Solar cell model

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 adds
the **Thermal Port** tab to the block dialog box.

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 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 irradation. 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.

**Parameterize by**Select one of the following methods for block parameterization:

`By s/c current and o/c voltage, 5 parameter`

— Provide short-circuit current and open-circuit voltage that the block converts to an equivalent circuit model of the solar cell. This is the default option.`By equivalent circuit parameters, 5 parameter`

— Provide electrical parameters for an equivalent circuit model of the solar cell using the 5-parameter solar cell model that makes the following assumptions:The saturation current of the second diode is zero.

The parallel resistor has infinite impedance.

`By equivalent circuit parameters, 8 parameter`

— Provide electrical parameters for an equivalent circuit model of the solar cell using the 8-parameter solar cell model.

**Short-circuit current, Isc**The current that flows when you short-circuit the solar cell. This parameter is only visible when you select

`By s/c current and o/c voltage, 5 parameter`

for the**Parameterize by**parameter. The default value is`7.34`

A.**Open-circuit voltage, Voc**The voltage across the solar cell when it is not connected. This parameter is only visible when you select

`By s/c current and o/c voltage, 5 parameter`

for the**Parameterize by**parameter. The default value is`0.6`

V.**Diode saturation current, Is**The asymptotic reverse current of the first diode for increasing reverse bias in the absence of any incident light. This parameter is only visible when you select one of the following settings:

`By equivalent circuit parameters, 5 parameter`

for the**Parameterize by**parameter`By equivalent circuit parameters, 8 parameter`

for the**Parameterize by**parameter

The default value is

`1e-06`

A.**Diode saturation current, Is2**The asymptotic reverse current of the second diode for increasing reverse bias in the absence of any incident light. This parameter is only visible when you select

`By equivalent circuit parameters, 8 parameter`

for the**Parameterize by**parameter. The default value is`0`

A.**Solar-generated current, Iph0**The solar-induced current when the irradiance is

*I*. This parameter is only visible when you select one of the following settings:_{r0}`By equivalent circuit parameters, 5 parameter`

for the**Parameterize by**parameter`By equivalent circuit parameters, 8 parameter`

for the**Parameterize by**parameter

The default value is

`7.34`

A.**Irradiance used for measurements, Ir0**The irradiance that produces a current of

*I*in the solar cell. The default value is_{ph0}`1000`

W/m^{2}.**Quality factor, N**The emission coefficient of the first diode. The default value is

`1.5`

.**Quality factor, N2**The emission coefficient of the second diode. This parameter is only visible when you select

`By equivalent circuit parameters, 8 parameter`

for the**Parameterize by**parameter. The default value is`2`

.**Series resistance, Rs**The internal series resistance. The default value is

`0`

Ω.**Parallel resistance, Rp**The internal parallel resistance. This parameter is only visible when you select

`By equivalent circuit parameters, 8 parameter`

for the**Parameterize by**parameter. The default value is`inf`

Ω.

**Number of series cells**The number of series-connected solar cells modeled by the block. The default value is

`1`

. The value must be greater than`0`

.

**First order temperature coefficient for Iph, TIPH1**The order of the linear increase in the solar-generated current as temperature increases. The default value is

`0`

1/K. The value must be greater than or equal to`0`

.**Energy gap, EG**The solar cell activation energy. The default value is

`1.11`

eV. The value must be greater than or equal to 0.1.**Temperature exponent for Is, TXIS1**The order of the exponential increase in the current from the first diode as temperature increases. The default value is

`3`

. The value must be greater than or equal to`0`

.**Temperature exponent for Is2, TXIS2**The order of the exponential increase in the current from the second diode as temperature increases. This parameter is only visible when you select

`By equivalent circuit parameters, 8 parameter`

for the**Parameterize by**parameter. The default value is`3`

. The value must be greater than or equal to`0`

.**Temperature exponent for Rs, TRS1**The order of the exponential increase in the series resistance as temperature increases. The default value is

`0`

. The value must be greater than or equal to`0`

.**Temperature exponent for Rp, TRP1**The order of the exponential increase in the parallel resistance as temperature increases. This parameter is only visible when you select

`By equivalent circuit parameters, 8 parameter`

for the**Parameterize by**parameter. The default value is`0`

. The value must be greater than or equal to`0`

.**Measurement temperature**The temperature at which the solar cell parameters were measured. The default value is

`25`

C. The value must be greater than`0`

.**Device simulation temperature**The temperature at which the solar cell is simulated. The default value is

`25`

C. The value must be greater than`0`

.

This tab appears only for blocks with exposed thermal ports. For more information, see Thermal Port.

**Thermal mass**The heat energy required to raise the temperature of the solar cell by one degree. When modeling more than one cell in series, specify the thermal mass for a single cell. This value gets multiplied internally by the number of cells to determine the total thermal mass. The default value is

`100`

J/K.**Initial temperature**The temperature of the solar cell at the start of simulation. The default value is

`25`

C.

The block has the following ports:

`Ir`

Incident irradiance

`+`

Positive electrical voltage

`-`

Negative electrical voltage

[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.

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