2.2 The sizing phase (iso-probability curves)
The sizing of the stand-alone PV systems consist of determine the reliability performance based on two dimensional parameters, the PV generator capacity which means the number of loads fed only by the PV array and the battery storage capacity indicates the number of days (hours) where the batteries are fully charged and with no energy income could feed the load (the hours where the load is supplied only by the batteries and not from the PV array) [1,3]. Those two parameters are defined by the following equations,
where is the used PV array area in (m2), is the mean hourly global solar radiation received on inclined surface in (Wh/m2). is the load value at time t in (W) and is the total panels' efficiency gave by the following equation,
Where, is the efficiency of a solar cell at a referenced solar radiation (i.e. 1000 W/m2), is the temperature coefficient is between (0.004-0.006), is the cell temperature in °C and is the reference temperature of the panel (generally equal to 25 °C with air mass AM= 1.5).
Where, is the maximum battery useful capacity in (Wh), is the number of batteries, is voltage for the unity of storage, is the nominal battery capacity in (Ah) and is the maximum depth of discharge.
The objective of sizing is the measure of the degree of the reliability in which the system (photovoltaic generator plus batteries) can supply the load demand at any time t. For that, the load loss of probability LLP is defined as the ratio between the energy deficit and energy demand for a specified load during the total operation time of the installation as expressed in the following equation
At each time t, the numerical method is applied to each configuration (panels and batteries) in an iterative way until the desired LLP is obtained. Once this task is completed, the parameters are saved and the reliability condition is reached. The summary of the modified algorithm based on numerical methods [17-18] is given by the following steps,
Step 1: Initialization of the data;
, Load at time t , , the panels’ efficiency, , the classified hourly solar radiation data on inclined surface (lowest hourly solar radiation obtained from the fuzzy c-means algorithm ), .
Step 2: Calculate the useful PV array area and the maximum useful battery capacity ;
, , , .
Step 3: calculate the state of the charge of the battery at the time t,
The energy supplied by the auxiliary generator , keep the battery fully charged if the load requirements is bigger than the energy stored in the batteries, that
The value is calculated over the number of available hours by the following equation,
Step 4: if then and go to step 5; Otherwise and go to step 5
Step 5: if go to step 3; else, go to the next step.
Step 6: saving pairs .
Step 7: if the values of are changes go to step 2;...