Improving the Active Power Filter Performance with a Prediction Based Reference Generation

Transcription

1 Improving the Active Power Fiter Performance with a Prediction Based Reference Generation M. Routimo, M. Sao and H. Tuusa Abstract In this paper a current reference generation method for a votage source shunt active power fiter is examined. The proposed method improves the harmonic fitering by compensating the deays in the system. In stationary operating point of the oad the method uses measurement data samped in previous periods to generate a reference prediction. Since in transient state of the oad the prediction no onger hods true, a computationa contro deay compensation agorithm is used in the reference generation instead of the prediction in this situation. Changing the agorithm according to the operating point guarantees effective harmonic compensation in a operating points. In this paper the system performance is examined with an active fiter simuation mode. Index terms digita contro, contro deay, current reference generation, shunt active power fiter I I. INTRODUCTION N recent years active power fiters (APFs) have been widey studied and severa methods to contro them have been proposed, e.g. [1] [4]. In harmonic fitering the active fiter current reference generation pays an important roe: if the reference is poor, a good fitering resut cannot be achieved. A common probem in votage source shunt active fiters (Fig. 1) is their abiity to fiter ony ow order harmonics effectivey. This is mainy caused by performing the digita contro agorithm and samping the measurement signas, which cause a deay. Because of this, the contro is aways ate and the active fiter cannot react fast enough to rapid changes in the oad current. As a resut the fitering of higher order harmonics is difficut but the compensation of ower order harmonics aso deteriorates. Methods to improve the active fiter performance with prediction based current reference generation methods have been presented in the iterature, e.g. [5] [6]. In [5] the prediction is based on the measurements of dc ink variabes of the individua oad. The method is very effective for harmonic fitering. However, with mutipe oads the number of measurements is increased. In addition the system uses an artificia neura network in the reference generation, thus a ot of computing is needed. In [6] the active fiter current reference is predicted based on the data samped in the previous fundamenta periods. The method is very effective with constant oad, but if the oad changes, the system performance deteriorates. This paper presents a simpe method to effectivey compensate a the harmonics up to 2 khz both in stationary and transient states of the oad. The method is based on the change of the reference generation agorithm according to the operating point. In the stationary state the reference generation is based on the prediction whie in the transient state a computationa contro deay compensation method is used instead. The theory behind the proposed method is presented and it is appied to the contro system of the votage source shunt active power fiter. The performance of the proposed method is examined with an active fiter simuation mode and the resuts are compared with other reference generation methods. II. CURRENT REFERENCE GENERATION In this section the active fiter current reference generation methods for the contro system based on the oad current feedforward connection are examined. The contro system is based on [7] and it is impemented in the synchronousy rotating reference frame, which is tied to the suppy votage vector. The basic idea in reference generation for this kind of contro system is to extract the harmonics from the measured oad currents. They are taken negative to the active fiter harmonic reference. In the reference frame the fundamenta current component can be seen as a dc component and as a consequence the harmonics can be extracted with a high pass fiter. A. A Conventiona Method In a conventiona method the harmonics are extracted with a high pass fiter. In [7] the high pass fiter is based on a fourth order Butterworth ow pass fiter, and in [8] and [9] to keep the extraction agorithm simpe high pass fitering is reaised utiizing the forward Euer discretized first order ow pass fiter. A bock diagram of the system is iustrated in Fig. 2, where i d is the measured oad current rea axis current component, i d0 a fundamenta current component u s i s i f L smooth i L f u f Non-inear oad C f u dc The authors are with Department of Eectrica Engineering, Institute of Power Eectronics in Tampere University of Technoogy, P.O. Box 692, FIN Tampere, FINLAND, phone: ; fax: ; e-mai: mikko.routimo@tut.fi. Active power fiter Fig. 1. Configuration of the votage source shunt APF.

2 i d Low pass fiter i d0 and i dh the harmonics. Since the aim is aso to compensate the reactive power, the oad current quadrature component is not high pass fitered. The main probem in the conventiona method is that because the contro system is impemented digitay, deays occur. Even if the high pass fiter woud perform perfecty, not a the harmonics coud be fitered because of the deays. The high pass fiter time constant is about 8 ms in [8] and [9]. That is, in the case of step change in the fundamenta oad current component it takes about 19 ms for the high pass fiter to remove 90 % of the new dc vaue. In addition, the system cannot competey compensate the unbaance of the oad currents (100 Hz component in the synchronous reference frame), because of the phase shift caused by the fiter. This coud be soved by choosing a bigger time constant, but this woud ead to even onger response time. B. Contro Deay Compensation A computationa contro deay compensation method is presented in [8] and [10]. The method improves the performance of the conventiona method. The first step in the method is to extract the harmonics, for exampe, based on the conventiona method and after that the current reference given by the high pass fiter is modified so that the deay wi be compensated. In the method the active fiter current reference is modified based on the knowedge of the fiter current behaviour in a case of step change in the current reference. The reference is corrected so that the fiter current behaves as desired. The agorithm can be written in discrete form as *s τc s s s ifh( k + 1 ) = ( ih( ih( k 1) ) ih(, (1) Ts where i *s fh is an active fiter harmonic current reference, i s h oad current harmonics in synchronous reference frame, τ c is a compensation time constant, T s samping interva and k a discrete time instant. The system performs we both in stationary and transient state of the oad and sinusoida suppy currents are achieved. A drawback of the method is that the high order harmonics increase. C. Prediction Symmetrica three-phase oads connected to sinusoida mains cause harmonics of the order n = 6p ± 1, p [1, 2, 3, ]. (2) In the synchronous reference frame, which is tied to the suppy votage vector, they are seen as the suppy frequency mutipes of the orders n s = 6p. (3) That is, when the oad operates in stationary state and the system is examined in the synchronous reference frame, the oad current frequency can be seen as a dc quantity with a rippe caused by the harmonics. The period of the rippe is T r = 1/(n s min f s ), (4) - + idh Fig. 2. Bock diagram of the high pass fiter. i d where n s min is the owest order harmonic in the synchronous reference frame and f s the suppy votage frequency. According to this the oad current behaviour at the next samping instant coud be predicted based on the oad current samped in the ast period T r. Unbaanced oad currents can be divided into positive and negative sequence components. In the synchronous reference frame the positive sequence current can be seen as a dc component and the negative as a harmonic with a frequency of 2f s. To aso observe the unbaance of the phase currents, the prediction shoud be done on the basis of the oad current measured time T u = 1/2f s ago. Since the period T u is a mutipe of T r, both the harmonics and unbaance can be predicted using the data coected during ast T u. The deay caused by samping the measurement signas and performing the contro agorithm can be approximated to be about 1.5T s, where T s is the samping interva. Since in the discrete time system ony mutipes of the samping interva can be handed, the deay is rounded to 2T s. Let us assume that we have stored m sampes of the oad current performance in a tabe during the ast period T u. According to the discussion above, we can now predict the oad current performance at the next samping instant t(k+1) and compensate the contro deay by using the data measured at time instant t(k (m 2)). This yieds the active fiter current reference equations: * i fdh( k + 1) = id0( id( k ( m 2)) (5) * i fqh ( k + 1) = iq( k ( m 2)), (6) where k denotes a discrete time instant, m the number of sampes in one period T u and i d0 the fundamenta oad current component in the synchronous reference frame. The prediction made based on the data samped in the previous period appies to the operating point where the oad is in stationary state. If the oad changes probems occur, since the prediction is no onger vaid. D. The Proposed Method A soution for the drawback in the prediction method is to use the prediction in stationary operating point and a more robust reference generation agorithm under the transient state operation. As was discussed, the computationa contro deay compensation method aso performs we in transient state operation. That is why we choose to use the method in the transient state. Athough a drawback of the method is that the high order harmonics increase, this is not a probem since we wi use the CDC method for ony a whie, that is during the transient state of the oad. The prediction is used to generate the reference in the stationary operating point. Since the two agorithms are used in the current reference generation, the contro system has to know whether the oad is in transient state or not. This can be done comparing the measured oad current to the vaue that is measured one period ago. In the stationary state we have s s i i ( k m) = 0. (7) In any case, because of the inaccuracies in the system (e.g. measuring noise), the new and the od current do not necessariy have exacty the same vaues. In the impementation of the system the condition of the transient becomes

3 s s i ( k m) i ( > e, (8) max where e max defines the accepted maximum error between the new and the od vaues. 1) Foating Average To make the reference prediction we have stored measurement data of the oad currents in the memory. Thus the fundamenta oad current component can be determined cacuating the average of the sampes of the oad current. To compensate the reactive power, ony the oad current d axis component is high pass fitered. The foating average agorithm is then i d0 k 1 = i m d k ( m 1) 1 = id, sum (9) m 1 = [ id, sum ( k 1) id ( k m) + id ] m If the dc component is cacuated as an average of the m sampes coected during the time period T u =1/2f s (10 ms with f s = 50 Hz), this kind of ow pass fiter competey damps a the frequencies that in the synchronous reference frame are mutipes of 2f s. This hods true with haf wave symmetrica oad currents. If this cannot be assumed, the measurement data coected during the whoe fundamenta period has to be used. In the case of step change in the fundamenta oad current component, the new dc vaue wi be removed after m sampes. As a concusion, with a high pass fiter based on the foating average a the harmonics in the oad current, incuding that caused by an unbaanced oad, can be extracted without any damping in magnitude or phase shift. III. CONTROL SYSTEM The proposed current reference generation method is used in the contro of a votage source shunt active power fiter. The contro system is introduced in Fig. 3. Subscripts s, and f refer to suppy, oad and active fiter variabes respectivey, h to harmonics and 0 to fundamenta frequency quantities in synchronous reference frame. Underined variabes refer to space vectors, the superscript s to a space vector in synchronousy rotating reference frame, * to reference vaue and subscripts d and q to rea and quadrature components respectivey. The system is based on the oad current feedforward connection. The measured oad current i is first transformed to the synchronous reference frame with a bock 3 2. The reference frame ange θ s is determined with a phase ocked oop (PLL) by observing the suppy votage u s. The current reference to compensate the harmonics is generated with the bock Reference Generation. The content of the bock is presented in Fig. 4. In the figure bock Average cacuates the foating average according to Equation (9) and the bock Tabe gives the oad current vaues samped m 2 time instants ago. The current reference i *s fh(k+1) is cacuated using Equations (5) and (6) and another reference candidate using the contro deay compensation method presented in Equation (1). The error signa e( is cacuated to find out if the oad operates in transient state. A switch in 3 2 i s i s ( i s Load L smooth the figure uses this information to decide which one of the two reference candidates is used in the active fiter current contro. The APF dc ink votage is controed with a fundamenta frequency d axis current reference component i * fd0. This is a dc quantity in a synchronousy rotating reference frame and it is added to the harmonic reference i * fh. The reactive power can be controed with a fundamenta frequency q axis reference i * fq0. A PID controer is used in cosed-oop contro of the fiter currents i s f. Finay the active fiter votage reference u *s f is produced by subtracting the fiter inductor votage reference u *s Lf from the suppy votage u s s. IV. SIMULATION RESULTS The performance of the proposed current reference generation method was examined through simuations. The simuation mode was made using Matab / Simuink. The modeed votage source shunt active power fiter was designed to compensate harmonics caused by a noninear oad of 5 kva nomina power. The simuation mode parameters are shown in Tabe I. A. Stationary State Operation First an active fiter performance was examined in stationary state operation. A three-phase diode rectifier with an RL oad was used as a harmonic producing oad. The oad resistance was 64 Ω and the inductance 10 mh. A phase-a oad current waveform is presented in Fig. 5a. In simuations three different methods to contro the active fiter were used. Figure 5b presents a phase-a suppy current, when a method based on [7] has been used.. Gitches can be seen in the suppy current waveform at time instants when the oad current changes suddeny. They are caused by the deays and the active fiter system dynamics. The harmonic content of the waveforms in Fig. 5 is presented in Tabe II. The computationa contro deay compensation method i i f u s u L f u f C f V u s θ s PLL θ s 3 2 i * fq0 i s f u s s Reference i *s u *s fh + + i *s Lf u *s f f PID Generation + i * Current fd0 controer Average Moduator Fig. 3. Contro system bock diagram. i d0 ( + - i d (k-m) i s (k-(m-2)) - + Tabe i s (k-m) + - i s h( e( CDC i *s fh(k+1) Pe 2 Dc-ink votage controer i *s fh(k+1) Fig. 4. Bock diagram of the reference generation. u dc - + u * dc i *s fh(k+1)

4 (CDC) improves the active fiter performance [8]. The fitering resut can be seen in Fig. 5c. The gitches have now been reduced and the harmonic distortion cacuated up to 2 khz (THD 2 khz ) has been haved. Athough the fitering performance with the ow order harmonics has been improved, the high order harmonics have been increased. This can be seen in Tabe II, where the THD cacuated up to 20 khz remains amost constant regardess of whether the conventiona or the CDC method is used. TABLE I ACTIVE FILTER PARAMETERS Suppy phase votage U s 230 V Suppy frequency f s 50 Hz Fiter inductor L f 5 mh Fiter inductor resistance R f 0.3 Ω Dc ink capacitor C f 1.1 mf Smoothing inductor L smooth 2.3 mh Switching frequency f sw 10 khz Sampe time T s 50 µs Sampes stored in memory m 200 Compensation time constant τ c 2T s Maximum accepted d axis error e dmax 1.5 A Maximum accepted q axis error e qmax 2.0 A n TABLE II HARMONIC CURRENT COMPONENTS RL Load i a(n) /i a(1) Shunt APF i sa(n) /i a(n) Shunt APF with CDC i sa(n) /i a(n) Proposed Method i sa(n) /i a(n) THD 2 khz THD 20 khz a b c d Fig. 5. Simuated phase-a current waveforms in stationary state operation. a) Load current. b) Suppy current with a conventiona method. c) Suppy current with computationa contro deay compensation method. d) Suppy current with the proposed reference generation method. a b Fig. 6. Simuated phase-a current waveforms, when a diode rectifier suppies an RC oad. a) The oad current. b) The suppy current with the proposed method.

5 a b c d Fig. 7. Simuated phase-a current waveforms in transient state. a) The oad current. b) The current reference is generated using a pure prediction. c) The contro deay compensation method is used. d) The proposed method is used. a b Fig. 8. Simuated phase-a current waveforms of transient state operation when the proposed method is used. a) Load current. b) Suppy current. When the proposed prediction based current reference generation has been used, the resuting suppy current waveform can be seen in Fig. 5d and the harmonic content of that in Tabe II. Thanks to the prediction, effects of contro deays have been competey compensated and a the harmonics up to 2 khz have been effectivey fitered. Figure 6 demonstrates that harmonics of RC type oad have aso been effectivey reduced. B. Transient State Operation As was discussed previousy, a purey prediction based reference generation causes probems if the oad changes. Figures 7a and b iustrate this situation. It can be seen that since the oad changes at time instant 44 ms, the prediction no onger hods true. This resuts in a highy distorted suppy current. Figure 7c demonstrates that the computationa contro deay compensation method aso performs we in the transient state operation and the suppy current is aso kept sinusoida at this operating point. Thus the proposed current reference generation method combines these two methods: in stationary state operation the reference is generated using the prediction and in transient state using the CDC method. The resut is shown in Fig. 7d. It can be seen in the figure that the suppy current is kept sinusoida in both of the operating points. If the oad changes stepwise, the new operating point is found in 10 ms, as can be seen. The CDC method is in use during this time interva. Figures 8a and b demonstrate the proposed method performance in the case of two changes in the oad. It can be seen that the method performs very we. V. CONCLUSIONS An active power fiter current reference generation method was examined in this paper. In stationary harmonic compensation condition the method predicted the current reference on the basis of the data coected during the previous period. When the oad changed and the prediction was not vaid, the computationa contro deay compensation method was used. Both the agorithms were simpe and no compicated computation was needed. The performance of the proposed current reference generation method was examined with simuation mode and the resuts were compared to other methods. Both the stationary and transient state operations were examined. The resuts showed that with the proposed method sinusoida suppy currents with a ow harmonic distortion were achieved both in stationary and transient state operation.

6 REFERENCES [1] Akagi, H., "New Trends in Active Fiters for Power Conditioning", IEEE Transactions on Industry Appications, Vo. 32, No. 6, pp , [2] Mendaek, N., A-Haddad, K., Dessaint, L. A., Fnaiech, F., "Noninear Contro Strategy Appied to a Shunt Active Power Fiter", IEEE 32 nd Annua Power Eectronics Speciaists Conference. PESC 01, Vo. 4, pp , [3] Chandra, A., Singh, B., Singh, B. N., A-Haddad, K., "An Improved Contro Agorithm of Shunt Active Fiter for Votage Reguation, Harmonic Eimination, Power-factor Correction, and Baancing of Noninear Loads", IEEE Transactions on Power Eectronics, Vo. 15, No. 3, pp , [4] Mattavei, P., "A Cosed-oop Seective Harmonic Compensation for Active Fiters", IEEE Transactions on Industry Appications, Vo. 37, No. 1, pp , [5] Marks, J. H., Green, T. C., "Predictive Transient-Foowing Contro of Shunt and Series Active Power Fiter", IEEE Transactions on Power Eectronics, Vo. 17, No. 4, pp , [6] Mariethoz, S., Rufer, A. C., "Open Loop and Cosed Loop Spectra Frequency Active Fitering", IEEE Transactions on Power Eectronics, Vo. 17, No. 4, pp , [7] Mendaek, N., A-Haddad, "Modeing and noninear contro of shunt active power fiter in the synchronous reference frame", Ninth Internationa Conference on Harmonics and Quaity of Power, Vo. 1, pp , [8] Routimo, M., Sao, M., Tuusa, H., "A Contro Deay Compensation Method for Votage Source Active Power Fiter", The Ninth European Power Quaity Conference. PCIM 2003 Europe, pp , [9] Routimo, M., Sao, M., Tuusa, H., "Wideband Harmonic Compensation with a Votage-Source Hybrid Active Power Fiter", Nineteenth Annua IEEE Appied Power Eectronics Conference. APEC 2004, Vo. 1, pp , [10] Sao M., Tuusa H., "A Nove Open-oop Contro Method for a Current-Source Active Power Fiter", IEEE Transactions on Industria Eectronics, Vo. 50, No. 2, pp , 2003.