________________________________________________________________________________________________
________________________________________________________________________________________________
Modeling and Simulation MPC-DSTATCOM for Power Quality Improvement
G GOPAL
EEE Department MGIT, Hyderabad, Telangana State, India Abstract :-In this paper, a novel model predictive current
control strategy is proposed for DSTATCOM to improve the power quality in distribution system. Unlike classical control schemes, the proposed method neither requires current PI controllers nor modulators at switching signal generation stage. The discrete-time model of the converter, filter and terminal voltage are used to predict the future behavior of the compensating currents for each of the eight possible switching states. The control method decides a switching state in which the actual currents are closer to their references. In this first part, proposed method is verified through extensive simulation in Matlab platform and a comparative analysis is made with HCC and SMC current control schemes. It has been found that total harmonic distortion of load compensation is well within the allowable range of IEEE standards with achievement of unit power factor.
Keywords—finite control set (FCS); model predictive control (MPC); Distribution Static Compensator; Power quality
I. INTRODUCTION
In recent decades due to proliferation of non-linear loads such as switched mode power supply (SMPS), Rectifiers, Adjustable speed drives(ASDs), Computers, Printers, Arc furnaces are the prime source of harmonic distortion which cause power quality (PQ) problems in power distribution network[1][2]. Load compensation which can solve the PQ problems like harmonic elimination and reactive power compensation.
Distribution Static Compensator ( DSTAT-COM) [3]
has been proved to be a suitable custom power device, which can eliminate harmonics and compensate reactive power in distribution network, is based on Power converter, suitable control strategy (reference generation) and current control schemes(current controller). Authors have already proposed a novel control strategy which is best suitable for distorted utility condition [4][5].In literature it has been found that hysteresis current control (HCC) and linear PWM(LPWM) current control schemes are well established for control of power converters [6][7].
However, in real time platform the implementation of new complex algorithms are possible due to evolution of powerful microprocessors and microcontrollers such as
fuzzy logic, sliding mode control (SMC), and model predictive control (MPC). Fuzzy logic is suitable for applications where the controlled system or some of its parameters are unknown. Sliding mode presents robustness and takes into account the switching nature of the power converters.
Model Predictive control [8]-[10] offers several advantages such as 1) No modulation 2) Direct digital implementation 3) Inclusion of constraints directly in the cost function 4) Switching frequency is controllable 5) Application to a variety of systems 6) Inclusion of Nonlinearities 7) Consideration of multivariable case. It has been implemented successfully in various fields like current control [11]-[13],torque and flux control[14], control of NPC converter[15],matrix converter[16] and flying capacitor converter[17]. However, due to availability of high speed microprocessors and microcontrollers today make it possible of MPC implementation in spite of its high computation time as compared to classical current control schemes.
In this paper performance of proposed FCS-MPC current control scheme is investigated in three phase three wire system for balanced/distorted source and non- linear balanced /unbalanced Load for mitigation of harmonics and compensation of reactive power which defines the problem statement. The measure of the performance is the source current total harmonic distortion.
Rest of the paper is organized as follows. In section II system configuration and in section III brief discussion on proposed reference generation strategy are presented.
In section IV classical control techniques and in section V real-time model, flow-graph of FCS-MPC controller are presented. In section VI the performance indices used for evaluation are discussed. Simulation results are described in section VII. Finally in section VIII, conclusion is drawn.
II. SYSTEM CONFIGURATION
Fig.1 shows the basic circuit diagram of a DSTATCOM [3] system with non-linear load connected to three phase three wire distribution system. A nonlinear load is
________________________________________________________________________________________________
realized by using a three phase full bridge diode rectifier. A three phase voltage source converter (VSC) working as a DSTATCOM is realized using six insulated gate bipolar transistors (IGBTs) with anti- parallel diodes. At ac side, the interfacing inductors are used to filter high frequency components of compensating currents. The MPC (model predictive control) controller is used to generate switching signals by prediction algorithm without use of any modulator as in classical technique like linear PWM, deadbeat current control scheme.
Fig.1 system configuration of DSTATCOM
III. REFERENCE GENERATION
The reference compensating current is equal to the difference between estimated source and load current.Fig.2 shows the control structure of reference generation. The peak source current is estimated as
Prime objective is to make source current balanced.
Let formulate all powers in time domain. Zero sequence, positive sequence and Negative sequence complex power are denoted as s0, s+ and s- . The real power of zero sequence, positive sequence and Negative sequence are denoted as p0,p+ and p-. The Imaginary power of zero sequence, positive sequence and Negative sequence are denoted as q0,q+ and q -.The instantaneous voltage and current of zero sequence ,positive sequence and Negative sequence are denoted as v0,v+ ,v- and i0,i+,i- respectively. Let zero sequence power is formulated as
Let calculate the positive sequence power.
Let calculate the negative sequence power.
where x = a, b, c and Ux1 is fundamental unit vector template.
In equation (4) putting ia+ib+ic=0 , We get
where x = a, b, c and Ux1 is fundamental unit vector template.
Fig.2 Control structure of proposed controller Fig.2 shows the basic control structure of proposed control strategy which constitutes one positive sequence detector; low pass filters (LPF1 and LPF2) and arithmetic calculators. The average power plav is obtained by filtering instantaneous power Pinst through
________________________________________________________________________________________________
LPF2. LPF1 is used to extract the fundamental from distorted PCC (point of common coupling) voltage.
IV. CLASSICAL CURRENT CONTROL TECHNIQUES
A. Hysteresis current control (HCC)
In this control strategy actual compensating currents are compared with reference compensating currents to determine the switching state of each leg. For implementation point of view this method requires simple circuit. The performance is good with fast dynamic response. Due to change in load parameters and operating conditions the switching frequency can be varied which is the major drawback of this controller.
Due to its resonance problem, high switching loss it is unacceptable in lower power level application.
B. Sliding mode control (SMC)
The sliding mode controller [18] maintains the system on sliding surface(s) so that actual compensating currents move closer to reference compensating currents. There are three steps required to design SMC 1) proposing a sliding surface, 2) verifying SMC existence and 3) analyzing stability into surface. Sliding surface is chosen in such a way that the control feature is to maintain system within surface. In order to guarantee the sliding mode existence ss <0, must be fulfilled and this fact guarantees the attraction of the system to surface. This controller has been widely applied to power converter due to its fastness, robustness and stability and takes into account the switching nature of the power converters. The sliding surface sx and switching signals gx can be formulated by the following equations.
where x = phase a, b and c respectively.
V FCS-MPC CONTROLLER
MPC, also referred to as receding horizon control, is so- called advanced control technique as compared to classical like PI, hysteresis and sliding mode control which has been implemented successfully in practical applications in recent decades. An attractive feature of MPC is that it can handle general constrained nonlinear systems with multiple inputs and outputs in a unified and clear manner. In this section, we will focus on FCS- MPC formulations, flow-graph and predictive model which control the states of the converter switches directly, i.e., without any intermediate modulators.
A. FCS-MPC Model
The proposed control model is based on finite number of switching states as show in Fig.3. The model of system is used to predict the behavior of switching variables of each state. A cost function q is used to optimize and select a state which is having minimum error. This state is applied to converter at same instant.
Fig.3 Predictive control model structure.
B. Converter Model
The switching states of the converter in fig.4 are determined by the gating signals ga, gb and gc as follows.
Fig.4 Power circuit of VSC
The switching variable ga, gb and gc can be expressed in vectorial form as
Where a = ej2π/ 3 and m1=2/3
The voltage space vector of converter can be defined as
________________________________________________________________________________________________
C. Discrete time model
A power circuit describing the source current model is presented in fig.4. Here vf is the voltage applied by the inverter and vt is the pcc voltage, i f is the compensating current through the filter inductance and resistance Lf and Rf, respectively.
By using indirect control technique a discrete-time form of source current for a sampling time Ts can predict the future value with measured pcc (point of common coupling) voltage and inverter voltage at the kth sample instant is as follows.
Seven possible voltage vectors results seven compensating current prediction. The voltage vector whose current prediction is closer to reference compensating current is applied by inverter. The voltage vector can be selected by use of the following cost function.
As the future value of reference current is unknown, it can be estimated by using Lagrange second order extrapolation which is estimated as follows
D. Algorithm & Flow Graph
The algorithm of model predictive controller illustrated in following steps and described in flow graph in fig.5.
• Apply the new switching state.
• Measure compensating current if , Vdc and terminal voltage vt and load current iL.
• Calculate the all seven possible vectors of VSC.
• Predict the compensating current .
• Estimate future reference current at next sample instant Ts.
• Apply optimization technique using cost function q.
• Select the g(iop) for which measured compensating current is closer to reference current.
Switching signals are generated from seven possible finite control state to drive the IGBTs in the VSC. The future source currents are predicted for each voltage vector. The cost function is evaluated for each prediction of source current. The index of the voltage vector that minimizes the cost function is stored. At the beginning of the next sampling period, the index value is used to read the table of switching states and generate the corresponding gate signals for the IGBTs.
Fig.5 Flow graph of proposed algorithm E. Real Time model
Fig.6 shows the real time model which has been developed in Matlab/Simulink software. This model consists of i*sv1, isv, vfv, vtv and predictive model &
optimization blocks to generate switching signals for voltage source inverter(VSI). The future reference current is generated through i*sv1 block by using Lagrange second order extrapolation (13) and converted to vector form with help of Clarke transformation. The actual source current vector is calculated from measured load current iL and compensating current if . Seven space vectors have been generated in vfv block by using measured DC-link voltage and switching vector gv. The terminal voltage and actual source current are converted to vector form by using Clarke transformation in vtv and isv block respectively. The Predictive model (10) and optimization algorithm (12) is implemented through embedded Matlab function in predictive and optimization block which can work in real time platform e.g. OPAL RT lab(Real Time Simulator).
________________________________________________________________________________________________
VI. PERFORMANCE INDICES
A. Total harmonic distortion
The total harmonic distortion (THD) [19] is used to define the effect of harmonics on the power system voltage. It is used in low-voltage, medium-voltage, and high-voltage systems. It is expressed as a percent of the fundamental and is defined as
Fig.6 MPC real-time model
According to IEEE-519 the permissible limit for distortion in the signal is 5%.
VII. RESULTS AND DISCUSSION
To investigate the performance of the DSTATCOM for proposed controller, simulations are performed on matlab platform. A three phase three wire distribution system with parameters given below is considered for simulation.
A. System Parameters:
Supply voltage: 50Vrms (L-N), 50Hz, three phase balanced
Source side line impedance: Rs=1Ω, Ls=5mH
Nonlinear load: Three phase full bridge diode rectifier with load ( LL=50mH,RL=20Ω),
DC-link storage Capacitor Cdc=2000μF Interface inductor Lf=5mH, Rf =1Ω DC Link voltage Vdc=115V
Unbalanced Linear load: Za=67+j31.42Ω ,Zb=37+j18.55Ω, Zc=28.5+j12.56Ω
Low pass butter-worth filter LPF1and LPF2:Cut-off frequency fc1=100Hz, fc2=25Hz, Sampling frequency fs=20kHz, Order-4th (2xsecond order section),
Structure: Direct form-II.MPC parameters C1=0.9900, C2=0.0100
B. Different cases
The performance of the proposed controller is evaluated based on three different cases.
Case1- Balanced Source and balanced Non-Linear load Case2- Balanced Source and Unbalanced Non-linear load.
Case3- Balanced distorted Source and Unbalanced Nonlinear load.
In case 1 the source is assumed to be sinusoidal and balanced whereas the load is considered as non- sinusoidal and balanced. Before compensation the THD of Source current is found to be 23.0553%. After compensation the THD of Source current for phase-a is listed in the Table1. In case 2 the source is balanced and sinusoidal but the load is unbalanced non –sinusoidal (Source current harmonic is found to be 20.8911%
before compensation) .The THD of the Source current for phase-a after compensation is summarized in Table1.
In case 3 the source is balanced and distorted (distorted voltage source harmonic is 11.6034%) but the load is unbalanced non sinusoidal (Source current harmonic is found to be 20.8911% before compensation). The THD of the Source current for phase-a after compensation is summarized in Table 1.
C. Case 3 – Simulation of Proposed MPC controller
________________________________________________________________________________________________
Fig. 7. (a) Three phase unbalanced Load current; (b) Distorted pcc voltage of phase-a; (c) DC link voltage;
(d) Three phase Source current after compensation; (e) Compensating current of phase-a; (f) Compensating current of phase-a; (g) Harmonics of Source current before compensation of phase-a and (h) Harmonics of
Source current after compensation of phase-a.
Fig.7 (a, b, c, d, e, f, g and h) shows the dynamic performance of the system.
D. Analysis
From the Table1 it has been found that performance of MPC controller is better than classical HCC and SMC current control scheme for harmonic mitigation and reactive power compensation. PI controller and modulator are not required for MPC controller to stabilize the DC-link voltage and generate the switching signals respectively.
TABLE I. Comparative Analysis of source current THD(% ) after compensation
VIII. CONCLUSION
This algorithm does not need internal current controllers and modulation stages. In all cases it is observed that proposed MPC controller is working fine and able to compensate the non-linear balanced/ unbalanced load successfully. The THD obtained here are within the limit of 5% prescribed by IEEE 519 standard.
REFERENCES
[1] Rosa, Francisco C. De La, “Harmonics and Power Systems,” NewYork, Taylor & Francis Group, LLC, 2006.
[2] H. Akagi, E. H. Watanabe, and M. Aredes,”
Instantaneous Power Theory and Applications to Power Conditioning”, Hoboken, NJ: Wiley, 2007.
[3] A Moreno-Munoz,”Power Quality: Mitigation Technologies in a Distributed Environment”.
London, U. K.: Springer-Verlag, 2007.
[4] G. Sahu,K. Mahapatra ,”Real time implementation of digital filter on control strategy of DSTATCOM for load compensation under distorted utility condition.”in Proc IEEE Conf. PrimeAsia, pp.164- 169,2013.
[5] Gokulananda Sahu,Kamalakanta Mahapatra”A novel control strategy of DSTATCOM for load compensation under distorted utility condition”,in Proc.IEEE conf. ICAEE,pp.1-6,2014.
[6] M. P. Kazmierkowski, R. Krishnan, and F.
Blaabjerg, Control in Power Electronics. New York: Academic, 2002.
[7] N. Mohan, T. M. Undeland, and W. P. Robbins, Power Electronics,2nd ed. Hoboken, NJ: Wiley, 1995.
[8] Linder and R. Kennel, “Model predictive control for electrical drives,”in Proc. IEEE PESC, Recife, Brazil, 2005, pp. 1793–1799.
[9] P. Cortés, J. Rodríguez, D. E. Quevedo, and C.
Silva, “Predictive current control strategy with imposed load current spectrum,” IEEE Trans.
Power Electron., vol. 23, no. 2, pp. 612–618, Mar. 2008.
[10] P. Antoniewicz and M. P. Kazmierkowski,
“Predictive direct power control of three-phase boost rectifier,” Bull. Pol. Acad. Sci., vol. 54, no.
3,pp.287–292, 2006.
[11] J. Rodríguez, J. Pontt, C. Silva, M. Salgado, S.
Rees, U. mmann,P. Lezana, R. Huerta, and P.
Cortés, “Predictive control of a threephase inverter,” Electron. Lett., vol. 40, no. 9, pp. 561–
562, Apr. 29, 2004.
[12] J. Rodriguez, J. Pontt, C. Silva, P. Cortes, U.
Amman, and S.Rees,“Predictive current control of a voltage source inverter,” in Proc. IEEE35th Annu. PESC, Jun. 2004, vol. 3, pp. 2192–2196.
[13] J. Rodríguez, J. Pontt, C. Silva, P. Correa, P.
Lezana, P. Cortés, and U. Ammann, “Predictive current control of a voltage source inverter,”IEEE Trans. Ind. Electron., vol. 54, no. 1, pp. 495–503, Feb. 2007.
[14] J. Rodríguez, J. Pontt, C. Silva, P. Cortés, S.
Rees, and U. Ammann,“Predictive direct torque control of an induction machine,” in Proc. 11th Int. EPE-PEMC, Riga, Latvia, Sep. 2–4, 2004.
________________________________________________________________________________________________
[15] R. Vargas, P. Cortes, U. Ammann, J. Rodriguez, and J. Pontt, “Predictive control of a three-phase neutral-point-clamped inverter,” IEEE Trans.
Ind.Electron., vol. 54, no. 5, pp. 2697–2705, Oct.
2007.
[16] S. Muller, U. Ammann, and S. Rees, “New time- discrete modulation scheme for matrix converters,” IEEE Trans. Ind. Electron., vol. 52, no. 6,pp. 1607–1615, Dec. 2005.
[17] E. I. Silva, B. P. McGrath, D. E. Quevedo, and G.
C. Goodwin, “Predictive control of a flying capacitor converter,” in Proc. Amer. Control Conf.,New York, Jul. 2007, pp. 3763–3768.
[18] Saetieo, S., Devaraj, R., and Torrey, D. A., “The design and implementation of a three phase
active power filter based on sliding mode control,” IEEE Trans. Ind. Appl., Vol. 31, No.
5,pp. 993–1000, September 1995.
[19] IEEE Recommended Practices and Requirements /or Harmonic Control in Electrical Power Systems, IEEE Standard 519, 1992.
[20] Gokulananda Sahu, Kamalakanta Mahapatra
“Model Predictive Control of DSTATCOM for Power Quality Improvement: Modeling, Simulation and Analysis-Part1” 2015 IEEE Power, Communication and Information Technology Conference (PCITC) Siksha „O‟
Anusandhan University, Bhubaneswar, India.
978-1-4799-7455-9/15/$31.00 ©2015 IEEE
