Finite-States Model Predictive Control with Increased Prediction Horizon for a 7-Level Cascade H-Bridge Multilevel STATCOM

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1 Proeedings of The 2th World Multi-Conferene on Systemis, Cybernetis and Informatis (WMSCI 216) Finite-States Model Preditive Control with Inreased Predition Horizon for a 7-Level Casade H-Bridge Multilevel STATCOM Raúl GREGOR*, Alfredo RENAULT*, Leonardo COMPARATORE*, Julio PACHER*, Jorge RODAS*, Derlis GREGOR *Laboratory of Power and Control Systems, Laboratory of Distributed Systems Faultad de Ingeniería, Universidad Naional de Asunión Luque, CP 26, Paraguay {rgregor, arenault, lomparatore, jpaher, jrodas & dgregor}@ing.una.py and Javier MUÑOZ, Maro RIVERA Department of Industrial Tehnologies, Universidad de Tala Tala, CP , Chile {jamunoz, maroriv}@utala.l ABSTRACT This paper presents a finite-states model preditive ontrol tehnique applied to the three-wire asade H-bridge multilevel onverters for stati synhronous ompensators. The fous of this paper is to examine the impats of inreasing the predition horizon on the ontrol performane in terms of reative power ompensation. The proposed approah predits the future behavior of the ontrol ations onsidering all possible swithing states onsidering a seond step of predition horizon in order to selets the optimal swithing vetor by using an optimization proess onsidering a defined ost funtion. The effetiveness of the proposed ontrol approah is analyzed through simulations. Keywords: Preditive ontrol, asade H-bridge onverter, reative power ompensation. 1. INTRODUCTION Power quality and effiieny issues have been atually onsolidated as a sientifi topi in the field of eletrial engineering due to the tehnial requirements for grid onnetion. In reent years, power fator (PF), voltage ollapse, unbalane, exessive harmonis, transients and osillations, have been a major onern in power transmission and distribution systems. Non-linear loads normally produe disturbanes in power transmission and distribution systems, ausing a high-level harmoni distortion in phase urrents and voltages. Moreover, reative loads produe a low PF, ausing an exessive reative power (VAR) restriting the maximum ative power transfer, adding losses to the power transmission and distribution systems affeting its stability and reliability [1]-[3]. Nowadays, several developments of flexible AC transmission system ontrollers, suh as VAR ompensators, have been suessfully implemented to overome the aforementioned drawbaks. In reent years, multilevel onverters have beome a popular alternative to overome the tehnologial restritions of the atual semiondutors devies that have limited power ratings [4]. Among all multilevel topologies, the asaded H-bridge (CHB) multilevel onverter is often onsidered as one of the most suitable onfiguration for highpower stati synhronous ompensator STATCOM, espeially useful for reative power ompensation []. CHB onverterbased STATCOM systems have been widely used in high-power appliations due to its inherent advantages, suh as: redued swithing losses, higher onversion effiieny, modular struture, salability to extended to more levels and higher number of redundant swithing states [6]-[8]. Furthermore, in terms of ontrol strategies, the CHB onverter topology inreases the degrees of freedom due to its modular feature whih allows it to impose an asymmetri ontrol approah. In the mentioned ontrol method ertain ells ould ompensate the PF assoiated with the fundamental frequeny and other ells ould ontrol the urrent harmoni distortion [9], [1]. The main ontribution of this paper omparing to previous works is fous on providing a bakground material about the finite-states model preditive ontrol with inreased predition horizon applied to a 7-level asade H-bridge multilevel STATCOM. This paper is organized as follows: Setion 2 desribes the threewire CHB multilevel STATCOM model. Setion 3 disusses the proposed finite-states model preditive ontrol tehnique with inreased predition horizon. Setion 4 disusses the simulation results and provides a omparative analysis with a onventional preditive ontrol tehnique. Finally, onluding remarks are summarized in Setion. 2. THREE-PHASE CHB STATCOM MODEL Fig. 1 (a) shows the proposed three-phase 7-level CHB onverter-based STATCOM topology, onsisting in three asade H-bridge ells per phase. The different H-bridge ells have an independent DC-link (C d ). Eah ell ontains four 1

2 Proeedings of The 2th World Multi-Conferene on Systemis, Cybernetis and Informatis (WMSCI 216) (a) (b) Fig. 1. Propose 7-level CHB onverter topology. (a) Three-phase 7-level CHB onverter-based STATCOM. (b) CHB onverter-based STATCOM onnetion. TABLE I ALLOWED COMBINATIONS OF ACTIVATION SIGNALS Sa 11 Sa 13 Sa 12 Sa 14 v a 1 1 +C d C d swithing devies, resulting in a total of 36 power swithes. Consequently, four swithing signals (S fij ) are needed in order to ontrol eah ell, where f represents the phase (a, b and ), i the ell number in the orresponding phase (1, 2 or 3) and j the swithing devie orresponding to the ell (1, 2, 3 or 4), respetively. Table I shows the allowed ombinations of ativation signals and the respetive output voltages orresponding to the Cell 1 of the phase a, where C d is the voltage of the apaitor. Similar allowed ombinations are defined for the other ells. Other possible ombinations are not permitted beause they ause a short iruit in the DC-link of the ell. To avoid this, only two ativation signals and they omplementary levels are used as shown in Fig. 1 (a) for the partiular ase of Cell 1. A. CHB onverter-based STATCOM model The dynami model of the iruit onfiguration shown in Fig. 1 (b) an be obtained by using Kirhhoff s iruit laws. For modeling purposes, it is assumed that the three-phase voltage soures are balaned and all modules have the same apaitane and voltage in their DC side. The CHB onverterbased STATCOM is onneted at the point of ommon oupling (PCC). Applying Kirhhoff s voltage law for the AC side of the STATCOM, the following equations are obtained: di ab dt = vab s dv ab d dt R f i ab ns f ij vd ab (1) = S f ij i ab vab d (2) C d R d C d where n is the number of ells, R d is a resistor onneted in parallel to the apaitor C d that onentrates the overall losses in the DC side and the resistor R f is the parasiti (series) resistane of the indutor. B. Finite-state preditive model For multilevel STATCOMs, the differential equation that models the AC side is [11]: di ab dt = vab s vab R f i ab. (3) The preditive model an be obtained by using a forward-euler disretization method from the ontinuous time-domain model represented by (3), whih provides the following equation: ( i ab [k+1] = 1 R ) f T { } s i ab [k] + Ts v ab s [k] v ab [k] where k identifies the atual disrete-time sample, T s is the sampling time, and i ab [k+1] is a predition of the STATCOM phase urrents made at sample k. However, if it is onsidered that the measured urrents and voltages at the beginning of the sampling time, whih are used in the ontrol loop, are not valid for the end of sampling time, when the miroontroller sends swithing states, due to a miroproessor alulation time delay and also to a fast dynami response of the system it is neessary to arry out a seond predition step as follow: ( i ab [k+2] = 1 R ) f T { } s i ab [k+1] + Ts v ab s [k+2] v ab [k+2] () where i ab [k+1] is alulated from (4) using measured STATCOM urrents (i ab [k]) and onsidering the onverter voltages (v ab [k]) seleted by the preditive ontrol in the previous sampling period assuming the ε = 2 2n voltage vetors, where n is the number of H-bridge ells per phase. If n = 3, sixty-four possible urrents (i ab [k+2]) are alulated using the possible voltage vetors v ab [k+2] per phase, whih an be applied in next sampling time. (4) 2

3 Proeedings of The 2th World Multi-Conferene on Systemis, Cybernetis and Informatis (WMSCI 216) Fig. 2. Blok diagram of the proposed ontrol sheme. 3. PROPOSED CONTROL TECHNIQUE Fig. 2 shows the blok diagram of the proposed finite-state model-based preditive ontrol tehnique applied to the threephase 7-level CHB onverter-based STATCOM system. In the proposed ontrol approah the predited errors are omputed for eah possible voltage vetor as: ei [k+2] = i ab [k+2] i ab [k+2] (6) being ei [k+2] the STATCOM urrent errors in the AC side. The ost funtion is evaluated sixty-four times by using an optimization proess. This ost funtion provides the ability to define different ontrol riteria inorporating another funtion objetives. The ost funtion has been typially defined as a quadrati measure of the predited error, whih an be defined as [12], [13]: A. Referenes generation g [k+2] = ei [k+2] 2. (7) The instantaneous ative and reative power referenes are obtained from the Clarke transformation approah in α β referene frame by using the following transformation matrix: T = (8) Applying (8), the α β urrent referenes in the AC side of the STATCOM are obtained from: [ i α i β ] [ 1 vsα v = sβ (v sα) 2 + (v sβ ) 2 v sβ v sα ] [ P where the supersript ( ) denotes the referene variables and P and Q are the instantaneous ative and reative power referenes, respetively. In order to allow an unitary power fator at the grid side and onsidering whih ideally the STATCOM do not absorb any ative power, the instantaneous power referenes an be written as: Q ] (9) P = (1) Q = Q L = v sαi Lβ v sβ i Lα (11) being Q L the instantaneous reative load power to be ompensate by the H-bridge onverter-based STATCOM system. The STATCOM phase urrents referenes used in the optimization proess are: i ab = T 1 [i α i β ] (12) where the supersript ( ) indiates the transposed matrix. B. Optimization proess The optimization is performed by exhaustive searh over all possible swithing vetors of the ontrol ation. Considering the sheme shown in Fig. 1 (a), where the number of H-bridge ells per phase (f {a, b, }) are three, then eah vetor S fij onsists in 2n hoie signals, where j {1, 2, 3}. During the optimization proess, both the ost funtion and the preditive model must be omputed 64 times at eah sampling period to guarantee optimality, sine there are 64 possible swithing vetors for the ase study. These swithing vetors represent all possible output voltages of the STATCOM, v a, v b and v, onneted at the PCC point. The output voltages an be represented by the following equation: v a v b v = v 1 v 2 v 3 v d (13) where v 1, v 2 and v 3 are the optimal levels of the three-phase 7-level CHB onverter-based STATCOM system ( 3, 2, 1,, 1, 2, 3). The first 1 swithing vetors for one phase (a) are shown in Table II. Finally, the optimization algorithm selets the optimum vetor S opt that minimizes the defined ost funtion represented by (7). Algorithm 1 summarizes the optimization proess. 4. SIMULATION RESULTS A MatLab/Simulink simulation environment has been developed to analyze the performane of the proposed preditive ontroller with inreased predition horizon tehnique applied to the 3

4 Proeedings of The 2th World Multi-Conferene on Systemis, Cybernetis and Informatis (WMSCI 216) TABLE II FIRST 1 SWITCHING VECTORS FOR A THREE-PHASE 7-LEVEL CHB CONVERTER-BASED STATCOM SYSTEM Sa 11 Sa 13 S aij Sa 21 Sa 23 Sa 31 Sa 33 η v Algorithm 1 Optimization algorithm 1. Initialize Jo a :=, Jo b :=, Jo :=, η := 2. Compute the STATCOM referene urrents (Eqn. 12) 3. Compute the first predition step (Eqn. 4) 4. while η ε do. S fij S η f ij i = 1, 2, 3 & j = 1, 2, 3 6. Compute the seond predition step (Eqn. ) 7. Compute the traking error (Eqn. 6) 8. Compute the ost funtion (Eqn. 7) 9. if J a < Jo a then 1. J a o J a, S opt a 11. end if 12. if J b < Jo b then 13. J b o J b, S opt b 14. end if 1. if J < Jo then 16. J o J, S opt 17. end if 18. η := η end while S aij S bij S ij 2. Apply the optimum vetor S opt {S opt a, S opt, S opt b } three-phase 7-level CHB onverter-based STATCOM system, onsidering the eletrial parameters shown in Table III. Numerial integration using Runge-Kutta method has been applied to ompute the evolution of the variables step by step in the time domain. The performane of the proposed finite-states model preditive ontrol method has been analyzed in terms of reative power ompensation as well as harmoni distortion onsidering a 4 khz of sampling frequeny, setting 114 V in the DC side as it is shown in Fig. 1 (a). Fig. 3 shows a simulation results performed in order to analyze the feasibility of the proposed ontrol tehnique under steady-state and transient onditions. Fig. 3 (upper) shows a step in the instantaneous reative power referene where it is possible to notie the effet of reative power ompensation. Moreover, Fig. 3 (middle), shows the traking urrent dynami performane for a step hange of the reative power referene. TABLE III PARAMETERS DESCRIPTION 7-Level CHB STATCOM PARAMETER SYMBOL VALUE UNIT Eletri frequeny of the grid f e Hz Voltage of the eletri grid v s 31.2 V Filter resistane R f.9 Ω Filter indutane 3 mh DC-link voltage v d 114 V Load parameters Load resistane R L 23.2 Ω Load indutane L L mh Preditive ontrol parameters Sampling time T s 2 µs Ative power referene P W Ideal Reative power referene Q Q L VAR, -, Fig. 3. CHB STATCOM transient response: (upper) reative power ompensation, (middle) traking urrent and (bottom) grid voltage and urrent. Finally, Fig. 3 (bottom) shows the effet of the grid urrent when the 7-level CHB STATCOM ompensates the reative power after t =.7 s. It an be observed from the simulation results that the phase of grid urrent represented in red olor, suddenly hanges to ompensate the reative power showing a fast dynami response during the transient. Next, in order to ompare quantitatively the proposed ontrol method with the onventional preditive ontrol tehnique the 4

5 Proeedings of The 2th World Multi-Conferene on Systemis, Cybernetis and Informatis (WMSCI 216) (a) (b) Fig. 4. Comparison performane onsidering: (upper) the grid urrent and (bottom) the THD of the grid urrent. (a) Seond predition step response. (b) First predition step response. mean squared error (MSE) and the total harmoni distortion (THD) are used as figures of merit. The equations are represented by (14) and (1), respetively: MSE(Ψ) = 1 N THD = 1 i 2 1 N Ψ 2 j (14) j=1 N i 2 i (1) i=2 where N is the number of vetor elements, i 1 is the amplitude of the fundamental frequeny of the analyzed urrent, and i i are the urrent harmonis. Fig. 4 shows a omparison analysis between the proposed seond predition step ontroller and the onventional first predition step ontroller onsidering; (upper) the grid urrent of the phase a and (bottom) the THD of the analyzed grid urrent. As shown in Fig. 4 (a) a better performane is obtained using the proposed seond predition step ontroller mainly in terms of lower THD when the delays are onsidered in the ontrol equations. This harateristi produes a well-defined disrete urrent spetra in ontrast with the onventional one step predition method. The improvement obtained in the THD performane parameter is about 6% (a drop from.16% to 1.82%) using the proposed method, onsidering the interval where the reative power is ompensated (after. s). Furthermore, the seond step preditive urrent ontrol loop is analyzed in more detail to quantify the improvements obtained using the proposed ontrol method in terms of MSE. Fig. shows the dynami response obtained when a step in the referene reative power (Q ) from 3, to -3, VAR at t =.2 s is applied. Under these operating onditions the obtained MSE performane parameters are also redued using the proposed method, from.9816 to.3224 whih represents an improvement of 67 %. As observed, from the simulation results, the urrent referene traking of the proposed method is very good, being even able to redue the harmoni distortion Fig.. CHB STATCOM urrent traking analysis: (upper) proposed method based on seond predition step and (bottom) onventional method. of the urrents without affeting the dynami response during the transient, whih is however very fast.. CONCLUSION In this paper an enhaned preditive urrent ontrol tehnique applied to the three-wire CHB multilevel onverters STATCOM has been proposed, analyzed and ompared with the onventional one step preditive ontrol approah. The simulation results onfirm the apability of the proposed ontrol tehnique to ompensate the instantaneous reative power and shows that it is possible inreased signifiantly the performane of the ontrol algorithm when is onsidered the miroproessor alulation time delay defining a seond step predition horizon.

6 Proeedings of The 2th World Multi-Conferene on Systemis, Cybernetis and Informatis (WMSCI 216) A omparative simulation results performed with referene to the onventional method show improvements in terms of total harmoni distortion as well as in terms of mean square error. Aknowledgment The authors would like to thank to the Paraguayan Government for the eonomial support provided by means of a CONACYT Grant projet 14-INV-96. In addition, they wish to express their gratitude to the anonymous reviewers for their helpful omments and suggestions. 6. REFERENCES [1] S. H. Jo, S. Son and J. W. Park, On Improving Distortion Power Quality Index in Distributed Power Grids, IEEE Trans. Smart Grid, vol. 4, no. 1, pp. 86 9, Mar [2] L. K. Haw, M. S. A. Dahidah and H. A. F. Almurib, A New Reative Current Referene Algorithm for the STATCOM System Based on Casaded Multilevel Inverters, IEEE Trans. Power Eletron., vol. 3, no. 7, pp , Jul. 21. [3] Y. Neyshabouri, H. Iman-Eini and M. Miranbeigi, State Feedbak Control Strategy and Voltage Balaning Sheme for a Transformerless STATi Synhronous COMpensator based on Casaded H- bridge Converter, IET Power Eletron., vol. 8, no. 6, pp , Jun. 21. [4] J. Muñoz, et al, Stati Compensators (STATCOMs) in Power Systems, Control of Multilevel STATCOMs, ISBN: , pp , 21. [] A. Marzoughi, Y. Neyshabouri and H. Imaneini, Control Sheme for Casaded H-bridge Converter-Based Distribution Network Stati Compensator, IET Power Eletron., vol. 7, no. 11, pp , Nov [6] C. D. Townsend, T. J. Summers and R. E. Betz, Phase-Shifted Carrier Modulation Tehniques for Casaded H-Bridge Multilevel Converters, IEEE Trans. Ind. Eletron., vol. 62, no. 11, pp , Nov. 21. [7] Y. Yu, G. Konstantinou, B. Hredzak and V. G. Agelidis, Operation of Casaded H-Bridge Multilevel Converters for Large-Sale Photovoltai Power Plants Under Bridge Failures, IEEE Trans. Ind. Eletron., vol. 62, no. 11, pp , Nov. 21. [8] G. Farivar, B. Hredzak and V. G. Agelidis, Deoupled Control System for Casaded H-Bridge Multilevel Converter Based STAT- COM, IEEE Trans. Ind. Eletron., vol. 63, no. 1, pp , Jan [9] X. Li, M. Su, Y. Sun, H. Dan and W. Xiong, Modulation Strategy Based on Mathematial Constrution for Matrix Converter Extending the Input Reative Power Range, IEEE Trans. Power Eletron., vol. 29, no. 2, pp , Feb [1] L. Sun, Z. Wu, F. Xiao, X. Cai and S. Wang, Suppression of Real Power Bak Flow of Nonregenerative Casaded H-Bridge Inverters Operating Under Faulty Conditions, IEEE Trans. Power Eletron., vol. 31, no. 7, pp , Jul [11] R. P. Aguilera, R. Baidya, P. Auna, S. Vazquez, T. Mouton and V. G. Agelidis, Model Preditive Control of Casaded H-Bridge Inverters based on a Fast-Optimization Algorithm, in Pro. IEEE IECON, Yokohama, Japan, 21, pp [12] R. P. Aguilera, P. Lezana, G. Konstantinou, P. Auna, B. Wu, S. Bernet and V. G. Agelidis, Closed-Loop SHE-PWM Tehnique for Power Converters Through Model Preditive Control, in Pro. IEEE IECON, Yokohama, Japan, 21, pp [13] R. P. Aguilera, Y. Yu, P. Auna, G. Konstantinou, C. D. Townsend, B. Wu and V. G. Agelidis, Preditive Control Algorithm to Ahieve Power Balane of Casaded H-Bridge Converter, in Pro. IEEE PRECEDE, Valparaiso, Chile, 21, pp