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A Novel Predictive Control Algorithm For Autonomous

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A Novel Predictive Control Algorithm For Autonomous
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  A Novel Predictive Control Algorithm For Autonomous Power Supply Systems Alexander G. Garganeev National Research Tomsk Polytechnic University, Tomsk, Russia E-mail: garganeev@rambler.ru Raef Aboelsaud Electrical Power & Machines Department, Faculty of Engineering, Zagazig University, Egypt National Research Tomsk Polytechnic University, Tomsk, Russia E-mail: aboelsaud@tpu.ru A. Ibrahim Electrical Power & Machines Department, Faculty of Engineering, Zagazig University, Egypt National Research Tomsk Polytechnic University, Tomsk, Russia E-mail: Ibragim@tpu.ru ABSTRACT A novel predictive control algorithm is proposed for predicting and regulating the load voltages of a four-leg inverter in an autonomous three-phase four-wire power supply system (APS). The control algorithm is developed to reduce the number of the mathematical operations required for the control system without affecting the control performance. The current information about the APS with its load voltages prediction is processed by using a discrete-time state space model. The simulation results show a good control performance in regulating the load voltages   , with fewer mathematical computations, under various load conditions   .   CCS Concepts   •  Applied computing Computer-aided design   Keywords Power supply system; model predictive control; autonomous inverte. 1.   INTRODUCTION  Nowadays, the autonomous power supply systems (APS) can effectively solve the problems in providing electrical power for remote areas. The advances of power electronics components, digital processing technologies make it possible to implement new  principles for the management of APS [1], [2]. APSs often operate in limiting conditions of input energy sources, as well as, they work with random nature of the loads which can be characterized by the number of phases and the degree of symmetry and nonlinearity. Unbalance and harmonic distortion of voltage can cause serious problems with the systems' equipment, such as vibration, overvoltage, overheating, etc [3], [4] . Load unbalances in the stand-alone four-wire systems can be handled by   the three-phase four-leg voltage source inverters (4-leg VSI) [1], [4]. In this topology, the neutral line is connected to the midpoint "n" between the transistor switches Sn, S'n in the fourth leg (see Fig. 1); this reduces the use of large and expensive dc link capacitors and provides a lower DC link voltage ripple in comparison with the other topologies.   To realize the benefits of 4-leg VSI scheme in APS, the Finite Control Set Model Predictive Control (FCS-MPC) can be employed which is recently considered as one of the most effective ways to control power electronics converters [5]  –  [9]. However, FCS-MPC   has no modulators and operates at a variable switching frequency. This method provides a fast dynamic response to the disturbing effect from the load side. Further tasks, such as minimizing switching frequency, spectrum formation and eliminating harmonics, can be solved by the controller algorithms. Moreover, the FCS-MPC concept is simple and provides an intuitive vision for  programming and implementation [10].   FCS-MPC gets the current information about the system by using the discrete-time model to predict the load voltages and then selects the switching state that minimizes the error between the  predicted voltage and reference voltage through the objective function estimation. Finally, the selected switching state is applied to the 4-leg VSI.   The model predictive control requires a large amount of calculations which are needed for predicting of variables changes and for control optimization. To implement predictive control in the "online" mode, a high-speed microprocessor is required which is currently available in the computer hardware market [11]   . In this paper, a new FCS-   MPC algorithm is proposed to decrease the number of calculations; this is resulting in reducing in the running time of the microprocessor software program used for digital implementation of the control system and at the same time shows very good static and dynamic control characteristics under different load conditions.   Permission to make digital or hard copies of all or part of this work for  personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to  post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Permissions@acm.org.  ICFET '18, June 25  –  27, 2018, Moscow, Russian Federation © 2018 Association for Computing Machinery. ACM ISBN 978-1-4503-6472- 0/18/06…$15.00   https://doi.org/10.1145/3233347.3233384 1 7    Figure 1. Three-phase APS containing 4-leg VSI with output LC filter 2.   SYSTEM   MODEL The three-phase APS consisting of 4-leg VSI with output LC-filter and loads is shown in Fig.1. The fourth leg is connected to the LC-filter and loads through a neutral inductor Ln which is used to minimize the ripple of the neutral current [2], [12]. The mathematical model of the APS is based on the relation  between switching states and output voltages. There are four control signals for the 4-leg VSI Sa, Sb, Sc and Sn [13]. These signals form a total of 24 = 16 possible switching states of the inverter. The switching states with the corresponding output line to neutral voltages are shown in Table 1. In the last two switching states, all upper or all lower switches are closed, the output phase voltages are equal to zero, providing zero vector states. The output voltages in accordance with the switching signals are described as follows: v an  = ( S  a   − S  n ) V  dc ,  (1) v  bn  = ( S   b   − S  n ) V  dc ,  (2) v cn  = ( S  c   −   S  n ) V  dc , (3) where Vdc is the input DC voltage. To simplify the analysis, the voltage and current vectors can be expressed as: v  = [ v an  v bn  v cn ] T  , (4) v o  = [ v oa  v ob  v oc ] T  , (5) i  = [ i a  i b  i c ] T ,  (6) i o  =[ i oa  i ob  i oc ] T  ,  (7) where v and vo are the vectors of the output inverter voltages and the load voltages, respectively, also i and io are the vectors of the output inverter currents and the load currents, respectively. Differential equations for the output LC filter in terms of voltage and current vectors are expressed as follows: v = L di/dt + v o  +L n  di n  /dt,   (8)   i = i o  + C dv o  /dt,  (9) i n  = i a  + i b  + i c .  (10) By solving (8) and (9), this model can be represented in a state space form as: o oo vv vd  A Bii idt                  , (11) where: 1 1eq eq6 6 6 6  0 I / C 0 I / C  A ,B L 0 L 0               , (12) eq 2 1 1 L 1 2 1 L1 1 2        , (13) where 0 and I are third-order zero and unit matrices, respectively. For the simplification, the inductances of the filter and the neutral line inductor are assumed to be equal (Ln = L). For performing a digital implementation, the discrete-time model of the system is required. Therefore, the discrete state space model can be extracted from the continuous state space model in (11) as follows: o oo v(k)v (k 1) v (k)Q J i (k)i(k 1) i(k)                  , (14) where Q  = e  ATs ,  J = A -1  (Q  –   I  6×6   ) B , T s  is the sampling time and k is the discrete sampling instant. 3.   PREDICTIVE   VOLTAGE   CONTROL   ALGORITHM The block diagram of the APS with the proposed predictive voltage control approach is shown in Fig. 2. The main concept of the FCS-MPC algorithm can be briefly described as follows [14]: the discrete state space model gives a complete presentation of the system to predict the load voltage vector for a one-step prediction time (k + 1), and then the objective function selects the best switching state according to the control objective. Finally, the selected switching state is applied to the 4-leg VSI switches. This algorithm is performed for each sampling period. The objective function can be defined as follows:   g = [v*(k+1)  –   v o (k+1)] 2   (15) where v*(k+1) is the extrapolated value of the reference voltage. The reduction in calculation time is based on the following considerations:      The switching states of 4-leg VSI are stored in a lookup table for the optimization function estimation. The two zero vector states (15th and 16th switching state in Table 1) can be considered as one combined zero vector state and the control algorithm selects between them randomly. Therefore, the control algorithm will require the calculation of 15 states instead of 16 for each sampling period as depicted in Fig. 3.   1 7 1  T ABLE 1.   S WITCHING S TATES O F 4- LEG VSI S a  S b  S c  S n   v  an  v  bn  v  cn   1 1000 V  dc 00 2 01000 V  dc 0 3 1100 V  dc V  dc 0 4 001000 V  dc 5 1010 V  dc 0 V  dc 6 01100 V  dc V  dc 7 1110 V  dc V  dc V  dc 8 0001 -V  dc -V  dc -V  dc 9 10010 -V  dc -V  dc 10 0101 -V  dc 0 -V  dc 11 110100 -V  dc 12 0011 -V  dc -V  dc 0 13 10110 -V  dc 0 14 0111 -V  dc 00 15 1111000 16 0000000   Figure 2. Block diagram of three-phase APS with the proposed FCS-MPC approach.    Because the sampling time Ts is very small, the reference voltage can be assumed to be constant through the sampling period. This assumption will eliminate the calculation time required for reference voltage extrapolation.      The load voltages and currents are assumed to  be measured by high-speed sensors. Thus, the estimation time of load current observation can be eliminated [15].   4.   SIMULATION   RESULTS   AND   CASE   STUDIES The simulation of the APS including the control algorithm is carried out in MATLAB/SIMULINK software. The parameters used in the simulation are shown in Table 2. The following two working cases are considered for demonstrating the proposed control algorithm. 4.1.   C ASE 1   Balanced loads are connected and then a step change of the loads is provided by connecting unbalanced loads after 0.2 seconds (see Fig. 4). The amplitude of the reference phase voltage is set at 310 V with a frequency of 50 Hz. The results show that the load voltages are symmetrical under load variations and very well track the reference voltages with low harmonic distortion - the total harmonic distortion (THD) is not more than 2.5%.   The control approach provides a fast dynamic response which is obvious at the moment of connecting the unbalanced load. The neutral current is zero in the case of a balanced load and starts to flow in the neutral line in the condition of unbalanced load connection. The DC-link capacitor voltage has low ripple level which begins increase with the unbalanced load connection with a  percentage ripple not exceeding 2%. Figure 3. Flowchart of the proposed control algorithm. 1 7    Figure 4. Load voltages, load currents, neutral current and DС -link capacitor voltage of APS in case 1.   Figure 5. Load voltages, load currents, neutral current and DC-link capacitor voltage of APS in case 2. 1 7  4.1.   C ASE 2 Unbalanced nonlinear loads are connected to the system which can be considered as three different nonlinear single phase loads as shown in Fig. 6. Load voltages, load currents, neutral current and DC-link voltage of the inverter are shown in Fig. 5. Due to the nonlinearity of the load, the neutral current is substantially non-sinusoidal and circulates through the fourth wire of the APS. At the same time, the load voltage of the APS remains sinusoidal and symmetrical with a good tracking of the reference voltage. The voltage harmonic distortion of the load is within the permissible limits, not exceeding 4%. Although the system operates under nonlinear and unbalanced load conditions, the proposed control approach provides small percentage ripple in DC-   link voltage.   TABLE I. S YSTEM P ARAMETERS   Parameters Values DC input voltage of the inverter V  dc  = 640 V Sampling time T   s  = 20 µs DC-link capacitance C dc  = 1000 µF LC filter L = 2.5 mH, C= 80 µF Balanced loads R  a  = R   b  = R  c  = 20 ohm Unbalanced loads R  a = 7 ohm, R   b  = 15 ohm, R  c   = ∞, L a  = 10 mH, L  b  = 30 mH Unbalanced nonlinear loads L a ' = 50 mH, R  a '=20 ohm, R   b 1'=1 ohm, R   b 2'=60 ohm, C  b '=3000 µF, L c '= 20 mH, R  c '=70 ohm, C c '= 5000 µF Figure 6. Topology of the three-phase nonlinear unbalanced loads. 4.   CONCLUSION The FCS-MPC approach is used to control the load voltages of 4-leg VSI with LC filter in APS. The control algorithm is developed to reduce the calculation time required for the digital implementation of the control system by decreasing the number of the mathematical operations while providing high control  performance. The analysis results show that the proposed control algorithm provides high load voltages quality in the APS with low DC-link voltage ripple in the inverter when operating under linear, nonlinear and unbalanced load conditions. Furthermore, the control performance shows good static and dynamic responses with load variations. 5.   REFERENCES [1]   M. R. Miveh, M. F. Rahmat, A. A. Ghadimi, and M. W. Mustafa, “Control techniques for three -phase four-leg voltage source inverters in autonomous microgrids: A review,” Renew. Sustain. Energy Rev., vol. 54, pp. 1592–  1610, 2016.   [2]   S. Haritonov , “Electromagnetic processes in systems of electric power generation for autonomous objects,”  Novosib. Izd. NGTU   , p. 536, 2011.   [3]   F. Shahnia, R. Majumder, A. Ghosh, G. Ledwich, and F. Zare, “Operation and control of a hybrid microgrid containing unbalanced and nonlinear loads,” Electr. Power Syst. Res., vol. 80, no. 8, pp. 954  –  965, 2010.   [4]   G. Zinovev, “Fundamentals of power electronics,” Novosib. Izd. NGTU   , p. 664, 2003.   [5]   R. T. Shrejner, A.A. Efimov, and I. A. Muhamatshin, “Predicts relay -active frequency converter vector control in AC electric drive systems,” Jelektrotehnika, vol. 10, pp. 43–  50, 2004.   [6]   A. A. Efimov, V. D. Kosulin, and S. V. Mel’nikov, “Predicts relay- vector control active current converters,” Information-control Syst., no. 4, pp. 48  –  53, 2014.   [7]   Diab A.A.Z., Kotin D.A., and Pankratov V.V., “   Direct vector control asynchronous electromotor using prediction mod els,” Vestn. Dona, vol. 1, no. 28, pp. 1  –  8, 2014.   [8]   A. A.Z. Diab, “Vector control of asynchronous electromotor  based on  prediction models,” Avtoreferat kand.  Nauk. Novosib., p. 20, 2009.   [9]   S. Bayhan, M. Trabelsi, H. Abu-Rub, and M. Malinowski, “Finite -control-set model-predictive control for a quasi-   z-source four- leg inverter under unbalanced load condition,” IEEE Trans. Ind. Electron., vol. 64, no. 4, pp. 2560  –  2569, 2017.   [10]   S. Kouro, P. Cortes, R. Vargas, U. Ammann, and J. Rodriguez, “Model predictive control a simple and  powerful method to control power converters,” Ind. Electron. IEEE Trans., vol. 56, no. 6, pp. 1826  –  1838, 2009.   [11]   S. Vazquez, J. Leon, and L. Franquelo, J. Rodriguez, H Young, A. Marquez and P. Zanchetta, “Model  predictive control: a review of its applications in power electronics,”  IEEE Ind. Electron. Mag.,  vol. 8, no. 1, pp. 16  –  31, 2014.   1 7
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