Optimization of Photovoltaic Power Systems pp 113-147 | Cite as

# Optimized Use of PV Arrays

## Abstract

The source of photovoltaic electrical energy is the solar cell. Commercial solar cells reach maximum conversion efficiencies of 20–21%, while an efficiency of 25% may be achieved in laboratory [62]. The overall efficiency of a module ranges from 15 to 17% [62]. Under real operating conditions, a lower efficiency than the nominal efficiency could be observed [73]. PV arrays must be installed so that they maximize the amount of direct exposure to the sun. This usually means placement in an area clear of shading, in a southward direction and at an angle equal to the latitude of the location. The power provided by the PV array varies with solar irradiance and temperature, since these parameters influence the I–V characteristics of solar cells. In order to optimize the energy transfer from the PV array to the load, it is necessary to force the working point to be at the maximum power point (MPP) [31, 63].

### Keywords

Sliding Mode### Symbols

*a*,*b*,*c*and*d*Coefficients determined by the sampling values of the photovoltaic voltage V

_{PV}*BN*Big negative

*BP*Big positive

- \( \frac{{dP_{\text{pv}} }}{{dV_{\text{pv}} }} \)
Derivative of PV power by the voltage

- \( I_{\text{L}} \)
Inductance current

*k*_{1}A constant of proportionality (\( 0.71\langle k_{1} \langle 0.78 \))

*k*_{2}A factor which depends on the current PV (\( 0.78\langle k_{2} \langle 0.92 \))

*K*_{G}A proportional gain

*k*_{c}A positive scaling constant

*MN*Means negative

*MP*Means positive

- \( R_{\text{pv}} \)
Equivalent load connect to the PV

*SN*Small negative

*SP*Small positive

- \( V_{\text{opt}} \)
Optimal voltage which gives maximum power

*Z*Zero

- \( \alpha \)
Duty cycle

- \( \alpha_{eq} \)
Equivalent duty cycle

- \( \Updelta P_{\text{pv}} \)
Power variation between two operating points

- \( \Updelta V_{\text{pv}} \)
Voltage variation between two operating points.