From A PV Array Driving A Three-phase Induction Motor. 1. H. Altas. Karadenir Technical University. Depqrtment of Electrical and Eleceonics. Engineering.
A Novel Fuzzy Logic Controller For Maxhnum Power Extraction From A PV Array Driving A Three-phase Induction Motor 1. H. Altas Karadenir Technical University Depqrtment of Electrical and Eleceonics Engineering 61OXO Trabzon, Turkey
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Design and prototype implementation of a novel fuzzy logic (FL) controller for maximum power extraction from a stand-alone photovoltaic (PV) array system are studied. The FL controller was designed and implemented using an IBM AT computer to trinsfer the maximum available output power of a PV array to a pulse-width modulated (PWM) inverter fed three-phase induction motor. A computer emulation model of the PV array including the effects of changing temperature and solar irradiation levels on the array output power was used in the laboratory prototype modelling. The computer emulation model was then interfaced with the load system using a Data Translation. DT2X2 I , data acquisition board and ATLAB driver software. The resultant performance of the FL controller was compared with that of a classical proportional plus integral (PI) controller. Abstmcl
The capability of PV solar cells converting light directly to electricity has stimulated new research on PV cells so that the PV array applications have emerged as an important solution to the growing enrrgy crisis since mid 1970s. Due to their high initial co\is. the PV cclls have not been preferred by electricity u w r y who are ablc to buy cheaper electrical energy from the utility grid. However. they have been used for water pumping, air conditioning. and irrigation purposes in remote and isolated areas H here electrical energy from utility grid is not available o r too expensive to transport. Fortunately, due to developing manufacturing processes. the PV cell prices have been reduced extensively during last decades. so that the cost of solar cells has dropped from .WHI to about $7 per peak watt between the years I965 and 19XOl.lj. Although, nowadays, grid isolated PY array applications are already attractive with a cost of 25-30 CentskWh 121. the United States Energy Research and developnxnt Administration (ERDA) plans to reach a production cost of SO. I - 0.3 per peak watt capacity by the year 2(MHJ 131. and under IO Cents per peak watt capacity by the year 2015 121. The PV array systems will be more competitive with the utility grid. once the cost of electricity from PV array systems drops.under IO Cents per peak watt 121.
array schemes resulting in the desired operating conditions[4]. In this paper, the performance of a novel FL controller that was used to keep the operating power of a stand-alone PV array at its maximum value while supplying power to a PWM inverter fed three-phase induction motor is studied. A similar FL controller for MPO of a PV array-dc motor load scheme is given in reference[4].
SYSTEM DESCRIPTION As shown in Figure I , the prototype expeljmental scheme has mainly four parts that are processed either as digital or as analog systems. The prototype model of the PV array and the controller (C) are processed digitally by an IBM AT computer while the PWM inverter and the three-phase inductio? motor are operated continuously as analog systems. The PV array model is represented by difference equations relating the continuous system load current I,, the temperature and solar irradiation disturbances Tx and S,, respectively. and the PV array output voltage Vpv In the prototype modelling of the PV array, the load current,IL, and the solar irradiation disturbance, S,, are two continuous system inputs to the computer emulationmodel via analog-to-digital (A-D) converters. The temperature disturbance, Tx, is entered as arbitrary digital numbers h m the keyboard of the computer. The change in the solar cell operating temperature due to changing solar irradiation level is included in the PV array modelling as explained in references [1,4]. The operating power, voltage, and current of the PV array model at the current temperature and solar irradiation level are calculated using its mathematical model and compared with their corresponding maximum power point (MAP) values, which were previously stored for the same temperature and solar irradiation level. The difference between the operating power point (OPP) and MAP results in the maximum power operating error (MPOE), e, that is used by the FL controller. The coneoller output, V,,,, and the PV array model output voltage, V,,, are sent to the continuous time physical process of the scheme via digital-toanalog (D-A) converters. The gain, K, of the power amplifier was set to such a value that the maximum voltage to the P W : inverter would be equal or lower than the maximum open circuit voltage of the PV array at the lowest operating temperature. The output voltage range of the power amplifier represents the output voltage range of the PV array configuration that is being considered. Therefore, the power amplifier is also a part of the PV array prototype laboratory model. As given in references [ 1,4], the solar array voltage is obtained as a function of the w a y current along with the solar irradiation level and cell temperature.
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Since a PI array is an expensive system to build, and the cost of electricity from the PV m y systems is more-expensive compared to ihe price of electricity from the utility grid. the user of such an expensive system naturilly wants to use all of the availablt: output power. Therefore, PV arriiy systems should be designed to operate at their maximum output power levels for any temperature and .solar irradiation level at all the time. The maximum power operating (MPO) controllers for PV arrays have bern considered in different solar powered dc and ac schemes. However. the MPO controllers used in do schemes are mostly considered for steady-state operating conditions of dc motor\ as the MPO controllers in ac schemes are mostly used for utility interfaced PV array systems rather than standalone PV mays. Moht of the controllers used in previous PV array application schemes are classical PI or PID conmollers. FL controllers have been applied in only a limited number of PV
. 0-7803-1772-6/94/$3.00 @ 1994 IEEE'
A. M. Sharaf The University of New Brunswick Department of Electrical Engineering P.O. Box 4400, Fredericton, NB Canada EBB SA3
Since the array current is directly proportional or equal to the load current &=IL), conml of the load current means the control of the PV array curfent, and therefore, control of the PV array voltage and power. Since the cumnt of an induction
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motor is a function of applied motor voltage, frequency and slip, without considering the load torque dependencies, at least one of these three variables must be controlled in order to have a desired induction motor current. As shown in Figure 1, the PWM inverter has two control inputs for frequency and voltage/frequency ratio (V/F) control of induction motors. The carrier and reference three-phase signals of the PWM inverter are generated by the HEF4752V (PWM-IC), which is an integrated circuit chip manufactured by Phillips for PWM inverters[5]. The frequency of the reference three-phase signals is controlled using an external control input signal such as the one that determined by the FL controller here. Due to the limited number of D-A output channels of the DT2821 board, only the frequency control input was regulated by the FL controller. The V/F ratio control signal was set manually to a constant value so that the magnetic saturation in the induction motor was avoided.
The subscript Q in Figure 2 indicates the quantized values. the implied relation among the fuzzy variables e, de, and du is expressed in terms of fuzzy conditional statements as: IF e is NS THEN (IF de is PM THEN du is PS) This logical expression is represented in terms of membership degrees as: p,(e,de,du)=min[p,,(e), ppM(de),ppS(du)l Since e, and de are the known fuzzy variables to the controller, the value of the control input change du is obtained by applying the compositional rule of inference: p*(du)=inax[min[p*,,(e), p*pM(de).p,(e,de,du)ll where * indicates the current measured and calculated values. This expression represents only one rule. Since there are seven fuzzy subsets for each fuzzy variable, the interpretation of these fuzzy subsets results in forty-nine rules as shown in Table I. After implementing all the rules, the final stage, defuzzification, is processed to yield the resultant control input change. During the defuzzification, the results of the fuzzy control rules are converted to actual values. Usually two algorithms, the maximum of maxima (MOM), or the centre of area (COA), are applied[9]. The COA method is also called centre-of-gravity algorithm[9] and defined as:
Design of the FL Controller Since its development by Zadeh[6], the fuzzy set theory has been applied in different fields of process control(71 where the mathematical models of systems are very complicated. Since the basic principle of a FL controller is to determine the control input directly from the output variables of the controlled system, a mathematical model of the system is not needed. Although a massive amount of work on the FL control systems has been appeared in the literature[S], very few of them deal with the application of FL controller to the PV array systems[8]. Therefore application of the FL controllers to a solar powered induction motor system is another step taken in the utilization areas of the FL controllers. The maximum power operating error (MPOE) e(k) and its rate of change de(k) are two selected inputs to the FL controller. The MPOE is obtained as the difference between the reference maximum power (RMP) and the operating power (OP). The RMP is an uncontrollable input because it is a function of temperature and solar irradiation levels which are uncontrollable disturbances to the PV array system. Therefore the reference input to the control system is not a constant as it is usually in other systems. In the FL controller, first of all, the inputs e(k) and de(k) are processed by thefuzzvier where their linguistic fuzzy subsets and fuzzy membership functions are defined. These fuzzy subsets and their fuzzy membership functions are then implemented as fuzzy conditional statements. The implementation of the fuzzy conditional statements results in a fuzzy subset and its membership function in the universe of discourse representing the control input change du(k). The actual value of du(k) is then found by converting this resultant fuzzy subset and its membership function into actual numbers. This conversion process is called defuuifwutwn. Final control action to be taken is obtained by adding the final value of du(k) to the previous control voltage u(k). In this paper, seven membership functions, which are also referred as fuzzy subsets, are defined in three universes of discourse representing error e, error change de, and control input change du. In order to reduce the process time and space, the three universes of discourse were quantized into one common universe of discourse by scaling the minimum and maximum ranges into the same level for e, de, and du. Therefore, seven fuzzy subsets, NL: negative large, NM: negative medium, NS: negative small, Z Z zero, PS: positive small, PM: positive medium, and PL: positive large, are represented in one common universe of discourse as shown in Figure 2.
49
du*
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This value, du* of the resultant control input change from the defuzzifier is the quantized value ant it should be re-scaled back to its original unit and its normal value using the scaling factor that was initially used for quantization. Then, the final control voltage is obtained by adding this change to the previous value of the control voltage: v(k)=v(k-I ) + du where k indicates the kth sampling.
RESULTS AND CONCLUSIONS Power-Voltage (P-V) characteristic of the PV array during startup and steady-state operation is given in Figure 3. The maximum power peaks that obtained for different temperature and solar irradiation levels using FL controller are shown in this figure. The lower peak represents the P-V characteristic for the operating condpions 25 "C and 50 mW/cm*. While the system is being operated at the lower peak, the operating conditions are changed to P O T and 100 mW/cm2, temperature and solar irradiation levels, respectively, in about five seconds resulting in the upper power peak. The time response of the PV array power giver in Figures 4 and 5 for FL and PI controllers, respectively, shows that the maximum power operating error is minimized quite well by both controllers. However, the system has overshoot and longer settling time with PI controller, while there is no overshoot with FL controller. The settling time is about 5 seconds with FL controller and 7 seconds with PI controller. This difference on the settling time of the PV array power is also reflected on the motor speed as shown in Figure 6, where the speed reaches the steady-state at about 12 seconds with FL controller while it takes about 14 seconds with PI controller. The magnitude of the steady-state speed is also reduced by the PI controller. As shown in Figure 6, the motor operates at 800 rpm with FL controller, and at 750 rpm with PI controller. The overall results indicate that the system is operated slightly better with FL controller than PI controller.
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ACKNOWLEDGEMENT The authors would Wte to acknowledge Karadeniz Technical University-Turkey, and NSERC & EMR-Canada. Figure 3. Power-Voltage characteristics of PV G a y during start-up and continuous operation.
Figure 1. The prototype experimental scheme
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Figure 3. Power-Voltage characteristics of PV array during starting-up and continuous operation. PV ARRAY POWE R PV ARRAY POWE R 1.2
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Figure 5. Time response of the PV array power using FL controller.
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Figure 6 . Induction motor speed. Table 1 -Fuzzy control rule decision table.
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(21. [3]. (41.
[5].
M. Buresch, "Photovoltaic Energy Systems Design and
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L.A. Zadeh, "Fuzzy Sets", Information and Control 8. 1965. pp.338-353. J.Maiers and Y.S. Sherif, "Applications of Fuzzy Set Theory". IEEE Transactions on Systems. Man, and Cybernetics. Vol. SMC-15, No.1, January/ February 19x5, pp. 175- 189. R.M. Tong, " A Control Engineering Review of Fuzzy Systems", Automatica, Vol. 13. Pergamon Press 1977, pp. 559-569. Y.F. Li and C.C. Lau. "Development of Fuzzy Algorithms for Servo Systems", IEEE, Control Syatems Magazine, April 1989, pp. 65-72.
