Multiobjective MPPT/Charging Controller for Standalone PV Power Systems under Different Insolation and Load Conditions

Zhenhua Jiang and Roger A. Dougal

Department of Electrical Engineering University of South Carolina Columbia, SC 29208, USA

Email: [jiang, dougal]@engr.sc.edu Phone: +1-803-777-7890

Fax: +1-803-777-8045

Abstract This paper presents a novel multiobjective control algorithm for standalone PV power systems that can track the maximum power point of the solar array while limiting the charging/discharging current and voltage of the battery under different insolation and load conditions. A state machine model of the multiobjective control algorithm is described. The large-signal stability of the system is analyzed. The controller design is verified by numerical simulation in the Virtual Test Bed (VTB) environment for orbital and land-based applications. Simulation results show that the control strategy is robust and demonstrate that the power converter can be appropriately regulated to meet multiple objectives required by standalone PV power systems.

Index Terms PV power system, battery charger, MPPT, multiobjective control, state machine model.

I. INTRODUCTION As the concerns of the fossil fuel exhaustion and the envi-

ronmental pollution increase, renewable energy conversion systems become more and more attractive. Among them, photovoltaic (PV) power generation systems stand out as an important solution because they produce electrical power without introducing environmental pollution by directly converting the solar energy into electricity and also because the solar energy is unexhausted. They can find various applications such as those for the household appliances, for the soldiers in the remote missions, for the solar cars, and even for the electric aircrafts [1]. They can be built into a power plant and then connected to the power grid through appropriate power conversion interfaces [2]. Also, they are ubiquitous in the spacecrafts where the sunlight is sufficient.

Since the solar insolation varies with time and the solar cell has a nonlinear voltage-current characteristic [3], subject to vary with the change of the operating conditions such as solar insolation, the ambient temperature, the load, wind, etc, the PV system has to track the maximum power point (MPP) by controlling a DC/DC converter interposed between the solar array and the power bus to ensure the efficient operation. The objective of maximum power point tracking (MPPT) is to continuously tune the power converter so that it draws maximum power from the solar array regardless of weather or load conditions. Many MPP tracking algorithms have been developed [4]-[9]. Perturb and Observe [4] and Incremental Conductance [5] are the most widely used methods. Other MPPT techniques include short-circuit

current method [6], and the open-circuit voltage method [7]. Recently, some other methods such as fuzzy controller or neural network controller have been developed for maximum power point tracking [8], [9]. The battery is generally used in a standalone PV power system to store energy when the solar insolation is sufficient or the load is light and to provide energy in the case of no sunlight or a heavy load [10], [11].

In existing MPPT systems, there are two kinds of configurations: series and parallel configurations. The series MPPT system, as shown in Figure 1, is considered here. In this system, in order to save components and to increase system efficiency, the power converter acts not only as a maximum power point tracker but also as a charger to manage the state-of-charge of the battery by regulating the charging current or voltage. In this case, control of the power converter is actually a multiobjective control problem [12], [13]. Rather than being controlled to serve as a sole voltage or current regulator, the power converter is required to regulate and balance the power flow between the solar array and the battery under different insolation and load conditions for three objectives: (1) to maximize the output power from the solar array when the load is heavy or the solar insolation is weak, (2) to limit the charging current of the battery when the load is light or the solar insolation is strong, and (3) to limit the voltage of the battery to prevent overcharging.

Figure 1. MPPT/charging configuration of a standalone PV power system.

This paper presents a multiobjective control algorithm for standalone PV power systems that can track the maximum power point while limiting the current/voltage of the battery under different insolation and load conditions. A state machine model of the multiobjective control algorithm is described. The mode changes and large-signal behaviors of the system are analyzed. The controller design is verified by simulation in the Virtual Test Bed (VTB) environment [14].

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II. MULTIOBJECTIVE MPPT/CHARGING ALGORITHM

A. Multiobjective Control Algorithm

In the MPPT/charging configuration shown in Figure 1, the only control input is the duty cycle of the power converter. By changing the duty cycle, the output current of the solar array and the current (or voltage) of the battery can be regulated, but not independently. The control strategy that we describe here has three regulation modes: maximum power point tracking (MPPT) mode, battery current limit (BCL) mode, and battery voltage limit (BVL) mode. The battery voltage is an important index of the regulation mode. If the battery voltage exceeds the voltage limit, which may correspond to the condition of high solar insolation, no load, or a light load coupled with high battery charge level, BVL mode applies to prevent the battery from overcharging. Under this mode, the output current of the solar array may be away from the current at MPP and the charging current of the battery should be below the current limit. If the battery voltage is below the voltage limit, which may correspond to the condition of low solar insolation, a heavy load or a light load coupled with low battery charge level, MPPT mode or BCL mode may apply, depending on solar insolation and the load. If the load demand makes the battery current to reach the current limit, the charging current of the battery may need to be regulated in order to protect the battery, i.e., BCL mode applies. In this case, the solar array current is unregulated. If the load demand is very high, the battery may be discharged or be charged at a lower rate and then MPPT mode may apply. In this case, the control strategy aims to draw as much power as possible from the solar array.

Figure 2 shows the state machine representation [15] of the multiobjective control strategy. The circles represent the regulation modes (states) of the system. The arrows indicate changes from one regulation mode to another (events). Each event happens under a corresponding condition that is unique to the current regulation mode (state). Initially, it always works in MPPT mode. If there is no load or a light load, the charging current of the battery may increase quickly to the limit current, and then BCL mode applies. Whenever the battery voltage reaches the voltage limit, BVL mode will apply. Under either BCL mode or BVL mode, if the load increases very quickly (i.e., both the battery voltage and the battery current are lower than their limits), MPPT mode will apply. Under any of these three modes, the load will be disconnected (DISC) if the battery discharging current exceeds the safe operating limit (for instance, 4 times the rated charging current), which corresponds to the condition that the load is extremely heavy, or if the battery voltage is lower than the low voltage limit.

At any time, the control strategy selects only one regulation mode and then the power converter has only one control objective. The duty cycle of the power converter is then set according to this objective. Whenever a change in the insolation, the battery or the load results in satisfaction of the

corresponding event condition, the control strategy will move to another regulation mode and the control output (the duty cycle of the power converter) is calculated afresh according to the new objective, which makes it possible to implement the multiobjective control strategy with only a single control variable. In the configuration shown in Figure 1, this control strategy accounts for all of the possible regulation modes and the corresponding conditions that result in the changes of regulation modes. Under any condition of the whether and the load, the control strategy can select the regulation mode appropriately, as will be shown later in this paper.

States: MPPT: Maximum Power Point Tracking mode BCL: Battery Current Limit mode BVL: Battery Voltage Limit mode DISC: Disconnecting the Load Conditions of Events: 1: Power on 2: Ib > Iref 3: Ib < Iref 4: Vb > Vref 5: Vb < Vref, Ib > Iref (This rarely happens) 6: Vb < Vref 7: Vb > Vref 8, 9, 10: Vb < Vref,, Ib < Idisc (for instance, Idisc = -4 x Iref. This happens under very heavy load)

Figure 2. State machine representation of the control strategy for MPPT/charging in a standalone PV power system.

B. Implementation of Control Algorithm

The control strategy is then coded in the VTB. The main functional blocks in this algorithm are the regulation mode select module, MPPT module and the compensation loop module. The regulation mode select module realizes the control strategy shown in Figure 2 and outputs the regulation mode selected. The regulation mode is determined according to the operating conditions (the previous regulation mode and the measured currents and voltages) and the logic of the control strategy. The compensation loop module is used to compute the duty cycle of the power converter according to the selected regulation mode (control objective).

Incremental conductance method is exploited in this study to track the maximum power point of the solar array. At any instant, as shown in Figure 1, the solar array output power Psa, although a function of the local insolation, the array temperature, and the array voltage, can be described by (1).

1155IAS 2004 0-7803-8486-5/04/$20.00 2004 IEEE

sasasa IVP = (1)

where Vsa and Isa are the sampled voltage and current of the solar array module. Differentiating (1) yields

sa

sa

sa

sa

sa

sa

sa dVdI

VI

dVdP

V+=

1 (2)

Lat us define the instantaneous conductance and incremental conductance of the solar array, respectively, as

sasa VIG = and sasa dVdIG = . Since the solar array voltage is positive, we can easily get the following from (2).

GGdVdPGGdVdPGGdVdP

sasa

sasa

sasa

>

if0 if0

if0 (3)

Equation (3) suggests that the operating voltage is below the voltage at MPP if the instantaneous conductance is greater than the incremental conductance, and vice versa. The MPPT algorithm is therefore to search the voltage operating point at which the instantaneous conductance is equal to the incremental conductance. The MPPT algorithm is illustrated in Figure 3.

Figure 3. Flow chart of Incremental Conductance algorithm for MPPT.

A full PID algorithm is used to regulate the charging current or voltage of the battery when the system operates at BCL or BVL mode. The compensation loops for current regulation and voltage regulation are, respectively, implemented as follows.

( ) ( ) ( ) ( )( )( ) ( ))1 )()()(

1

,0

,

+ ++=

=

I(nnIkkIkIk

nInIkndnd

idn

krefii,

refip (4)

( ) ( ) ( ) ( )( )( ) ( ))1V )()()(

1

,0

,

+ ++=

=

(nnVkkVkVk

nVnVkndnd

vdn

krefvi,

refvp (5)

where d(n) and d(n-1) are duty cycles at the current and previous sampling steps respectively, I(n) and V(n) are, respectively, the sampled current and voltage of the battery at the current step, Iref(n) is the reference current of the battery,

and Vref is the reference voltage of the battery, kp,i and kp,v are the current and voltage proportional gains, ki,i and ki,v are the current and voltage integral gains, and kd,i and kd,v are the current and voltage derivative gains.

III. LARGE-SIGNAL STABILITY ANALYSIS Due to nonlinearities in the solar array, the battery and the

load, the system may often have multiple equilibrium points, wherein only one is desirable. The multiobjective control algorithm may cause the system to frequently change from one mode to another. The need to ensure large-signal stability of the system may require some basic understanding of large-signal behavior of the system. In the following, the changes of operation mode and the large-signal behaviors of the system are analyzed.

A. Changes of Operation Mode

While the control algorithm has three regulation modes, the system may have five operating modes: battery-only discharging mode, MPPT discharging mode, MPPT charging mode, constant current charging mode, constant voltage charging mode. At the first three operating modes, the controller regulates the system at MPPT mode. The changes of operation mode are described as follows.

During the total darkness period, the solar array does not produce electric power and only the battery is discharged to the load. Whenever sunlight is present and there is not enough power for the solar array to source the load, the power converter begins to track the maximum power from the solar array and the battery discharges. When the increasing insolation makes the capacity of the solar array to exceed the load demand, the extra power automatically flows into the battery and then the battery is charged. If the irradiance is so great or the load becomes so low that the charging current of the battery exceeds the safe limit, then the power converter begins to regulate the charging current within the safe range. Whenever the battery voltage reaches the high limit, the power converter starts to regulate the battery voltage so that it stands at a constant level. Any change in the insolation and load may cause the operating mode to change to another. B. Large-Signal Behaviors

During the darkness mode, only the battery powers the load, therefore the system stability is guaranteed. When the system operates at the MPPT discharging mode, the solar array operates at the maximum power point, and therefore the source line 1 must be a constant power line. Source line 2, a varying voltage source, represents the output of the battery. The battery provides an appropriate amount of current to compensate for the discrepancy between the source line 1 and the load line, as shown in Figure 4-a. Thus only one equilibrium point exists. Assuming a constant power load line, the output power of the battery is constant; thus the battery current depends on the voltage. The source line 2 will move leftwards or rightwards on the state plane.

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When the system operates at the MPPT charging mode, the solar array operates at the maximum power point while the battery acts as a varying voltage sink. The extra power from the solar array will flow into the battery to compensate for the discrepancy between the source line 1 and the load line, as shown in Figure 4-b. Thus only one equilibrium point exists. Assuming a constant power load line, the input power of the battery is constant; thus the battery charging current depends on the voltage. The change from MPPT discharging mode to MPPT charging mode or vice-versa does not cause any stability problem, since the power converter always tracks the maximum power point of the solar array. The only difference between these two changes is that the current flows into or out of the battery.

When the battery charging current is regulated at constant current or the battery voltage at constant voltage, the battery, seen by the solar array, is a constant power load line at any instant. We can get a single constant power load line by combining it with the series regulator load line, as illustrated in Figure 4-c. It can be seen that there are three equilibrium points. At this time, the solar array output voltage is not regulated and becomes floating. It has been shown in [16] that the operating point will move from the voltage at MPP to the desirable stable equilibrium point near the solar array open-circuit voltage (Figures 4-c). The constant power load line will move along the v-i curve of the solar array, depending on the load demand, and the solar array output voltage will vary with the load demand. When the load is increased so that the equilibrium points become only one, the system will switch to MPPT mode (Figures 4-a, and 4-b).

(a) (b)

(c)

Figure 4. Illustration of large-signal behaviors of the system.

IV. APPLICATION I: SATELLITE POWER SYSTEM The multiobjective control algorithm can be employed in

different applications. To investigate the performances of the control strategy, two case studies are conducted by numerical simulation in the VTB, respectively, for orbital and land-based applications. While a satellite power system is considered in this section, a wearable PV power source will be studied in the next section.

Figure 5 shows the VTB schematic view of a 3kW satellite power system under study. The simulation model comprises a solar irradiance model to illuminate the solar cells, a solar array to convert the solar illumination into electrical power, a lithium-ion battery array, a buck converter, a resistive load, a pulsed power load, and a bus voltage regulator [17], [18]. Several auxiliary components in the system are responsible for appropriate and efficient operation of the entire system. The primary energy conversion device is a 220 x 40 (series by parallel connections) array of single junction silicon cells. Each cell has an active area of 2.4 x 6.6 cm2, and a responsivity of 0.35 A/W. The battery is a 20 x 20 array of Li-Ion cells, each having a voltage of 4.2V at full charge and a capacity of 1.5 A-hrs. The initial state-of-charge of the battery is 0.5. All the solar array cells and all the battery cells are lumped into a single model for this particular simulation.

Figure 5. VTB schematic view of a satellite power system.

The payload consists of a constant power load of 1kW and a pulsed power load alternately drawing 1.5kW and 0.5kW. The limit of the battery charging current is set at 20A, according to the maximum safe charging rate. The battery voltage during charging is limited to 84V. The bus voltage is regulated at 120V. The satellite is running on the low Earth orbit (LEO) at the attitude of 798 km. The simulation is run for 100 minutes, and the simulation results are shown in Figures 6 through 9. Figure 6 shows the voltages of the solar array, the battery, and the load. Figure 7 shows the currents from the solar array, from the battery and to the load. The calculated state-of-charge of the battery is plotted in Figure 8. Figure 9 displays the changes of regulation mode in the controller.

It is shown in Figure 7 that, when the satellite is initially in the sunlight and the load draws a high current, MPPT mode applies (see Figure 9). At this moment, the solar array

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provides about 33A current and the battery is charged at 10A, which is lower than the current limit. When the load draws low power, the charging current increases to 20 A (the current limit) and then BCL mode applies (see Figure 9). At this time, the solar array supplies about 30A current and the voltage of the solar array increases a little bit. But the output power of the solar array is a little lower than the maximum power available. When the battery voltage reaches the limit at 3300s, CBV mode applies and the battery voltage is regulated at 84V. The charging current of the battery begins to decrease and so does the solar array output current; consequently, the voltage of the solar array increases a little. When the satellite is in eclipse, the voltage and current of the solar array drop to zero. During this time, the battery is discharged at a current between 20A and 32A, depending on the load, and the battery voltage decreased gradually after a sudden drop (Figure 6). When the satellite moves to the next cycle, MPPT mode applies again. The state-of-charge of the battery, as shown in Figure 8, increases when the battery is charged and decreases when it is discharged. During each cycle, the net increase of the state-of-charge is positive. This is because the average power of the load is a little less than the average output power of the solar array and the net input power to the battery is positive during each cycle. Figure 9 shows that the regulation mode is selected correctly according to the insolation conditions, the battery charge levels and the load.

Simulation results show that the solar array current, battery current and battery voltage are regulated properly. Simulation results also suggest that the single power converter can be regulated to meet the multiple objectives required by the satellite PV power system. In the satellite, the solar arrays are built oversized in order to still make them workable at end of life after years of meteorite damage. The loads do not necessarily undergo large power fluctuations; thus the battery is usually sized to meet the basic power requirement of the satellite during eclipse. Thus, the control algorithm makes more sense in respect of limiting the battery charging current and voltage than MPPT.

0 1000 2000 3000 4000 5000 60000

20

40

60

80

100

120

T ime(s)

Volta

ge(V

)

SABatteryLoad

Figure 6. Voltages of the solar array, the battery, and the load.

0 1000 2000 3000 4000 5000 6000-40

-30

-20

-10

0

10

20

30

40

Time(s)

Curr

en

t(A)

SABatteryLoad

Figure 7. Currents from the solar array, from the battery, and to the load.

0 1000 2000 3000 4000 5000 60000.4

0.5

0.6

0.7

0.8

0.9

1

T ime(s)

Stat

e-o

f-cha

rge

Figure 8. Calculated state-of-charge of the battery.

0 1000 2000 3000 4000 5000 60000

0.5

1

1.5

2

2.5

3

3.5

4

Time(s)

Regu

latio

n m

ode

Figure 9. Change of the regulation mode (1: MPPT, 2: BCL, 3: BVL).

V. APPLICATION II: WEARABLE PV POWER SOURCE With the development of flexible thin-film photovoltaic

technologies, solar technologies are being integrated into clothing. Developed to meet the needs for portable power of

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todays mobile devices, the solar jacket is offering a personal solar power solution [19]. The wearable PV power source is thus becoming an attractive solution to the portable power source. In the wearable PV power source, the size and weight of the system is an important consideration; the solar array is sized to meet the basic power requirement of electronic equipment while the battery is sized to provide power when the solar array is fully or partially shaded by the tree, cloud, building, etc. In this application, the proposed multiobjective MPPT/charging algorithm has a capability to accomplish the power management requirement of the system.

Figure 10 shows the schematic view of a 100W wearable PV power source under study. The solar panel on the jacket is configured as two arrays of 60 x 5 cells, each cell having an active area of 1.2 x 0.5 cm2, and a responsivity of 0.305 A/W. The battery is a 4 x 2 array of Li-Ion cells. The bus voltage is regulated at 24V. The power source is assumed to be located at the latitude 34N and longitude 82W. The system is operated from 13:00PM to 14:00PM, May 12, 2004. The ambient temperature is assumed to be 300K constantly during the operation. A scenario that the solar arrays both are totally shaded by the cloud, tree or building and a scenario that the solar arrays each are partially shaded at different time is studied to verify the control algorithm. The initial state-of-charge of the battery is 0.5. The load draws 88W of peak power and 56W of basic power alternately. The limit of the battery charging current is set as 2A, according to the maximum safe charging rate. The voltage of the battery is limited to 16.8V. Simulation results are shown in Figures 11 through 14. Figure 11 shows the received solar insolation. The voltages of the solar array, the battery, and the load are shown in Figure 12. Figure 13 shows the currents from the solar array, from the battery and to the load. The change of regulation mode is plotted in Figure 14.

Figure 10. VTB schematic view of a residential power system.

The solar insolation during one hour of operation is almost constant but the received insolation is less than the solar insolation when the solar array is partially shaded and is zero when the solar array is totally shaded (see Figure 11). When the load initially draws peak power, MPPT mode applies (see Figure 14). At this moment, each solar array provides about

2A current (the current at MPP) and the battery is charged at a current between 0A and 1A, which is lower than the current limit. When the load draws low power, the charging current increases to 2A (the battery current limit) and then BCL mode applies (see Figure 14). At this time, each solar array supplies about 1.5A current and the voltage of the solar array increases a little bit. But the output power of the solar array is a little lower than the maximum power available.

When the solar arrays are totally shaded at 800s, the voltage and current of the solar array drop to zero. During this period, the battery powers the load and is discharged at 4A (Figure 13). When one solar array is partially shaded, the shaded array outputs a smaller current (Figure 12) but the controller can still track the MPP and the output voltages of the two arrays are almost the same (Figure 13). At 2800s, the battery voltage reaches the limit and then the controller begins to operate at BVL mode and the battery voltage is regulated at 24V (Figure 12). Less current flows into the battery and thus the output current of the solar array declines, resulting in the increase of the solar array output voltage. Figure 15 shows the regulation mode is selected correctly.

0 500 1000 1500 2000 2500 3000 35000

200

400

600

800

1000

Time(s)

Re

ceiv

ed

sola

r in

sola

tion

(W/m

2)

SA1SA2

Figure 11. Received solar insolation.

0 500 1000 1500 2000 2500 3000 35000

5

10

15

20

25

30

35

Time(s)

Volta

ge(V

)

SA1SA2BatteryLoad

Figure 12. Voltages of the solar array, the battery, and the load.

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0 500 1000 1500 2000 2500 3000 3500-4

-3

-2

-1

0

1

2

3

4

5

T ime(s)

Curr

en

t(A)

SA1SA2BatteryLoad

Figure 13. Currents from the solar array, from the battery, and to the load.

0 500 1000 1500 2000 2500 3000 35000

0.5

1

1.5

2

2.5

3

3.5

4

T ime(s)

Reg

ula

tion

m

ode

Figure 14. Change of the regulation mode (1: MPPT, 2: BCL, 3: BVL).

Simulation results demonstrate that the controller regulates the solar array outputs and the battery voltage and current properly, and show that the single power converter can be regulated to meet the requirements of the wearable PV power source under different insolation and load conditions.

VI. CONCLUSION This paper has presented a multiobjective controller for

standalone PV power systems that can track the maximum power point of the solar array while limiting the current/ voltage of the battery under different insolation and load conditions. A state machine model of the multiobjective control algorithm is described. The mode changes and large-signal behaviors of the system are analyzed. The controller design is verified by numerical simulation in the VTB environment for both orbital and land-based applications.

Simulation results show that the control strategy is robust and that the power converter can be appropriately regulated to meet the multiple objectives required by standalone PV power systems. Simulation results also demonstrate that the proposed multiobjective control algorithm is capable to accomplish the power management requirement of an interes-ting wearable PV power source.

VII. ACKNOWLEDGEMENTS This work was supported by the US Office of Naval

Research under contract N000140310952.

VIII. REFERENCES [1] L. McCarthy, J. Pieper, A. Rues, C. H. Wu, Performance monitoring

in UMR's solar car, IEEE Instrumentation & Measurement Magazine, Vol. 3, No. 3, pp. 19-23, Sept. 2000.

[2] H. J. Wenger, C. Jennings, J. J. Iannucci, Carrisa Plains PV power plant performance, Conference Record of 21st IEEE Photovoltaic Specialists Conference, vol.2, pp. 844-849, May 1990.

[3] R. C. Neville, Solar Energy Conversion: The Solar Cell, Elsevier Scientific, New York, 1978.

[4] O. Wasynczuck, Dynamic Behavior of a Class of Photovoltaic Power Systems, IEEE Trans. Apparatus and Systems, Vol. PAS-102, No. 9, pp. 3031-3037, 1983.

[5] K. Hussein, I. Muta, T. Hoshino, and M. Osakada, Maximum Photovoltaic Power Tracking: An Algorithm for Rapidly Changing Atmospheric Conditions, IEE Proc.-Generation, Transmission, Distribution, Vol. 142, No.1, pp. 59-64, January, 1995.

[6] T. Noguchi, S. Togashi, R. Nakamoto, Short-Current Pulse-Based Maximum-Power-Point Tracking Method for Multiple Photovoltaic-and-Converter Module System, IEEE Trans. on Industrial Electronics, vol. 49, pp. 217-223, Feb. 2002.

[7] J. H. R. Enslin, M. S. Wolf, D. B. Snyman and W. Swiegers, Integrated Photovoltaic Maximum Power Point Tracking Converter, IEEE Trans. on Industrial Electronics, vol. 44, pp. 769-773, Dec. 1997.

[8] M. Veerachary, T. Senjyu, K. Uezato, Neural-network-based maximum-power-point tracking of coupled-inductor interleaved-boost-converter-supplied PV system using fuzzy controller, IEEE Trans. on Industrial Electronics, Vol. 50, No. 4, pp. 749 758, Aug. 2003.

[9] M. Veerachary, T. Senjyu, K. Uezato, Feedforward maximum power point tracking of PV systems using fuzzy controller, IEEE Transactions on Aerospace and Electronic Systems, Vol. 38, No. 3, pp. 969 981, July 2002.

[10] V. A. Pacheco, L. C. Freitas, J. B. Vieira, E. A. A. Coelho, V. J. Farias, Stand-alone photovoltaic energy storage system with maximum power point tracking, Proceedings of IEEE Applied Power Electronics Conference and Exposition, Vol. 1, pp. 97-102, 9-13 Feb. 2003

[11] S. J. Chiang, K. T. Chang, C. Y. Yen,Residential photovoltaic energy storage system, IEEE Industrial Electronics, Vol. 45, No. 3, pp. 385 394, June 1998.

[12] P. Stewart, G.W Jewell, R. E Clark, P. J. Fleming, Controllability analysis of multi objective control systems, Proceedings of IEEE International Symposium on Computer Aided Control System Design, Vol. 1, pp. 74 -79, Sept. 2002.

[13] M. Trentini, J. K. Pieper, A case study of multi-objective control: synthesis and analysis, Proceedings of IEEE International Conference on Control Applications, Vol. 2, pp. 1001-1005, Sept. 1998.

[14] T. Lovett, A Monti, E. Santi, R. Dougal, A multilanguage environment for interactive simulation and development of controls for power electronics, Proceedings of IEEE 32nd Annual Power Electronics Specialists Conference, Vol. 3, pp. 1725 1729, 2001.

[15] D. Drechsel, An adaptive control system modelled as finite state machine, Proceedings of IEEE Annual Convention and Exhibition in India, pp. 124-128, Jan. 1990.

[16] B. Cho, J. Lee, and F. Lee, Large-Signal Stability Analysis of Spacecraft Power Processing Systems, IEEE Transactions on Power Electronics, Vol. 5, No. 1, pp. 110-116, Jan. 1990.

[17] S. Liu and R. A. Dougal, Dynamic Multi-physics Model for Solar Array, IEEE Transactions on Energy Conversion, Vol. 17, No. 2, pp. 285-294, June 2002.

[18] Z. Jiang, S. Liu, and R. Dougal, Design and Testing of Spacecraft Power Systems Using VTB, IEEE Transactions on Aerospace and Electronic Systems, Vol. 39, No. 3, pp. 976-989, July 2003.

[19] Solar SCOTTeVEST jacket, designed to carry, connect and charge mobile devices, will stage at CTIA 2004 Fashion in Motion Show, [online] http://www.scottevest.com/htmlemail/icp_release/ctia2.html

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