VOLTAGE AND FREQUENCY DEPENDENT MODEL FOR PV MODULE DYNAMIC IMPEDANCE T. Chayavanich1,2,3,*, C. Limsakul 3, N. Chayavanich2,3, D. Chenvidhya3, C. Jivacate3, K.Kirtikara3 1. School of Energy, Environment and Materials, 2. Electrical Engineering Department, 3. CES Solar Cell Testing Center (CSSC) King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand * Corresponding Author:
[email protected]
ABSTRACT In this paper, the modeling of voltage and frequency dependence for dynamic impedance of PV module is proposed. In our previous works, we developed measurement technique to measure the dynamic impedance of solar cells and modules, and found that parameters in their dynamic models having either voltage or voltage and frequency dependent characteristics. Therefore in this work, the transition capacitance and diffusion capacitance which measured in term of a parallel capacitance is modeled in a mathematical voltage frequency dependent equation. The proposed model can be used to investigate dynamic behavior of PV module by using the measurement values of the dynamic impedance. The proposed model is verified by simulating the dynamic behavior of I-V characteristics of PV modules. The dynamic I-V characteristic simulation using the model and I-V measurement data measured under a flash solar simulator are compared. 1. INTRODUCTION The dynamic impedance of a solar cell consists of series (Rs), shunt resistance (Rsh), voltage dependent dynamic resistance and transition capacitance, frequency and voltage dependent diffusion capacitance. In previous work, we have developed measurement technique to measure the dynamic impedance of solar cell and modules of which transition capacitance (CT) and diffusion capacitance (CD) are measured in term of a parallel capacitance (CP) and it is voltage and frequency dependent [1]. In this paper, the modeling of voltage and frequency dependent model of dynamic impedance of PV module is proposed. The parallel capacitance is modeled in a mathematical equation which is voltage and frequency dependent. The proposed model can be used to investigate dynamic behavior of PV module by using the measurement values of the dynamic impedance.
2. DYNAMIC IMPEDANCE OF PV MODULE The dynamic impedance of PV module is shown in Fig. 1. Series resistance (Rs) and shunt resistance (Rsh) are voltage independent. Dynamic resistance (Rd) is voltage dependent. Parallel capacitance (CP) is voltage and frequency dependent. The diode exponential equation, either single exponential or double exponential is used to perform the dynamic resistance characteristics. Parallel capacitance can be measured under dark condition using impedance spectroscopy technique. Rs
I ph
D1
D2
CP
R sh
Fig. 1 AC Equivalent circuit of PV module (double diode model).
3. EXPERIMENT 3.1 Static I-V Characteristics In our experiment, we examine the I-V characteristics at STC of 120 W polycrystalline silicon (p-Si) module, under flash solar simulator using measurement time 10 ms. The parameters in the double exponential equation, Rs and Rsh are extracted by curve fitting using the I-V curve measurement and the static model of PV module[2]. 3.2 Modeling of Parallel Capacitance Dynamic impedance of the module is measured under dark condition. Input voltage signals consisting biasing voltage and modulating signal are applied to the modules. Forward bias voltage of 0.1 - 0.5V/cell are used. The frequencies of modulating signals are varied from 10 Hz to 100 kHz. From output signals, we calculated CP, then CP under illuminated condition are calculated from the CP under dark condition[3]. The
mathematical model of CP at various frequency of modulating signal (f) and bias voltage (V) is identified by curve fitting using eqn. 1 [4]. A
C P V , f
1 V / B 1 / 2
1/ 2 ª C § V ·º exp¨ ¸» 1 E ( 2Sf ) 2 1 « © D ¹¼ ¬ 2Sf (1)
Where A, B, C, D and E are fitting parameters.
3.3 Simulation of Dynamic I-V Characteristics In order to verify our dynamic model, the dynamic IV characteristics with short voltage sweep rates, 1 and 5 ms, are simulated using Simulink and compared with the I-V forward and reverse measurement under flash solar simulator. The effect of CP can be modeled as the capacitive current and is simulated using eqn.2. IC
CP
dV dC P V dt dt
(2)
4. RESULTS AND DISCUSSION 4.1 Static I-V Characteristics The result of the simulation of static I-V curve at STC using the static model with the fitting parameters has an error of maximum power and fill factor within 0.1%. 4.2 Modeling of Parallel Capacitance The value of CP from the voltage and frequency dependent model is comparable to the value of measurement at different bias voltage and frequency as shown in Fig.3- 4. 1.00E-05 Maesurement Model
9.00E-06
7.00E-06 Cp (Farad)
4.3 Simulation of Dynamic I-V Characteristics The simulation results are compared with the I-V measurement data measured under flash solar simulator. Table I. Maximum Power from I-V measurement and simulation at different voltage sweep rates. Sweep time
Reverse sweep
Forward sweep
Measurement
Simulation
Measurement
Simulation
Pmax (W)
Pmax (W)
Pmax (W)
Pmax (W)
1
124.095
118.836
113.906
115.536
5
118.622
117.234
116.537
116.527
10
116.930
117.045
116.764
116.686
(ms)
The simulation using the CP model shows a good agreement with the measurement. 5. CONCLUSIONS Voltage and frequency dependent model for dynamic impedance of PV module is proposed. Parallel capacitance of PV module is measured and is modeled in term of voltage and frequency dependent equation. The model will enable us to investigate dynamic behavior of PV module. ACKNOWLEDGEMENT This work is supported by the Department of Alternative Energy Development and Efficiency and the Pilot Plant Development and training Institute.
8.00E-06
6.00E-06 5.00E-06 4.00E-06 3.00E-06 2.00E-06 1.00E-06 0.00E+00 1
10
100
1000
10000
100000
Frequency (Hz)
Fig. 3 CP vs. frequency curves from the model and the measurement at 0.5V bias voltage. 5.00E-06
Measurement Model
4.50E-06 4.00E-06 3.50E-06 Cp (Farad)
The CP value from the model also shows that it is voltage dependent at voltage below 0.3 V., and it conforms with the module capacitance dominated by CT.
3.00E-06 2.50E-06 2.00E-06 1.50E-06 1.00E-06 5.00E-07 0.00E+00 0
0.1
0.2
0.3 Voltage (V)
0.4
0.5
0.6
Fig. 4 CP vs. bias voltage curves from the model and the measurement at 200 Hz.
REFERENCES [1] D.Chenvidhya et al., “PV module dynamic impedance and its voltage and frequency dependencies”, Solar Energy Materials & Solar Cells, 86 (2005). [2] J.A. GOW, C.D. Manning, “Development of a photovoltaic array model for use in powerelectronics simulation studies”, IEE Proc.Electr.Power Appl., 146, 2 (1999). [3] R. Anil. Kumar et al., “GaAs/Ge solar cell AC parameters under illumination” , Solar Energy, 76 (2004). [4] Robert F. Pierret, “Semiconductor device fundamentals”, Addison-Wesley Publishing Company,Inc.,1996.
