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CommunityCategory: XMODELModeling a photovoltaic (PV) cell

XMODEL

Modeling a photovoltaic (PV) cell

SA Support Team Staff 2022-11-30

I’d like to model an energy harvesting system tracking the maximum power point (MPP) of photovoltaic (PV) cells. Can you show an example of modeling a PV cell so that it exhibits I-V and P-V characteristics as shown below. These graphs are from the paper titled “Optimization of Perturb and Observe Maximum Power Point Tracking Method” published in the IEEE Transactions on Power Electronics in July 2005 by N. Femia, et al.

1 Answers
SA Support Team Staff 2022-11-30

Sure. You can model the PV cells using one of the equivalent circuit models known in literature. For example, the model shown below is called a single diode equivalent circuit model, of which detailed description can be found in this link. It is made of a current source producing the light-generated current Iph, a diode modeling the voltage-dependent current ID lost due to recombination, and resistors with equivalent shunt and series resistances, Rshunt and Rseries, respectively. The ID-VD characteristics of the diode is governed by the Shockley’s exponential model: ID = IS ·exp(VD/nVT) where IS is the reverse saturation current, VT is the thermal voltage (=kT/q), and n is the diode’s ideality factor. When this model is describing a set of NS serially-connected PV cells, the equivalent ideality factor n may increase with NS.

Writing this equivalent circuit model in XMODEL is straightforward using the circuit primitives. The schematic cellview 'sandbox.pvcell:schematic' shown below describes this PV cell model using the 'isource', 'diode', and 'resistor' primitives. Among them, the 'diode' primitive is selecting the exponential model, which can specify the reverse saturation current and ideality factor directly using the parameters 'Is' and 'N', respectively. Its series resistance parameter 'Rs' is set to 1% of the PV cell’s series resistance Rseries, because the value of 'Rs' must be greater than 0.

This schematic cellview 'sandbox.tb_pvcell:tb_meas_iv' describes a testbench to measure the I-V characteristics of the PV cell model. Basically, it is using the 'probe_dc' primitive to measure the current 'IL' delivered by the PV cell while sweeping the voltage 'VL' across its two terminals.

The testbench view 'sandbox.pvcell:tb_meas_iv' configures the simulation and plotting commands for this testbench as shown below. Basically, it adds a '--sweep' option to repeat the simulation while varying the 'Iph' parameter for the PV cell representing the light-generated current (i.e., the irradiance level), and overrides the simulation and plotting commands using the 'meas_dc' script. A more detailed explanation on the use of '--sweep' option and 'meas_dc' script can be found in this Q&A posting.

Below are the I-V characteristic curves of the PV cell model simulated using the described testbench. The assumed parameters for the PV cell model are IS=10-8A, n=20, Rseries=0.5Ω, and Rshunt=200Ω, and the plotted I-V curves are for Iph=1, 3, and 5A.

Using a similar approach, the schematic cellview 'sandbox.tb_pvcell:tb_meas_pv' shown below measures the power-voltage (P-V) characteristics of the PV cell model. The only difference with the 'tb_meas_iv' testbench is that the 'probe_dc' primitive is measuring the power 'PL' computed as a product between 'IL' and 'VL' as a function of 'VL'.

Finally, the simulated P-V characteristic curves of the PV cell assuming the same set of parameter values are shown below. There exists an optimal voltage level that maximizes the power delivered to the output, called the "maximum power point (MPP)". The maximum power point may change depending on the irradiance level, temperature, and so on.

Attachment: pvcell_20221130.tar.gz

XMODEL

태양전지(PV셀)의 모델링

SA Support Team Staff 2022-11-30

태양전지, 즉 PV셀의 최대전력점을 트랙킹하는 에너지 하베스팅 시스템을 모델링하려고 합니다. 아래 그래프에 보이는 I-V 그리고 P-V 특성을 가지도록 PV 셀을 모델링하는 예제를 보여주실 수 있나요? 참고로 아래 그래프는 2005년 7월 IEEE Transactions on Power Electronics에 출판된 N. Femia 외, “Optimization of Perturb and Observe Maximum Power Point Tracking Method”라는 그래프에서 발췌한 것입니다.

1 Answers
SA Support Team Staff 2022-11-30

Sure. You can model the PV cells using one of the equivalent circuit models known in literature. For example, the model shown below is called a single diode equivalent circuit model, of which detailed description can be found in this link. It is made of a current source producing the light-generated current Iph, a diode modeling the voltage-dependent current ID lost due to recombination, and resistors with equivalent shunt and series resistances, Rshunt and Rseries, respectively. The ID-VD characteristics of the diode is governed by the Shockley’s exponential model: ID = IS ·exp(VD/nVT) where IS is the reverse saturation current, VT is the thermal voltage (=kT/q), and n is the diode’s ideality factor. When this model is describing a set of NS serially-connected PV cells, the equivalent ideality factor n may increase with NS.

Writing this equivalent circuit model in XMODEL is straightforward using the circuit primitives. The schematic cellview 'sandbox.pvcell:schematic' shown below describes this PV cell model using the 'isource', 'diode', and 'resistor' primitives. Among them, the 'diode' primitive is selecting the exponential model, which can specify the reverse saturation current and ideality factor directly using the parameters 'Is' and 'N', respectively. Its series resistance parameter 'Rs' is set to 1% of the PV cell’s series resistance Rseries, because the value of 'Rs' must be greater than 0.

This schematic cellview 'sandbox.tb_pvcell:tb_meas_iv' describes a testbench to measure the I-V characteristics of the PV cell model. Basically, it is using the 'probe_dc' primitive to measure the current 'IL' delivered by the PV cell while sweeping the voltage 'VL' across its two terminals.

The testbench view 'sandbox.pvcell:tb_meas_iv' configures the simulation and plotting commands for this testbench as shown below. Basically, it adds a '--sweep' option to repeat the simulation while varying the 'Iph' parameter for the PV cell representing the light-generated current (i.e., the irradiance level), and overrides the simulation and plotting commands using the 'meas_dc' script. A more detailed explanation on the use of '--sweep' option and 'meas_dc' script can be found in this Q&A posting.

Below are the I-V characteristic curves of the PV cell model simulated using the described testbench. The assumed parameters for the PV cell model are IS=10-8A, n=20, Rseries=0.5Ω, and Rshunt=200Ω, and the plotted I-V curves are for Iph=1, 3, and 5A.

Using a similar approach, the schematic cellview 'sandbox.tb_pvcell:tb_meas_pv' shown below measures the power-voltage (P-V) characteristics of the PV cell model. The only difference with the 'tb_meas_iv' testbench is that the 'probe_dc' primitive is measuring the power 'PL' computed as a product between 'IL' and 'VL' as a function of 'VL'.

Finally, the simulated P-V characteristic curves of the PV cell assuming the same set of parameter values are shown below. There exists an optimal voltage level that maximizes the power delivered to the output, called the "maximum power point (MPP)". The maximum power point may change depending on the irradiance level, temperature, and so on.

Attachment: pvcell_20221130.tar.gz