Electrical Engineering (2005) 87: 33–39 DOI 10.1007/s00202-003-0219-x
O R I GI N A L P A P E R
Merih Palando¨ken Æ Mehmet Tu¨may Æ Murat Aksoy
A novel approach to active power filter control
Received: 16 October 2003 / Accepted: 3 December 2003 / Published online: 11 February 2004 Springer-Verlag 2004
Abstract This paper introduces a three-phase active power filter operating with fixed switching frequency and controlled by a fuzzy logic controller in the inner current control loop for each phase and a proportional– integral controller in the outer voltage control loop to compensate the reactive power and the current harmonic components simultaneously from the nonlinear loads. Keywords Active power filter Æ Harmonic compensation Æ Fuzzy logic controller Æ Energy quality Æ Pulse width modulation
1 Introduction Conventionally, passive second order filters are used to compensate current harmonics and improve the power factor in power systems. However, series or parallel resonance of these filters with the power system and the other loads connected across the nonlinear load and the constraint of using these filters for each harmonic frequency to be eliminated are the disadvantages from the point of operability. In addition to these, fixed compensation characteristics for fixed values of L and C and their bulk size are the other disadvantages from the points of cost and realizability [1, 2]. To overcome all these problems, active power filters (APF) with the principle of injecting current/voltage harmonics that have same amplitude but reverse phase of the current/voltage of the nonlinear load, with their respective control strategies, are proposed [1, 2, 3, 4, 5, 6, 7, 8].They have a smaller size, are capable of reducing the effect of distorted current/voltage waveforms as well as compensating the fundamental displacement component, are precisely controllable, have a quick response, M. Palando¨ken Æ M. Tu¨may (&) Æ M. Aksoy EEE Department, University of Cukurova, 01330, Balcali-Adana, Turkey E-mail:
[email protected]
and do not cause resonance unlike in the use of passive filters. In this paper, a three-phase current controlled voltage source PWM inverter having reference current tracking capability by using a fuzzy logic controller in the inner control loop and self-controlled proportional–integral (PI) DC link voltage control loop in the outer loop so as to compensate reactive power and current harmonic components simultaneously from nonlinear loads is proposed. The use of a fuzzy logic controller in the inner control loop will decrease the cost of APF because there is no need to use more accurate devices to measure the nonlinear load current and obtain a reference current. It will provide an easy enhancement of the whole control system besides allowing the modeling of nonlinear loads for control purposes with less effort than the ones encountered in the conventional control schemes [8, 9, 10]. Current control is achieved with fixed switching frequency, which has better performance than hysteresis current control [2]. The operational and structural difference between the proposed APF and the system described in [11] is that in the previous system the construction of APF for threephase harmonic compensation was achieved by three independently operating single phase APFs with an additional three triacs, capacitors, inductances, and fuzzy logic controllers. In order to achieve the desired control strategy this required an under uncoupling structure with balanced capacitor voltages at the inverter and the connections with all these parts. The proposed system and its control strategy allow for the elimination of this excessive number of components in the APF configuration. The procedure presented in this paper includes an explanation of how most conventional switching signals are determined by the rule-based fuzzy logic controller and the power circuit needed to realize this operation. The design criteria for an interface reactor and DC capacitor are also explained. The results of to what degree this control scheme eliminates harmonic components and reactive power are verified by the
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simulation for a single-phase AC power system using MATLAB. The simulation uses a single-phase power system because this control scheme can easily be extended for three-phase power systems by the application of this control scheme to each phase. This is due to decoupling each phase from each other when the neutral point potential of the DC side of APF is held at the same level with the neutral point potential of the three-phase AC mains.
2 Proposed APF circuit configuration The topology of the proposed APF is shown in Fig. 1. In this scheme, the power circuit that will be controlled as the APF and the power factor corrector is a three-phase PWM force commutated voltage source inverter connected to DC capacitors. It has six MOSFET switches with antiparallel diodes across each one to switch the capacitor voltage in order to achieve the desired action. There are two voltage levels at the AC terminal of APF, VDC/2 and )VDC/2. In the control scheme of the proposed APF, a fuzzy logic controller in combination with a PI controller is employed in the inner current control loop to adjust the conduction times of the corresponding switching devices of each phase and to track closely the reference current of each line current. The fuzzy logic controller is also helpful for the reduction in the required cost for measuring the load current and the APF output current and control of the APF output current. A PI voltage controller is employed in the outer capacitor voltage control loop due to its ability to provide zero steady state error, thus leading to an almost constant capacitor voltage. The PI controller in the inner loop is used to filter out noise signals that are out of the band of harmonic components and dominate the interested band of the error signal to determine the switching signals. These
Fig. 1 Block diagram of APF
noise signals are inherited from the switching of capacitor voltage and thus controlled alteration of current of the synchronous link reactor.
3 Principle of APF operation The main section of APF shown in Fig. 1 is a forcecommutated three-phase voltage source inverter having constant capacitor voltage on the DC side. The current harmonics elimination is achieved by the injection of equal but opposite phase of harmonic components of the nonlinear load current at the point of connection. Therefore, the reference harmonic current must be generated for each phase. This reference current generation unit for one phase is shown in Fig. 2. The nonlinear load current can be expressed for one phase, say for Vmax·sin(xt)120), as: iL ðtÞ ¼
1 X
IL;n sinðnxtÞ þ hn 120Þ
n¼1
¼ IL;1 cosðh1 Þ sinðxt 120Þ þ IL;1 sinðh1 Þ 1 X IL;n sinðnxt þ hn 120Þ cosðxt 120Þ þ n¼2
¼ ip ðtÞ þ iq ðtÞ þ in ðtÞ ð1Þ where x is the fundamental angular frequency of the nonlinear load current; hn and IL,n are the phase shift and amplitude of the nth order current harmonics, respectively; ip, iq, and ih are the active, reactive, and harmonic current components of nonlinear load current for the corresponding mains phase, respectively. For harmonic current elimination and power factor correction, APF must supply the required harmonic current components and reactive current component to the nonlinear load. In addition to this, AC mains must
35 Fig. 2 Block diagram of reference current generation unit for one phase
supply the active current component of APF for the losses inherited due to high frequency switching and the active current component of nonlinear load. To generate the active current component of the nonlinear load, the nonlinear current is multiplied by the sine wave as shown in Fig. 2. The phase lock loop (PLL) is used to obtain the unit sinusoidal wave in phase with the respective mains voltage. This synchronization signal is necessary to obtain the current reference for reactive power compensation. By the multiplication of the one phase load current with the synchronization signal, the signal spectrum of the one phase load current will be shifted x units and result in the active current component located at zero frequency as shown in Eq. 2. Then this component can be obtained by a low pass filter having a bandwidth smaller than x angular frequency and an amplifier with gain 2. The output of the amplifier is the amplitude of the active current component of the nonlinear load current. To obtain the sine wave having this amplitude, this DC signal in addition to the signal obtained from the DC bus voltage control loop is multiplied by the synchronization signal to obtain the total active current that the respective phase of AC mains must supply for proper operation of both voltage source inverter and the nonlinear load. This total active current is subtracted from the nonlinear load current to obtain the harmonic current and reactive current to be eliminated.
The fuzzy logic controller is used in the inner current control loop to increase the tracking capability of APF in addition to PWM and the PI controller so as to generate the necessary switching signals. Each DC capacitor voltage is selected to be greater than the amplitude of one phase mains voltage to give the capacitor switching the dominant role in increasing or decreasing the APF output current. For one phase equivalent circuit topology, when the capacitor voltage is greater than the AC mains voltage at any instant of time, the switching of this capacitor voltage will cause the APF output current to increase and switching this voltage in the opposite direction will cause the APF output current to decrease. The block diagram for the control system of the proposed APF is shown in Fig. 3. When the necessary command is obtained from the fuzzy logic controller, with the execution of equally affecting but differently weighting rules depending on the value of control variables, the switches on each arm will be operated by switching signals produced from the comparison of this command with the high frequency sawtooth carrier wave. The use of potential difference across the inductance as one of the control inputs for the fuzzy logic controller in the inner current control loop also provides satisfactory operation for APF even though these two capacitors do not have equal potential across their terminals.
iL ðtÞ sinðxt 120Þ 1 X IL;n sinðnxt þ hn 120Þ sinðxt 120Þ ¼
4 Control algorithm
n¼1 1 1 X IL;n ðcosððn þ 1Þxt þ hn 240Þ ¼ 2 n¼1
cosððn 1Þxt hn ÞÞ 1 1 ¼ IL;1 cosðh1 Þ IL;1 cosð2xt þ hn 240Þ 2 2 1 1 X IL;n ðcosððn þ 1Þxt þ hn 240Þ 2 n¼2 cosððn 1Þxt hn ÞÞ ð2Þ
In fuzzy logic, the linguistic variables are expressed by fuzzy sets defined by their respective universes of discourse. In the control algorithm of the proposed APF, the linguistic variables used to express the rules for control are the difference (error) between the reference signal having the reactive and harmonic current components of the nonlinear current and the APF output current, the rate of change of error, and the potential difference between the capacitor voltage and the voltage of the concerned phase during the necessary action. Theoretically, the rate of change of the APF output current and thus the actual current value is determined
36 Fig. 3 Block diagram of the APF control system for one phase
by only two variables. These variables are the conduction time of the power switches during one switching period and the instantaneous value of the potential difference between the capacitor and the mains phase voltage at that instant. Thus the data about the difference between the actual current and the reference current and the potential difference across the synchronous link reactor are all the necessary input variables for the fuzzy controller in addition to the rate of change of the error value. The additional control input related to the voltage across the inductance also provides satisfactory operation for APF even though there is potential difference between the voltages of two identical capacitors. By the inference of the corresponding rules, the actual APF output current is forced to track the reference signal. The linguistic rules will result in the necessary action for the output current by interpreting all the rules and contributions of each and aggregating all the implied results and then determining the optimum decision for the current change [9, 10]. The change in the actual APF output current will be different according to the error, the change in error level, and the instantaneous value of the potential difference across the inductance. The error rate and the voltage difference determine the degree of increase or decrease in APF output current by affecting only the amplitude of the signal at the output of the fuzzy controller. But the error signal determines effectively which action will be processed, i.e., increase or decrease in the APF output current, by affecting the sign of the PWM input signal as shown in Fig. 4. By the inspection of Fig. 4, it is also interpreted that for low values of voltage difference across the inductance and high values of error signal, the actuating signal for the power switches is high enough to obtain large conduction time intervals to compensate for high error value. For a constant error value, the increase in the value of voltage difference across the inductance causes a reduction in the amplitude of the actuating signal, leading to less but sufficient conduction time due to increasing value of voltage difference. Thus according to the sign of the error, the switching action and the resulting voltage across the inductance are determined. Then this voltage magnitude is used to determine the magnitude of the conduction time for that value of error
Fig. 4 Decision surface of the fuzzy rules with two of three inputs
and error rate. The hard limiter in the control system is used to determine the sign of the error signal. Multiplication of the negative value of the output of the hard limiter with capacitor voltage gives the voltage at one end of the inductor. Using the magnitude of voltage across the inductance, the inputs of the fuzzy controller are completed. Then the PWM signal is obtained by the comparison of the fuzzy controller crisp output with the high frequency sawtooth carrier signal. The result of comparison will be positive for an increase, negative for a decrease with their respective width denoting how fast the APF output current must be increased or decreased, respectively. The constant switching frequency will cause reduced voltage distortion at the interface reactor [2]. Current compensation is carried out in the time domain leading fast time response.
5 Power circuit design The selection of the DC capacitor and AC link reactor directly affects the performance of APF. The inductance is used to reduce the high frequency current components of the APF current and to provide the necessary tracking requirement. The selection criterion for the AC link reactor is that the value of inductance must be capable of compensating the current change at that conduction time interval in one switching period. The selection of the AC link reactor depends on the level of harmonic
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current to be eliminated, DC capacitor voltage, and the switching frequency of the PWM signal generator. ðV capdc V acðampÞÞ Dref current fswitching
\L\
ðV capdc þV acðampÞÞ Dref current fswitching 2
ð3Þ
where Dref current is the max reference current change; fswitching is the switching frequency of the PWM carrier wave; and VcapDC,Vac(amp) are the voltage across one DC capacitor and the amplitude of one phase of AC mains voltage, respectively. To compensate the maximum current change when the maximum potential difference across the terminals of the inductor is obtained, the conduction time value for an increase will be half of the switching period. During this time, the inductance current will increase and during the rest of the switching period, this current will decrease, resulting in the necessity to compensate the maximum current change twice. Thus, the average of this current change, or namely the maximum current change, will be compensated. The capacitor value is selected in order to satisfy low voltage fluctuation when there is transient alteration in the nonlinear load power. The optimum capacitor value can be expressed as: R t1 þDt 1 ð4Þ C ¼ DV Icap dt t1 where t1 is the starting time of the voltage fluctuation; Dt is the duration of the voltage fluctuation; Icap is the capacitor current during voltage fluctuation; DV is the allowable change in the capacitor voltage; and C is the required value of capacitance needed to limit the voltage change during power fluctuation.
6 Simulation results The effectiveness of the proposed control algorithm can be evaluated by the ability of three-phase APF to deliver Fig. 5 Time responses of reference and APF output current
a PWM compensating signal that contains only harmonic components, reactive current components, and a small amount of active current components of APF. This criterion is tested by investigating to what degree the error signal between the actual APF current and the reference current is reduced. The simulation is done for single-phase APF but the results obtained from this simulation can be extended for three-phase systems easily due to the decoupled operation of each phase when the neutral point potential of the DC capacitors is held at the same level with the neutral point of the threephase AC mains. That condition is achieved by the connection from the neutral point of the three-phase AC mains to the neutral point of two capacitors. The resulting error signal in the simulation study will have the cumulative harmonic and reactive current components for the power system. The simulation results are obtained under some assumptions: – The PI DC link will stabilize the DC voltage of one capacitor to the desired value, which is greater than the amplitude of the one phase of AC mains voltage. This assumption is realizable for such closed loop control systems with a PI voltage controller [2, 3, 7]. – The reference signal is obtained from the reference signal generation unit accurately. This assumption is also valid because the active current component of the nonlinear load current can be extracted by the low pass filter with ease at its zero frequency location by the modulation. If there is uncertainty in the system topology, this will be overcome by the adjustment of the fuzzy logic controller rules and its membership functions [9, 10]. The main characteristics of the fuzzy controller in this simulation study are the following:
38 Fig. 6 Frequency responses of error and reference current
– – – – – – –
Nineteen rules Three fuzzy sets for each of the three inputs Five fuzzy sets for the output Triangular and trapezoidal membership functions Fuzzification using continuous universe of discourse Implication using the ‘‘min’’ operator Defuzzification using the ‘‘centroid’’ method
The APF output current and the reference current are shown in Fig. 5 to illustrate the performance of the proposed three-phase APF. The harmonic content of the error signal between the APF output current and the reference current intended to be eliminated is the other criterion to be investigated to determine how well the APF operates in case the resultant harmonic current of AC mains can be identified. The harmonic content of the error signal between the APF output current and the reference signal and the harmonic content of the APF current are shown in Fig. 6. Fast Fourier transform over six periods of time (1.2 s) with 76,754 samples was used for the figure. From Fig. 6, the reduction of the current harmonics and the elimination of the reactive current component of the nonlinear load current are quite satisfactory. The amplitude of the error at the fundamental frequency corresponding to the amplitude of the reactive current component is 0.012 and the amplitude of the nonlinear current at that frequency is 6. This resultsin a rejection ratio of 500 times the reactive current component of the nonlinear current. The rejection ratios of the harmonic current components at 150 Hz, 250 Hz, and 350 Hz are 59.5077, 16.0896, and 9.56, respectively.
7 Conclusion In this paper, a three-phase fuzzy-controlled APF that operates with fixed switching frequency has been
presented and analyzed. The proposed APF forces the mains current to be sinusoidal and in phase with the mains voltage, thus compensating the harmonic and reactive current components from the nonlinear loads. The use of a fuzzy controller in combination with a PWM generator in the inner loop makes the control strategy simple, cost effective, reliable, and easily adaptable for different conditions. The switching signals are generated by using not only the data on error and the rate of change of error but also the potential difference across the inductance to evaluate the optimum value for the conduction time. With the addition of the data on the potential difference across the interface reactor to the controller inputs, the needed control inputs for controlling the APF output current are included completely. The performance of APF regarding current harmonic and reactive current compensation is investigated by using artificially generated harmonics. The tracking capability of the APF output current and in what ratio the harmonic and reactive current components are suppressed are described.
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