Instruction FACTA UNIVERSITATIS Series: Electronics and Energetics Vol. 33, N o 3, September 2020, pp. 429-444 https://doi.org/10.2298/FUEE2003429T © 2020 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND TECHNIQUE OF CONTROL PMSM POWERED BY PV PANEL USING PREDICTIVE CONTROLLER OF DTC-SVM Fadila Tahiri, Abdelkader Harrouz, Djamel Belatrache, Fatiha Bekraoui, Ouledali Omar, Ibrahim Boussaid Department of Hydrocarbon and Renewable Energy, Laboratory LDDI, University of Ahmed Draya, Adrar, Algeria Abstract. The present paper is a part of the study of Direct Torque Control based (DTC) on space vector modulation using predictive controller (Predictive SVM) of a permanent magnet synchronous motor (PMSM) powered by a photovoltaic (PV) source. In the conventional direct torque control (DTC) of a permanent magnet synchronous motor (PMSM), hysteresis controllers are used to choose the proper voltage vector resulting in large torque ripples. The direct torque control can accelerate the torque responses but increases the torque ripple at same time. Nowadays, exist some other alternative approaches to reduce the torque ripples based on (Predictive SVM) technique. This method is based on the replacement of hysteresis comparators (used in conventional DTC) by Proportional Integral (PI) regulators and the selection table by space vector modulation (SVM). The simulation results confirm that this proposed method where the control of the switching frequency is well controlled, allows us to reduce the oscillations of the electromagnetic torque and flux by 20 % and 30%, respectively with a good dynamic response compared with conventional DTC. Key words: photovoltaic, PMSM, DTC, DTC-SVM, predictive controller. NOMENCLATURE I0 Reverse saturation current of the diode (A) I0r Reverse saturation current K Constant of Boltzmann (1.38.10-23J / K) q Charge of the electron (1.6.10-19C) a p-n junction ideality factor EG Band gap G, Gr Real and reference solar radiation Icc Short-circuit current s v , sv sI , sI s , s Current, voltage and magnetic flux of stator (α,β)axes Received December 31, 2019; received in revised form May 17, 2020 Corresponding author: Abdelkader Harrouz Department of Renewable Energy and Hydrocarbon, Faculty of Technology and Sciences, Ahmed Draïa University - Adrar, Algeria E-mail: harrouz.onml@gmail.com 430 F. TAHIRI, A. HARROUZ, D. BELATRACHE, F. BEKRAOUI, O. OMAR, I. BOUSSAID  The speed of rotation of the machine (rotor)(rad/s) f  Permanent magnet flux linkage (web) Rs The stator resistance (Ω) Ls The inductance of the stator(H) J Moment of inertia f Coefficient of friction P Number of pairs of poles cba V ,, , cbaI ,, Three-phase voltage and current 1. INTRODUCTION The demand for electrical energy increases daily to cover human needs; the use of renewable energy is becoming the key solution to this serious energy crisis and environmental pollution [1]. Algeria has great potential from solar energy, because it has a vast desert area and very high solar radiation [2-3]. For this reason, the optimal solution to energy production in our study is solar energy [4]. In the field of variable speed, the permanent magnet synchronous machine are extensively accepted due to their high efficiency, high power density, high precision, low maintenance costs, simple structure, and its high torque density [5-6]. Among the most used applications for the permanent magnet synchronous motor (PMSM) are drones, portable robots, and vacuum pumps for decades of diversity and performance. Especially in electric and hybrid cars [7]. Vector controlled PMSM drive provides better dynamic response and lesser torque ripples, and necessitates only a constant switching frequency [8]. PMSM modeling has been tackled in the literature in various ways, commonly using a transition of the electrical component from the physical 3-phase structure to an equivalent 2-phase right-angled structure, enabled by the Clark Transformation [9]. Due to the presence of external disturbances and parameter variation in PMSM over the past decades, performance has been improved by developing various powerful control technologies. [10] However, the widely used approach consists in using linear control theory with the disturbance estimate [11]. It is therefore interesting to find a way to make their independent control to improve their performance. The most suitable solution now is direct torque control (DTC). This method has been first proposed for induction machines [7-12]. It is used in variable frequency drives where the stator flux and machine electromagnetic torque are directly used to generate the control pulses for voltage- source inverter through a predefined switching table [13], DTC owns the advantages of simplicity, quick dynamic response and robustness, which makes it a powerful motor control method in various applications [14]. However, it is known that DTC is troubled by the disadvantages of large torque/flux ripples and unstable switching frequency [15], which hinders its practiitcal applications. In order to tackle the problems associated with conventional DTC, lots of modified DTC methods are proposed to improve the control performance [16]. Abdelkarim Ammar et al [17], are present the space vector modulation (SVM) based Direct Torque Control strategy (DTC) for induction motor (IM) in order to overcome the drawbacks of the classical DTC. Moreover, they proposed model based loss minimization strategy for efficiency optimization, the proposed SVM-DTC algorithm was investigated by using Matlab/ Simulink with real time interface based on dSpace 1104 signal card. The simulation and experimental validation gives similar results, they showed Direct Torque Control (DTC) SVM Predictive of a PMSM Powered by Photovoltaic Source 431 that LMC reduces losses, improved efficiency at zero and low loads operation. Therefore, DTC-SVM it’s a good solution in general to overcome the drawbacks of classical DTC. A comprehensive review has been provided by R H Kumar et al [18] of recent advancements of DTC of induction motor (IM) for the past one decade. Strategies adopted to improve the performance of DTC based on switching table, constant switching frequency operation, intelligent control, sensor less control and predictive control are extensively discussed with its key results and algorithms. The simulation results of DTC Predictive show a reduction in torque and stator flux ripples by 14.94 and 23%, respectively, compared with conventional DTC drive. In this paper, we use the control Predictive DTC-SVM applied to Permanent Magnet Synchronous Motor, to obtain a constant switching frequency after it was variable in conventional DTC (because of the use of hysteresis comparators) and minimize the ripple of torque and flux. This method of control (Predictive DTC-SVM) is based on the replacement of hysteresis comparators (used in conventional DTC) [17] by Proportional Integral (PI) regulators and the selection table by space vector modulation (SVM).[21] 2. MODELING SYSTEM 2.1. Photovoltaic System The solar cells are generally connected in series and in parallel, in parallel with Nph cells to increase the current and in series with Nsh cells to increase the voltage then increase the PV power. A PV generator is made up of interconnected modules to form a unit producing high continuous power compatible with conventional electrical equipment [19]. The used model is shown in Figure.1, which consists of four components: a current generator Iph, a diode, a parallel resistance Rsh and a serial resistance Rse [20]. Fig. 1 Equivalent diagram of a photovoltaic cell. The output current is given by the following equation [22]: sh sh s sepv sh s pv s sepv sh s pv 0shphshPV R N N R I N N V 1 akTn R I N N Vq exp IN-IN=I                                         (1) 432 F. TAHIRI, A. HARROUZ, D. BELATRACHE, F. BEKRAOUI, O. OMAR, I. BOUSSAID Where, the cell reverse saturation current is related to the temperature (T) as follows                     T 1 298 1 ka qE exp T T I=I G 3 r 0r0 (2) Similarly, the photocurrent Iph depends on the solar radiation (G) and the cell temperature (T) [21]: ) G G (I=I r ccph (3) 2.2. Model of PMSM Accounting for the hypothesis commonly considered in AC machine modelling, the electrical equations of the PMSM in a (α, β) reference frame, are                        dt d TfIPIP dt d J dt dI LIRv dt dI LIRv rsfsf f s ssss f s ssss .cos...sin.. cos.. sin... (4) The electromagnetic torque Te is given from [23, 38]: e s 3 T p( ) 2 s s S I I        (5) 2.2.1. Simulation and interpretation In the first step, we use a simulation of the (PMSM) operation in the reference frame (α, β) powered directly by 50v, 50Hz network. The software used in this simulation is MATLAB / SIMULINK. We see in (Figure 2.a) that the space of speed reaches the steady state very quickly with an acceptable response time. After applying the load at the moment (0.3s - 0.4s) we found that the speed decreases and then returns to its reference value. The torque peaks at the first start moment, then reaches his value when the speed decreases (under load) and is proportional to the current. (Figure 2.d) shows the temporal evolution of the stator flux, which has a disturbed sinusoidal shape. Direct Torque Control (DTC) SVM Predictive of a PMSM Powered by Photovoltaic Source 433 Fig. 2 The variation with time: (a) Speed variation, (b) Torque variation, (c) Current variation, (d) Flux variation. 3. DIRECT TORQUE CONTROL OF PMSM The block scheme of the investigated direct torque control (DTC) for a voltage source inverter fed PMSM is presented in Figure.3 Fig. 3 General structure of the DTC. 434 F. TAHIRI, A. HARROUZ, D. BELATRACHE, F. BEKRAOUI, O. OMAR, I. BOUSSAID The direct torque control of a permanent magnet synchronous machine is based on direct determination of the control sequence to be applied to a voltage inverter [24]. The switching states is selected from the two comparator output (error) of both torque and flux, where the estimated values of torque and flux are compared with the reference values and depending upon the hysteresis comparator error, the result may increase or decreases [25]. The estimation of reference torque, flux and position of flux vector is done by using machine input voltages and currents as shown in Figure.3 [26] The stator electric equations of the PMSM, in a (α, β) reference frame are given by [27]: s s 3 I . 2 1 ( ) 2 I . sa S sb sc s S I I I I I j I                 (6) The stator voltage: s s 3 1 3 1 v . ( ) . ( ) 2 2 2 2 1 1 ( ) ( ) 2 2 V . a b c dc a b c S b c dc b c s S V V V U S S S V V V U S S V j V                                   (7) Two-level inverter is capable of producing six non-zero voltage vectors and two zero vectors. Figure.4. shows the complex plane of the eight voltage vectors [28] Fig. 4 Different vectors of stator voltages provided by a two levels inverter. Direct Torque Control (DTC) SVM Predictive of a PMSM Powered by Photovoltaic Source 435 Table 1 shows the switching states to select a suitable V for selecting the switches in the inverter. This voltage sector is generated from the two-comparator output (error) of both torque and flux [25]. The switching table receives 6 active and 2 zero vector from the comparator output and generates 8 possible switching vector for the inverter [27, 29]. DTC select the active voltage switching vector states for doubling the sampling period and select an appropriate V[30]. Table 1 Switching table for DTC 6sector[29]. The conventional DTC control is more robust compared against the conventional methods (field-oriented control for example). It does not require a mechanical measurement such as that the speed or position of the machine, moreover the sensitivity to the parameters of the machine is clearly attenuated in the case of DTC, since the flux is made according to a single parameter namely the stator resistance. In addition, SVM (space vector modulation) is replaced in this command by a simple switching table that makes it easier [31]. 4. PREDICTIVE DTC-SVM The strategy of the control DTC-SVM with a predictive controller uses a SVM with a fixed and constant switching frequency [28]. This control strategy ensures the decoupling between the stator flux vectors amplitude and its arguments. Indeed, the stator flux amplitude will be imposed. Nevertheless, the argument is calculated to obtain high performance like the reduction of the stator flux and the electromagnetic torque ripples. The difference between the conventional DTC and this control strategy is that the latter is based on the PI controllers and the SVM in order to fix the switching frequency, which consequently reduces the stator flux and the torque ripples as well as the harmonic waves of the stator current. The switching table and the hysteresis regulators used in the conventional DTC are eliminated. The voltage vector was calculated by using a predictive controller. [29] The block diagram of the predictive (DTC-SVM) control of a PMSM powered by a voltage inverter from a PV source is shown in Figure 5, the PI Predictive Controller is shown in Figure 6. [32] sector S1 S2 S3 S4 S5 S6 V2 V3 V4 V5 V6 V6 V7 V0 V7 V0 V7 V0 V6 V1 V2 V3 V4 V5 V3 V4 V5 V6 V1 V2 V0 V7 V0 V7 V0 V7 V5 V6 V1 V2 V3 V4 436 F. TAHIRI, A. HARROUZ, D. BELATRACHE, F. BEKRAOUI, O. OMAR, I. BOUSSAID Fig. 5 PMSM system control based on Predictive DTC-SVM. Fig. 6 PI Predictive Controller. 4.1. Predictive Controller The relationship between the torque pulses: [33]       KK T T sref s s eref e (8) Where Teref the reference is torque, s and ∆φ are respectively the deviations from s and φ which are defined by: ssrefs  ssref  (9) Where Ks and Kφ are the constants derived from the PMSM specifications. The torque ripple is actually caused by∆∅s, ∆φ and the influence of ∆∅s is considerably lower than ∆φ. As a result, the torque ripple can be attenuated if ∆φ is kept close to zero. For DTC-SVM control, the generation of the control pulses (Sa, Sb, Sc) applied to the inverter switches is generally based on the use of a predictive controller, which receives information about the error of the controller. ∆Te= (Te-ref -Te) the reference stator flux amplitude ∅ref, the amplitude and the position of the estimated stator flux vector and the current value to be measured [34]. The predictive controller determines the control reference stator voltage Direct Torque Control (DTC) SVM Predictive of a PMSM Powered by Photovoltaic Source 437 vector in the polar coordinates Vs= [Vsref ∆φ]. The equation shows that the relationship between the torque error and the increment of the angle ∆φ is linear. Therefore a Proportional Integral (PI) predictive Controller which generates the load angle changing to minimize the instantaneous error between the reference torque and the actual torque, is applied. From the structure of the predictive torque and stator flux controller shown in Figure.6. We noted that the torque error ∆Te and the stator reference flux are delivered to the predictive controller, which gives the deviation of the stator flux angle ∆φ [32]. From figure 6; α, β axes components of the stator reference voltage VSref, are calculated as:                    ss e srefsref refs ss e srefsref refs IR T V IR T V sinsin coscos (10) 4.2. Space Vector Modulation (SVM) The SVM method generates the switching signals based on the instantaneous position of the rotating reference vector in the voltage vector space of the converter [14, 37] as shown in the figure.3. In the space vector diagram SVD of a two-level inverter [35], every sector (represented as Si, i = 1 to 6) is an equilateral symmetrical triangle of height h (=√3/2). The edge vectors (V1 to V6) are named active vectors and (V0, V7) zero vectors. The three closest switching vectors (one zero vector and two active vectors), allows us to calculate the SVM switching time in any sector. The movement of the reference vector V * positioning inside the sector synthesizing the switching times. Figure 7 allows us to understand the two-level switching of SVD. The determination of the volts-second of V * and their time integral is shown in equation 11. [36] Fig. 7 Sector-1 for two-level SVD The reference voltage V*volts-sec is calculated by the following equation; V T+V T+V T=TV 002211s * (11) 438 F. TAHIRI, A. HARROUZ, D. BELATRACHE, F. BEKRAOUI, O. OMAR, I. BOUSSAID Where T0, T1 and T2 are the work times of basic space voltage vector V0, V1 and V2 respectively. V0 state can be either [000] or [111] switching state, or else both. Equation (12) can be used to determine the position of the angle V * (θ) in the sector; V V arctg            s s (12) The θ values sample the V* in different sector (Example, θ =115 ° , the V* approach sector-2, since sector-2 lies in an angle between 61°-120°). According to the V* position, whether inside or outside the hexagonal SVD (Figure.7), SVD is divided into linear modulation and over modulation equal Ma ≤0.907and Ma > 0.907, respectively. TS = T1 + T2 + T0. We calculated T1 and T2 from projecting V* position along α-axis and β-axis with respect to SVD origin (zero point). Henceforth, the volts-sec equations for α- axis and β-axis are VSα0 and VSβ0, TS= T1 + 0.5T2 and TS = hT2, respectively. Thus, T2 = TS VSβ0/h and T1 = TS (VSα0 − VSβ0)/2h. The active vector times T1 and T2, help to find the zero voltage time TS, from the given switching frequency. [37] 5. SIMULATION AND INTERPRETATION Both the simulations (simulation result of DTC conventional and Predictive DTC- SVM) were proceeded at the same conditions regarding motor parameters, switching frequency of inverter transistors and nominal condition (irradiation, temperature) of PV source. For constant flux operating condition, the flux amplitude produced by permanent magnet is the value of reference amplitude of stator flux. The system consists of photovoltaic sources, inverter, and permanent magnet synchronous motor. Table 2 Machine and control parameters Rated motor power Pn 1.1 kW Nominal motor voltage Vn 220V Power factor Cos φ 0.38 nominal frequency f 50Hz Stator resistance Rs 0.6 Ohm Direct stator induction aLd 2.8mH Quadratic stator induction Lq 1.4mH Flux of magnets 0.12Web Number of pole pairs P 4 Moment of Inertia J 1.1*10 -3 N.m.s 2 Coefficient of friction f 1.4*10 -3 nominal torque Te 10 N.m 5.1. Simulation Results of Conventional DTC In Fig.8.b, the electromagnetic torque is illustrated, that begins with a value of approximately 5Nm then its follows the reference torque to return the machine to the previously speed defined by the set point with a reversal of direction of rotation (t = 0.2 to 0.25), finally returns to zero until we apply a load of 5N.m at t= 0.3. We observe in Direct Torque Control (DTC) SVM Predictive of a PMSM Powered by Photovoltaic Source 439 Fig. 9.a. the stator current temporal evolution, which has an almost sinusoidal shape when we apply a load with an oscillation equal 4 A. The stator flux module follows its reference without exceeding. It shows no sensitivity to the load application. We noted that the electromagnetic torque is full of ripples caused by the used of hysteresis controllers for the stator flux and the electromagnetic torque ,which introduce limitations such as a variable switching frequency, high flux ripples and current distortion. Fig. 8 (a) –The variation of speed responses, (b) –The variation of stator torque responses Fig. 9 (a) –The variation of current responses, (b) –The variation of flux responses Fig. 10 (a) –The variation of stator flux (α, β) axes responses, (b) –The variation of stator flux (alpha) as a function of stator flux (beta). 440 F. TAHIRI, A. HARROUZ, D. BELATRACHE, F. BEKRAOUI, O. OMAR, I. BOUSSAID 5.2. Simulation Results of Predictive DTC-SVM Fig. 11 The block diagram of the simulation of PMSM system control based on Predictive DTC-SVM In the same operating condition (We apply a load of 5N.m at t = 0.3 and reverse direction of rotation at t = 0.2-0.25). In Fig.12.a, we note that the rotation speed makes a small overshoot at startup and then stabilizes at the rated speed 140 rad/s during a response time equal to 0.02 s. This overrun is justified by regulator values that have not been satisfactory and require adjustments. The electromagnetic torque, which is illustrated in Fig.12.b, perfectly follows its reference with an oscillation of 0.5N.m. On the curve of Fig.13.a, we see the stator current evolution which has a near sinusoidal shape with few fluctuations compared with the current of the DTC control. Concerning the Fig.13.b, we noticed that the modulus of the estimated stator flux revolves around its reference in a band of very narrow width that of the DTC. The presentation of the flow in the complex plane Fig.14.b shows that the stator flow starts from the point (0, 0) and then turns in the trigonometric direction to follow a circle of radius fixed by the instruction. Generally, we notice a decrease in torque and flux oscillations due to Predictive DTC- SVM control. Switching frequency in Predictive DTC-SVM is constant due to the excluded of the switching table and hysteresis regulators used in the conventional DTC and its replacement with PI controllers and SVM, which reduces the torque and flux oscillations as well as harmonic waves of constant current. Direct Torque Control (DTC) SVM Predictive of a PMSM Powered by Photovoltaic Source 441 Fig. 11 (a) – The variation of speed responses, (b) –The variation of stator torque responses Fig. 12 (a) –The variation of current responses, (b) –The variation of flux responses Fig. 13 (a) –The variation of stator flux (α, β) axes responses, (b) –The variation of stator flux (alpha) as a function of stator flux (beta). 442 F. TAHIRI, A. HARROUZ, D. BELATRACHE, F. BEKRAOUI, O. OMAR, I. BOUSSAID The following table shows the difference between the conventional DTC and Predictive DTC-SVM: Table 3 Various oscillations between the conventional DTC and Predictive DTC-SVM oscillation Torque (Nm) Flux (wb) Current (A) DTC 2.5 0.01 4 DTC-SVM predictive 0.5 0.003 1.75 6. CONCLUSION The work presented in this paper focuses on the study of Direct Torque Control (DTC) based on space vector modulation using predictive controller (Predictive SVM) of a permanent magnet synchronous motor (PMSM); indeed, this strategy is based on the direct determination of control sequence applied to the inverter. This control is less sensitive to the variation of the machine parameters and does not require mechanical sensors that are fragile. It has been concluded that the predictive SVM DTC control is to minimize ripple at the torque and flux, with a high switching frequency. From the results of the simulation can be summarized as follows:  The oscillation of torque and flux is important in the conventional DTC because of the use of hysteresis regulators, which introduce limitations such as a high and uncontrollable switching frequency  In DTC-SVM, we replace the hysteresis regulators and switching table with PI controller and SVM, the reducing of the oscillations in the torque and the flux produced by:  Inverter switching frequency is constant, which consequently reduces the flux stator and torque ripples as well as the harmonic waves of the stator current.  Distortion caused by sector changes are eliminated.  Zero low sampling frequency is required.  Dynamic performance of DTC-SVM are comparable with selection table based DTC. In the end, the torque, flux and current was recorded 0.5, 0.003 and 1.75, respectively in DTC-SVM predictive and 2.5, 0.01 and 4 respectively in conventional DTC. 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