Solar
Module Electrical Model |

An electrical model for the solar module
will allow us to determine the true operating conditions imposed by the
battery and regulator, and the loss of efficiency that occurs. In this
study the efficiency of the solar power system is studies for different
types of regulators.- A regulator that simply connects the solar module to the battery, so that the voltage output of the module is fixed at the battery voltage.
- A Maximum
Power Point Tracking (MPPT) regulator that follows the Maximum Power
Point of the solar module, transforming the module power output to a
voltage level that matches the battery. Such MPPT regulators can
generally only achieve about 92%-97% efficiency at best in the
transformation process (some top range ones claim as much as 99%), so
some of the gain achieved by these regulators will be lost. A good MPPT
regulator can also boost low module voltages up to the battery voltage,
thus allowing charging to continue under very low light levels.
The system diagram for this model is as follows: As a solar cell develops a voltage across a p-n junction in response to incident light, a simple model can be devised that consists of a current source (dependent on the incident illumination) and a parallel diode. Internal resistance can be significant for some cells, but we shall ignore this for the moment. Thus: I
= I
_{sc} - I_{0} (e^{V/Vk}-1)where I is the module current delivered to the battery, I _{sc} is the light dependent
current, equal to the short circuit current in the case of zero series resistance, and I_{0}
is a diode reverse bias current. V is the voltage across the cell and
Vk is another diode characteristic parameter proportional to
temperature. We
can obtain the two diode parameters by curve fitting to three points on
the characteristic V-I curve that is usually published for a solar
module. The three points that are normally specified are the short
circuit current, open circuit voltage, and maximum power point voltage
and current.If internal series resistance R _{s} of a cell is considered then the voltage V must be replaced by V+IR_{s} which is the voltage across the ideal diode. Thus we get:I
= I
_{sc} - I_{0} (e^{(V+IRs)/Vk}-1)The total voltage across a module is then the sum of the individual series cell voltages. Note that V and R _{s} refer to an individual cell. For a module which has total series resistance R_{sm} and voltage V_{m} it is necessary to divide by the number of cells in series N_{s}.As an example, the BP module BP3125, a 125W specified module, has the following datasheet values at an incident sunlight power of 1000W/m² and at 25 ^{o}C:- Short circuit current 8.02A
- Maximum power point current 7.23A
- Maximum power point voltage 17.3V
- Open circuit voltage 22.1V
- Number of cells in series N
_{s}
_{0} = 0.185mA, and Vk = 0.058V. The latter is double that of the theoretical 0.026V for an
ideal pn junction, however we will assume that Vk has the usual
linear temperature proportionality and that neither characteristic parameter
depends on light intensity. A plot of the V-I curve for this model is
shown
below.The model of the solar module as described above is combined with the model for the insolation of the module: - for the simple regulator, limiting the output of the solar module to the battery voltage and determining the current.
- for the MPPT regulator, determining the module's maximum
power point and converting the voltage/current at that point to match
the battery voltage at 100% efficiency.
- If the module followed the sun and the panel output voltage was fixed:: 22.5 AH
- If the module followed the sun and the panel output voltage was at the MPP: 28.3 AH
- If the module were fixed to north and the panel output voltage was fixed: 19.6 AH
- If the module were fixed to north and the panel output voltage was at the MPP: 24.4 AH
To model a cloudy day, the sunlight intensity was reduced by a factor of 10. The results showed that an MPP regulator provided very little gain over a simple regulator, as the module output was close to 12V most of the time. This conclusion may vary with other modules whose output may be less than 12V in certain conditions, and a good MPP regulator could provide a small advantage. A number of runs of the model under various conditions did not show MPP regulator gains greater than 30%. Some manufacturers claim over 40% gain for their products. The gain will increase as the open-circuit module voltage increases above the battery voltage. |

First created 26 June 2007

Last Modified 21 June 2015

© Ken Sarkies 2007