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I. NOMENCLATURE C, Ca Filter, array capacitance Voltage-Based Maximum d1 , d2 Duty ratios of switch S1 , S2 DP1 , DP2 Diodes of individual boost cells Power Point Tracking Control IA SCA current IAb SCA current with boost converter of PV System IAd SCA current with IDB converter Im SCA current at maximum power operation Iab Average load current with boost converter Iaid Average load current with IDB converter MUMMADI VEERACHARY, Student Member, IEEE Iph Insolation dependent photo current TOMONOBU SENJYU, Member, IEEE I0 Cell reverse saturation current KATSUMI UEZATO L1 , L2 Inductances of individual boost cells University of the Ryukyus Japan Ns , Np Number of SCA cells in series, parallel Pgb , Pgd SCA power output with boost, IDB converter Pm Maximum power of the SCA Photovoltaic (PV) generators exhibit nonlinear v-i R1 , R2 Inductor series resistances characteristics and maximum power (MP) points that vary Rs Cell series resistance with solar insolation. An intermediate converter can therefore R Load resistance increase efficiency by matching the PV system to the load and S1 , S2 Switches of individual boost cells by operating the solar cell arrays (SCAs) at their maximum V ,V Ab Ad SCA voltage with boost, IDB converter power point. An MP point tracking algorithm is developed using Vm SCA voltage at maximum power only SCA voltage information thus leading to current sensorless operation tracking control. The inadequacy of a boost converter for array V ,V ab aid Average load voltage with boost, IDB voltage based MP point control is experimentally verified and an converter improved converter system is proposed. The proposed converter ´b , ´id Efficiency of the boost, IDB converter system results in low ripple content, which improves the array ª Solar insolation. performance and hence a lower value of capacitance is sufficient on the solar array side. Simplified mathematical expressions for II. INTRODUCTION a PV source are derived. A signal flow graph is employed for modeling the converter system. Current sensorless peak power The rapid trend of industrialization of nations and increased interest in environmental issues recently tracking effectiveness is demonstrated through simulation results. led us to explore the use of renewable forms such Experimental results are presented to validate the proposed as solar energy. Photovoltaic (PV) generation is method. gaining increased importance as a renewable source [1—2] due to its advantages like absence of fuel cost, little maintenance, and no noise and wear due to the absence of moving parts, etc. In particular, energy conversion from solar cell arrays (SCAs) received considerable attention in the last two decades. The PV generator exhibits a nonlinear v-i characteristic, and its maximum power (MP) point varies with the solar insolation and temperature. At a particular solar Manuscript received March 14, 2000; revised July 3, 2001; released insolation, there is a unique operating point of the for publication July 26, 2001. PV generator at which its power output is maximum. IEEE Log No. T-AES/38/1/02589. Therefore, for maximum utilization efficiency, it is necessary to match the PV generator to the load such Refereeing of this contribution was handled by I. Batarseh. that the equilibrium operating point coincides with the Authors’ address: Dept. of Electrical and Electronics Engineering, MP point of the PV source. However, since the MP Faculty of Engineering, University of the Ryukyus, 1 Senbaru, point varies with insolation and seasons, it is difficult Nishihara-cho, Nakagami, Okinawa 903-0213, Japan. to maintain MP operation at all solar insolations. To overcome this problem, use of an intermediate 0018-9251/02/$17.00 ° 2002 IEEE c dc-dc converter is proposed [3—5], which continuously 262 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 38, NO. 1 JANUARY 2002 adjusts the voltage, current levels and matches the PV source to the load. The MP point tracking is applied to PV systems to extract maximum available power from the SCAs at all solar insolations. Different methods of peak power tracking schemes have been proposed by using different control strategies [6—9]. Boost converter based MP point tracking using fuzzy logic is reported [10]. These studies show that the fuzzy control algorithm is capable of improving the tracking performance as compared with conventional methods. However, in fuzzy implementation several parameters are selected on a trial and error basis, which mainly depends on designer experience and Fig. 1a. Experimental setup of PV system. intuition. To overcome some of the disadvantages mentioned above, a fuzzy neural network based MP stresses, fault tolerance for the system, flexibility in point tracking is proposed [11]. All these methods the system design, etc. depend on the SCA power output and/or load power This paper presents MP point tracking of SCA detection using the instantaneous voltage and current employing an intermediate interleaved dual boost information, requiring voltage and current sensors. (IDB) converter using only the array voltage Neural network based real time MP tracking controller information, eliminating the array current detection for PV grid connected systems has been reported [12]. and hence achieving current sensorless peak power The studies emphasize that the SCA operating point tracking. This paper is organized as follows. is shifted to its MP point by using a voltage control In Section III, we present the development of type inverter, which utilizes the array voltage together mathematical models for the PV generator and power with pilot cell voltage information. Array voltage converters. Maximum power point tracking control based MP point tracking using dc-dc converters is process is discussed in Section IV. Experimental currently under investigation by various researchers. system description is given in Section V. Section VI This method of MP tracking has advantages like presents experimental results, and conclusions are straightforward array voltage measurement (which is provided in Section VII. inexpensive as compared with the measurements of solar insolation, and other environmental factors), no need of current sensors, (which introduces losses and III. MATHEMATICAL MODEL OF SYSTEM complexity in the system) etc. The authors have tried Fig. 1(a) shows the overview of the combined to implement boost converter array voltage based MP system, which mainly consists of SCA, IDB converter, point control. The experimental investigations show and data acquisition system. The analysis of the that boost converters are not suitable for array voltage system is carried out under the following assumptions. based MP point tracking control as this leads to an undesirable operation. An alternate converter scheme 1) Switching elements (MOSFET and diode) of (interleaved dual boost (IDB) converter) is proposed the converter are assumed to be ideal, i.e., forward by the authors for array voltage based MP extraction, voltage drops and ON-state resistances of the switches by simple addition of one more boost cell in parallel are neglected. to the existing boost cell and controlling these two 2) The equivalent series resistance of the boost cells in an interleaved fashion. capacitance and stray capacitances are neglected. The advantages of the present converter system 3) Passive components (R, L, C) are assumed to be are 1) ripple cancellation both in the input and output linear, time invariant, and frequency independent. waveforms to the maximum extent possible, 2) lower 4) The two parallel boost cells are identical and value of ripple amplitude, and high ripple frequency operate in the continuous inductor current mode. in the resulting input and output waveforms, and 3) 5) The switches (S1 , S2 ) operate in interleaved reduced electromagnetic interference (EMI) because fashion. of low ripple amplitude of SCA current. Although Mathematical models for individual components the interleaving technique increases the number of are developed in the following sections. components, the actual increase of cost may not be significant. This is because more boost cells can A. PV Generator Model share the current flow in the inductors and switching devices, so lower current rating devices may be The PV generator is formed by the combination employed. Further, parallel connection of converters of many PV cells connected in series and parallel to has many desirable properties such as reduced device provide the desired output voltage and current. This VEERACHARY: VOLTAGE-BASED MAXIMUM POWER POINT TRACKING CONTROL OF PV SYSTEM 263 PV generator exhibits a nonlinear insolation dependent v-i characteristic, mathematically expressed for the SCA consisting of Ns cells in series and Np cells in parallel [1] as Ã ! µ ¶ ( ) Ns Ns Np Iph ¡ IA V = ¡IA Rs A + ln 1 + (1) Np ¤ Np I0 where ¤ = (q=AKT), q–electric charge; A–completion factor; K–Boltzmann’s constant; T–absolute temperature; Rs –cell series resistance; Iph –photo current; I0 –cell reverse saturation current; Fig. 1b. Equivalent circuit of system. IA , V are the SCA current and voltage, respectively. A For given values of SCA parameters, the V ¡ IA A characteristic depends on the solar insolation and the then the reflected equivalent load on the SCA side is MP point varies with the solar insolation. Rewriting given by the following equation (1) as Ã ! µ ¶ Req = ´b (1 ¡ d)2 R (7) Ns Ns V = ¡IA Rs A + i.e., Np ¤ V " µ Ã !# Ab = ´b (1 ¡ d)2 R: (8) ¶ IAb Ipha IA £ ln + ln 1 ¡ (2) Power extracted by the boost converter from the SCA I0 Np Ipha is where Ipha = Iph + I0 . Expanding the term V2 Ab Pgb = : (9) ln(1 ¡ (IA =Np Ipha )) into Taylor series and neglecting ´b (1 ¡ d)2 R higher order terms [5] results in the following From the above expression the array power Pgb equation Ã ! µ ¶· µ depends on the load and converter duty ratio. For a ¶¸ 2Ns Ns Ipha given load, the array power continuously increases V = ¡IA Rsg + A + ln : with duty ratio, theoretically resulting in minimum ¤Np Ipha ¤ I0 power at d = 0 and infinite power at d = 1, at which (3) the SCA voltage collapses, leading to an undesirable Simplifying the above equation for the SCA current operation. Furthermore, the power Pgb is continuously results in the following equation. increasing with duty ratio, and hence with this power · µ ¶ ¸ comparison method it may not be possible to reach 1 Ns Ipha IA = Ã ! ln ¡VA (4) the MP point. To overcome this disadvantage an 2Ns ¤ I0 Rsg + identical boost branch is connected in parallel to ¤Np Ipha the existing one and controlls these two branches in complementary fashion. The analytical discussion of where Rsg = Ns Rs =Np . The equations (3) and (4) are this converter is given in the following section. used in the simulation studies. B. Boost Converter Model C. IDB Converter Model The intermediate boost converter produces a The intermediate IDB converter produces a chopped output voltage and controls the average dc chopped output dc voltage and controls the average voltage applied to the load. Further, the converter dc voltage applied to the load. Further, the converter continuously matches the output characteristic of the continuously matches the output characteristic of the PV generator to the input characteristic of the load. PV generator to the input characteristic of the load so The steady-state voltage and current relations of the that MP is extracted from the SCA. The steady-state boost converter operating in continuous current mode voltage and current relations of the IDB converter are operating in continuous current mode are derived VAb using signal flow graph (SFG) technique [13]. The V = ab (5) (1 ¡ d) steady-state signal flow graph of the IDB converter is Iab = ´b (1 ¡ d)IAb (6) obtained as shown in Fig. 2. Voltage gain is derived by employing the well-known Mason’s gain formula. where ´b is the efficiency of the boost converter, To start with various possible forward paths and loops V , IAb are the array voltage and current, respectively. Ab are identified from the steady-state SFG (Fig. 2). The Transforming the load to the SCA side (Fig. 1(b)), forward paths transmittances formed by the nodes 264 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 38, NO. 1 JANUARY 2002 Fig. 2. Steady-state SFG of IDB converter. (V ¡ V ¡ IL1 ¡ I0 ¡ V ), (V ¡ V ¡ IL2 ¡ I0 ¡ V ) are g 1 0 g 2 0 i.e., V d R Ad = ´id (2d2 ¡ 2d + 1)2 R: (19) P1 = 2 (10) IAd R1 Substituting the IAd = IA expression (from (4)) in the d R above expression then P2 = 1 : (11) R2 · µ ¶ ¸ [´id (2d2 ¡ 2d + 1)2 R] Ns Ipha V = Ã Ad ! ln ¡V : Ad In this steady-state SFG two loops formed by the 2Ns ¤ I0 nodes (V ¡ IL2 ¡ I0 ¡ V ), (V ¡ IL1 ¡ I0 ¡ V ¡ V ) exist 2 2 1 0 1 Rsg + ¤Np Ipha and their loop transmittances are 2 (20) ¡Rd1 L1 = (12) On simplification the array voltage equation becomes R2 · µ ¶¸ ¡Rd22 [´id (2d2 ¡ 2d + 1)RNs ] Ipha L2 = : (13) V = Ad ln R1 ¤[K + ´id (2d2 ¡ 2d + 1)R] I0 (21) Applying Mason’s gain formula the steady-state where K = (Rsg + (2Ns =¤Np Ipha )). Power extracted by voltage gain obtained as the IDB converter from the SCA is Vaid R(R1 d1 + R2 d2 ) V2 = 2 2 (14) Pgd = Ad : (22) VAd R1 R2 + R(R1 d1 + R2 d2 ) Req where d1 , d2 are the duty ratios of the switches Substituting (18) and (21) in (22) then the resulting S1 , S2 , respectively. The IDB converter switching SCA power expression is devices (S1 , S2 ) are activated in complementary mode · µ ¶¸ with duty ratios d1 and d2 , satisfying the relation (´id RNs2 ) Ipha 2 d1 + d2 = 1. If the two parallel boost cells are identical Pgd = 2 ln : ¤ [K + ´id (2d2 ¡ 2d + 1)R]2 I0 (R1 = R2 = r; R À r) then the above equation becomes (23) VAd From (23) it can be noticed that, for given values V = aid : (15) 2 (d1 2 + d2 ) of the array parameters and load, the SCA power (Pgd ) depends on the duty ratio of the IDB converter. Substituting d1 = d, d2 = (1 ¡ d), the above equation Suitable adjustment of converter duty ratio results in can be written as V = V , which in turn results in extraction of MP Ad m VAd from the SCA. V = aid : (16) (2d2 ¡ 2d + 1) Using power balance, the current expression is IV. MAXIMUM POWER POINT TRACKING obtained as CONTROL PROCESS 2 2 Iaid = ´id (d1 + d2 )IAd (17) The control flow chart is given in Fig. 3, which where ´id is the efficiency of the IDB converter, controls the tracking process of the PV supplied V , IAd are the array voltage and current, respectively. converter system. The tracking process can be started Ad Transforming the load to the SCA side (Fig. 1b), then by outputting the command signal either 0 or 5 V to the reflected equivalent load on the SCA side is given the pulsewidth modulation (PWM) generator, which by the following equation corresponds to duty ratio of zero or one, respectively. Whatever may be the duty ratio (0-1) the array power Req = ´id (2d2 ¡ 2d + 1)2 R (18) (Pg ) is computed from the (22) using the already VEERACHARY: VOLTAGE-BASED MAXIMUM POWER POINT TRACKING CONTROL OF PV SYSTEM 265 Fig. 4. Power tracking process with duty ratio. V. EXPERIMENTAL SYSTEM DESCRIPTION The basic configuration of the proposed PV system is shown in Fig. 1(a). The data acquisition system is set up by using PC, interface AZI-3503 card, which mainly consists of 8-channel 12-bit A/D, D/A converters. For power measurements a digital power meter (YOKOGAWA-WT130) is used, through which Fig. 3. Flow chart for MP point tracking. a GPIB interface is connected to the PC to record the SCA power data. The PWM modulator is a voltage comparator made of LF311 operational amplifier. sensed array voltage. Change (increase or decrease) The reference signal to this comparator is the signal the duty ratio and then measure the instantaneous obtained from the D/A converter, generated by means array power. This power is compared with the of the MPPT algorithm. A synthesized YOKOGAWA previous power and a decision on whether to increase function generator (FG120) was used to obtain phase or decrease the duty ratio is taken depending on the displaced triangular carrier signals to the PWM location of the operating point and direction of its generator. The experimental prototype circuit was built movement as indicated in Fig. 4. As a consequence, with an International Rectifier IRF530N MOSFET there are four possibilities (two if the operating with suitable driver circuit, and the diode FML-32S. point is left of the MP point, two if the operating The artificial sun is realized in the laboratory by point is right of the MP point) for the operating means of incandescent lamp set. Further, the solar point movement. The duty ratio control signal is insolation level illuminated on the solar panel is continuously adjusted to maximize the array power adjusted by controlling the power to this incandescent by following the equation d = d § ¢d. The sign of lamp set. the incremental duty ratio (¢d) is determined by the incremental power (¢P) and operating point VI. EXPERIMENTAL RESULTS AND DISCUSSIONS movement as indicated in Fig. 4. If ¢P is positive and the operating point is left of MP point, then The simple boost converter is not able to track MP d = (d + ¢d), otherwise d = (d ¡ ¢d). Along similar point by sensing only the array voltage information. lines, if the ¢P is negative and the operating point is This is because the equivalent load impedance (in left of the MP point, then d = (d + ¢d), otherwise d = (7)) seen by the SCA is continuously decreasing with (d ¡ ¢d). This tracking control process repeats increasing the duty ratio. Further, from the (9) for a itself until the peak power point is reached and given load, the array power continuously increases then oscillates within an allowable range about with the duty ratio, resulting in minimum power at this point. In the simulated MP point tracking d = 0 and infinite power at d = 1, which is physically process the instantaneous array voltage and power an unrealizable condition. This phenomena is verified are computed employing the models developed in experimentally and the corresponding characteristics preceding sections, whereas in real time computer are shown in Fig. 5. To overcome this disadvantage implementation the instantaneous array voltage, and to extract MP from the SCA using only the power information is obtained by means of array voltage, an identical boost cell is connected data acquisition system. The MP point tracking in parallel to the existing boost cell as shown in process both in simulation and real time computer the experimental setup (Fig. 1(a)). These two boost implementation are same except the above mentioned branches are controlled in an interleaved fashion using difference. phase shift between the gate signals. This converter 266 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 38, NO. 1 JANUARY 2002 Fig. 5. Array characteristics with boost converter. Fig. 7. Comparison of experimental SCA power tracking characteristics. TABLE I SCA and Converter Parameters Np 1 Ns 27 Rs 0.04 − ¤ 13.68 V¡1 Io 0.00045 A R1 0.044 − R2 0.063 − L1 0.250 mH L2 0.250 mH C 220 ¹F Fig. 6. Experimental V ¡ IA characteristics of SCA module for A different solar insolations. Ca 2200 ¹F fs 25 kHz R 50 − is capable of reducing the ripple in the source current EMI and avoids the discontinuous input current mode even though the individual boost branches enter into converter system (shown in Fig. 1(a)). Comprehensive discontinuous current mode. simulation studies were made to investigate the Prototype PV-supplied converter (SCA and influence of IDB converter as an intermediate converter parameters are given in Table I) system MP point tracker for the PV supplied system. A was bread boarded to study the array voltage simulation software is developed for MP point based maximum power point tracking. The V ¡ IA A tracking employing the equations derived in the characteristics of the experimental PV generator for preceding sections and the control flow chart given in three different solar insolations (ª2 = 30%, ª3 = Fig. 3. In these studies the PV array is simulated using 60%, and ª5 = 100%) are shown in Fig. 6. The 100% (3) and (4). The simulated dynamic MP point tracking solar insolation represents a standard intensity of characteristics at 100% solar insolation are plotted in 1000 W/m2 . The data acquisition system measures Figs. 8 and 9. At this solar insolation the experimental the instantaneous array voltage information. For a dynamic MP tracking characteristics are also obtained given load, the MP point control algorithm computes and they are superimposed in Figs. 8 and 9. The the SCA power (Pg ) from the known instantaneous simulation and experimental results are in close array voltage information V . The algorithm tracks g agreement. Discrepancies between simulation and the maximum power point continuously by adjusting experimental results may be due to 1) the difficulties the converter duty ratio such that the array power is in realizing the identical solar insolation conditions maximum. At solar insolation ª5 the experimental in the experimental setup, and 2) the fact that the power tracking characteristic is shown in Fig. 7. For analysis was made on the assumption that the two verification, the output power of the SCA is measured boost branches are identical. by sensing the SCA voltage and current. The power The experimental array power tracking characteristic so obtained is superimposed in the same characteristics for three different solar insolations (ª2 , figure. These two characteristics are closely matching ª3 and ª5 ) are also obtained as shown in Fig. 10. For each other. Slight discrepancies may be due to errors verification of the MP points of the SCA, experiments in the measuring system, drops in parasitics, etc. were conducted on the SCA by connecting a variable The simulation program was developed in load resistance. The experimental MP points obtained the MATLAB environment for the PV-supplied at different solar insolations are tabulated in Table VEERACHARY: VOLTAGE-BASED MAXIMUM POWER POINT TRACKING CONTROL OF PV SYSTEM 267 TABLE II Experimental Maximum Power Points of SCA % Solar Insolation Maximum Power (W) ª1 2.65 ª2 8.17 ª3 17.63 ª4 21.44 ª5 23.03 Fig. 8. Comparison of experimental and simulated SCA power tracking characteristics. Fig. 11. SCA power tracking characteristic for variable solar insolations. Fig. 9. Comparison of experimental and simulated duty ratio tracking characteristics. Fig. 12. Experimental SCA power tracking characteristic for partial shading conditions. SCA power output decreases and settles to a new MP point as evidenced by Fig. 12. Fig. 10. SCA power tracking characteristics for different solar insolations. VII. CONCLUSIONS II. Comparing the tracking characteristics (Fig. 10) with MP points, it can be noticed that the duty ratio of Current sensorless SCA voltage based on a MP the converter is so adjusted such that MP is extracted point tracking algorithm is developed for an IDB from the SCA. Experimental studies are also made to converter supplied PV system. Analytical expressions observe the effectiveness of the developed tracking for the SCA, and power output expressions with algorithm for changing solar insolations. Experimental converters are derived. The SFG approach is used observations (Fig. 11) show that the developed in modeling the IDB converter. Simulation and algorithm is capable of tracking MP point even for experimental results for MP tracking are presented variable solar insolations. The tracking capability of for changing solar insolations and partial shading the IDB converter system is verified under partial conditions. The inadequacy of the boost converter shading conditions also. For illustration, array power for array voltage based MP point tracking scheme tracking characteristics when few cells (4) are shaded is verified. The experimental results demonstrate by 50% are shown in Fig. 12. Under this condition the that in the array voltage based peak power tracking 268 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 38, NO. 1 JANUARY 2002 scheme the IDB converter is suitable for extracting [6] Kislovski, A. S. (1993) MP from the SCA as compared with boost converter Power tracking methods in photovoltaic applications. Proceedings of Power Conversion, (1993), 513—528. supplied PV system. Furthermore, the use of an IDB [7] Hua, C., Lin, J., and Shen, C. (1998) converter avoids the discontinuous input current mode Implementation of a DSP controlled photovoltaic system of operation and reduces the ripple in the array input with peak power tracking. current. As a consequence the reduced ripple in the IEEE Transactions on Industrial Electronics, 45 (1998), array current results in improved SCA performance. 99—107. [8] Matsui, M., Kitano, T., Xu, D.-H., and Yang, Z.-Q. (2000) New MPPT control scheme utilizing power balance at DC ACKNOWLEDGMENTS link instead of array power detection. In Proceedings of International Power Electronics Conference (IPEC), 2000, 158—163. The first author wishes to acknowledge the [9] Sharif, M. F., Alonso, C., and Martinez, A. (2000) Government of Japan for granting MONBUSHO A simple and robust maximum power point control for scholarship and JNT University authorities for ground photovoltaic generators. permission to attend these research studies. Proceedings of International Power Electronics Conference (IPEC), 2000, 164—169. [10] Won, C.-Y., Kim, D.-H., and Kim, S.-C. (1994) REFERENCES A new maximum power point tracker of photovoltaic [1] Appelbaum, J. (1986) arrays using fuzzy controller. Starting and steady-state characteristics of dc motors In Proceedings of Power Electronic Specialist Conference, powered by solar cell generators. 1994, 396—403. IEEE Transactions on Energy Conversion, 1 (1986), [11] Senjyu, T., Arashiro, Y., Uezato, K., and Hee, H. K. (1998) 17—23. Maximum power point tracking control of photovoltaic [2] Fam, W. Z., and Balachander, M. K. (1988) array using fuzzy neural network. Dynamic performance of a dc shunt motor connected to Proc. of International Conference on Power Electronics photovoltaic array. (ICPE), 1998, 987—992. IEEE Transactions on Energy Conversion, 3 (1988), [12] Hiyama, T., Kouzuma, S., Imakubo, T., and Ortmeyer, T. H. 613—617. (1995) [3] Salameh, Z., and Taylor, D. (1990) Evaluation of neural network based real time maximum Step-up maximum power point tracker for photovoltaic power tracking controller for PV system. arrays. IEEE Transactions on Energy Conversion, 10 (1995), Solar Energy, 44 (1990), 57—61. 543—548. [4] Alghuwainem, S. M. (1992) [13] Smedley, K., and Cuk, S. (1994) Steady-state performance of dc motors supplied from Switching flow-graph nonlinear modeling technique. photovoltaic generators with step-up converter. IEEE Transactions on Power Electronics, 42 (1994), IEEE Transactions on Energy Conversion, 7 (1992), 405—413. 267—272. [5] Alghuwainem, S. M. (1997) A close form solution for the maximum power operating point of a solar cell array. Solar Energy Materials and Solar Cells, 46 (1997), 249—257. VEERACHARY: VOLTAGE-BASED MAXIMUM POWER POINT TRACKING CONTROL OF PV SYSTEM 269 Mummadi Veerachary was born in Survail, AP, India in 1968. He obtained his Bachelors degree from College of Engineering Anantapur, JNT University, Hyderabad, India, in 1992 and Master of Technology from Regional Engineering College, Warangal, India in 1994. In 1994 he joined as an Assistant Professor in the Dept. of Electrical Engineering, JNTU College of Engineering, Anantapur, India. Presently, he is at the Dept. of Electrical and Electronics Engineering, University of the Ryukyus, Okinawa, Japan for his research studies. His fields of interest are power electronics, modeling and simulation of power electronics and application to photovoltaic solar energy utilization. Mr. Veerachary was the recipient of the IEEE Industrial Electronics Society student travel grant award for the year 2001. Tomonobu Senjyu was born in Saga prefecture, Japan, in 1963. He received the B.S. and M.S. degrees in electrical engineering from University of the Ryukyus, Okinawa, Japan, in 1986 and 1988, respectively, and the Ph.D. degree in electrical engineering from Nagoya University, Nagoya, Japan, in 1994. Since 1988, he has been with the Department of Electrical and Electronics Engineering, Faculty of Engineering, University of the Ryukyus, where he is currently a Professor. His research interests are in the areas of stability of ac machines, advanced control of electrical machines, and power electronics. Dr. Senjyu is a member of the Institute of Electrical Engineers of Japan. Katsumi Uezato was born in Okinawa prefecture, Japan, in 1940. He received the B.S. degree in electrical engineering from the University of the Ryukyus, Okinawa, Japan, in 1963, the M.S. degree in electrical engineering from Kagoshima University, Kagoshima, Japan, in 1972, and the Ph.D. degree in electrical engineering from Nagoya University, Nagoya, Japan, in 1983. Since 1972, he has been with the Department of Electrical and Electronics Engineering, Faculty of Engineering, University of the Ryukyus, where he is currently a Professor. He is engaged in research on stability, control of synchronous machines and power electronics. Dr. Uezato is a member of the Institute of Electrical Engineers of Japan. 270 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 38, NO. 1 JANUARY 2002

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