Voltage-Based Maximum Power Point Tracking Control of PV System

Transcription

1 I. NOMENCLATURE Voltage-Based Maximum Power Point Tracking Control of PV System MUMMADI VEERACHARY, Student Member, IEEE TOMONOBU SENJYU, Member, IEEE KATSUMI UEZATO University of the Ryukyus Japan Photovoltaic (PV) generators exhibit nonlinear v-i characteristics and maximum power (MP) points that vary with solar insolation. An intermediate converter can therefore increase efficiency by matching the PV system to the load and by operating the solar cell arrays (SCAs) at their maximum power point. An MP point tracking algorithm is developed using only SCA voltage information thus leading to current sensorless tracking control. The inadequacy of a boost converter for array voltage based MP point control is experimentally verified and an improved converter system is proposed. The proposed converter system results in low ripple content, which improves the array performance and hence a lower value of capacitance is sufficient on the solar array side. Simplified mathematical expressions for a PV source are derived. A signal flow graph is employed for modeling the converter system. Current sensorless peak power tracking effectiveness is demonstrated through simulation results. Experimental results are presented to validate the proposed method. Manuscript received March 14, 2000; revised July 3, 2001; released for publication July 26, IEEE Log No. T-AES/38/1/ Refereeing of this contribution was handled by I. Batarseh. Authors address: Dept. of Electrical and Electronics Engineering, Faculty of Engineering, University of the Ryukyus, 1 Senbaru, Nishihara-cho, Nakagami, Okinawa , Japan /02/$17.00 c 2002 IEEE C, C a Filter, array capacitance d 1, d 2 Duty ratios of switch S 1,S 2 D P1, D P2 Diodes of individual boost cells I A SCA current I Ab SCA current with boost converter I Ad SCA current with IDB converter I m SCA current at maximum power operation I ab Average load current with boost converter I aid Average load current with IDB converter I ph Insolation dependent photo current I 0 Cell reverse saturation current L 1, L 2 Inductances of individual boost cells N s, N p Number of SCA cells in series, parallel P gb, P gd SCA power output with boost, IDB converter P m Maximum power of the SCA R 1, R 2 Inductor series resistances R s Cell series resistance R Load resistance S 1, S 2 Switches of individual boost cells V Ab, V Ad SCA voltage with boost, IDB converter V m SCA voltage at maximum power operation V ab, V aid Average load voltage with boost, IDB converter b, id Efficiency of the boost, IDB converter ª Solar insolation. II. INTRODUCTION The rapid trend of industrialization of nations and increased interest in environmental issues recently led us to explore the use of renewable forms such as solar energy. Photovoltaic (PV) generation is 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 insolation, there is a unique operating point of the PV generator at which its power output is maximum. Therefore, for maximum utilization efficiency, it is necessary to match the PV generator to the load such that the equilibrium operating point coincides with the MP point of the PV source. However, since the MP point varies with insolation and seasons, it is difficult to maintain MP operation at all solar insolations. To overcome this problem, use of an intermediate dc-dc converter is proposed [3 5], which continuously 262 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 38, NO. 1 JANUARY 2002

2 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 intuition. To overcome some of the disadvantages mentioned above, a fuzzy neural network based MP point tracking is proposed [11]. All these methods depend on the SCA power output and/or load power detection using the instantaneous voltage and current information, requiring voltage and current sensors. Neural network based real time MP tracking controller for PV grid connected systems has been reported [12]. The studies emphasize that the SCA operating point is shifted to its MP point by using a voltage control type inverter, which utilizes the array voltage together with pilot cell voltage information. Array voltage based MP point tracking using dc-dc converters is currently under investigation by various researchers. This method of MP tracking has advantages like straightforward array voltage measurement (which is inexpensive as compared with the measurements of solar insolation, and other environmental factors), no need of current sensors, (which introduces losses and complexity in the system) etc. The authors have tried to implement boost converter array voltage based MP point control. The experimental investigations show that boost converters are not suitable for array voltage based MP point tracking control as this leads to an undesirable operation. An alternate converter scheme (interleaved dual boost (IDB) converter) is proposed by the authors for array voltage based MP extraction, by simple addition of one more boost cell in parallel to the existing boost cell and controlling these two boost cells in an interleaved fashion. The advantages of the present converter system are 1) ripple cancellation both in the input and output waveforms to the maximum extent possible, 2) lower value of ripple amplitude, and high ripple frequency in the resulting input and output waveforms, and 3) reduced electromagnetic interference (EMI) because of low ripple amplitude of SCA current. Although the interleaving technique increases the number of components, the actual increase of cost may not be significant. This is because more boost cells can share the current flow in the inductors and switching devices, so lower current rating devices may be employed. Further, parallel connection of converters has many desirable properties such as reduced device Fig. 1a. Experimental setup of PV system. stresses, fault tolerance for the system, flexibility in the system design, etc. This paper presents MP point tracking of SCA employing an intermediate interleaved dual boost (IDB) converter using only the array voltage information, eliminating the array current detection and hence achieving current sensorless peak power tracking. This paper is organized as follows. In Section III, we present the development of mathematical models for the PV generator and power converters. Maximum power point tracking control process is discussed in Section IV. Experimental system description is given in Section V. Section VI presents experimental results, and conclusions are provided in Section VII. III. MATHEMATICAL MODEL OF SYSTEM Fig. 1(a) shows the overview of the combined system, which mainly consists of SCA, IDB converter, and data acquisition system. The analysis of the system is carried out under the following assumptions. 1) Switching elements (MOSFET and diode) of the converter are assumed to be ideal, i.e., forward voltage drops and ON-state resistances of the switches are neglected. 2) The equivalent series resistance of the capacitance and stray capacitances are neglected. 3) Passive components (R,L,C) areassumedtobe linear, time invariant, and frequency independent. 4) The two parallel boost cells are identical and operate in the continuous inductor current mode. 5) The switches (S 1,S 2 ) operate in interleaved fashion. Mathematical models for individual components are developed in the following sections. A. PV Generator Model The PV generator is formed by the combination of many PV cells connected in series and parallel to provide the desired output voltage and current. This VEERACHARY: VOLTAGE-BASED MAXIMUM POWER POINT TRACKING CONTROL OF PV SYSTEM 263

3 PV generator exhibits a nonlinear insolation dependent v-i characteristic, mathematically expressed for the SCA consisting of N s cells in series and N p cells in parallel [1] as V A = I A R s à N s N p! + µ ( Ns ln 1+ N p I ph I ) A N p I 0 (1) where =(q=akt), q electric charge; A completion factor; K Boltzmann s constant; T absolute temperature; R s cell series resistance; I ph photo current; I 0 cell reverse saturation current; I A, V A are the SCA current and voltage, respectively. For given values of SCA parameters, the V A I A characteristic depends on the solar insolation and the MP point varies with the solar insolation. Rewriting (1) as Ã! µ N V A = I A R s Ns s + " ln N p µ Ipha I 0 +ln Ã!# 1 I A N p I pha (2) where I pha = I ph + I 0. Expanding the term ln(1 (I A =N p I pha )) into Taylor series and neglecting higher order terms [5] results in the following equation Ã! V A = I A R sg + 2N µ µ s Ns Ipha + ln : N p I pha I 0 (3) Simplifying the above equation for the SCA current results in the following equation. µ 1 Ns Ipha I A = Ã! R sg + 2N ln V I A (4) s 0 N p I pha where R sg = N s R s =N p. The equations (3) and (4) are used in the simulation studies. B. Boost Converter Model The intermediate boost converter produces a chopped output voltage and controls the average dc voltage applied to the load. Further, the converter continuously matches the output characteristic of the PV generator to the input characteristic of the load. The steady-state voltage and current relations of the boost converter operating in continuous current mode are V ab = V Ab (5) (1 d) I ab = b(1 d)i Ab (6) where b is the efficiency of the boost converter, V Ab,I Ab are the array voltage and current, respectively. Transforming the load to the SCA side (Fig. 1(b)), Fig. 1b. Equivalent circuit of system. then the reflected equivalent load on the SCA side is given by the following equation R eq = b(1 d) 2 R (7) i.e., V Ab = I b(1 d) 2 R: (8) Ab Power extracted by the boost converter from the SCA is P gb = V 2 Ab b(1 d) 2 R : (9) From the above expression the array power P gb depends on the load and converter duty ratio. For a given load, the array power continuously increases with duty ratio, theoretically resulting in minimum power at d = 0 and infinite power at d =1,atwhich the SCA voltage collapses, leading to an undesirable operation. Furthermore, the power P gb is continuously increasing with duty ratio, and hence with this power comparison method it may not be possible to reach the MP point. To overcome this disadvantage an identical boost branch is connected in parallel to the existing one and controlls these two branches in complementary fashion. The analytical discussion of this converter is given in the following section. C. IDB Converter Model The intermediate IDB converter produces a chopped output dc voltage and controls the average dc voltage applied to the load. Further, the converter continuously matches the output characteristic of the PV generator to the input characteristic of the load so that MP is extracted from the SCA. The steady-state voltage and current relations of the IDB converter operating in continuous current mode are derived using signal flow graph (SFG) technique [13]. The steady-state signal flow graph of the IDB converter is obtained as shown in Fig. 2. Voltage gain is derived by employing the well-known Mason s gain formula. To start with various possible forward paths and loops are identified from the steady-state SFG (Fig. 2). The forward paths transmittances formed by the nodes 264 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 38, NO. 1 JANUARY 2002

4 Fig. 2. Steady-state SFG of IDB converter. (V g V 1 I L1 I 0 V 0 ), (V g V 2 I L2 I 0 V 0 )are P 1 = d 2 R R 1 (10) P 2 = d 1 R : (11) R 2 In this steady-state SFG two loops formed by the nodes (V 2 I L2 I 0 V 2 ), (V 1 I L1 I 0 V 0 V 1 )exist and their loop transmittances are L 1 = Rd2 1 R 2 (12) L 2 = Rd2 2 : (13) R 1 Applying Mason s gain formula the steady-state voltage gain obtained as V aid R(R = 1 d 1 + R 2 d 2 ) V Ad R 1 R 2 + R(R 1 d1 2 + R 2 d2 2 ) (14) where d 1,d 2 are the duty ratios of the switches S 1,S 2, respectively. The IDB converter switching devices (S 1,S 2 ) are activated in complementary mode with duty ratios d 1 and d 2, satisfying the relation d 1 + d 2 = 1. If the two parallel boost cells are identical (R 1 = R 2 = r; R À r) then the above equation becomes V Ad V aid = (d1 2 + (15) d2 2 ): Substituting d 1 = d, d 2 =(1 d), the above equation can be written as V V aid = Ad (2d 2 2d +1) : (16) Using power balance, the current expression is obtained as I aid = id (d1 2 + d2 2 )I Ad (17) where id is the efficiency of the IDB converter, V Ad,I Ad are the array voltage and current, respectively. Transforming the load to the SCA side (Fig. 1b), then the reflected equivalent load on the SCA side is given by the following equation R eq = id (2d 2 2d +1) 2 R (18) i.e., V Ad = id (2d 2 2d +1) 2 R: (19) I Ad Substituting the I Ad = I A expression (from (4)) in the above expression then V Ad = [ id(2d2 2d +1) 2 µ R] Ns Ipha Ã! R sg + 2N ln V I Ad : s 0 N p I pha (20) On simplification the array voltage equation becomes µ V Ad = [ id(2d2 2d +1)RN s ] Ipha [K + id (2d 2 ln 2d +1)R] I 0 (21) where K =(R sg +(2N s = N p I pha )). Power extracted by the IDB converter from the SCA is P gd = V2 Ad : (22) R eq Substituting (18) and (21) in (22) then the resulting SCA power expression is P gd = ( id RN 2 s ) 2 [K + id (2d 2 2d +1)R] 2 ln µ Ipha I 0 2 : (23) From (23) it can be noticed that, for given values of the array parameters and load, the SCA power (P gd ) depends on the duty ratio of the IDB converter. Suitable adjustment of converter duty ratio results in V Ad = V m, which in turn results in extraction of MP from the SCA. IV. MAXIMUM POWER POINT TRACKING CONTROL PROCESS The control flow chart is given in Fig. 3, which controls the tracking process of the PV supplied converter system. The tracking process can be started by outputting the command signal either 0 or 5 V to the pulsewidth modulation (PWM) generator, which corresponds to duty ratio of zero or one, respectively. Whatever may be the duty ratio (0-1) the array power (P g ) is computed from the (22) using the already VEERACHARY: VOLTAGE-BASED MAXIMUM POWER POINT TRACKING CONTROL OF PV SYSTEM 265

5 Fig. 4. Power tracking process with duty ratio. V. EXPERIMENTAL SYSTEM DESCRIPTION Fig. 3. Flow chart for MP point tracking. sensed array voltage. Change (increase or decrease) the duty ratio and then measure the instantaneous array power. This power is compared with the previous power and a decision on whether to increase or decrease the duty ratio is taken depending on the location of the operating point and direction of its movement as indicated in Fig. 4. As a consequence, there are four possibilities (two if the operating point is left of the MP point, two if the operating point is right of the MP point) for the operating point movement. The duty ratio control signal is continuously adjusted to maximize the array power by following the equation d = d d. The sign of the incremental duty ratio ( d) is determined by the incremental power ( P) and operating point movement as indicated in Fig. 4. If P is positive and the operating point is left of MP point, then d =(d + d), otherwise d =(d d). Along similar lines, if the P is negative and the operating point is left of the MP point, then d =(d + d), otherwise d = (d d). This tracking control process repeats itself until the peak power point is reached and then oscillates within an allowable range about this point. In the simulated MP point tracking process the instantaneous array voltage and power are computed employing the models developed in preceding sections, whereas in real time computer implementation the instantaneous array voltage, power information is obtained by means of data acquisition system. The MP point tracking process both in simulation and real time computer implementation are same except the above mentioned difference. 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 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. The reference signal to this comparator is the signal obtained from the D/A converter, generated by means of the MPPT algorithm. A synthesized YOKOGAWA function generator (FG120) was used to obtain phase displaced triangular carrier signals to the PWM generator. The experimental prototype circuit was built with an International Rectifier IRF530N MOSFET with suitable driver circuit, and the diode FML-32S. The artificial sun is realized in the laboratory by means of incandescent lamp set. Further, the solar insolation level illuminated on the solar panel is adjusted by controlling the power to this incandescent lamp set. VI. EXPERIMENTAL RESULTS AND DISCUSSIONS The simple boost converter is not able to track MP point by sensing only the array voltage information. This is because the equivalent load impedance (in (7)) seen by the SCA is continuously decreasing with increasing the duty ratio. Further, from the (9) for a given load, the array power continuously increases with the duty ratio, resulting in minimum power at d = 0 and infinite power at d = 1, which is physically an unrealizable condition. This phenomena is verified experimentally and the corresponding characteristics are shown in Fig. 5. To overcome this disadvantage and to extract MP from the SCA using only the array voltage, an identical boost cell is connected in parallel to the existing boost cell as shown in the experimental setup (Fig. 1(a)). These two boost branches are controlled in an interleaved fashion using phase shift between the gate signals. This converter 266 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 38, NO. 1 JANUARY 2002

6 Fig. 5. Array characteristics with boost converter. Fig. 7. Comparison of experimental SCA power tracking characteristics. TABLE I SCA and Converter Parameters Fig. 6. Experimental V A I A characteristics of SCA module for different solar insolations. 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 discontinuous current mode. Prototype PV-supplied converter (SCA and converter parameters are given in Table I) system was bread boarded to study the array voltage based maximum power point tracking. The V A I A characteristics of the experimental PV generator for three different solar insolations (ª 2 = 30%, ª 3 = 60%, and ª 5 = 100%) are shown in Fig. 6. The 100% solar insolation represents a standard intensity of 1000 W/m 2. The data acquisition system measures the instantaneous array voltage information. For a given load, the MP point control algorithm computes the SCA power (P g ) from the known instantaneous array voltage information V g. The algorithm tracks the maximum power point continuously by adjusting the converter duty ratio such that the array power is maximum. At solar insolation ª 5 the experimental power tracking characteristic is shown in Fig. 7. For verification, the output power of the SCA is measured by sensing the SCA voltage and current. The power characteristic so obtained is superimposed in the same figure. These two characteristics are closely matching each other. Slight discrepancies may be due to errors in the measuring system, drops in parasitics, etc. The simulation program was developed in the MATLAB environment for the PV-supplied N p 1 N s 27 R s V 1 I o A R R L mh L mh C 220 ¹F C a 2200 ¹F f s 25 khz R 50 converter system (shown in Fig. 1(a)). Comprehensive simulation studies were made to investigate the influence of IDB converter as an intermediate MP point tracker for the PV supplied system. A simulation software is developed for MP point tracking employing the equations derived in the preceding sections and the control flow chart given in Fig. 3. In these studies the PV array is simulated using (3) and (4). The simulated dynamic MP point tracking characteristics at 100% solar insolation are plotted in Figs. 8 and 9. At this solar insolation the experimental dynamic MP tracking characteristics are also obtained and they are superimposed in Figs. 8 and 9. The simulation and experimental results are in close agreement. Discrepancies between simulation and experimental results may be due to 1) the difficulties in realizing the identical solar insolation conditions in the experimental setup, and 2) the fact that the analysis was made on the assumption that the two boost branches are identical. The experimental array power tracking characteristics for three different solar insolations (ª 2, ª 3 and ª 5 ) are also obtained as shown in Fig. 10. For verification of the MP points of the SCA, experiments were conducted on the SCA by connecting a variable load resistance. The experimental MP points obtained at different solar insolations are tabulated in Table VEERACHARY: VOLTAGE-BASED MAXIMUM POWER POINT TRACKING CONTROL OF PV SYSTEM 267

7 TABLE II Experimental Maximum Power Points of SCA % Solar Insolation Maximum Power (W) ª ª ª ª ª 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. Fig. 10. SCA power tracking characteristics for different solar insolations. II. Comparing the tracking characteristics (Fig. 10) with MP points, it can be noticed that the duty ratio of the converter is so adjusted such that MP is extracted from the SCA. Experimental studies are also made to observe the effectiveness of the developed tracking algorithm for changing solar insolations. Experimental observations (Fig. 11) show that the developed algorithm is capable of tracking MP point even for variable solar insolations. The tracking capability of the IDB converter system is verified under partial shading conditions also. For illustration, array power tracking characteristics when few cells (4) are shaded by 50% are shown in Fig. 12. Under this condition the SCA power output decreases and settles to a new MP point as evidenced by Fig. 12. VII. CONCLUSIONS Current sensorless SCA voltage based on a MP point tracking algorithm is developed for an IDB converter supplied PV system. Analytical expressions for the SCA, and power output expressions with converters are derived. The SFG approach is used in modeling the IDB converter. Simulation and experimental results for MP tracking are presented for changing solar insolations and partial shading conditions. The inadequacy of the boost converter for array voltage based MP point tracking scheme is verified. The experimental results demonstrate that in the array voltage based peak power tracking 268 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 38, NO. 1 JANUARY 2002

8 scheme the IDB converter is suitable for extracting MP from the SCA as compared with boost converter supplied PV system. Furthermore, the use of an IDB converter avoids the discontinuous input current mode of operation and reduces the ripple in the array input current. As a consequence the reduced ripple in the array current results in improved SCA performance. ACKNOWLEDGMENTS The first author wishes to acknowledge the Government of Japan for granting MONBUSHO scholarship and JNT University authorities for permission to attend these research studies. REFERENCES [1] Appelbaum, J. (1986) Starting and steady-state characteristics of dc motors powered by solar cell generators. IEEE Transactions on Energy Conversion, 1 (1986), [2] Fam, W. Z., and Balachander, M. K. (1988) Dynamic performance of a dc shunt motor connected to photovoltaic array. IEEE Transactions on Energy Conversion, 3 (1988), [3] Salameh, Z., and Taylor, D. (1990) Step-up maximum power point tracker for photovoltaic arrays. Solar Energy, 44 (1990), [4] Alghuwainem, S. M. (1992) Steady-state performance of dc motors supplied from photovoltaic generators with step-up converter. IEEE Transactions on Energy Conversion, 7 (1992), [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), [6] Kislovski, A. S. (1993) Power tracking methods in photovoltaic applications. Proceedings of Power Conversion, (1993), [7] Hua, C., Lin, J., and Shen, C. (1998) Implementation of a DSP controlled photovoltaic system with peak power tracking. IEEE Transactions on Industrial Electronics, 45 (1998), [8] Matsui, M., Kitano, T., Xu, D.-H., and Yang, Z.-Q. (2000) New MPPT control scheme utilizing power balance at DC link instead of array power detection. In Proceedings of International Power Electronics Conference (IPEC), 2000, [9] Sharif, M. F., Alonso, C., and Martinez, A. (2000) A simple and robust maximum power point control for ground photovoltaic generators. Proceedings of International Power Electronics Conference (IPEC), 2000, [10] Won, C.-Y., Kim, D.-H., and Kim, S.-C. (1994) A new maximum power point tracker of photovoltaic arrays using fuzzy controller. In Proceedings of Power Electronic Specialist Conference, 1994, [11] Senjyu, T., Arashiro, Y., Uezato, K., and Hee, H. K. (1998) Maximum power point tracking control of photovoltaic array using fuzzy neural network. Proc. of International Conference on Power Electronics (ICPE), 1998, [12] Hiyama, T., Kouzuma, S., Imakubo, T., and Ortmeyer, T. H. (1995) Evaluation of neural network based real time maximum power tracking controller for PV system. IEEE Transactions on Energy Conversion, 10 (1995), [13] Smedley, K., and Cuk, S. (1994) Switching flow-graph nonlinear modeling technique. IEEE Transactions on Power Electronics, 42 (1994), VEERACHARY: VOLTAGE-BASED MAXIMUM POWER POINT TRACKING CONTROL OF PV SYSTEM 269

9 Mummadi Veerachary was born in Survail, AP, India in 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 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 Tomonobu Senjyu was born in Saga prefecture, Japan, in 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 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 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 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