Documentation |
Solar cell model
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_{ph} is the solar-induced current:
$${I}_{ph}={I}_{ph0}\times \frac{{I}_{r}}{{I}_{r0}}$$
where:
I_{r} is the irradiance (light intensity) in W/m^{2} falling on the cell.
I_{ph0} is the measured solar-generated current for the irradiance I_{r0}.
I_{s} is the saturation current of the first diode.
I_{s2} is the saturation current of the second diode.
V_{t} is the thermal voltage, 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_{2} is the quality factor (diode emission coefficient) of the second diode.
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 T:
$${I}_{ph}(t)={I}_{ph}*\left(1+TIPH1*\left(T-{T}_{meas}\right)\right)$$
where:
TIPH1 is the First order temperature coefficient for Iph, TIPH1 parameter value.
T_{meas} is the 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 T:
$${I}_{s1}(T)={I}_{s1}*{\left(\frac{T}{{T}_{meas}}\right)}^{\left(\raisebox{1ex}{$TXIS1$}\!\left/ \!\raisebox{-1ex}{$N$}\right.\right)}*{e}^{\left(EG*\left(\frac{T}{{T}_{meas}}-1\right)/\left(N*{V}_{t}\right)\right)}$$
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 T:
$${I}_{s2}(T)={I}_{s2}*{\left(\frac{T}{{T}_{meas}}\right)}^{\left(\raisebox{1ex}{$TXIS2$}\!\left/ \!\raisebox{-1ex}{${N}_{2}$}\right.\right)}*{e}^{\left(EG*\left(\frac{T}{{T}_{meas}}-1\right)/\left({N}_{2}*{V}_{t}\right)\right)}$$
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 T:
$${R}_{s}(T)={R}_{s}*{\left(\frac{T}{{T}_{meas}}\right)}^{TRS1}$$
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 T:
$${R}_{p}(T)={R}_{p}*{\left(\frac{T}{{T}_{meas}}\right)}^{TRP1}$$
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.
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.
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.
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.
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.
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.
The solar-induced current when the irradiance is I_{r0}. 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 7.34 A.
The irradiance that produces a current of I_{ph0} in the solar cell. The default value is 1000 W/m^{2}.
The emission coefficient of the first diode. The default value is 1.5.
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.
The internal series resistance. The default value is 0 Ω.
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.
The number of series-connected solar cells modeled by the block. The default value is 1. The value must be greater than 0.
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.
The solar cell activation energy. The default value is 1.11 eV. The value must be greater than or equal to 0.1.
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.
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.
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.
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.
The temperature at which the solar cell parameters were measured. The default value is 25 C. The value must be greater than 0.
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.
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.
The temperature of the solar cell at the start of simulation. The default value is 25 C.