# Dimensioning of a PV system

## What is the purpose of sizing an installation?

The purpose behind the sizing of installation is to fix the modalities of implementation according to technical and financial criteria.

Technical studies concern the design and sizing of photovoltaic fields and system components.

These components are mainly:

– Inverters
-The batteries
– Regulators (or converters)
– The dimensioning allows:
– an evaluation of the energy produced
– Optimization of the PV system taking into account the factors influencing the system (shading, loss of energy, dirt, temperature, ct)

– The sizing aid tools are software like Homer, RETSCREEN, PV-CHART, TRNSYS, etc.

sizing of a PV system requires knowledge of:
– The nature of the installation (autonomous, injection into the network or hybrid)
– The nature of the load and the energy requirements
– The characteristics of PV modules.
– The characteristics of the site (sunshine weather conditions, etc.
– The modes of use of PV modules (fixed or mobile orientation (solar tracking)
-The angle of inclination.
– The technology and characteristics of the storage system (battery)
– Characteristics of regulators
– Characteristics of inverters.

#### Energy balance of the PV system

Sizing a system is a fairly complicated task due to:

– The random and intermittent nature of solar radiation reaching the photovoltaic modules.

– The effects of soil reflection (albedo).

– The orientation of the PV module (tilt, rotation, and azimuth orientation)

– Soiling of the modules
– Etc.

Therefore, there are several models for sizing a PV system; among these models are:
a) The simplified model
b) The pressure drop probability model.

#### a) Simplified design model

In this model, the energy balance in a PV system is established by assuming that the energy consumption over a period of time of the load is equal to the energy produced by the PV modules.
So we have
Psol = LPsol: energy produced by PV modules

L: energy consumption of the load as Psol = Pc.Ne.Ce
Pc: peak power of the modules.
Ne: equivalent number of hours.
Cp: ​​loss coefficient.

Then  L = Pc.Ne.Cp

As the solar irradiation depends on the state of the sky and the season, the choice of Ne depends:
– The nature of the application. For example, if we have a water pumping system for the summer, we take Ne which corresponds to the summer.
– If the application is for the whole year.
– Two options are generally considered:

• The case design of the most unfavorable case. Here, we size the system considering the case of the month with the lowest solar irradiation.

—–which gives us the smallest value of Ne —–  (Ne) min
In this case, we have:
L = Pc. (Ne) min. cp
In this case, we will always have a generation of excess energy (except for the month of low irradiation).
•  Medium sizing case:

In this case, we take the daily irradiation as the average value of the irradiations for all the year
In this case, we take Ne = Ne and we therefore have
L = Pc (Ne) .Cp

• If the PV field is formed by N modules

N= Ns.Np

Or Ns: number of modules in series
Np: number of modules in parallel

So this case and ensuring the identical modules:
Pc=Ns.Np.P0c
Pc= N. P0c
Or  P0puissance crête of a  module

From here we shoot
L = N. P0c.Nc.Cp
Hence the number of modules to meet the needs of a load consuming energy is:
N =L/P0c.Nc.Cp

Assuming that the module operates at the point of maximum power
P0c = Im.Vm
With Im: current at maximum power
Vm: voltage at maximum power
N=L/Im.Vm.Nc.Cp

N=Ns.Np

Ns: serial number of modules
Np: parallel number of modules

Assuming the load operates at direct current
The voltage across the load is then Vcc and the current through the load is Ic.

with :Vcc= Ns.Cs.Vm
So :Ns=Vcc/Cs.Vm
therefore : Np=L/Im.Vm.Nc.Cp.Ns

Cs is called the safety factor
Cs is taken greater than 1 (oversizing on the system)
The number of modules in parallel is determined using the equations
Np=L/Im.Vm.Nc.Cp.Ns