**Introduction** The use of solar off-grid energy supply is becoming increasingly popular for domestic, industrial and municipal applications. Due to the variable nature of renewable energy sources, many of the installations include an energy storage system to enable supply for peak demands and when energy generation is limited. There are alternative storage technologies but the method of calculating the size of the lead acid battery required is common to all chemistries. To ensure a system that satisfies the usage requirements it is necessary to obtain a reasonably detailed picture of the loading and run time autonomy of the battery. Allowances must be made for the efficiency of the components in the system in converting energy from the input source to the demand on the battery. For this, the size of individual load, the total load and the individual run times are crucial factors in calculating an accurate battery capacity for the system requirement. Whether as the sole source of electricity or as a hybrid fuel supply, the characteristics of the equipment and the application need to be thoroughly understood to design and specify an effective and trouble-free installation. To provide electricity during the night, either all or in part, from a solar photovoltaic array requires batteries for storage of electrical energy. A meticulous approach to calculating the autonomy load will also ensure that the solar battery selection will be accurate. A correct battery specification will ensure not only a satisfactory autonomy but also a long and cost-effective battery life. The following is a guide to obtaining the detailed and correct information necessary to calculate the size of battery required to maximise its performance, energy efficiency and cost effectiveness.

Summary of methodThis section provides an understanding of the overall method to provide an explanation of the methodology used to obtain the data. The detailed calculation and methods of obtaining loads and efficiencies are given in the operations section.

Estimation of the autonomy in hours (H)This is the time that the battery must operate without recharging. This is designated as

HGenerally, there is more than one load from various devices and these loads may not be operating continuously. For these individual loads there will be individual autonomies. These will be listed separately as load 1, 2, 3 etc., with corresponding times in operation, i.e. corresponding autonomies. These individual autonomies are designated ash1, h2. h3etc.

Calculation of the total and average load (Lt and La)It is important to assess the total number of ampere hours which the battery needs to supply during its operation. However, it is also important to know the variation in loads and the type of load which is used. The load calculation can be done in 2 ways:

Estimation from equipment rating

Direct measurement of the load

For estimation from the component rating it is important to know not only the indicated value but also the power factor. Many loads have an inductive element such as a TV, refrigerator or LED lights. The individual loads (in watt hours) are designated

l1, l2, l3etc. The nameplate rating of the load must be adjusted for its power factor by multiplying the load by the power factor. If the load is obtained by measurement then this step is unnecessary and the measured value can be used directly. The load and average load can be calculated by taking the sum of the individual loads or the maximum load measured (Lt) then dividing by the number of hours for the battery operation (H) to give the average load (La). A more accurate method is to look at the individual loads and their time of operation. To calculate the total watt hours required, the loads are multiplied by their operating time.

Efficiency of the systemThe basic principle of operation for a Solar Photovoltaic or renewable energy supply is that it has to convert power (watts) into a form which has a controlled voltage for either storage or direct use through an inverter or DC:DC converter where there is a constant voltage supply. Each operation from the power supply to the load will have an efficiency loss which must be considered when calculating the amount of energy available for the autonomous period. The total efficiency of the system depends upon the number of stages between the power supply, the load and the % efficiency at each stage. For example, the total efficiency of a simple system without energy storage would be:

PV array ————> DC:DC ————-> Inverter ————–> LoadOutput from the solar panels x DC converter efficiency (

EDC) x Inverter Efficiency (EI)= total available output.With energy storage, the efficiency of the battery charger, the efficiency of the battery chemistry on discharge and charge must also be considered. The voltage loss through the cables is another factor to be added in for calculating the battery output requirement.

Output required from the Solar battery.It is possible to calculate the output requirement simply from the total watt hours required over the autonomy period using either the measured or calculated values, as explained in section 2. However, the size of the Solar battery required to deliver this output requires a more detailed approach. The following parameters should be known:

The minimum state of charge of the battery at the end of the autonomy

The maximum state of charge of the battery at the end of the charging period

The peak load on the battery during the autonomy period

The time when the peak load occurs

The voltage loss between the battery and DC load and the voltage loss between the inverter and the AC load

Operating temperature of the battery

These maximum and minimum state of charge are important to ensure that the battery not only provides sufficient energy for the autonomy period, but also that the battery obtains the expected cycle duty and will have sufficient energy input during the recharge period to complete the duty cycle. The peak loads and their occurrence during the discharge period are important as this will cause a voltage drop. The solar battery should be sized to prevent this drop, including the voltage losses in the system, from falling below the required operating voltage for the loads or inverter. The solar battery capacity will vary with temperature. The lower the temperature then the lower the capacity. The life of the battery will also depend upon the battery operating temperature: generally the higher the temperature the shorter the battery life. This information regarding capacity and life will be provided by the Microtex technical team, you can contact them here.

Estimation of available battery capacity using average loadThe average load may be calculated by any of the methods described, which incorporate the inefficiencies, the run time, the peak loads and the time they occur during the discharge. This should be used to estimate the available capacity required by the battery. However, it is not only the total energy required that is important as it is unlikely that there will be a uniform current draw over the whole autonomy. The peak load is important particularly if it occurs near the end of the discharge period as it may cause the battery voltage to drop below the minimum necessary to operate the equipment, despite the battery having sufficient capacity to provide the total energy requirement.

**Input required for battery charging**

The charger should have sufficient output current to recharge the battery up to the state of charge required to complete the autonomy period. It is important to obtain the correct re-charging regime from Microtex for the type of solar battery used and also that there is sufficient time for the required recharge. It is necessary to consider the efficiency of the charger and the efficiency of the battery being charged. The charger efficiency will be dependent upon the losses due to conversion from the power source to the battery. Whether it is a transformer, switch mode or high frequency charger will determine the conversion efficiency. There are further losses due to the differences between the battery charging voltage and discharge voltage which will be dependent upon the charging profile used and the percentage state of charge that the battery must reach. The energy efficiency i.e. amps x volts x time (watt hours) must not be confused with coulombic efficiency i.e. amps x time (ampere hours). The majority of battery companies quote only coulombic recharge efficiency in their literature. This is not a true measure of the system efficiency which should be measured in watt hours. The Microtex technical team will advise on the charge regime and the efficiency for calculation purposes. Feel free to call us for support on sizing of your solar battery requirements.

**Final sizing of solar battery and charger**

Once the output requirement is fully understood using the methodologies described, and the recharge characteristics identified, the solar battery size can be calculated. This is the equation:

Total watts including inefficiencies taken out of the battery = total watts including inefficiencies put into the battery.

Two more factors are the ambient temperature and the depth of discharge and recharge to provide the required cycle life and recharge time for the operation of the battery. The amount of battery capacity used can be expressed as a fraction e.g. Minimum SOC = 20% and maximum SOC = 95% the capacity fraction is 75% or 0.75. The operating temperature will provide the compensation for capacity and the DOD and %SOC will determine the battery size so that:

Battery size = (total watts out/capacity fraction) x temperature compensation

This will give the correct battery size with no margin for error. It is recommended that there is a contingency of +5% added to this final value to ensure a trouble-free operation.

Dr Mike – CTO Microtex