Solar Cell

Photovoltaic solar cell

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Description

The Solar Cell block represents a solar cell current source.

The solar cell model includes the following components:

• Solar-Induced Current

• Temperature Dependence

• Thermal Port

Solar-Induced Current

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/m², 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.

• N₂ 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.

Temperature Dependence

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:

$$I_s(T)=I_s*{\left(\frac{T}{T_{meas}}\right)}^{\left(\raisebox{1ex}{$TXIS1$}\!\left/ \!\raisebox{-1ex}{$N$}\right.\right)}*e^{\left(EG*\left(\frac{T}{T_{meas}}-1\right)/\left(N*V_t\right)\right)}$$

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.

Thermal Port

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 i² · 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.

Ports

Input

Ir — Incident irradiance

physical signal

Physical signal associated with the solar cell incident irradiance.

Conserving

+ — Positive voltage

electrical

Electrical conserving port associated with the solar cell positive voltage

- — Negative voltage

electrical

Electrical conserving port associated with the solar cell negative voltage

Parameters

Cell Characteristics

Parameterize by — Block parameterization

By s/c current and o/c voltage, 5 parameter (default) | By equivalent circuit parameters, 5 parameter | By equivalent circuit parameters, 8 parameter

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.

• 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 — Short-circuit current

7.34 A (default)

Current that flows when you short-circuit the solar cell.

Dependencies

This parameter is visible only when you select By s/c current and o/c voltage, 5 parameter for the Parameterize by parameter.

Open-circuit voltage, Voc — Open-circuit voltage

0.6 V (default)

Voltage across the solar cell when it is not connected.

Dependencies

This parameter is visible only when you select By s/c current and o/c voltage, 5 parameter for the Parameterize by parameter.

Diode saturation current, Is — First diode saturation current

1e-6 A (default)

Asymptotic reverse current of the first diode for increasing reverse bias in the absence of any incident light.

Dependencies

This parameter is visible only when you select By equivalent circuit parameters, 5 parameter or By equivalent circuit parameters, 8 parameter for the Parameterize by parameter.

Diode saturation current, Is2 — Second diode saturation current

0 A (default)

Asymptotic reverse current of the second diode for increasing reverse bias in the absence of any incident light.

Dependencies

This parameter is visible only when you select By equivalent circuit parameters, 8 parameter for the Parameterize by parameter.

Solar-generated current for measurements, Iph0 — Solar-generated current for measurements

7.34 A (default)

Solar-induced current when the irradiance is I_r0.

Dependencies

This parameter is visible only when you select By equivalent circuit parameters, 5 parameter or By equivalent circuit parameters, 8 parameter for the Parameterize by parameter.

Irradiance used for measurements, Ir0 — Irradiance used for measurements

1000 W/m2 (default)

Irradiance that produces a current of I_ph0 in the solar cell.

Quality factor, N — First diode emission coefficient

1.5 (default)

Emission coefficient of the first diode.

Quality factor, N2 — Second diode emission coefficient

2 (default)

Emission coefficient of the second diode.

Dependencies

This parameter is visible only when you select By equivalent circuit parameters, 8 parameter for the Parameterize by parameter.

Series resistance, Rs — Series resistance

0 Ohm (default)

Internal series resistance.

Parallel resistance, Rp — Parallel resistance

inf Ohm (default)

Internal parallel resistance.

Dependencies

This parameter is visible only when you select By equivalent circuit parameters, 8 parameter for the Parameterize by parameter.

Configuration

Number of series cells — Series-connected solar cells

1 (default) | positive scalar

Number of series-connected solar cells modeled by the block. The value must be greater than 0.

Temperature Dependence

First order temperature coefficient for Iph, TIPH1 — First order temperature coefficient for Iph

0 1/K (default) | nonnegative scalar

Order of the linear increase in the solar-generated current as temperature increases. The value must be greater than or equal to 0.

Energy gap, EG — Energy gap

1.11 eV (default)

Solar cell activation energy. The value must be greater than or equal to 0.1.

Temperature exponent for Is, TXIS1 — Temperature exponent for Is

3 (default) | positive scalar

Order of the exponential increase in the current from the first diode as temperature increases. The value must be greater than 0.

Temperature exponent for Is2, TXIS2 — Temperature exponent for Is2

3 (default) | nonnegative scalar

Order of the exponential increase in the current from the second diode as temperature increases. The value must be greater than or equal to 0.

Dependencies

This parameter is visible only when you select By equivalent circuit parameters, 8 parameter for the Parameterize by parameter.

Temperature exponent for Rs, TRS1 — Temperature exponent for Rs

0 (default)

Order of the exponential increase in the series resistance as temperature increases. The value must be greater than or equal to 0.

Temperature exponent for Rp, TRP1 — Temperature exponent for Rp

0 (default) | nonnegative scalar

Order of the exponential increase in the parallel resistance as temperature increases. The value must be greater than or equal to 0.

Dependencies

This parameter is visible only when you select By equivalent circuit parameters, 8 parameter for the Parameterize by parameter.

Measurement temperature — Measurement temperature

25 degC (default) | positive scalar

Temperature at which the solar cell parameters were measured. The value must be greater than 0.

Device simulation temperature — Device simulation temperature

25 degC (default) | positive scalar

Temperature at which the solar cell is simulated. The value must be greater than 0.

Thermal port

This tab is visible only if you expose the thermal port on this block.

Thermal mass — Thermal mass

100 J/K (default)

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.

Initial temperature — Initial temperature

25 degC (default)

The temperature of the solar cell at the start of simulation.

Model Examples

Solar Cell Power Curve

Generate the power-voltage curve for a solar array. Understanding the power-voltage curve is important for inverter design. Ideally the solar array would always be operating at peak power given the irradiance level and panel temperature.

References

[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.

Extended Capabilities

C/C++ Code Generation
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