Residential Photo Voltaic Energy Storage System

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 45, NO. 3, JUNE 1998

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Residential Photovoltaic Energy Storage System S. J. Chiang, K. T. Chang, and C. Y. Yen

Abstract—This paper introduces a residential photovoltaic (PV) energy storage system, in which the PV power is controlled by a dc–dc converter and transferred to a small battery energy storage system (BESS). For managing the power, a pattern of daily operation considering the load characteristic of the homeowner, the generation characteristic of the PV power, and the powerleveling demand of the utility is prescribed. The system looks up the pattern to select the operation mode, so that powers from the PV array, the batteries, and the utility are utilized in a cost-effective manner. As for the control of the system, a novel control technique for the maximum power-point tracking (MPPT) of the PV array is proposed, in which the state-averaged model of the dc–dc converter, including the dynamic model of the PV array, is derived. Accordingly, a high-performance discrete MPPT controller that tracks the maximum power point with zero-slope regulation and current-mode control is presented. With proposed arrangements on the control of the BESS and the current-to-power scaling factor setting, the dc–dc converter is capable of combining with the BESS for performing the functions of power conditioning and active power filtering. An experimental 600-W system is implemented, and some simulation and experimental results are provided to demonstrate the effectiveness of the proposed system. Index Terms— Active power filtering, battery energy storage system, maximum power-point tracking, power conditioning.

I. INTRODUCTION

T

HE residential photovoltaic (PV) system has great potential of being a significant market, due to the following advantages [1]: 1) translating the utility value into an allowable system cost using the homeowner economic parameters and 2) the PV system is able to utilize the roof for support structure, eliminating land and direct structure expense. However, it suffers an interface issue with the utility that should be solved before a large number of them are applied [2]. The small battery energy storage system (BESS) that possesses the functions of power conditioner, active power filter, and uninterruptible power supply (UPS) has been demonstrated to be effective for interfacing with the utility and providing reliable power to the load [3], [4]. In this paper, the PV power is controlled by a dc–dc converter and transferred to the BESS proposed in [3] and [4] to form a residential PV energy storage system. In addition to the advantages of the BESS, the proposed system possesses flexible capability in power usage. In Section II, it will be shown that, if load characteristic of the homeowner, generation characteristic of the PV power, and load demand of the utility have been prescribed, the proposed system is able to allow an optimal Manuscript received January 13, 1997; revised August 24, 1997. The authors are with the Department of Electrical Engineering, National Lien Ho College of Technology and Commerce, Miao-Li, Taiwan, R.O.C. Publisher Item Identifier S 0278-0046(98)03557-6.

power management strategy to be used, so that all powers in the system are utilized in a cost-effective manner. As for the control of the proposed system, to increase the conversion efficiency of the PV power, the dc–dc converter is used for tracking the maximum power point of the PV array. It is appropriate to employ current-mode control of the dc–dc converter in the proposed system to coordinate the PV power with the power conditioning function of the BESS in the best way. Although some papers [5]–[11] have proposed different maximum power-point tracking (MPPT) algorithms in the past, MPPT with current-mode control was seldom addressed. In addition, these MPPT control algorithms do not consider the dynamic behavior of the PV array, thus, stability and performance of the MPPT control are hard to evaluate. In Section III, the derivation of the small-signal model of the dc–dc converter, including the dynamic model of the PV array, is proposed first. Based on this model, a novel discrete MPPT controller that tracks the maximum power point with zero-slope regulation and current-mode control is presented. As a result, the MPPT controller, including the current-mode controller, is able to be designed quantitatively, and good control performance is achieved. Following suitable arrangements on the current-to-power scaling factor setting and the controllers of the BESS, the dc–dc converter is able to cooperate with the BESS for performing the functions of power conditioning and active power filtering. In each mode, the power flows in the system are balanced and programmable with significant stability. Since it is difficult to change the operating condition in the real field tests, the performance of the proposed MPPT controller is examined first by simulation in Section IV. In Section V, an experimental 600-W system is implemented, and its effectiveness is demonstrated by some measured results. Finally, some conclusions are made in Section VI. II. POWER MANAGEMENT OF THE PROPOSED SYSTEM The power circuit of the proposed PV energy storage system is shown in Fig. 1. It consists of a PV array, a dc–dc converter and a single-phase battery energy storage system that is formed by a bidirectional converter and connects with the batteries, the load, and the utility. There is one power source (the PV array), one power sink (the load), and two power sources/sinks (the batteries and the utility), which are paralleled in the system. According to possible power flow conditions among these parallel components, operation of the proposed system can be cataloged into four operation modes, as shown in Fig. 2. Since each component has its own cost and characteristics for power generation or consumption, operation of the proposed system is designed with consideration of the following factors:

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Fig. 1. The power circuit of proposed PV energy storage system.

(a)

Fig. 3. A pattern of daily operation of the proposed system. (b)

(c)

(d) Fig. 2. Four operation modes of the proposed system. (a) Mode 1. (b) Mode 2. (c) Mode 3. (d) Mode 4.

A. Load Characteristic of the Homeowner From the viewpoint of the homeowner, the best policy is to minimize the kilowatthour cost from the utility and sell excess power to the utility in the peak-load period of the utility. For this reason, the load characteristic of the homeowner should be explored. It is usually case by case and dependent on the homeowner preference. B. Generation Characteristic of the PV Power For a roof-mounted PV array, the insolating level and the solar path are changed with time, and the daily generation characteristic of the PV power should be analyzed for determining the best way to utilize the PV power. C. Power-Leveling Demand of the Utility A typical power-leveling demand of the utility is to share the peak-load burden of the utility with the stored energy and

restore the energy with the off-peak utility power to reshape the power level of the utility [12]. Based on these considerations, if the daily power profile related to each factor is prescribed, it is possible to determine an optimal pattern of daily operation from the viewpoint of the utility, as well as the homeowner. Fig. 3 shows a design example, where the homeowner is a typical modern family. The daily operation is formed by the operation modes shown in Fig. 2 and arranged in a sequence as follows. Off-Peak Load Period (Mode 1): From midnight to daybreak, the PV power is absent, and the utility recharges the batteries and supplies the load power simultaneously. Low-Insolation Period (Mode 2): In early morning, the PV power is present, yet not large enough to charge the batteries and supply the load power; the insufficiency is supplied by the utility. High-Insolation Period (Mode 3): From late morning to middle evening, the PV power is larger than the demand for charging the batteries and supplying the load power; the excess power can be fed to the utility. Discharging Period (Mode 4): From late evening to midnight, the utility power is minimized, the load power is supplied by the PV array and the discharging batteries initially; as PV power gradually decreases to zero, the load power is finally supplied all by batteries. It is evident that the pattern of daily operation described above is cost effective, since the charge of batteries is in terms of the free PV power and the off-peak utility power that is low cost in power generation; the discharging power of batteries is used to supply the peak-load power of the homeowner to save the kilowatthour cost from the utility. Furthermore, if the power policy is permissible, the excess PV power can be sold to the utility in the peak-load period of the utility. It should be noted that, if the characteristic of any factor is changed, the pattern of daily operation should be redesigned

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Fig. 4. Configuration of the proposed system.

based on the aforementioned considerations. There is no unique solution applicable for any case, however, the proposed four operation modes indeed provide a flexible circumstance for the homeowner to program his/her own system in the best way. III. CONTROL

OF THE

PROPOSED SYSTEM

The configuration of the proposed PV energy storage system is shown in Fig. 4, in which the dc–dc converter is a boost type used to step up the PV voltage to the level of the dc link of the single-phase system; the bidirectional converter of the BESS is a single-phase full-bridge converter. The control system consists of three parts, namely, the PV control section, the BESS control section, and the operation mode control section. The PV control section is used to control the dc–dc converter for transferring maximum power from the PV array to the dc link. The BESS control section is used to control the bidirectional converter for performing the functions of power conditioning and active power filtering. Based on a prescribed pattern of operation and the operating condition, the operation mode control section generates the mode selection

signal for controlling the switch SW. Detailed descriptions of these control sections follow. A. PV Control Section The PV control section employs multiloop control with the inductor current of the boost converter in the inner loop for achieving fast dynamic response. The outer loop is the MPPT controller that tracks the maximum power point of the PV array to produce the converter current command ; the inner loop then executes the current-mode control to let the converter current follow closely. The theoretical base and the design of the PV control section follow. B. MPPT Controller Under a stable insolation, the P–V and I–V characteristics of a roof-mounted PV array are monotonous. As shown in Fig. 5(a), they are functions of voltage, insolation level, and temperature [7], [11]. From these characteristics, some important properties for the design of the proposed MPPT controller are concluded, as follows.

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(a)

(b)

(c) Fig. 5. The characteristics of PV array. (a) I–V and P–V characteristics. (b) m and b characteristics (25  C/1sun). (c) dPP V =dVP and IP characteristics (25  C/1sun).

1) The PV array consists of two segments; one is the constant voltage segment, and the other is the constant current segment. Therefore, it is reasonable to approximate the I–V characteristics in both segments as (1) where and are positive reals. Fig. 5(b) shows the values of and that are obtained from the I–V characteristic of Fig. 5(a). is equivalent to the output conductance of the PV array. In the constant-current segment, is small, so the PV array exhibits a high negative output impedance. On the contrary, it exhibits a small negative output impedance in the constant-voltage segment. 2) There are no local maximum power points; the only one maximum power point is global and occurs at the knee of the characteristic, i.e., at where the slope of is zero. In the constant-current segment

0 mVP

the slope is positive, while in the constant the slope is negative. With the voltage segment approximation of (1), the slope can be written as (2) Fig. 5(c) shows that this approximation is very accurate. 3) If the PV array is controlled by current, in order to move the operating point toward the zero slope point and, thus, the maximum power point, should decrease for positive slope and increase for negative slope. From the input side of the boost converter, one can obtain (3) is equal to the converter current in steady state. Therefore, adjustment of also can move the operating point toward the maximum power point.

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(a)

(b) Fig. 6. Control block diagram of the PV control section. (a) MPPT controller. (b) Current-mode controller.

Based on the above properties and the current equation listed in (3), a novel MPPT controller that tracks the maximum power point with zero slope regulation and current-mode is the control is proposed, as shown in Fig. 6(a). Where gain of the current sensor, the dynamic models of the slope and the converter model are obtained from the linearization of (2) and (3), respectively, under the assumption that the current is equal to by current-mode control. “ ” is used to represent the small variation around the operating point. A proportional integral (PI) controller is adopted for regulating the slope; it is designed as (4) is the slope error of , and and where are the proportional and integral gains of PI controller, respectively. From Fig. 6(a), the regulating performance of the closed-loop system can be derived as

where and

is the discrete time sequence,

is the sampling time,

(7) The second issue is that there exists a right-half-plane zero ; in addition, varies a lot from the constant-voltage segment to the constant-current segment. Therefore, the regulating performance of MPPT control may not be good if the right-half-plane zero is too small; it is also sensitive to the operating point if the parameters of PI controllers are fixed. To cope with these difficulties, the right-half-plane zero is made large by adopting a small input capacitor , and the regulating performance is improved by an adaptive PI controller. The adaptive rule in the proposed system is

for

constant voltage segment for

constant current segment (8)

(5)

Examining (5), there exist two control issues. First, the desires a pure differentiation that is hard slope to be realized with analog circuits in practice, so it is realized in a discrete manner in this paper. By using the backward difference approximation [13], the difference equation of the PI controller listed in (4) is derived as (6)

and are positive reals. The design where object is to make the MPPT control be usually started from the constant-voltage segment to approach the zero slope point. Since is large enough in this segment, it is easy to make and the regulating performance well by assigning proper The adaptive gains and are set large to move the operating point from the constant-current segment toward the constant-voltage segment quickly. It should be noted that the dynamic model of the converter, including the PV array shown in Fig. 6(a), should be transferred to a discrete form. Accordingly, the PI controllers are

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able to be designed quantitatively, thereby, the stability and performance of the MPPT control also can be evaluated.

control block diagram of Fig. 6(b), if the variation of can the tracking performance of be fully eliminated by to can be obtained as

C. Current-Mode Controller For the boost converter, the converter current described by

(16)

can be where

is on

(9) (17) is off

(10)

With pulsewidth modulation (PWM) switching, (9) and (10) can be averaged using the state-space averaging method [14] as

is equivalent to the bandwidth of the current loop, and a larger results in a wider bandwidth. However, a stable current loop is such that the slew rate of the amplified current error signal does not exceed that of the ramp signal. Therefore,

(11) where is the duty ratio. The small-signal equation corresponding to (11) is then obtained by a linearization procedure as

(18) is the frequency of the ramp and is, thus, the where is the maximum voltage of the switching frequency. PV array. Equation (18) limits the maximum gain of

(12) is the steady-state duty ratio. Since the where duty ratio is obtained by comparing the control signal with the ramp signal the variation of duty ratio can be expressed as (13) is the amplitude of where (12), one can obtain

Substituting (13) into

(14) where (15) The proposed current-mode controller is designed as shown in Fig. 6(b), where the small-signal model of the power stage is plotted with (14). For achieving good current-tracking and must be performance, the effect of variation of of batteries voltage is small reduced. Assume the variation and very slow, such that it is neglected in the design of is the proposed current-mode controller. As a result, owing to MPPT control, its seen as a constant. As to variation is large. In order to compensate this variation, a is employed. Owing to its ease feedforward control signal of implementation and no need for the slope compensation, the conductance current-mode control [15], [16] is adopted for the proposed system. Usually, the P or the PI controller is employed in the conductance current-mode control. Due to the batteries, the output voltage of the dc–dc converter is assumed to be constant, such that the I control to eliminate the effects of the low-frequency zero/pole created by the load and output capacitor of a conventional dc–dc converter is not necessary [15]. Therefore, a P control of the current-mode controller is enough for the proposed system. Based on the

(19) Substituting (19) and (15) into (17), the maximum bandwidth is obtained as Hz

(20)

Compared with the MPPT control, this bandwidth is large enough, so it is reasonable to assume that the current-loop gain is unity in the design of the MPPT controller. D. BESS Control Section The BESS control section shown in Fig. 4 mainly consists of four parts, namely, the current-forced switching scheme, the the discharging controller active power filter controller , and the charging controller [3], [4]. These four parts form a multiloop control system; the innermost loop is the current-forced switching scheme, the object of which is to let the converter currents closely follow its command that is generated by its outer-loop controller The active power filter controller not only regulates the real power of the bidirectional converter in a way to follow its command but also controls the converter to compensate for the reactive power and harmonic current of the load to let the utility current be of low distortion and near unity power factor. is generated by the outermost loop controller or and selected by the mode selection switch SW. For balancing various power flows in the system and achieving the power conditioning function in each mode described previously, it desires a suitable current-to-power scaling factor setting and controller design of the BESS as the PV control section is combined with the BESS control section. The proposed design is shown in Fig. 4, and detailed description follows. When the system is operated in modes 1–3, is generated by the charging controller, and the current command from the PV control section is multiplied by a factor ; then,

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Fig. 7. The operation mode control section.

subtract the battery charging command where power command

to generate the

(21) to the output current of is the scaling factor to transform the boost converter, and is the factor for scaling the current with With such an arrangement, the command power flows are balanced in each mode and flow as follows: 1) in mode 1, the real power command is only for battery charging, so the utility supplies the load real power (2) and simultaneously charges the batteries with power in mode 2, if is smaller than the batteries are charged by the PV array and the utility, as well; however, all the load real power is supplied by the utility. On the contrary, if is is not enough for supplying all the load larger than , yet real power, the PV array charges the batteries and supplies the load with real power and the difference between the load real power and is supplied from the utility automatically; is larger than and is larger than and 3) in mode 3, the load real power, so the PV panel charges the batteries and supplies all the load real power, and the difference between and the load real power is fed to the utility. is generated When the system is operating in mode 4, by the discharging controller since the utility real power command is set as zero; if is successfully regulated to

be zero, all the load real power is supplied by the PV array and batteries. As decreases to zero, all the real power is supplied by the discharging batteries. In all four modes, due to the active power filtering function of all the load harmonics and reactive power are compensated for by the bidirectional converter. The detailed design of the BESS control section is described in [3] and [4] and is neglected in this paper. E. Operation Mode Control Section The block diagram of the operation mode control section is shown in Fig. 7, which is designed based on the case shown in Fig. 3. The mode selection signal for SW is generated by looking up the ROM’s with the current time and the operating condition. In the daytime period (06:00–18:00), if it is judged as a the PV power is present normal condition,and the mode selection signal is generated by ROM1. Otherwise, it is judged as an abnormal condition, and the mode selection signal is generated by ROM2. ROM1 is programmed according to the operating pattern shown in Fig. 3 by noting that is generated by the charging controller in modes 1–3. In the abnormal condition, since the PV power is absent, the system is equivalent to a BESS. Therefore, ROM2 is programmed based on the load demand of the utility. In the evening (18:00–22:00), if the voltage of the batteries is higher than the preset value it is judged as a

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(a) Fig. 8.

(b)

Simulated results of MPPT control. (a) An increasing step change in Ip . (b) A decreasing step change in Ip .

normal condition, and the system is operated in the discharging mode (selected by ROM1). Otherwise, it is operated in the charging mode (selected by ROM2). In the nighttime period (22:00–24:00, 0:00–06:00), since it is designed to operate in charging mode, regardless of whether in normal or abnormal condition, the operation mode can be determined by ROM1 or ROM2. In this case, it is selected by ROM2. There exists a possibility that the voltage of the batteries falls below a preset level. Under this condition, the system is forced to operate in charging mode until the voltage of the batteries has returned to its normal level. IV. SIMULATION

OF THE

MPPT CONTROL

Since it is hard to adjust the operating condition of the PV array, such as the insolating level and temperature in the real field test, the following simulations are carried out instead to confirm the performance of the proposed MPPT control technique. The I–V characteristic of the PV array is described by a simplified model [11]: (22) and are the operating voltage and current of a where cell, respectively, is the charge of the electron, is the Boltzmann’s constant, is the absolute temperature, is the short-circuit current, and is the inverse saturation current of the cell. The operating voltage and current of the PV array are (23) and are the series and parallel number of cells of where the PV array, respectively. By changing the short-circuit level and temperature, various operating conditions can be set. Fig. 8 shows the simulated results of the MPPT control under a step change (thus, a step change of In Fig. 8(a), the maximum PV power is changed from about 1000 to 500 W. First, the operating point is around the 1000-W maximum power point by the MPPT control. Due to the right-half-plane zero of (5), a step decrease of makes the slope response a

instantaneous dip (marked as “ ”) with reverse polarity. This dip of the slope pushes the operating point into the constantcurrent segment. The adaptive PI controller then forces the operating point back to the constant-voltage segment quickly; since is large in this segment, MPPT is achieved with good control performance. Fig. 8(b) shows the simulated results, that the maximum PV power is changed from about 500 to 1000 W. A reverse results in a response to Fig. 8(a), the step increase of dip of the slope, and the operating point is pushed into the constant voltage segment. The MPPT is then achieved with good regulating performance. The MPPT control performance is also good when the PV array is subjected to the variation of temperature. Due to the limitation of scope, its simulated result is neglected in this paper. V. EXPERIMENTAL RESULTS Based on the above theoretical bases, a 600-W experimental system is designed and implemented as follows: each with

PV array batteries

A

C

V

AH

V W/cm

utility single-phase 110 V/60 Hz H

F V/50 kHz

ms

power switch MOSFET 450 V/13 A (boost converter) IGBT module 600 V/50 A (bidirectional converter). All of the controllers are implemented with analog circuits, and the MPPT controller are executed except that the gain

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(a)

(b) Fig. 9.

Measured waveforms of ic , i3c , and

dP

P V =dVP in MPPT control.

(a)

on a 486 PC with 1-ms sampling interval. Some typical measured results are as follows. A. MPPT Control The experiment is carried out in different insolating levels and temperatures of the PV array. Fig. 9(a) shows the and measured waveforms of one case; the close traces of show that the tracking performance of the current-mode is controller is excellent. In addition, the slope adjusted to approximate zero after a short period (about 25 sampling intervals). The related MPPT control locus is shown in Fig. 9(b); the maximum power point is about 320 W at 82 V. These results confirm that the MPPT control is successfully achieved and its performance is excellent. B. BESS Control For testing the control performance of the proposed PV energy storage system in various operation modes, the load is set as 250 W (48 full-wave resistor) at light-load condition and 630 W (48 full-wave resistor plus 16 half-wave resistor) at heavy-load condition, the charging power of batteries is set as 150 W, and the PV power from the dc–dc converter is fixed at about 500 W in the low- and high-insolation periods for testing convenience. Due to the limit of scope, only the measured waveforms of the system changed from mode 3 (high insolating period) to mode 2 (low insolating period) are

(b) Fig. 10. System operations. (a) Measured waveforms when system is changed from mode 3 to mode 2, where subscripts o; L; and u are used to represent the BESS, the load, and the utility, respectively. (b) Measured real power waveforms in various operation modes.

provided and shown in Fig. 10(a), and the mode change is carried out by changing the load from the light-load to the heavy-load condition. Initially, in the high insolating period, the PV power charges the batteries and supplies the load real power, and the excess power (about 100 W) is fed to the utility. As the load change happens, the sudden inversion indicates the insufficient power for charging batteries, of and load real power is drawn from the utility; much can be observed from the measured real power waveforms of and Owing to the active power filter controller, not only is adjustable, but, also, the reactive power the real power and harmonics current of the load are compensated for by the

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system. This can be observed from the utility current that is low distortion, even under nonlinear load at the heavy-load condition. To demonstrate the overall system operation, Fig. 10(b) shows the power waveforms of the system that operates in the sequence of mode 1, mode 3, mode 2, to mode 4. Smooth balance of power flows and successful power transformation can be observed form these measured power waveforms. VI. CONCLUSIONS This paper has proposed a residential PV energy storage system, where the PV power is controlled by a dc–dc converter and transferred to a small BESS. The proposed system, possessing the functions of power conditioner and active power filter, is capable of providing an optimal interface with the utility. The additional PV power makes the system flexible in power usage, so that all powers in the system can be utilized in a cost-effective manner. Some control techniques for realizing the functions of the proposed system, including the MPPT control of the PV array and control of power flows in the system, have been presented. A prototype 600-W system was implemented, and some simulated and experimental results were provided to demonstrate the effectiveness of the proposed system. Although the setup cost of the proposed system is high, such that it is hard to compete with the current utility power, we believe that the capital issue will be resolved if there is a political encouragement in the kilowatt price and the market is large enough.

[10] C. Y. Won, D. H. Kim, S. C. Kim, W. S. Kim, and H. S. Kim, “A new maximum power point tracker of photovoltaic arrays using fuzzy controller,” in Conf. Rec. IEEE Power Electronics Specialists Conf., 1994, pp. 396–403. [11] A. S. Kislovski and R. Redl, “Maximum-power-tracking using positive feedback,” in Conf. Rec. IEEE Power Electronics Specialists Conf., 1994, pp. 1065–1068. [12] A. Pivec, B. M. Radimer, and E. A. Hyman, “Utility operation of battery energy storage at the best facility,” IEEE Trans. Energy Conversion, vol. EC-1, pp. 47–54, Mar. 1986. [13] K. J. Astrom and B. Wittenmark, Computer-Controlled Systems: Theory and Design. Englewood Cliffs, NJ: Prentice-Hall, 1990. [14] N. Mohan, T. M. Undeland, and W. P. Robbins, Power Electronics: Converters, Applications and Design. New York: Wiley, 1995. [15] D. O’Sullivan, H. Spruyt, and A. Crausaz, “PWM conductance control,” in Conf. Rec. IEEE Power Electronics Specialists Conf., 1988, pp. 351–359. [16] A. S. Kislovski, “Small-signal, low frequency analysis of a buck type PWM conductance controller,” in Conf. Rec. IEEE Power Electronics Specialists Conf., 1990, pp. 88–95.

S. J. Chiang was born in Taiwan, R.O.C., in 1965. He received the B.S. and Ph.D. degrees from the Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan, R.O.C., in 1987 and 1994, respectively. Since 1995, he has been an Associate Professor in the Department of Electrical Engineering, National Lien Ho College of Technology and Commerce, Mioa-Li, Taiwan, R.O.C. His research interests are in the areas of power electronics, control systems, and motor drives.

REFERENCES [1] G. J. Jones, “The design of photovoltaic systems for residential applications,” in Conf. Rec. IEEE Photovoltaic Specialists Conf., 1981, pp. 805–810. [2] G. L. Campen, “An analysis of the harmonics and power factor effects at a utility intertied photovoltaic system,” IEEE Trans. Power App. Syst., vol. PAS-101, pp. 4632–4639, Dec. 1982. [3] C. M. Liaw, T. H. Chen, S. J. Chiang, C. M. Lee, and C. T. Wang, “Small battery energy storage system,” Proc. Inst. Elect. Eng., vol. 140, pt. B, no. 1, pp. 7–17, 1993. [4] S. J. Chiang, “Design and implementation of multi-functional battery energy storage systems,” Ph.D. dissertation, Dep. Elect. Eng., National Tsing Hua University, Hsin-Chu, Taiwan, R.O.C., 1994. [5] Z. Salameh and D. Taylor, “Step-up maximum power point tracker for photovoltaic arrays,” Sol. Energy Proc., vol. 44, no. 1, pp. 57–61, 1990. [6] D. B. Snyman and J. H. R. Enslin, “Analysis and experimental evaluation of a new MPPT converter topology for PV installations,” in Conf. Rec. IEEE Power Electronics Specialists Conf., 1992, pp. 542–547. [7] J. H. R. Enslin and D. B. Snyman, “Simplified feed-forward control of the maximum power point in PV installations,” in Conf. Rec. IEEE Industrial Electronics Conf., 1992, pp. 542–547. [8] U. Herrmann, H. G. Langer, and H. Broeck, “Low cost DC to AC converter for photovoltaic power conversion in residential applications,” in Conf. Rec. IEEE Power Electronics Specialists Conf., 1993, pp. 588–594. [9] V. Arcidiacono, S. Corsi, and L. Lambri, “Maximum power point tracker for photovoltaic power plants,” in Conf. Rec. IEEE Photovoltaic Specialists Conf., 1982, pp. 507–512.

K. T. Chang was born in Taiwan, R.O.C, in 1964. He received the M.S.E.E. degree from the National Taiwan University of Science and Technology, Taipei, Taiwan, R.O.C., in 1991. During 1988, he was an Engineer with ChungHwa Electrical Communication Company, Taiwan, R.O.C. In 1990, he joined the Two-Way Automatic Controlled System Group, Taiwan Power Power Company. Since 1991, he has been a Lecturer in the Department of Electrical Engineering, National Lien Ho College of Technology and Commerce, Miao-Li, Taiwan, R.O.C. His research interests are in the areas of power electronics and power systems.

C. Y. Yen was born in Taiwan, R.O.C., in 1959. He received the B.S.E.E. degree from the National Taiwan University of Science and Technology, Taipei, Taiwan, R.O.C., in 1986. He is presently a Lecturer in the Department of Electrical Engineering, National Lien Ho College of Technology and Commerce, Miao-Li, Taiwan, R.O.C. His research interests are in the areas of motor drives, power electronics, and control systems.