Comparison of Current Control Strategies for Four-Leg Shunt Active Power Filter in Matlab-Simulink

Transcription

1 Kamil ANTONIEWICZ, Marisz MALINOWSKI Faclty of Electrical Engineering, Warsaw University of Technology, l. Koszykowa Warsaw Comparison of Crrent Control Strategies for For-Leg Shnt Active Power Filter in Matlab-Simlink Streszczenie. W artykle przedstawiono porównanie trzech metod sterowania dwpoziomowym czterogałęziowym aktywnym filtrem mocy. Dwie z metod stanowią rozwiązania klasyczne, natomiast trzecia metoda proponowana jest, jako rozwiązaniem alternatywne. W pierwszej metodzie zastosowano teorię mocy chwilowych oraz reglatory histerezowe; drga metoda bazje na reglatorach PI oraz modlacji PWM. Trzecia metoda to sterowanie predykcyjne wykorzystjące model o ograniczonej ilości stanów (FS-MPC). Porównanie dokonane zostało na podstawie symlacji w programie Matlab-Simlink. Porównanie trzech metod sterowania dwpoziomowym czterogałęziowym aktywnym filtrem mocy Abstract. This paper presents a comparison of three control strategies that were applied in the simlation model of a for-leg Shnt Active Power Filter based on two-level voltage-sorce converter. The research considered two classical methods and one proposed as an alternative. In the first an instantaneos power theory is sed for the references calclation and hysteresis controllers for gates signals generation. The second employs PI controllers and PWM modlation. The third method is Model Predictive Control with a finite control-states set nmber (FS-MPC). The comparison is based on simlations performed in Matlab-simlink. Słowa klczowe: predykcyjne, równoległy aktywny filtr mocy, czterogałęziowy APF, sterowanie, symlacje. Keywords: predictive, Shnt Active Power Filter, for leg SAPF, control, simlation. doi:.95/pe.4..5 Introdction Fast growth of electrical energy consmption increases an importance of energy qality aspect. This is a high significance isse, while the correct operation of electrical devices is sally dictated by delivered electrical energy parameters. Modern grid-side transistor based converters are controlled with the algorithms which assres a reqired vale of the crrent THD and reactive power. Here, three control methods for two-level for-leg Shnt Active Power Filter (SAPF) are presented and compared in simlation model. The first method is based on instantaneos power theory which is sed to calclate the reference crrents for SAPF. Gate signals are generated by hysteresis controllers, which compare crrent references with measred vales [- 6]. The second reqires coordinates transformation from the natral do rotating d-q with fndamental 5Hz freqency. It employs linear crrent controllers (proportional-integral, PI) to calclate the SAPF reference voltage for a plse-width modlator [,7-9]. The third method belongs to the category of predictive control. It s generally based on the model of the controlled system, which is sed for calclation of ftre vales of state variables. Depending on the type of application and desired control properties different ways of sing prediction can be chosen. In the case of SAPF a Model Predictive Control with a finite control states set (FS-MPC) [,-8] has been selected as the most sitable. For this method it is assmed that the system can represent a finite nmber of control states in every time period which is correct for power electronics devices. It also offers a very high operation dynamics what meets SAPF control reqirement. FS-MPC featres make it competitive to the aforementioned strategies. The comparison of three control methods was performed in Matlab-Simlink. The sbseqent sections of this paper give a system overview and introdce the three methods, showing the advantages and ddvantages of each of them. Next, the simlation reslts will be presented. Finally, according to the chosen criterions, the reslts comparison is performed, giving the conclsions in the last section. For-Leg Shnt Active Power Filter System Overview Figre presents the system overview. For-leg SAPF is connected to the Point of Common-Copling (PCC) throgh a passive indctive filter. SAPF compensates distortions introdced by the nonlinear and asymmetrical load, which, for the prpose of this comparison is represented by three-arm 6-plse diode-bridge with load and three-leg resistive-indctive load with the netral point connected to the netral line at PCC. Instantaneos Power Theory Based Control With Hysteresis Controllers (P-Q Theory Based) This type of SAPF control represents the classical approach to obtain the compensation of crrent harmonics, as well as the reactive power (see fig. ). It reqires load crrents and grid voltages measrement. First, transformation to stationary coordinates is performed, sing eqation: () x x x x C x x a b c, where C and x is a vector of instantaneos vales of grid voltage PCC or load crrent i L. Transformed vectors are sed for load power calclation, which for three-phase grid with symmetrical voltages is expressed with: pl PCC PCC il () ql PCC PCC il Next, a variable component P vr of P L is extracted with a high-pass filter []. Finally, inclding SAPF DC-capacitor voltage control with P dudc component, the expression for the reference crrents is given as: i (3) i Cref Cref PCC PCC PCC PCC PCC PCC p q comp comp, where P comp =P vr -P dudc. In case of asymmetrical load, the non-zero netral wire crrent mst be also compensated by SAPF. Its reference vale is calclated sing the Kirchoff s law, as a sm of the three phase crrents. 4 PRZEGLĄD ELEKTROTECHNICZNY, ISSN 33-97, R. 9 NR /4

2 Calclated reference crrents are delivered to hysteresis controllers which compare them with the measred compensation crrents. This way the gates signals are generated. Fig. General system overview Fig. General system overview Fig. Instantaneos power theory based control scheme for SAPF This method gives a very simple soltion for SAPF control. Thanks to the se of hysteresis controllers a high operation dynamics in transient states and very good reference tracking can be reached. The robstness is extremely high, what is a great advantage of this method. On the other hand, classical hysteresis controllers operate with a variable freqency, which is, in fact, a very important isse. Spectral analysis shows that a wide range of harmonic freqencies can be generated. As the main conseqences, a problematic otpt filter design shold be mentioned. However, soltions for this problem have already been proposed. With a variable width of hysteresis band a fixed freqency can be achieved. The variation is dependent on the instantaneos otpt voltage and DC voltage, as described in []. It s realized with a phaselocked loop or a feed-forward loop. Linear crrent controllers Another classical approach represents the linear crrent control method. This soltion is based on coordinates transformation and PI controllers. However, this method also brings several isses. The linear PI controllers have a limited bandwidth, what also brings limitation to the SAPF performance. It cannot reach a zero steady state error when operates on an alternate signal. A partial soltion is to transform coordinates system from stationary to rotating [7-9]. This operation reqires the grid voltage phase angle and low-pass filters for DC vales extraction (fndamental freqency crrent becomes a DC vale), what is similar to previos method. The block scheme is presented in figre 3. Load crrents are transformed from the natral abc to rotating d-q- coordinates system, synchronized with the grid voltage phase angle Φ( PCC ) sing eqations: (4) i i i Ld cos sin PCC sin PCC cos Lq PCC PCC L i i i L The components of compensation crrents can be individally extracted, similarly to instantaneos power theory, with low-pass filters. Here, also the DC-capacitor voltage error component in d coordinate is injected. Next, the reslting reference crrents are compared with measred vales. Errors for d and q components are delivered to PI controllers. After decopling of the d and q otpt components, the final reference voltage is delivered to the implemented modlation techniqe. This techniqe, thanks to the modlation, has a great advantage of fixed freqency, what is very helpfl in the matter of the otpt filter design. This control loop works qite well with reactive power compensation and loworder harmonics. However, higher-order harmonics exceed PI bandwidth, so the SAPF crrents cannot track the references with a desired qality and ths the compensation becomes nsatisfactory. Finite Control-States Set Model Predictive Control This control strategy belongs to calclation demanding. In case of power electronics application it was a serios barrier. However, modern control platforms, at last broght soltions for an effective digital implementation, so the poplarity of this control strategy grows [-8]. Figre 4 depicts the scheme of a typical FS-MPC strctre. The idea is based on system model which is sed for state variables vales prediction [,3,5]. So first of all, the model mst be as exact as possible, becase the control performance is highly dependent on the parameters (indctances, capacitances) precision. Using measred vales of compensation crrents, their vales in the forthcoming sampling can be predicted sing (5), with respect to available control states S(a, b, c). It mst be done for all states in every sampling period. Fig. 3 Linear crrent control scheme for SAPF Fig. 3 Linear crrent control scheme for SAPF The correction of the predicted vale also improves the prediction precision [9]. In this simlation, the coefficient K was chosen,6 (see fig. 4), what gave the best operation performance. The reference vales can be calclated with any available method. For this comparison the L L PRZEGLĄD ELEKTROTECHNICZNY, ISSN 33-97, R. 9 NR /4 5

3 instantaneos power theory based method was employed with eqations () and (3). Fig. 4 FS-MPC scheme for SAPF For each state predicted crrents errors are smmed p in the cost fnction (7). Whole Predictive Control can be expressed with eqations: (5) (6) I pre, mk CvV C, mk Ci I C, mk V C, mk U DC S mk U PCC, mk (7) J k k S m m a, b, c Cref, m I pre, m I, where m corresponds to phase a, b, c or netral leg n; I pre,m (k+), I C,m (k) predicted and measred compensation crrent in, respectively (k) and (k+)-th step; U DC - SAPF DC capacitor voltage; S m states; U PCC,m (k+)=u PCC,m (k)+(u PCC,m (k)-u PCC,m (k-)); C v,=t s /(L g +R g T s ), C i =L g /(L g +R g T s ) - constants dependent on the otpt filter parameters and sampling time T s. The cost fnction J(S m ) can also inclde other parameters that shold be covered like the nmber of, DC-capacitor voltage etc. Finally, the control otpt is the state that minimizes the cost fnction. Considering power converters, it is clear that they can represent only a finite nmber of states ( states). Focsing only on SAPFs applications, as it was described before, the main objectives are high precision in references tracking and ths high operation dynamics. FS-MPC, thanks to its capabilities can reach these high demands, while it natrally eliminates possible delays. It operates with a finite nmber of control states, choosing the converter s state that gives an optimal references tracking. However, it sffers from an inaccracy of the given circit parameters, what can possibly bring an error in every prediction. This control strategy doesn t employ the modlation. The states are set directly, what leads to a variable freqency, if only crrents control is considered. Nevertheless, how was mentioned above, the cost fnction can cover that isse, throgh inclding the nmber of as the parameter. FS-MPC, thanks to the cost fnction, has great capabilities of control. However, for the comparison with the classical control strategies only the basic form was chosen. The prediction and cost fnction incldes only compensation crrents, while the references are obtained with the instantaneos power theory, which was described in the previos section. Simlation Reslts The comparison was performed in Matlab-Simlink sing a SimPowerSystems library. To analyze the performances in the compensation of reactive power and crrent harmonics, two types of load were considered: three-phase 6-plse diode-bridge with resistive load and asymmetrical three-phase resistive-indctive (Load and Load - see figre ). The main system parameters are collected in the table. Table. Main parameters of simlation model Qantity Vale Load Power [kva] 5 Grid phase voltage [V rms ] 3 SAPF DC voltage [V] 7 Sampling freqency [khz] Hysteresis controllers Linear crrent reglators FS- MPC 4 4 Passive filter indctance L g [mh].5 Passive filter resistance R g [Ω]. Bridge load R/L [Ω]/[mH] 3/ Bridge switched load R [Ω] 6 Three phase load R/L [Ω]/[mH] /3 Three phase load phase A switched load R [Ω] 3 Reslts are in two grops. All the figres present system performance dring a load step change. The first grop corresponds to an asymmetrical three-phase load. Here, to standardize operating conditions in the comparison a criterion was chosen: redction of Total Harmonic Distortion (THD) of phase A grid crrent below 4%. To reach this criterion, the sampling freqency of linear control was set to khz, while FS-MPC and control based on instantaneos power theory operate on 4kHz. The other grop corresponds to a nonlinear load, where each method operates with the same sampling freqency respectively. Figres 5, 6 and 7 represent the first grop. They compare phase shift compensation effectiveness, while the load is symmetrical and, after a load change in one phase, also compensation of netral wire crrent. The classical methods give similar THD vale 3,9%, however, with the instantaneos power theory based control, a nmber of is mch lower. Comparing THD it mst be noted, that FS-MPC gave the lowest vale of this factor. The research showed that it was 3%. Moreover also this method reqired the lowest nmber of. All methods assred a similar and very good compensation of asymmetry. Fig. 5 SAPF with instantaneos power theory based control; Load - operation performance, from the top: phase A grid voltage V a and crrent i sa (THD=3,9%) and netral crrent i sn, load crrents with netral crrent, compensation crrents, nmber of in SAPF phase A per grid voltage period (ms) 6 PRZEGLĄD ELEKTROTECHNICZNY, ISSN 33-97, R. 9 NR /4

4 4 Va/ icn Fig. 6 SAPF with linear crrent control; Load - operation performance, from the top: phase A grid voltage V a and crrent i sa (THD=3,9%) and netral crrent i sn, load crrents with netral crrent, compensation crrents, nmber of in SAPF phase A per grid voltage period (ms) 4 Va/ icn Fig. 7 SAPF with FS-MPC; Load - operation performance, from the top: phase phase A grid voltage V a and crrent i sa (THD(i sa )=3%) and netral crrent i sn, load crrents with netral crrent, compensation crrents, nmber of in SAPF phase A per grid voltage period (ms) The second stage of this comparison relates to the second type of load. This analysis gave a view on the three methods operations in dynamic states, with load crrents step changes. 4 Va/ icn Fig. 8 SAPF with instantaneos power theory based control; Load - operation performance, from the top: phase A grid voltage V a and crrent i sa (THD=9,5%), load crrents, compensation crrents, nmber of in SAPF phase A per grid voltage period (ms) As can be seen in figres 8, 9 and the methods present different performances. Control based on instantaneos power theory and FS-MPC redces THD to 9,5%. Taking a look on figres 8 and, it mst be noted that FS-MPC reqires mch lower nmber of, what is noticeable on grid crrent ripples. The second classical method, linear control, gives mch worse reslts. With this nonlinear load THD reached over 7%. It can be explained with a limited bandwidth of PI controllers, which cannot assre good error correction for rapidly changing references. Even thogh, it reqires the highest nmber of it cannot reach the other two methods performances. 4 Va/ icn Fig. 9 SAPF with linear crrent control; Load - operation performance, from the top: phase A grid voltage V a and crrent i sa (THD(i sa )=7,5%), load crrents, compensation nmber of in SAPF phase A per grid voltage period (ms) Va/ icn Fig. SAPF with FS-MPC; Load - operation performance, from the top: phase A grid voltage V a and crrent i sa (THD(i sa )=9,5%), load crrents, compensation crrents, nmber of in SAPF phase A per grid voltage period (ms) The analysis of figre shows clearly that FS-MPC gives a better operation precision, than the other two methods. It gives the same THD vale as control based on instantaneos power theory, bt keeps the nmber of at the lowest level. The compensation crrents can trace references with a high accracy. Table. Comparison of the three SAPF control methods proprieties. P-Q Theory Linear Crrent Criterion FS-MPC based Control Calclations Calclation per sampling Low High (high freqency) Sensitivity to Low system sensitivity parameters Gate signals generation Hysteresis controllers (variable freqency) High Low calclation Sensitive Modlator (constant freqency) Low (depends on model) High calclation Very sensitive to (otpt filter) Direct states set (variable freqency) PRZEGLĄD ELEKTROTECHNICZNY, ISSN 33-97, R. 9 NR /4 7

5 Table collects and gives comparison of the proprieties of the three control methods. Conclsions This paper presented a comparison of three Shnt Active Power Filter control techniqe performances. Two of proposed techniqes are considered as the basic form of the classical approach to the SAPF control isse. These are: linear crrent control and instantaneos power theory based control with hysteresis controllers. The third method was Finite Control-State Set Model Predictive Control (FS- MPC). The idea was to compare MPC with the classical methods, as a possible alternative for the control strategy. This comparison was based on the SAPF simlation model, bilt in Matlab-Simlink. It considered two types of operation, regarding to the type of load. The first stage of research was focsed only on a three phase RL load with the netral wire connected to the grid netral point. At the next point a diode-bridge with an RL load, connected in parallel with switched resistive load was considered. To standardize operating conditions the criterion was chosen: redction of phase A grid crrent THD to 4% for a symmetrical linear load. It was reached with a sampling freqency of khz for linear control and 4kHz for the other two methods. Next a crrent phase shift compensation of a three phase symmetrical linear load was simlated and stdied. In this case, with sinsoidal references, FS-MPC operated with the best precision, what can be noticed on the grid crrent THD of 3%. This reslt was reached with a significantly lower nmber of (per grid voltage period), than the other two methods. Linear control and instantaneos power theory based control gave a similar THD 3,9%, however, the linear control reqired more. At the next point, the analysis was performed for an asymmetrical load. It showed that all methods assred very similar compensation of a crrent phase shift and very good netral wire crrent compensation. The second type of load gave the reslts of the three control methods operation with a nonlinear load. This comparison showed that the best operation performance is given by FS-MPC. Althogh, similarly to control based on instantaneos power theory, THD increased to 9,5%, for FS-MPC the nmber of is significantly lower. Linear control presents mch worse performance. With a limited bandwidth of PI controllers it cannot assre a good tracking of dynamically changing references, worsening compensation effectiveness. This comparison shows that, proposed FS-MPC can be a good alternative to the classical methods. With a lower freqency, this method assred better compensation performance than the other two methods. Considering the idea of predictive control and FS-MPC, this method can assre a very high operation and filtration dynamics what is highly reqired in SAPF applications. 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[7] Wang Xiaogang, Xie Ynxiang, Shai Dingxin, Three-Phase For-Leg Active Power Filter Based on Nonlinear Optimal Predictive Control, Proceedings of the 7th Chinese Control Conference, Vol. (8), 7-. [8] Rivera M., Yaramas V., Llor A., Rodrigez J., W B., Fadel M., Digital Predictive Crrent Control of a Three-Phase For- Leg inverter, Trans. on Indstrial Electronics, isse: 99 (),. [9] Xiao-gang W., Yn-xiang X., Ding-xin S., Simplified Model Predictive Control for a Shnt Active Power Filter, Power Electronics Specialists Conference, PESC 8 (8), Athors: M.Sc. Kamil Antoniewicz, antoniek@ee.pw.ed.pl; Ph.D. Marisz Malinowski WUT Professor, malin@isep.pw.ed.pl; Faclty of Electrical Engineering, Warsaw University of Technology, l. Koszykowa Warsaw 8 PRZEGLĄD ELEKTROTECHNICZNY, ISSN 33-97, R. 9 NR /4