Photovoltaic solar cell

**Library:**Simscape / Electrical / Sources

The Solar Cell block represents a solar cell current source.

The solar cell model includes the following components:

The block represents a single solar cell as a resistance
*R _{s}* that is connected in series
with a parallel combination of the following elements:

Current source

Two exponential diodes

Parallel resistor

*R*_{p}

The following illustration shows the equivalent circuit diagram:

The output current *I* is

$$I={I}_{ph}-{I}_{s}*\left({e}^{(V+I*{R}_{s})/(\text{N}*{V}_{t})}-1\right)-{I}_{s2}*({e}^{\left(V+I*{R}_{s}\right)/\left({N}_{2}*{V}_{t}\right)}-1)-\left(V+I*{R}_{s}\right)/{R}_{p}$$

where:

*I*is the solar-induced current:_{ph}$${I}_{ph}={I}_{ph0}\times \frac{{I}_{r}}{{I}_{r0}}$$

where:

*I*is the irradiance (light intensity), in W/m_{r}^{2}, falling on the cell.*I*is the measured solar-generated current for the irradiance_{ph0}*I*._{r0}

*I*is the saturation current of the first diode._{s}*I*is the saturation current of the second diode._{s2}*V*is the thermal voltage,_{t}*kT/q*, where:*k*is the Boltzmann constant.*T*is the**Device simulation temperature**parameter value.*q*is the elementary charge on an electron.

*N*is the quality factor (diode emission coefficient) of the first diode.*N*is the quality factor (diode emission coefficient) of the second diode._{2}*V*is the voltage across the solar cell electrical ports.

The quality factor varies for amorphous cells, and is typically
`2`

for polycrystalline cells.

The block lets you choose between two models:

An 8-parameter model where the preceding equation describes the output current

A 5-parameter model that applies the following simplifying assumptions to the preceding equation:

The saturation current of the second diode is zero.

The impedance of the parallel resistor is infinite.

If you choose the 5-parameter model, you can parameterize this block in terms of the preceding equivalent circuit model parameters or in terms of the short-circuit current and open-circuit voltage the block uses to derive these parameters.

All models adjust the block resistance and current parameters as a function of temperature.

You can model any number of solar cells connected in series using a single
Solar Cell block by setting the parameter
**Number of series cells** to a value larger than 1. Internally
the block still simulates only the equations for a single solar cell, but scales up
the output voltage according to the number of cells. This results in a more
efficient simulation than if equations for each cell were simulated
individually.

If you want to model *N* cells in parallel, you can do so for
single cells by scaling the parameter values accordingly. That is, multiply
short-circuit current, diode saturation current, and solar-generated currents by
*N*, and divide series resistance by *N*. To
connect solar cell blocks in parallel, where each block contains multiple cells in
series, make multiple copies of the block and connect accordingly.

Several solar cell parameters depend on temperature. The solar cell temperature is
specified by the **Device simulation temperature** parameter
value.

The block provides the following relationship between the solar-induced current
*I _{ph}* and the solar cell temperature

$${I}_{ph}(t)={I}_{ph}*\left(1+TIPH1*\left(T-{T}_{meas}\right)\right)$$

where:

*TIPH1*is the**First order temperature coefficient for Iph, TIPH1**parameter value.*T*is the_{meas}**Measurement temperature**parameter value.

The block provides the following relationship between the saturation current of
the first diode *I _{s}* and the solar cell
temperature

$${I}_{s1}(T)={I}_{s1}*{\left(\frac{T}{{T}_{meas}}\right)}^{\left(\raisebox{1ex}{$TXIS1$}\!\left/ \!\raisebox{-1ex}{$N$}\right.\right)}*{e}^{\left(EG*\left(\frac{T}{{T}_{meas}}-1\right)/\left(N*{V}_{t}\right)\right)}$$

where *TXIS1* is the **Temperature
exponent for Is, TXIS1** parameter value.

The block provides the following relationship between the saturation current of
the second diode *I _{s2}* and the solar cell
temperature

$${I}_{s2}(T)={I}_{s2}*{\left(\frac{T}{{T}_{meas}}\right)}^{\left(\raisebox{1ex}{$TXIS2$}\!\left/ \!\raisebox{-1ex}{${N}_{2}$}\right.\right)}*{e}^{\left(EG*\left(\frac{T}{{T}_{meas}}-1\right)/\left({N}_{2}*{V}_{t}\right)\right)}$$

where *TXIS2* is the **Temperature
exponent for Is2, TXIS2** parameter value.

The block provides the following relationship between the series resistance
*R _{s}* and the solar cell temperature

$${R}_{s}(T)={R}_{s}*{\left(\frac{T}{{T}_{meas}}\right)}^{TRS1}$$

where *TRS1* is the **Temperature
exponent for Rs, TRS1** parameter value.

The block provides the following relationship between the parallel resistance
*R _{p}* and the solar cell temperature

$${R}_{p}(T)={R}_{p}*{\left(\frac{T}{{T}_{meas}}\right)}^{TRP1}$$

where *TRP1* is the **Temperature
exponent for Rp, TRP1** parameter value.

The block has an optional thermal port, hidden by default. To expose the thermal port,
right-click the block in your model, and then from the context menu select
**Simscape** > **Block
choices** > **Show thermal port**.
This action displays the thermal port **H** on the block icon, and
exposes the **Thermal Port** parameters.

The thermal port model, shown in the following illustration, represents just the thermal mass
of the device. The thermal mass is directly connected to the component thermal port
**H**. An internal Ideal Heat Flow Source
block supplies a heat flow to the port and thermal mass. This heat
flow represents the internally generated heat.

The internally generated heat in the solar cell is calculated according to the equivalent
circuit diagram, shown at the beginning of the reference page, in the Solar-Induced Current section. It is
the sum of the *i*^{2} ·
*R* losses for each of the resistors plus the losses in
each of the diodes.

The internally generated heat due to electrical losses is a separate heating effect to that of the solar irradiation. To model thermal heating due to solar irradiation, you must account for it separately in your model and add the heat flow to the physical node connected to the solar cell thermal port.

[1] Gow, J.A. and C.D. Manning. “Development of a
Photovoltaic Array Model for Use in Power-Electronics Simulation Studies.”
*IEEE Proceedings of Electric Power Applications*, Vol. 146,
No. 2, 1999, pp. 193–200.