Vector control of an induction motor fed by a photovoltaic generator

Transcription

1 Applied Energy 74 (2003) Vector control of an induction motor fed by a photovoltaic generator M. Arrouf*, N. Bouguechal Department of Electrical Engineering, Faculty of Engineering Sciences, University of Batna, Algeria Abstract With the continuous decrease of the cost of solar cells, there is an increasing interest in photovoltaic (PV)system applications. Electric motors powered by solar-cell generators are one of the most important applications, such as in water pumping systems. This paper investigates a photovoltaic-electro mechanic chain, composed of a PV generator, an impedance adapter DC DC converter, a storage battery and a vector controlled induction machine. The PV generator is forced to operate at its maximum power point by using an appropriate search algorithm, and a balance between battery charge and motor supply is also ensured in all insolation conditions. Simulation results show the effectiveness and feasibility of such an approach. # 2003 Elsevier Science Ltd. All rights reserved. Keywords: PV generator; Impedance adapter; Storage battery; Vector control and induction machine 1. Introduction In addition to its advantages, such as speed capability, robustness, cheapness and ease of maintenance, when used with a field-oriented control scheme, the induction motor can compete with the DC motor in high-performance applications [3]. In this way, the vector-controlled induction machine became of great interest because of the perfect decoupling control of flux and electromagnetic torque, and a lot of industrial applications are based upon this type of drive. The operating point of the system moves from the maximum power point of the current voltage (I V)Characteristic of the PV array if the insolation and ambient temperature vary from the nominal level. In such a case, neither the PV array nor the induction motor is optimally used. In order to enhance the cost-effectiveness of * Corresponding author. Fax: address: m.arrouf@univ-batna.dz (M. Arrouf) /03/$ - see front matter # 2003 Elsevier Science Ltd. All rights reserved. PII: S (02)

2 160 M. Arrouf, N. Bouguechal / Applied Energy 74 (2003) PV array-powered systems, the electric power generated by the PV arrays should be efficiently utilized, and any improvement in efficiency is considered to be precious. This work employs an impedance adapter DC DC converter after the PV array to make it work at the maximum power output level for all conditions (insolation, temperature and load). The function of the storage battery is to keep the operating voltage of the association hysteresis controlled voltage source inverter (VSI)induction motor within certain allowed limits, and a bang-bang control is adopted to drive the inverter supplying the motor. 2. Solar-cell generator The solar cell is a semiconductor device that converts the solar insolation directly to electrical energy. The cell is a non-linear device and can be represented by the I V terminal characteristics, or by an approximate electrical equivalent circuit as shown in Fig. 1 [1,2]. The cells are connected in series and in parallel combinations in order to form an array of the desired voltage and power levels. Fig. 2 represents the I V and P V characteristics of the solar-cell generator for five insolation levels (in percentages). The I g V g equation of the solar cell generator, which consists of N s cells in series and N p cells in parallel, is given by: Fig. 1. Solar-cell equivalent circuit. Fig. 2. Characteristics of a solar-cell generator.

3 M. Arrouf, N. Bouguechal / Applied Energy 74 (2003) Vg ¼ IgRs N s Ln 1 þ N pi p I g N p N p I o ð1þ with A ¼ q akt where I p : cell photocurrent (amps), proportional to the insolation; I o cell reverse saturation current; R s cell series resistance; q: electron charge, a completion factor; K Boltzmann s constant; and T absolute temperature. 3. Impedance adapter The solar cell is a non-linear device; it can only provide maximum power at specific voltage and current levels. Due to the relatively expensive PV modules, it is highly desirable to match the load to the PV array. To force the PV array to deliver the maximum power to the load [4], a DC DC buck converter (impedance adapter) is included between the PV generator and the storage battery, as shown in Fig. 3. The average load voltage V 2 is given by: V 2 ¼ kv 1 ð2þ where 0<k<1 is the duty cycle and V 1 is the output voltage of the PV array. The load voltage is therefore controlled by the duty cycle of the chopper. 4. Search for the maximum power point It is reasonable to assume that the DC DC converter is loss free, that is, all power converted by the PV array can be transformed to the load [7], hence, P ¼ V 1 I 1 ¼ V 2 I 2 ð3þ Fig. 3. Schematic of the conversion chain.

4 162 M. Arrouf, N. Bouguechal / Applied Energy 74 (2003) The firing angle of the chopper m which corresponds to the maximum power point is found and tracked by the following algorithm [11]: ¼ hsign ðþ¼hsign " P iþ1 ¼ i þ iþ1 where h is a positive constant. The search is started with a large increment until the first overshoot of the maximum power point (indicated by the changing of the sign of "). Then the search process will continue in the inverse direction of variation of with the reduced amplitude 2 ¼ 1 2 until a new change of the sign of " ensues, etc. This process is repeated until n is negligible. The (n 1)computed power values are compared to find the firing angle m, which corresponds to the maximum power. The search process will start again when a variation of insolation or temperature is detected. We verify in Fig. 4 that it is possible to track the maximum power point with the coordinates: m1 ¼ 4:0778rd; Pm1 ¼ 6115:1W m2 ¼ 4:2248rd; Pm2 ¼ 4696:5W m3 ¼ 4:4208rd; Pm3 ¼ 3334:9W m4 ¼ 4:7149rd; Pm4 ¼ 2049:2W m5 ¼ 5:4010rd; Pm5 ¼ 878:8641W ð4þ With this strategy, the maximum power point can be closely tracked for all insolations and temperatures as well as load conditions. Fig. 4. Firing angle-generator power characteristic.

5 5. Induction machine model It is well known that the dynamic performance of a squirrel-cage induction motor (SCIM)can be analysed mathematically using the d q axis theory by the following equations [9,10]: where Vds ¼ RsIds þ dds wsqs dt Vqs ¼ RsIqs þ dqs þ wsds dt 0 ¼ RrIdr þ ddr wslqr dt 0 ¼ RrIqr þ dqr þ wsldr dt Ce Cr ¼ J d dt þ f Ce ¼ plmðiqsidr IdsIqrÞ ð6þ d; q: axes corresponding to the synchronous reference frame s, r subscripts corresponding to stator and rotor respectively Ls; Lr : stator and rotor main inductances respectively Rs, Rr : stator and rotor resistances respectively Lm : intrinsic self-inductance Ts; Tr: stator and rotor time-constants Ts ¼ Ls Lr Rs ; Tr ¼ Rr s;r: stator and rotor leakage-coefficients s ¼ Lm Ls Lr 1;r ¼ Lm 1 : total leakage coefficient ¼ 1 Lm2 LsLr p: number of pole pairs S: differential operator Ce : electromechanical torque s;r: stator and rotor electrical angles Cr : load torque sl: slipping angle f: friction coefficient : mechanical speed ¼ wr p J : total inertia If, on the other hand, the rotor flux is so positioned that it coincides with the d- axis component (dr=r and qr =0), it becomes possible to control the torque independently by the q-axis stator current, and the rotor flux can be controlled with the d-axis stator current with a delay. In this case, the torque can be expressed as: Ce ¼ plm Lr M. Arrouf, N. Bouguechal / Applied Energy 74 (2003) riqs Then, by keeping the rotor flux constant, the motor torque can directly be controlled as in the case of a separately-excited DC machine. The expression of the rotor flux can be given by: ð5þ ð7þ

6 164 M. Arrouf, N. Bouguechal / Applied Energy 74 (2003) Lm r ¼ Ids TrS þ 1 ð8þ 6. Field oriented control of the induction motor In the following, we discuss the simulation results of: (a)the simplified indirect field-oriented control [6,8] Fig. 5. (b)the inverter fed by a linear-voltage source [5]. (c)the inverter fed by a non-linear voltage source (a) Without inverter For a mechanical speed reversal, Fig. 6 shows that the motor speed and torque follow their references without steady-state errors nor overshoot. Fig. 5. Block-diagram of an indirect field-oriented control. Fig. 6. Speed and torque responses without inverter.

7 M. Arrouf, N. Bouguechal / Applied Energy 74 (2003) (b) With inverter (linear source) The inverter works on the principle of bang-bang control with three independent hysteresis controllers. The calculated values of the three-phase stator currents are compared with the reference values and the inverter elements are switched accordingly to impress the necessary terminal voltages to the motor phases. The simulation results of the associated inverter-induction motor fed by a linear source are given in Fig. 7, with the hysteresis band i ¼ 1A. A harmonic analysis is to be performed to determine the hysteresis band to remain within reasonable limits in order to avoid the undesirable pulsations of the torque With inverter (photovoltaic source) The function of the battery is to keep the operating voltage of the association VSI inverter-induction motor within certain allowed limits in order to operate the motor at high efficiency. Let us consider now how the battery storage operates. If the output current of the DC DC down converter (I2)is greater than the input VSI inverter Fig. 7. Simulation results with the inverter (Cr=0). Fig. 8. Voltage and state of charge of the battery.

8 166 M. Arrouf, N. Bouguechal / Applied Energy 74 (2003) Fig. 9. Simulation results (Cr=0). Fig. 10. Simulation results (Cr=15 Nm,). current (I3), then the battery is charging by the current (I2 I3). On the other hand, if the current (I2)is smaller than motor current (I3)then the battery is discharging with a current equal to (I2 I3) We have simulated the operation of the cascade: PV array-impedance DC DC converter- storage battery-vsi inverter and the induction motor for different load torque values (Cr=10, 15, 20 Nm). The global time of the simulation of the cascade has been divided into five period times of insolation as follows: 60, 80, 100, 80 and 60% of insolation, respectively. The state of charge and the voltage of the battery are given for different insolation and load torque values as shown in Fig. 8. Figs. 9 and 10 show that the induction machine dynamic is not affected by the insolation level, battery charge level and load-torque variations. 7. Conclusion The drive system performance has been simulated for different solar insolations and it has been found to be satisfactory. We can say that the speed motor is not

9 M. Arrouf, N. Bouguechal / Applied Energy 74 (2003) affected by the variation of the insolation: on the other hand, the other parameters such as torque and the d q components of stator current vary with the insolation level, but their average values remains constant. References [1] Appelbaum J. Starting and steady-state characteristics of DC motors powered by solar cell generators. IEEE Trans on energy conversion March 1986;EC-1(1): [2] Langridge D, Lawrence W, Wichert B. High-efficiency solar water pumping systems using a BDC motor. In: 12th European photovoltaic solar energy conference, Netherlands; p [3] Hamid M, Metawally B, Annis WR. Performance analysis of PV pumping systems using switched reluctance motor drives. Solar energy 1996;56(2):161. [4] Alghuwainem SM. Application of a DC chopper to maximize utilization of solar-cell generators. pp. 91 WM, EC, 1991 IEEE/PES 1991 winter meeting, New York, 3 7 February [5] Golea A. Me thodologie de conception des associations convertisseurs-machines. The` se doctorat, INP. Grenoble, France; [6] Leonhard W. Control of electric drives. New York: Springer Verlag; [7] Bose BK. Power electronics an emerging technology. IEEE Trans. Ind. Electronics, vol.36, no.3, pp [8] Capolino GA, Fu YY. Field oriented control of induction machines principle, methodology and simulation [in French]. Proc. SEE Meeting, Valence, pp. 4/1 17. [9] Ho EY, Sen PC. Decoupling control of induction motor drives. IEEE Trans. Ind. Electronics, vol. 35, No. 2, pp [10] Wade S, Dunnigan MW, Williams BW. Modeling and simulation of induction machine vector control with rotor resistance identification. IEEE Trans Power Electronics 1997;12(3). [11] Mostafa RM. Etude et re alisation d une chaine de conversion d énergie photovoltaique-electromécanique et de sa commande numérique. The` se de Doctorat, Université Paris VI; 1983.