 shows the frequency response of the passive power filter current to the load harmonic current under different damping resistors. In this figure, the passive power filter is tuned at 300 Hz. In general, an inductor is connected in series with the power capacitor for reactive power compensation in order to suppress the inrush current. Hence, its frequency response is similar to Fig. 2. The figure shows that the resonant amplification is suppressed effectively after applying a damping resistor, and a larger damping resistor provides better suppression effect. However, a large damping resistor will result in excessive power loss. Fig. 3 shows the power circuit of the proposed method for protecting the power capacitor/passive power filter. The basic operation theory of the proposed protection method is to add a damping resistor when the power capacitor/passive power filter is over-voltage or over-current. From Eq. (2), it can be found that the power capacitor/passive power filter current depends on the value of damping resistor. It means that the damping resistor can effectively suppress the power capacitor/passive power filter current not only for the power
Fig. 3. The power circuit of the proposed method.
resonance but also for the excessive harmonic current injection of un-compensated neighboring nonlinear load. However, the value of damping resistor is expected to vary with the voltage or current of the power capacitor/passive power filter to avoid excessive power loss. Hence, the proposed power circuit consists of a resistor and a bi-directional switch. The bi-directional switch is controlled by the pulse-widthmodulation (PWM) control operated in high frequency with the variable duty ratio. The value of effective damping resistor depends on the duty ratio of bi-directional switch. 2.2. Inrush current suppression The system impedance is inductive in the practical industrial power distribution system. Hence, the power system with the power capacitor/passive power filter can be regarded as a series R–L–C circuit, and it can be simplified as Fig. 4. In this figure, the voltage is represented as vs (t) = vm sin(wt)
Fig. 4. The circuit of series R–L–C.
(3)
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If the damping resistor is neglected, the circuit equation of Fig. 4 can be written as LC
d2 vc (t) + vc (t) = vm sin(ωt) dt 2
(4)
ing resistor. It means that the transient-state current will decay to zero in the steady state, and the decay rate is proportional to the value of the damping resistor. Hence, the insertion of a damping resistor in the R–L–C circuit has the performance of suppressing the transient-state current.
The solution of Eq. (4) can be written as vc (t) = K0 vm sin(ωt) + K1 cos ω0 t + K2 sin ω0 t
(5)
where K0 is K0 =
1/ωC 1/ωC − ωL
(6)
and ω0 is the natural frequency of the capacitor and inductance and can be shown as ω0 = √
1 LC
(7)
If the capacitor has a residual voltage or the switch is not turn-on at instant of zero crossing point of voltage, it can be regarded that an initial voltage V0 exists in the capacitor. Due to the existence of L, the initial current of the capacitor is equal to zero. Then, the parameters K1 and K2 can be derived as K1 = v0 K2 =
−ωvm ω0
(8) (9)
3. Operation and control principle At the instant of applying the power capacitor/passive power filter to the power feeder, the conventional switch is turned on and the PWM switch is turned off, and a damping resistor is inserted to suppress the inrush current. And then, the PWM switch is shorted to bypass the damping resistor after a short duration of applying the power capacitor/passive power filter. The damping resistor is operated only a few utility periods. The proposed protection device performs over-current and over-voltage protection of power capacitor when the rootmean-square (RMS) values of power capacitor voltage and current are higher than the setting values. Hence, the rootmean-square values of power capacitor voltage and current must be calculated. If the power capacitor voltage contains harmonic components, the capacitor voltage can be represented as vc (t) =
(10)
For the right-hand side of Eq. (10), the first term is the steadystate current and the second and third terms are the transientstate current. From Eq. (10), it can be found that closing the switch will result in a transient-state current, and the value of transient-state current is proportional to the initial voltage V0 and the natural frequency ω0 . After applying the damping resistor, the capacitor current can be re-derived as i(t) = K0 ωCVm cos(ωt) + e−αt (K1 cos ωd t + K2 sin ωd t) (11) where K0 , K1 and K2 are constant values, and they are almost equal to K0 , K1 and K2 because the damping resistor is very small as compared with the impedance of inductor L and capacitor C, and R 2L ωd = ω02 − α2
(14)
Then, the capacitor current can be derived as
ic (t) = K0 ωCVm cos(ωt) − ω0 CV0 sin(ω0 t)
α=
Vcn sin(nωt + φn )
n=1
The capacitor current can be derived as
− ωCVm cos(ω0 t)
∞
(12) (13)
Comparing Eqs. (10) and (11), it can be found that the transient-state current needs to be multiplied by an exponential function with negative exponent after applying the damp-
ic (t) =
∞
nωCVcn cos(nωt + φn )
(15)
n=1
As seen in Eq. (15), every order harmonic amplitude of capacitor current can be calculated by the every order harmonic amplitude of capacitor voltage. The RMS values of power capacitor voltage and current can be calculated as ∞ 2 Vcn Vc = (16) 2 n=1
∞ (nωCVcn )2 Ic = 2
(17)
n=1
Hence, both RMS values of the power capacitor voltage and current can be obtained by only detecting and calculating every harmonic order of the capacitor voltage. Fig. 5 shows the control function block of the proposed PWM controlled variable damping resistor. The power capacitor voltage is detected firstly and sent to the RMS values calculation block. The RMS values calculation block calculates the amplitude of the power capacitor voltage by the fast Fourier transformation (FFT) analysis. Since the dominant harmonic in the practical industrial power system is less than
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Fig. 5. The control function block of the PWM controlled variable damping resistor.
the 25th order, the RMS value calculation block only calculates the harmonic amplitude of the power capacitor voltage below the 25th order harmonic to simplify the FFT calculation. The results of FFT analysis are used to calculate the RMS values (Vc and Ic ) of the power capacitor voltage and current shown in Eqs. (16) and (17). The output signals of RMS values calculation block are the RMS values of power capacitor voltage and current. The RMS values of power capacitor voltage and current are sent to the comparison block and compared with their upper tolerance values, respectively. The compared errors of the RMS values of the power capacitor voltage/current and their upper tolerance are added to be the output signal of the comparison block. The output signal of the comparison block is sent to the PI controller. If the output of PI controller is positive, it will be limited at zero and the integrator of PI controller is reset. It can avoid the saturation of integrator in PI controller when the power capacitor is operated normally. The control signal (Vcon ) is obtained by adding the output of PI controller to an offset value (Voff ). The control signal is sent to the PWM block to compare to a high frequency triangle signal (Vtri ). The output of PWM block is sent to drive the PWM switch. The offset value is the peak value of the high frequency triangular signal. Under the normal condition, the RMS values of power capacitor voltage and current are smaller than their upper tolerance values, and then the output of the PI controller is zero. The control signal is just the offset value. This means that the PWM switch is turned on completely, and the duty ratio of PWM switch is unity. In this condition, the damping resistor is disabled completely and the power capacitor/passive power filter is operated normally. As the RMS values of power capacitor voltage and current are higher than their upper tolerance values due to the resonance or excessive neighboring harmonic current injection, the output of PI controller will be toward negative value and the integrator of PI controller can operates. The control signal begins to decrease and the duty ratio of PWM switch is smaller than unity. The PWM switch will operate in the high switching frequency, and a controllable damping resistor is inserted into the power capacitor/passive power filter circuit to suppress the resonance or decrease the harmonic current injection of power capacitor/passive power filter. The value of variable damping resistor can be derived as R = (1 − D)Rdam
found that the equivalent value of damping resistor depends on the duty ratio of PWM switch. As the duty ratio is equal to zero, it means that the PWM switch is completely turn-off and the total damping resistor Rdam is inserting into the circuit. At the instant of applying the power capacitor/passive power filter to the power feeder, a switching-on signal will be applying to the control circuit. The switching-on signal is sent to the one-shot circuit to generate a short-term (about two cycles) actuated signal to actuate the switch SW. Then, the control signal is connected to ground. Hence, the PWM switch is opened completely during the actuated period of one-shot circuit that the power capacitor is connected to the power feeder, and then the total damping resistor Rdam is connected in series with the power capacitor to suppress the inrush current.
4. Design specifications The tolerance operation voltage and current of the power capacitor ruled by the standards of IEC 831 and IEC 871 are 110 and 130% RMS of the nominal rated voltage and the nominal rated current respectively. Hence, the upper tolerance value of the power capacitor voltage is set as 1.08 times of the nominal rated voltage, and the upper tolerance value of the power capacitor current is set as 1.2 times of the nominal rated current for protecting the power capacitor effectively. If the voltage and current of power capacitor after inserting the total damping resistor Rdam (the PWM switch is completely turned off) is still higher than the set upper tolerance values, the conventional switch is turned off to remove the power capacitor/passive power filter away from the power feeder. The PWM switch is a bi-directional switch configured by the power electronic devices such as IGBT and GTO, and it is shown in Fig. 6. The selection of PWM switch is dependent on the power rating of power capacitor/passive power filter. In general, IGBT is often used in the middle power rating and GTO is adequately for the large power rating. The selection
(18)
where Rdam is the resistor parallel with the PWM switch and D is the duty ratio of the PWM switch. From Eq. (18), it can be
Fig. 6. The configuration of the PWM switch.
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Table 1 The major parameters of simulation system System impedance Inductor of passive power filter Power capacitor Resistor, Rdam
0.05 mH + 0.01 0.47 mH 600 F 1
of the switching frequency for PWM switch must consider the switching loss and ripple current limitation. In general, the switching frequency of the power electronic device is several kHz. The practical power loss depends on the value of the controllable damping resistor R shown in Eq. (16) not on Rdam . The selection of resistor Rdam is dependent on the suppression ranges of the resonant current and the resonant voltage. The suppression rate of the resonant current and the resonant voltage depends on the quality factor, which is the ratio of reactance and resistance of power capacitor/passive power filter circuit. The value of resistor Rdam determines the minimum quality factor and maximum suppression rate. A conventional switch is also connected in series with the power capacitor/passive power filter. It can further protect the power capacitor/passive power filter when Rdam cannot suppress the current or voltage to below their upper tolerance values. Besides, the heat problem is an important consideration in selection Rdam .
5. Simulation results To verify the proposed protection device for power capacitor/passive power filter, a three-phase simulation system with 380 V and 60 Hz is established. The major parameters of the simulation system are shown in Table 1.
Fig. 7 shows the simulation results at the instant of turning on the power capacitor without and with the variable damping resistor. As seen in Fig. 7(a), a very large inrush current (more than eight times the amplitude of the normal current) is generated at the instant of the turning on the power capacitor. Fig. 7(b) shows the simulation result that the power capacitor is in series with the variable damping resistor and the conventional switch is turned on at 0.19 ms. The PWM switch is opened completely at the instant of switching the power capacitor to the power feeder, and then the total damping resistor Rdam is connected in series with the power capacitor to suppress the inrush current. For avoiding the power loss caused by the variable damping resistor, the PWM switch is completely turned on for shorting the resistor Rdam at 0.23 ms. Fig. 7(b) shows that the inrush current is suppressed to less than two times the amplitude of the normal current when the power capacitor is turned on with the resistor Rdam . This verifies that the proposed device can effectively suppress the inrush current at the instant of turning on the power capacitor. Fig. 8 shows the simulation results at the instant of turning on the passive power filter without and with the variable damping resistor. Fig. 8(a) shows that a large inrush current is generated when the passive power filter is turned on without the variable damping resistor. Since an inductor is connected in series with the power capacitor in the passive power filter, the inrush current is suppressed and the oscillation frequency becomes lower. This result coincides with the above analysis. In Fig. 8(b), it shows the simulation result that the variable damping resistor is in series with the passive power filter and the conventional switch is turned on at 0.19 ms. The PWM switch is opened completely at the instant of turning on the passive power filter, and then the resistor Rdam is connected in series with the power capacitor to suppress the inrush current. For avoiding the power loss and obtaining the good filter
Fig. 7. The simulation results of the power capacitor at the instant of turning on: (a) without the variable damping resistor and (b) with the variable damping resistor.
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Fig. 8. The simulation results of the passive power filter at the instant of turning on: (a) without the variable damping resistor and (b) with the variable damping resistor.
performance, the PWM switch is completely turned on for shorting the resistor Rdam at 0.23 ms. Fig. 8(b) shows that the inrush current is suppressed effectively by inserting the resistor Rdam . The above result verifies that the proposed PWM controlled variable damping resistor can suppress the inrush currents of the power capacitor and the passive power filter effectively. Figs. 9–11 show the simulation results of the passive power filter under the condition of harmonic resonance. In the practical application of the passive power filter, the parameters of the passive power filter are often drifted due to aged or temperature problems. For intensifying the effect of the harmonic resonance, it is assuming that the inductor of the passive power filter is drifted to 0.43 mH. Fig. 9 shows
the simulation result of the passive power filter without the variable damping resistor under applying the nonlinear load. In Fig. 9, the nonlinear load is applied at 1 s. As seen in Fig. 9(a), the current of passive power filter is amplified to three times the amplitude of the normal current after applying the nonlinear load. It will result in the over-current of the passive power filter. Fig. 10 shows the simulation result after applying the variable damping resistor to the passive power filter for suppressing the resonance amplification. It shows that the current of the passive power filter is amplified at the instant of applying the nonlinear load. However, the control circuit detects that the RMS values of the power capacitor voltage and current are higher than their upper tolerance values, and then the duty ratio of PWM switch is decreased to less
Fig. 9. The simulation results of the passive power filter without the variable damping resistor under applying the nonlinear load: (a) the passive power filter current and (b) the load current.
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Fig. 10. The simulation results of the passive power filter with the variable damping resistor under applying nonlinear load: (a) the passive power filter current, (b) the load current and (c) the value of variable damping resistor.
than unity and inserted the variable damping resistor to the passive power filter. Hence, the amplification of resonance is suppressed. From Fig. 10(c), the final value of variable damping resistor inserted into the passive power filter is only about 0.2 . Since the FFT algorithm is used in the control circuit, the response time for detecting the over-voltage and over-current is more than one utility period. Hence, it can be found that the resonance amplification exists about two utility periods in Fig. 10. The current of the power capacitor is about 1.2 times of its normal current in the steady state after applying the variable damping resistor R, and it is the upper tolerance value for the power capacitor current in the control circuit. For reducing the transient duration, a fast control loop shown in Fig. 11 should be added into the control circuit. The fast control loop contains a low-pass filter, a precision rectifier, a comparison circuit and a one-shot circuit.
The detected power capacitor voltage is sent to a low-pass filter with wide bandwidth to filter out the undesired high frequency interference, and then the output of low-pass filter is sent to a precision rectifier to obtain its absolute value. The absolute value is sent to a comparison block to compare with a preset value. The compared result is sent to actuate a one-shot circuit with a predetermined actuated duration. The predetermined actuated duration of one-shot circuit is about one cycle of the utility voltage. The output of one-shot circuit is subtracted from the output of comparison block by a subtractor. If the detected power capacitor voltage is higher than the setting value, the output of one-shot circuit is actuated and output a high level signal. Then, the duty ratio of PWM switch is decreased to zero and the resistor Rdam is inserted into the passive power filter immediately. After about one cycle of the utility voltage, the RMS values calculation block is
Fig. 11. The control function block of the PWM controlled variable damping resistor with fast control loop.
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Fig. 12. The simulation results of the passive power filter with the variable damping resistor (modified method) under applying the nonlinear load: (a) the passive power filter current, (b) the load current and (c) the value of variable damping resistor.
operated and the output of one-shot circuit is returned to low level. Then, the RMS values calculation block takes over the duty of the controller to adjust the duty ratio of PWM switch. Hence, the response time of variable damping resistor is fast. Fig. 12 shows the simulation result of the variable damping resistor with the fast control loop. From Fig. 12, it can be found that the variable damping resistor is 1 (the duty ratio is zero) at the instant of applying the nonlinear load, and then it decreases to about 0.2 after the RMS values calculation block has operated. As seen in Fig. 12, the response
time is very fast. Hence, the proposed protection device has the excellent performance to protect the passive power filter from the over-current damage. Fig. 13 shows the spectrum of the load current, the passive power filter current without the variable damping resistor and the passive power filter current with the variable damping resistor under the steady-state duration of 1.2–1.4 s. From Fig. 13(a) and (b), it can be found that the fifth harmonic current of the passive power filter is more than two times the amplitude of the load current before applying the variable damping resistor, this means that
Fig. 13. The spectrum of: (a) the load current, (b) the passive power filter current without the variable damping resistor and (c) the passive power filter current with the variable damping resistor.
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the harmonic resonance occurs between the passive power filter and system impedance. As seen in Fig. 13(c), the fifth harmonic of passive power filter current is suppressed after applying the variable damping resistor. 6. Conclusions The active power facilities can solve the problems of harmonic pollution and power factor improvement, however, the high cost limits the wide spread use of these facilities. Although the power capacitor/passive power facilities have the risk of the harmonic resonance and the inrush current at the instant of turning on, these passive power facilities are still widely used in industrial power system due to their low cost. Hence, how to protect the passive power facilities is an important issue in today’s power system. In this paper, a PWM controlled variable resistor is proposed to act as a damping resistor for protecting the power capacitor/passive power filter. It can improve the problem of inrush current at the instant of turning on the power capacitor/passive power filter and avoid the over-voltage/overcurrent damage of the power capacitor/passive power filter due to the harmonic resonance. Hence, the proposed PWM controlled variable damping resistor can solve the major problems of power capacitor/passive power filter and reduce the power rating of the switch used for turning on/off the power capacitor/passive power filter, and extend the life of power capacitor. The simulation results show that the proposed PWM controlled variable damping resistor has the expected performance. Acknowledgement The authors would like to express their gratitude to the financial support given by the National Science Council of ROC under the contract NSC 89-2213-E-244-010.
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A PWM controlled variable damping resistor for protecting the power capacitor/passive power filter Jinn-Chang Wua , Hurng-Liahng Joub,∗ , Kuen-Der Wub b
a Department of Electrical Engineering, Kun Shan University of Technology, Tainan Hsien 710, Taiwan, ROC Department of Electrical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 80782, Taiwan, ROC
Received 31 October 2003; received in revised form 13 June 2004; accepted 13 June 2004 Available online 8 September 2004
Abstract A protection device for the power capacitor/passive power filter has been proposed. This device includes a control circuit, a conventional switch, a PWM switch and a resistor. The PWM switch is connected in parallel with a resistor to form a variable damper, serially connected to the power capacitor/passive power filter, in order to avoid the resonant amplification phenomenon. A conventional switch is used to switch on/off the power capacitor/passive power filter to the power distribution system. The control circuit calculates the voltage and the current of the power capacitor/passive power filter and compared to their upper tolerance values. The compared results are adapted to determine the duty ratio of PWM switch and the operation of conventional switch in order to protect the power capacitor/passive power filter circuit from the damage of over-voltage/over-current. Besides, this protection device can also improve the inrush current problem of the power capacitor/passive power filter at the instant of turning on. The performance of the proposed protection device has been verified by computer simulation. The simulation results show that the proposed PWM controlled variable damping resistor has the expected performance. © 2004 Elsevier B.V. All rights reserved. Keywords: PWM; Capacitor; Passive power filter; Damper
1. Introduction Most loads in the electric power system have the characteristic of inductance. The phase of inductive load current lags with the utility voltage. As a result, the current in the transmission or distribution power system contains not only the active current but also the reactive current. Therefore, it reduces the power transmission efficiency in the transmission or distribution power system and degrades the voltage regulation at the load terminal. In order to solve those problems, utilities or electric power users install a capacitor set or an automatic power factor regulator (APFR) in the power feeder to improve the power factor. The capacity of power capacitor set used in a power system is about 25–35% of the total capacity of power system. The capacity even reaches to 50% ∗ Corresponding author. Tel.: +886 7 3814526x5519; fax: +886 7 3921073. E-mail address: [email protected] (H.-L. Jou).
0378-7796/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2004.06.003
in some power systems [1]. Evidently, the power capacitor is widely used in the power system. With the development of power electronics, the power electronic facilities, such as uninterruptible power supply (UPS), motor driver and battery charger, have been used for power conversion application to improve the energy efficiency and the operation performance. The input characteristic of power electronic facilities is nonlinear, and its input current has the characteristics of high harmonic current and poor power factor. The voltage waveform of the power system is distorted due to the harmonic current, and the distorted waveform results in the degradation of power quality [2]. Because of low hardware and maintenance cost of the passive power filters, this problem has been solved conventionally by using passive power filters that consist of inductors and capacitors [3,4]. However, the power capacitor/passive power filter may result in the problem of power resonance. Although some active power facilities have been developed to solve the problems
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of harmonic pollution and power factor improvement [5–7], the high cost limits the wide spread use of these facilities. The power capacitor/passive power facilities are still widely used in the industrial power system due to the low cost. The resonance phenomenon occurs in the power capacitor for reactive power compensation or in the passive power filter for harmonic suppression. The resonance phenomenon between the impedance of a power distribution system and the power capacitor/passive power filter occurs frequently due to serious harmonic pollution in the modern industrial power system. The resonance phenomenon results in the over-voltage/over-current of power capacitor/passive power filter [8–11]. When the power distribution system contains the harmonic whose frequency is near to the resonant frequency, the amplitude of the harmonic voltage/current may be amplified more than 10 times producing over-voltage/overcurrent causing the damage of the power capacitor/passive power filter. However, the voltage/current rating of power capacitor/passive power filter is selected based on its normal operation value. Hence, the damage of power capacitor/passive power filter caused by the harmonic resonance includes over-voltage resulting in insulation damage, or overcurrent resulting in overheating damage. The investigation of harmonic events in Japan shows that the inductor damage is 65% and the capacitor damage is 26% in the power system [12]. Obviously, the damage of power inductor/capacitor due to harmonics is a very serious problem. In order to prevent the power capacitor/passive power filter from over-voltage/over-current caused by the harmonic resonance, the voltage/current rating of the power capacitor is increased conventionally. This solution not only increases the overall cost but also fails to protect the power capacitor/passive power filter from damage due to harmonic resonance. If the current rating of the inductor does not increase simultaneously, the inductor will be damaged due to overcurrent caused by the resonance phenomenon. This may be the reason behind the fact that the inductor damage is more (about 65%) when compared to the capacitor damage (26%). Consequently, the conventional solution is ineffective. A protection method for power capacitor/passive power filter, based on controlling the effective value of an inserting damping resistor by a PWM switch and a resistor, is proposed in this paper. This method can protect the power capacitor/passive power filter from over-voltage/over-current and the inrush current at the instant of turn-on by inserting a PWM controlled variable damping resistor. Finally, computer simulation is made to verify its performance.
2. Basic theory 2.1. The over-voltage and over-current protection Fig. 1(a) shows a simplified industrial power system with power capacitor/passive power filter. The load in the industrial power system is a nonlinear load, which is named as the
Fig. 1. The simplified industrial system with power capacitor/passive power filter: (a) the circuit diagram and (b) the equivalent circuit.
un-compensated nonlinear load. The neighboring power facilities may also contain nonlinear loads, which names as the un-compensated neighboring nonlinear load. Hence, Fig. 1(a) may contain two harmonic sources, an un-compensated nonlinear load and an un-compensated neighboring nonlinear load. To simplify the analysis, both nonlinear loads are simplified as the harmonic current sources (ILh , Inh ). Fig. 1(b) shows the harmonic equivalent circuit of Fig. 1(a). As seen in Fig. 1(b), the harmonic current injected into the power capacitor/passive power filter (Ich ) can be derived as Ich =
Zsh (ILh + Inh ) Zch + Zsh
(1)
where h is the index for representing the harmonic order. The power resonance occurs when the denominator of Eq. (1) approaches to zero. It will result in a large harmonic current injecting into the power capacitor. The amplitude of the injected harmonic current may be several times larger than the amplitude of harmonic current source. In the same time, the harmonic voltage across the capacitor will also be amplified. Hence, the power resonance may result in overvoltage/over-current and cause damage to the power capacitor/passive power filter. From Eq. (1), it can be found that the power capacitor/passive power filter cannot distinguish the harmonic currents generated by the un-compensated nonlinear load or the un-compensated neighboring nonlinear load. It means that the power capacitor/passive power filter supplies a low impedance path of harmonic current not only for the uncompensated nonlinear load but also for the un-compensated neighboring nonlinear load. In the industrial distribution system, the harmonic current of the un-compensated neighboring nonlinear loads will flow into the power capacitor/passive power filter and result in over-current. Hence, the investigation of harmonic sources is necessary before designing power
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Fig. 2. The frequency response of the passive power filter current to the load harmonic current under different damping resistors.
capacitor/passive power filter. Otherwise, the installation of power capacitor/passive power filter may further degrade the distortion of the utility current leading to its damage. The harmonic damage of power capacitor/passive power filter is mainly due to the resonance with the power system impedance and the excessive injection of harmonic current from the un-compensated neighboring nonlinear load. Based on the basic circuit theory of resonance, it can be found that the resonance will be suppressed by inserting a damping resistor in series with the power capacitor/passive power filter. If a damping resistor (R) is inserted in series with the power capacitor/passive power filter, Eq. (1) can be rewritten as Ich =
Zsh (ILh + Inh ) Zch + Zsh + R
(2)
From Eq. (2), it can be found that a term R is added in the denominator. Hence, the value of denominator is enlarged at the resonant frequency, and the resonance can be effectively suppressed. Fig. 2 shows the frequency response of the passive power filter current to the load harmonic current under different damping resistors. In this figure, the passive power filter is tuned at 300 Hz. In general, an inductor is connected in series with the power capacitor for reactive power compensation in order to suppress the inrush current. Hence, its frequency response is similar to Fig. 2. The figure shows that the resonant amplification is suppressed effectively after applying a damping resistor, and a larger damping resistor provides better suppression effect. However, a large damping resistor will result in excessive power loss. Fig. 3 shows the power circuit of the proposed method for protecting the power capacitor/passive power filter. The basic operation theory of the proposed protection method is to add a damping resistor when the power capacitor/passive power filter is over-voltage or over-current. From Eq. (2), it can be found that the power capacitor/passive power filter current depends on the value of damping resistor. It means that the damping resistor can effectively suppress the power capacitor/passive power filter current not only for the power
Fig. 3. The power circuit of the proposed method.
resonance but also for the excessive harmonic current injection of un-compensated neighboring nonlinear load. However, the value of damping resistor is expected to vary with the voltage or current of the power capacitor/passive power filter to avoid excessive power loss. Hence, the proposed power circuit consists of a resistor and a bi-directional switch. The bi-directional switch is controlled by the pulse-widthmodulation (PWM) control operated in high frequency with the variable duty ratio. The value of effective damping resistor depends on the duty ratio of bi-directional switch. 2.2. Inrush current suppression The system impedance is inductive in the practical industrial power distribution system. Hence, the power system with the power capacitor/passive power filter can be regarded as a series R–L–C circuit, and it can be simplified as Fig. 4. In this figure, the voltage is represented as vs (t) = vm sin(wt)
Fig. 4. The circuit of series R–L–C.
(3)
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If the damping resistor is neglected, the circuit equation of Fig. 4 can be written as LC
d2 vc (t) + vc (t) = vm sin(ωt) dt 2
(4)
ing resistor. It means that the transient-state current will decay to zero in the steady state, and the decay rate is proportional to the value of the damping resistor. Hence, the insertion of a damping resistor in the R–L–C circuit has the performance of suppressing the transient-state current.
The solution of Eq. (4) can be written as vc (t) = K0 vm sin(ωt) + K1 cos ω0 t + K2 sin ω0 t
(5)
where K0 is K0 =
1/ωC 1/ωC − ωL
(6)
and ω0 is the natural frequency of the capacitor and inductance and can be shown as ω0 = √
1 LC
(7)
If the capacitor has a residual voltage or the switch is not turn-on at instant of zero crossing point of voltage, it can be regarded that an initial voltage V0 exists in the capacitor. Due to the existence of L, the initial current of the capacitor is equal to zero. Then, the parameters K1 and K2 can be derived as K1 = v0 K2 =
−ωvm ω0
(8) (9)
3. Operation and control principle At the instant of applying the power capacitor/passive power filter to the power feeder, the conventional switch is turned on and the PWM switch is turned off, and a damping resistor is inserted to suppress the inrush current. And then, the PWM switch is shorted to bypass the damping resistor after a short duration of applying the power capacitor/passive power filter. The damping resistor is operated only a few utility periods. The proposed protection device performs over-current and over-voltage protection of power capacitor when the rootmean-square (RMS) values of power capacitor voltage and current are higher than the setting values. Hence, the rootmean-square values of power capacitor voltage and current must be calculated. If the power capacitor voltage contains harmonic components, the capacitor voltage can be represented as vc (t) =
(10)
For the right-hand side of Eq. (10), the first term is the steadystate current and the second and third terms are the transientstate current. From Eq. (10), it can be found that closing the switch will result in a transient-state current, and the value of transient-state current is proportional to the initial voltage V0 and the natural frequency ω0 . After applying the damping resistor, the capacitor current can be re-derived as i(t) = K0 ωCVm cos(ωt) + e−αt (K1 cos ωd t + K2 sin ωd t) (11) where K0 , K1 and K2 are constant values, and they are almost equal to K0 , K1 and K2 because the damping resistor is very small as compared with the impedance of inductor L and capacitor C, and R 2L ωd = ω02 − α2
(14)
Then, the capacitor current can be derived as
ic (t) = K0 ωCVm cos(ωt) − ω0 CV0 sin(ω0 t)
α=
Vcn sin(nωt + φn )
n=1
The capacitor current can be derived as
− ωCVm cos(ω0 t)
∞
(12) (13)
Comparing Eqs. (10) and (11), it can be found that the transient-state current needs to be multiplied by an exponential function with negative exponent after applying the damp-
ic (t) =
∞
nωCVcn cos(nωt + φn )
(15)
n=1
As seen in Eq. (15), every order harmonic amplitude of capacitor current can be calculated by the every order harmonic amplitude of capacitor voltage. The RMS values of power capacitor voltage and current can be calculated as ∞ 2 Vcn Vc = (16) 2 n=1
∞ (nωCVcn )2 Ic = 2
(17)
n=1
Hence, both RMS values of the power capacitor voltage and current can be obtained by only detecting and calculating every harmonic order of the capacitor voltage. Fig. 5 shows the control function block of the proposed PWM controlled variable damping resistor. The power capacitor voltage is detected firstly and sent to the RMS values calculation block. The RMS values calculation block calculates the amplitude of the power capacitor voltage by the fast Fourier transformation (FFT) analysis. Since the dominant harmonic in the practical industrial power system is less than
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Fig. 5. The control function block of the PWM controlled variable damping resistor.
the 25th order, the RMS value calculation block only calculates the harmonic amplitude of the power capacitor voltage below the 25th order harmonic to simplify the FFT calculation. The results of FFT analysis are used to calculate the RMS values (Vc and Ic ) of the power capacitor voltage and current shown in Eqs. (16) and (17). The output signals of RMS values calculation block are the RMS values of power capacitor voltage and current. The RMS values of power capacitor voltage and current are sent to the comparison block and compared with their upper tolerance values, respectively. The compared errors of the RMS values of the power capacitor voltage/current and their upper tolerance are added to be the output signal of the comparison block. The output signal of the comparison block is sent to the PI controller. If the output of PI controller is positive, it will be limited at zero and the integrator of PI controller is reset. It can avoid the saturation of integrator in PI controller when the power capacitor is operated normally. The control signal (Vcon ) is obtained by adding the output of PI controller to an offset value (Voff ). The control signal is sent to the PWM block to compare to a high frequency triangle signal (Vtri ). The output of PWM block is sent to drive the PWM switch. The offset value is the peak value of the high frequency triangular signal. Under the normal condition, the RMS values of power capacitor voltage and current are smaller than their upper tolerance values, and then the output of the PI controller is zero. The control signal is just the offset value. This means that the PWM switch is turned on completely, and the duty ratio of PWM switch is unity. In this condition, the damping resistor is disabled completely and the power capacitor/passive power filter is operated normally. As the RMS values of power capacitor voltage and current are higher than their upper tolerance values due to the resonance or excessive neighboring harmonic current injection, the output of PI controller will be toward negative value and the integrator of PI controller can operates. The control signal begins to decrease and the duty ratio of PWM switch is smaller than unity. The PWM switch will operate in the high switching frequency, and a controllable damping resistor is inserted into the power capacitor/passive power filter circuit to suppress the resonance or decrease the harmonic current injection of power capacitor/passive power filter. The value of variable damping resistor can be derived as R = (1 − D)Rdam
found that the equivalent value of damping resistor depends on the duty ratio of PWM switch. As the duty ratio is equal to zero, it means that the PWM switch is completely turn-off and the total damping resistor Rdam is inserting into the circuit. At the instant of applying the power capacitor/passive power filter to the power feeder, a switching-on signal will be applying to the control circuit. The switching-on signal is sent to the one-shot circuit to generate a short-term (about two cycles) actuated signal to actuate the switch SW. Then, the control signal is connected to ground. Hence, the PWM switch is opened completely during the actuated period of one-shot circuit that the power capacitor is connected to the power feeder, and then the total damping resistor Rdam is connected in series with the power capacitor to suppress the inrush current.
4. Design specifications The tolerance operation voltage and current of the power capacitor ruled by the standards of IEC 831 and IEC 871 are 110 and 130% RMS of the nominal rated voltage and the nominal rated current respectively. Hence, the upper tolerance value of the power capacitor voltage is set as 1.08 times of the nominal rated voltage, and the upper tolerance value of the power capacitor current is set as 1.2 times of the nominal rated current for protecting the power capacitor effectively. If the voltage and current of power capacitor after inserting the total damping resistor Rdam (the PWM switch is completely turned off) is still higher than the set upper tolerance values, the conventional switch is turned off to remove the power capacitor/passive power filter away from the power feeder. The PWM switch is a bi-directional switch configured by the power electronic devices such as IGBT and GTO, and it is shown in Fig. 6. The selection of PWM switch is dependent on the power rating of power capacitor/passive power filter. In general, IGBT is often used in the middle power rating and GTO is adequately for the large power rating. The selection
(18)
where Rdam is the resistor parallel with the PWM switch and D is the duty ratio of the PWM switch. From Eq. (18), it can be
Fig. 6. The configuration of the PWM switch.
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Table 1 The major parameters of simulation system System impedance Inductor of passive power filter Power capacitor Resistor, Rdam
0.05 mH + 0.01 0.47 mH 600 F 1
of the switching frequency for PWM switch must consider the switching loss and ripple current limitation. In general, the switching frequency of the power electronic device is several kHz. The practical power loss depends on the value of the controllable damping resistor R shown in Eq. (16) not on Rdam . The selection of resistor Rdam is dependent on the suppression ranges of the resonant current and the resonant voltage. The suppression rate of the resonant current and the resonant voltage depends on the quality factor, which is the ratio of reactance and resistance of power capacitor/passive power filter circuit. The value of resistor Rdam determines the minimum quality factor and maximum suppression rate. A conventional switch is also connected in series with the power capacitor/passive power filter. It can further protect the power capacitor/passive power filter when Rdam cannot suppress the current or voltage to below their upper tolerance values. Besides, the heat problem is an important consideration in selection Rdam .
5. Simulation results To verify the proposed protection device for power capacitor/passive power filter, a three-phase simulation system with 380 V and 60 Hz is established. The major parameters of the simulation system are shown in Table 1.
Fig. 7 shows the simulation results at the instant of turning on the power capacitor without and with the variable damping resistor. As seen in Fig. 7(a), a very large inrush current (more than eight times the amplitude of the normal current) is generated at the instant of the turning on the power capacitor. Fig. 7(b) shows the simulation result that the power capacitor is in series with the variable damping resistor and the conventional switch is turned on at 0.19 ms. The PWM switch is opened completely at the instant of switching the power capacitor to the power feeder, and then the total damping resistor Rdam is connected in series with the power capacitor to suppress the inrush current. For avoiding the power loss caused by the variable damping resistor, the PWM switch is completely turned on for shorting the resistor Rdam at 0.23 ms. Fig. 7(b) shows that the inrush current is suppressed to less than two times the amplitude of the normal current when the power capacitor is turned on with the resistor Rdam . This verifies that the proposed device can effectively suppress the inrush current at the instant of turning on the power capacitor. Fig. 8 shows the simulation results at the instant of turning on the passive power filter without and with the variable damping resistor. Fig. 8(a) shows that a large inrush current is generated when the passive power filter is turned on without the variable damping resistor. Since an inductor is connected in series with the power capacitor in the passive power filter, the inrush current is suppressed and the oscillation frequency becomes lower. This result coincides with the above analysis. In Fig. 8(b), it shows the simulation result that the variable damping resistor is in series with the passive power filter and the conventional switch is turned on at 0.19 ms. The PWM switch is opened completely at the instant of turning on the passive power filter, and then the resistor Rdam is connected in series with the power capacitor to suppress the inrush current. For avoiding the power loss and obtaining the good filter
Fig. 7. The simulation results of the power capacitor at the instant of turning on: (a) without the variable damping resistor and (b) with the variable damping resistor.
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Fig. 8. The simulation results of the passive power filter at the instant of turning on: (a) without the variable damping resistor and (b) with the variable damping resistor.
performance, the PWM switch is completely turned on for shorting the resistor Rdam at 0.23 ms. Fig. 8(b) shows that the inrush current is suppressed effectively by inserting the resistor Rdam . The above result verifies that the proposed PWM controlled variable damping resistor can suppress the inrush currents of the power capacitor and the passive power filter effectively. Figs. 9–11 show the simulation results of the passive power filter under the condition of harmonic resonance. In the practical application of the passive power filter, the parameters of the passive power filter are often drifted due to aged or temperature problems. For intensifying the effect of the harmonic resonance, it is assuming that the inductor of the passive power filter is drifted to 0.43 mH. Fig. 9 shows
the simulation result of the passive power filter without the variable damping resistor under applying the nonlinear load. In Fig. 9, the nonlinear load is applied at 1 s. As seen in Fig. 9(a), the current of passive power filter is amplified to three times the amplitude of the normal current after applying the nonlinear load. It will result in the over-current of the passive power filter. Fig. 10 shows the simulation result after applying the variable damping resistor to the passive power filter for suppressing the resonance amplification. It shows that the current of the passive power filter is amplified at the instant of applying the nonlinear load. However, the control circuit detects that the RMS values of the power capacitor voltage and current are higher than their upper tolerance values, and then the duty ratio of PWM switch is decreased to less
Fig. 9. The simulation results of the passive power filter without the variable damping resistor under applying the nonlinear load: (a) the passive power filter current and (b) the load current.
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Fig. 10. The simulation results of the passive power filter with the variable damping resistor under applying nonlinear load: (a) the passive power filter current, (b) the load current and (c) the value of variable damping resistor.
than unity and inserted the variable damping resistor to the passive power filter. Hence, the amplification of resonance is suppressed. From Fig. 10(c), the final value of variable damping resistor inserted into the passive power filter is only about 0.2 . Since the FFT algorithm is used in the control circuit, the response time for detecting the over-voltage and over-current is more than one utility period. Hence, it can be found that the resonance amplification exists about two utility periods in Fig. 10. The current of the power capacitor is about 1.2 times of its normal current in the steady state after applying the variable damping resistor R, and it is the upper tolerance value for the power capacitor current in the control circuit. For reducing the transient duration, a fast control loop shown in Fig. 11 should be added into the control circuit. The fast control loop contains a low-pass filter, a precision rectifier, a comparison circuit and a one-shot circuit.
The detected power capacitor voltage is sent to a low-pass filter with wide bandwidth to filter out the undesired high frequency interference, and then the output of low-pass filter is sent to a precision rectifier to obtain its absolute value. The absolute value is sent to a comparison block to compare with a preset value. The compared result is sent to actuate a one-shot circuit with a predetermined actuated duration. The predetermined actuated duration of one-shot circuit is about one cycle of the utility voltage. The output of one-shot circuit is subtracted from the output of comparison block by a subtractor. If the detected power capacitor voltage is higher than the setting value, the output of one-shot circuit is actuated and output a high level signal. Then, the duty ratio of PWM switch is decreased to zero and the resistor Rdam is inserted into the passive power filter immediately. After about one cycle of the utility voltage, the RMS values calculation block is
Fig. 11. The control function block of the PWM controlled variable damping resistor with fast control loop.
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Fig. 12. The simulation results of the passive power filter with the variable damping resistor (modified method) under applying the nonlinear load: (a) the passive power filter current, (b) the load current and (c) the value of variable damping resistor.
operated and the output of one-shot circuit is returned to low level. Then, the RMS values calculation block takes over the duty of the controller to adjust the duty ratio of PWM switch. Hence, the response time of variable damping resistor is fast. Fig. 12 shows the simulation result of the variable damping resistor with the fast control loop. From Fig. 12, it can be found that the variable damping resistor is 1 (the duty ratio is zero) at the instant of applying the nonlinear load, and then it decreases to about 0.2 after the RMS values calculation block has operated. As seen in Fig. 12, the response
time is very fast. Hence, the proposed protection device has the excellent performance to protect the passive power filter from the over-current damage. Fig. 13 shows the spectrum of the load current, the passive power filter current without the variable damping resistor and the passive power filter current with the variable damping resistor under the steady-state duration of 1.2–1.4 s. From Fig. 13(a) and (b), it can be found that the fifth harmonic current of the passive power filter is more than two times the amplitude of the load current before applying the variable damping resistor, this means that
Fig. 13. The spectrum of: (a) the load current, (b) the passive power filter current without the variable damping resistor and (c) the passive power filter current with the variable damping resistor.
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the harmonic resonance occurs between the passive power filter and system impedance. As seen in Fig. 13(c), the fifth harmonic of passive power filter current is suppressed after applying the variable damping resistor. 6. Conclusions The active power facilities can solve the problems of harmonic pollution and power factor improvement, however, the high cost limits the wide spread use of these facilities. Although the power capacitor/passive power facilities have the risk of the harmonic resonance and the inrush current at the instant of turning on, these passive power facilities are still widely used in industrial power system due to their low cost. Hence, how to protect the passive power facilities is an important issue in today’s power system. In this paper, a PWM controlled variable resistor is proposed to act as a damping resistor for protecting the power capacitor/passive power filter. It can improve the problem of inrush current at the instant of turning on the power capacitor/passive power filter and avoid the over-voltage/overcurrent damage of the power capacitor/passive power filter due to the harmonic resonance. Hence, the proposed PWM controlled variable damping resistor can solve the major problems of power capacitor/passive power filter and reduce the power rating of the switch used for turning on/off the power capacitor/passive power filter, and extend the life of power capacitor. The simulation results show that the proposed PWM controlled variable damping resistor has the expected performance. Acknowledgement The authors would like to express their gratitude to the financial support given by the National Science Council of ROC under the contract NSC 89-2213-E-244-010.
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