New single-phase active power filterH.-L. JOU J.-C. WU H.-Y. Chu Indexing term: Filters andfiltering Abstract: A new algorithm for a single-phase active power filter, based on calculation of the real part of the fundamental load current, is proposed in the paper. The algorithm proposed can maintain the input power factor of the mains close to unity and force the mains current to be a sinewave under distorted or nondistorted mains voltage. A prototype is developed and tested to verify its performance. The experimental results show that the algorithm proposed can compensate for the reactive power and suppress the harmonics of the nonlinear load effectively. List of symbols uJt) = mains I,, = output of the PI controller C, L, = DC busbar capacitor = filter inductor u,(t) = DC capacitor voltage = average voltage of the DC capacitor CC(t) = voltage fluctuation of the DC capacitor V, idc(t) = DC busbar current idr = DC component of the DC busbar current ;( ,t ) = high-order i,(t) = low-order harmonic components of the DC busbar current harmonic components of the DC busbar current 1 Introduction voltage iL(t) = load current I, = nth-order harmonic of load current = angular frequency of the mains w 0. = phase of the nth-order harmonic of load current V, = peak value of mains voltage i,(t) = reference sinusiodal signal value of the fundamental component of the load current = amplitude of the real part of the fundamental load i, current T = period of the mains i,(t) = reference compensation signal i&) = mains current i,(t) = calculated mains current I,, = peak value of the mains current p&) = power supplied from the mains P, = DC component of p*(r) p&) = AC component of pJr) pL(t)= power consumed by the load P, = DC component of p L ( f ) h ( t ) = AC component of pL(t) p,(t) = power injected into the convertor P, = DC component of p,(t) P,o, = power loss of the convertor p,(t) = AC component of p&) K, = proportion constant of the PI controller K, = integration constant of the PI controller I, = peak 0IEE, 1994 Paper 9938B (P4, P6), reaived 25th June 1993 Harmonics is a problem in power systems that has become serious recently owing to the wide use of power electronics-related equipment. Furthermore, the input power factor of most of this equipment is poor. Conventionally, a passive power filter and capacitor were used to attenuate the harmonics and improve the input power factor. However, they have many disadvantages, such as large size, resonance, fixed compensation characteristic etc. [l]. To solve the problems of power-factor correction, many different configurations of static VAR compensators (SVCs) have been proposed [2, 31. Unfortunately, some SVC configurations generate lowerorder harmonics themselves [SI, and the response time of some SVC configurations may be too long to be acceptable for fast-fluctuating loads. Many harmonics-suppression methods based on the technique of power electronics have been developed [3-171 to solve harmonics problems. One of them is the active power filter. The configurations of active power filter developed include three-phase and single-phase systems. The three-phase system implemented by a threephase bridge inverter is suitable for large capacity. However, three single-phase bridge inverters, rather than a single three-phase bridge inverter, are more suitable for serious unbalanced loads [3]. That is, each phase must be compensated for independently. The investigation in this paper concentrates on the single-phase active power filter. Many single-phase algorithms have been developed, but the performance of some still needed to be improved. The half-cycle integration algorithm has the inherent problem that it produces a large error when the load current contains even-order harmonics [3]. The current-sampling detection algorithm The authors would like to acknowledge the support of the National Science Council, Taiwan, under contract NSC-81-0115-E151-07. 129 H.-L. is with the Department of Electrical Engineering, National Jou Kaohsiung Institute of Technology, Kaohsiung, 80782 Taiwan J.-C. Wu is with the Department of Electrical Engineering, Kao Yuan Junior College of Technology & Commerce, Kaohsiung, Taiwan H.-Y. Chu is with the Department of Electrical Engineering, National Cheng Kung University, Tainan, 70101 Taiwan IEE Proc.-Electr. Power Appl., Vol. 141, No.3, M o y 1994 (t) [iL(t)i. 141. The output of the integrator and the output of the reference signal are fed to the input terminals of a multiplier. The performances of the full-cycle integration algorithm and synchronous detection algorithms are better than the above two algorithms [3. The load in this diagram may be a rectifier or other nonmins generatw Fig.(t) = I. Finally. the output of the multiplier is fed to a linear integrator.(t) and ic.(t) = iL(t). the performance of all these algorithms will be degraded under distorted mains voltage.(r).(t) (6) = I. As the reference signal is in phase with the mains voltage.) 10A per 5V per division + 1 I. The simulation and test results show that the prototype has the performance desired. sin (not + e.i. The load current and the reference signal are fed to the input terminals of a multiplier. i. The mains voltage is fed multiplier integrator multiplier Fig. the calculated compensation current can be obtained by subtracting eqn.) . IEE Proc. 131.) . 2 Basic theory Hence. 1 load I (1) Power circuit ofthe proposed actiue powerfilter linear load.. = = I. Fig.cannot compensate effectively as the load current is seriously distorted [3]. 2. It shows that the calculated i. it is represented as d t ) = V. M a y I994 .(t) must be fed to a power convertor to generate the practical compensation current. sin (ot) 130 current are shown in Figs. sin (ot + e. 3n and b.(t).I . Assuming the mains voltage is a pure sinewave.-Electr. the output of the multiplier is the real part of the fundamental load current.(t) = sin (ot) 5V per division 5ms per division (4) the amplitude of the real part of the fundamental load current can be extracted using the Fourier algorithm and represented as I. 2 Block diagram of the cornpensation current calculated circuit for the proposed actiue powerfilter I Fig. the real part of the fundamental load current can be obtained by multiplying I. 6. and it is represented as i. i.(t) are shown in Figs. respectively.=l 160V per division 'fdivisim It can be subdivided into the fundamental and harmonic components as iJt) = I. 3 shows the test results of the compensation current calculated circuit. cos 6 . The mains voltage and the load 1 1.(t) is a pure sinewave and in phase with u. 3 Test results oftke proposed actiue powerfilter controller 0 Mains voltage ". Then. 2 from eqn.(t). The calculated i. 3c and d. Then. sin (not + 63 n=2 (3) d Assuming a reference sinusoidal signal is represented as i. No.(t) COS dt (5) e. and that it has the performance of reactive-power compensation and harmonics suppression of the nonlinear loads. sin (ot) The nonlinear load current can be represented as iL(t) = m to the reference sinusoidal signal generator to generate a reference signal i. 3. A prototype is developed and tested to verify its performance. It is shown as i. However. Fig. 1 shows the power circuit of the active power filter. cos e. sin (ot) "=I (7) 3 Calculated circuit of the compensation current The block diagram for implementing the proposed active power filter is shown in Fig. by i.(t) = m 1 1. Vol. sin (not + e. A new algorithm for an active power filter is proposed in this paper to improve compensation accuracy under distorted mains voltage. it can be concluded that the proposed algorithm can be implemented by an analogue circuit. The output of the integrator is the amplitude of the real part of the fundamental load current if the parameters of the integrator are designed suitably. From this Figure. the compensation current iJt) can be obtained by a subtract circuit that subtracts iJt) from the load current iL(t). Power Appl.(I) b Load current i&) c Fundamental load current i) & d Reference compensation cumnt i. For practical application. and j. This problem can be solved by controlling the amplitude of the mains current. is the proportion constant that determines the dynamic response of the DC capacitor voltage. a DC busbar capacitor and a filter inductor. can be represented as P. The DC busbar current can be subdivided into three parts and represented as where I . 5.COS ((n + (cos ((n . V I n=2 cos (20t + e..1 Single-phase full-bridge convertor FL(t)is the AC component and is represented as -v PL(t) = + -+ I. The mains current after compensation can be represented as i J t ) = I. the magnitude of P .W where P . and it is rewritten as is@) = (I. I. and the switching device used is the insulated gate bipolar transistor (IGBT).(t) are the DC and AC components of p. Vol. It consists of three main parts: a singlephase full-bridge convertor. is the integration constant that determines its settling time. this can be achieved by using small passive reactive elements for storing energy in the active power filter. 4 PI controller used in DC busbar voltage control sin (wt) (8) The real power supplied from the mains can be represented as Pa@) = udt)i.. Nevertheless. the reactive power is compensated for by the passive reactive components. where P . I. The DC busbar capacitor is used to store the energy to mantain the constant DC voltage and to reduce the voltage fluctuation under load variation. Vrei Fig. is the output of the PI controller.. I.(t) is the AC component. and F. and they do not affect the average voltage of the DC capacitor. 8 must be modified to compensate for the loss of the power convertor. l .. . The average values of Fs(r) and BL(t) during a mains cycle are zero.) + 8. is the DC component.1)wt + 8. the AC components of B. + I g t ) (19) =J( V.(t) and FL(t) may result in voltage fluctuation of the DC capacitor. I1 COS 81 . It supplies the real power to the DC busbar of the convertor to maintain a constant DC voltage and generates a compensation current to compensate for the load current. Its transfer function can be represented as H(s) = K . and C&) is the fluctuating voltage. COS 8. + dL(t) (10) where P .) (12) The power that is injected into the convertor is represented as 1)ot 2 .(t) in eqn.(t) of the convertor cannot be kept constant. where K.(t). and idc(t) is the higher-order harmonics due to the switching operation. cos ( 2 4 (9) = p. = V’I. is the average voltage of the DC capacitor. 141. The control strategy used is the unipolar PWM. = ~ ( V . No. owing to the power loss of the convertor circuit as no suitable DC voltage control circuit is used. is the DC component and is represented as P. 5 Power circuit (18) v. M a y 1994 . LC(t)is the lower-oFder harmonic components due to the load current. C where V. respectively.-Electr. . + Ice.f v. V. the DC busbar voltage can be represented as U&) = v.) and $C AV: thus AK = (P. 4.(t) =$ Therefore i. The instantaneous power consumed by the load is P d t ) = %(t)iL(t) = p. is the DC component. and K. some assumptions are made and stated as follows : 131 The average voltage of the DC capacitor can be controlled by adjusting the amplitude of the mains current i&). A PI controller used to control the DC capacitor voltage is shown in Fig. V.) sin (wt) where I.)) The convertor used in the active power filter is a fullbridge convertor... 2 The power circuit of the developd active power filter is shown in Fig. Hence.Plod At - 5 2 Energy storage element Conventionally.. The convertor is used to supply the desired compensation and charging power. The passive reactive element of the voltage-source active power filter is a capacitor located in the DC busbar. To simplify the analysis of the DC busbar voltage fluctuation.2P~..4 Control circuit of the DC busbar voltage The DC busbar voltage u. If the power loss of the convertor is assumed to be a constant and is represented as Plasa. .. However. 1. Power Appl. The convertor is a multifunctional convertor in practice. The filter inductor is used to smooth the compensation current supplied from the convertor. and the harmonics is suppressed by a passive filter. 3. cos 8. I. K +$ I E E Proc. This essentially requires large reactive elements. + F. DC busbar capacitor = 2200 pF. a prototype was developed and tested in a singlephase power system with 11OV. The major parameters of the prototype are as follows: DC busbar voltage = 200 V. 6 and 7 show the € However. No. 5 shows the mains voltage and current under the half-wave rectifier load before compensation. In other words. 26. the lower the frequency. smoothing inductor = 10 mH. the gain of the error amplifier can affect this phenomenon also. eqn. Nevertheless. . (c) In the steady state. Then. idc(t) be neglected. it may cause the problem of multicrossing phenomenon because the change rate of the convertor output current is larger than the slope of the triangle carrier signal. However. a large capacity capacitor is expected to suppress the voltage fluctuation to a limited level. (b) The energy stored in the filter inductor is negligible. %(t)idAt) = i&) (24) As I. The performance of the proposed active power filter under distorted mains voltage is also discussed. The lower-order harmonics current supplied from the DC capacitor can be represented as ijc(t) is very small compared with However. an inductor is required to filter out the switching ripple current. .(t)..24 kHZ. this problem can be solved by suitable design of the size of the inductor and the gain of the error amplifier. 3. In addition. 141. Fig. Rectifier loads were used in the test. d In the steady state. 132 Fig. Power Appl. It may cause the problem of core saturation and result in the transformer connected in the same feeder burning out. that is. 7 Simulation P. ( ) The power convertor is lossless. the voltage fluctuation of the DC capacitor due to i&) is very small and can be neglected. or the larger the magnitude of the AC power component i. the size of this inductor must be as small as possible.PL=0 and test results i&) (22) also can be represented as i&) = P. 7.(t) -iL(t) Besides. the voltage of the DC capacitor and the capacity of the DC capacitor.(a) Because the switching frequency is very high. or the load current to be compensated for contains the subharmonic current. For a good dynamic response. the capacity of the DC capacitor depends on the power rating of the active power filter and the load type.1 Half. 6 Filter inductor Ly lOOVper 5ms perdivision Fig.the larger the capacity of the DC capacitor required. the average voltage can be maintained constant. This is a serious problem in practical applications. the voltage fluctuation of the DC capacitor can be obtained and represented as ijdc(t)= cd 1 1 ' 0 id&) dt The voltage fluctuation of the DC busbar must be regulated to an acceptable level to obtain a good compensating accuracy and high operation efficiency. the voltage fluctuation of the DC capacitor depends on the order and the magnitude of the AC power component i c ( ~ ) . This has the result that the switching frequency is higher than the carrier signal frequency. 6 Simulation results o the proposed active power filter under f half-wave rectifier load a Mains voltage b Mains currem IEE Proc. From eqn.. the input instantaneous power must be equal to that of the output. = 0 and I . the positive halfcycle is not symmetrical with the negative half-cycle for both mains voltage and current.(d = $. it cannot suppress the switching ripple current. Vol. 6 Test results under haf-wave recrifler load before compensation a Mains voltage b Mains current To ensure that the compensation current generated by the convertor is a smooth current. Fortunately. the mains voltage will contain a DC offset voltage as well.-Electr. if the inductor is too small. When a large power rating of the active power filter is developed. switching frequency = 10. cos (not 9") 1 m + I=1 To verify the performance of the proposed active power filter. Figs.wave rectifier load For a power source with a high source impedance. = 0. The half-wave rectifier load is a typical unsymmetrical nonlinear load. In the Figure. M a y 1994 . that is. the fluctuating voltage of the DC capacitor is very small compared with the average voltage of the DC capacitor. (21) It implies P. and the amplitude of can V . is zero. 13 can be rewritten as PAt) = i.as the even-order harmonics when the load current is unsymmetrical. 3. Fig. and the mains current is nearly in phase with the mains voltage. To solve this problem. .. The total harmonics distortion of the mains voltage is 12%. . power systems have been seriously polluted by harmonics.-Electr. 5rns per division Fig. .. 9-12 show the test results under distorted mains voltage.Hz 1 Ok O2 0 021 022 m 023 024 025 b b f Fig.. That is. . 11 and 12 show the simulation and test results after compensation. frequency Hz . 7 Test results o the proposed active powerfilter under hal/-waue rect8er load a Mains voltage b Mains current b Mains current 00 frequency. As c lOOVper division Figs. Power Appl. M a y 1994 . time. . Fig. It can be seen c 6A per division b 5rns per divislon 5rnsper division Fig. .simulated and experimental compensation results of the proposed active power filter under the half-wave rectifier load. s 50 O m a that the mains current is nearly a sinewave and still in phase with the mains voltage.b 1 Ok Mains voltage before any load applied Waveform o the mains voltage f b Spectrumor the mains voltage a Fig. have limited not only voltage harmonics but also current harmonics. The feedback harmonics may cause distortion of the mains voltage. they generate the problem of harmonics feedback. the input power factor is close to unity after compensation. 9 Recently. such as IEC 555-2. . electrical standards. Many countries have restricted the voltage harmonics generated by power equipment. 133 IEE Proc. 10 Test results under distorted mains voltage before compensation ( I Mains voltage f Fig. 12 Test results o the proposed active powerfilter under distorted f mains voltage a Mains voltage b Mains cumnt 35V per division 00 r t . 8 shows the spectrum of the mains current before and after compensation. . Figs. 10 shows the mains voltage and the mains current under a full-wave rectifier load. Therefore the proposed active power filter can force the mains current to be a sinewave and obtain unity displacement power factor under distorted mains voltage. it can be seen that not only the mains current but also the mains voltage are pure sinewave. 8 Spectrum o the mains current f a Jkfore compensation E lOOVper division b After compensation above. 141. However. the problem is not effectively countered. . 8 Conclusions 12 t I I. No. 7. 9a and b show the waveform and spectrum of the mains voltage before any load is applied. Vol. it can be found that the proposed active power filter can compensate for the unsymmetrical load current and improve the voltage distortion due to the nonlinear current flowing through the system impedance. Fig. 11 Simulation results o the proposed active power filter under distorted mains voltage a Mains voltage b Mains current Fig. From these Figures.2 Performance under distorted mains voltage Because nonlinear loads are widely used. . the single-phase active power filter proposed is superior to conventional active power filters.: ‘Harmonic .D. 3. IECI-23.. 1989.: ‘Power electronics in electric utilities: static VAR compensators’. SEM-KOA.. pp... the mains voltage is often distorted in practical power systems. IEEE PESC88 Record.M. OKUMA. Siemens Com-ponents Publication. 9-15 17 AKAGI.F..H. NABAE. 1986 10 DIXON. AKAGI. 9 References ‘Harmonic current and reactive power compensation with an active filter’.H.. (l). IE-37. IEEE Trans.: ‘A single-phase controlled-current PWM rectifier’. 1990..: ‘An SMR topology with suppressed DC link components and predictive line current waveshap ing’. A. IEE. and MIRBOD. This results in the problem that the calculated mains current is not a sinewave. Vol. PE5. M.D. IEEE Trans. 1987 9 HERFURTH.. P. (b) It can compensate for the power factor and suppress the harmonics of symmetrical and unsymmetrical nonlinear loads. 141. 1986.R. IKEDA. T. S.pp. 1988. r e d d o n in ‘multiplex converters by triple-frequency current injection’. as the mains voltage is distorted. 1988 11 MANIAS. Power Appl.: ‘Instantaneous reactive power compensators comprising switching devices without energy storage components’. pp.. MARSH. K. and McLELLAN.: ‘A new injection method for AC harmonic elimination by active power filter’. (7). IE-35.. K. 453-459 13 HARASHIMA. (3)... (3). H. J. April 1988.F. (I). 1990. 1976.. Proc. the performance of conventional active power filters is degraded... T. M.H.:‘Control strategy of active power filters using multiple voltage-source PWM converters’. 1988. IEEE Trans. B. pp. IA-22. pp.. Siemens Components Publication. 1984.: ‘Generalized method of harmonic reduction in AC-DC converters by harmonic current injection’.L.H.. INABA. H. M. pp. pp. . J. 1987. M. 116. (4). M. Y.: ‘A closed-loop control for the reduction of reactive power required by electronic converters’. IEE. (3. IEEE Trans. 427-433 6 AMETANI.. G. IA-20.: ‘Active harmonic filtering for line rectifiers of higher power output’.: ‘High power factor preregulators for off-line power supplies’.. 86-89 15 AKAGI. pp. Unfortunately. (4). 1988. 1986. (4). and ARITSUKA. The active power filter proposed has two important features as follows: (a) It can force the mains current to be a sinewave even when the mains voltage is distorted. M. (4). IEEE Trans. and ATOH. and TSUBOI. and PARK. 1730-1734 8 HERFURTH. pp. 625630 16 PENG. A. IEEE Trans. A.: ‘A study of active power filters using quard-series voltage-source PWM converters for harmonic compensation’.: ‘A study on the theory of instantaneous reactive power’. 14 FURUHASHI. H. pp. F..The active power filter is a better solution to harmonics problems. (3). PWR-I.. The mains voltage is used in the calculation process of most conventional active power filter algorithms. PE-4..: ‘TDA 4814intearated circuit for sinusoidal line Current consumption’.-Electr. A. 141-147 CHOE. and PARK. 1174-1179 GYUGYI.Z. P. IEEE Trans. B. S. (l).: 2 3 4 5 power filter with optimized injection’.: ‘Analysis and control of active 1 TAKEDA. 1969. Above all. H. 483-494 COX. Unitrode power supply Seminar Handbook. A. and UCHIKAMA.G. Y. IEEE Trans. 857-864 7 BIRD. S. IEEE Trans. 119. pp. G. Hence. and NABAE. and 0 0 1 . M a y 1994 ..and NABAE.. pp. 1972. (lo). 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