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The entire design of a PV system is based on the size of the load. The load influences every aspect of design of the different PV system components (Bhuiyan & Asgar, 2003). Hence, its estimation must be efficient and reliable. Overestimation of the load will result to over sizing of the system which will not be cost-effective. On the other hand, an underestimation of the load will result to under sizing of the system and the generated power will not be able to power the required load.

A variety of literature exists on the design and sizing of PV systems. Authors have used different mathematical models for the sizing of the different PV system components. However, these models fall under either of the two general methods for sizing PV systems: kW method and the Ah method.

2.8.1 Sizing of array

According to Alamsyah, Sopian & Shahrir (2003), the size of a PV array can be computed using Equation 3.

𝐴𝑃𝑃= _𝐻 𝑈𝑒𝑒

𝑎𝑎𝑎𝑥ŋ𝑃𝑃 𝑥ŋ𝐵𝑥ŋ𝑖𝑥𝑇𝐶𝐶 Equation 3

Where; APV is the required PV array area in m2, Lel is the required electric load in kW h d-1,

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Havg is the average daily irradiation of the location in kW h m-2 d-1,

ŋPVis the PV panel efficiency in %, ŋi is the efficiency of the inverter in % while TCF is the temperature correction factor.

In their study, Abdul & Anjum (2015), considered the battery and inverter efficiency to be 85% and 90% respectively. Caisheng, and Nehrir (2008) used a TCF of 80% in their study.

The peak power of the PV (PPVP) panel under STC can be calculated using the peak solar irradiance and the efficiency of the PV panel as indicated in Equation 4 (Mahmoud and Ibrik, 2006).

𝑃𝑃𝑃𝑃=𝐴𝑃𝑃 𝑥𝐼𝑝 𝑥ŋ𝑃𝑃

Equation 4

Where; Ip is taken as 1000 W m-2 (irradiance at STC).

Bhuiyan and Asgar (2003) used another method for the sizing of the PV array which entails the use of current to describe the requirement of the load. According to the authors, the PV array is sized to replace the daily load using average weather conditions. Normally, the array is sized in the design month corresponding to the month with the minimum solar insolation in order to ensure that the power generated by the array is able to reliably operate the load. The derated design current of the array (IDE) is computed using Equation 5 (Bhuiyan & Asgar, 2003).

𝐼𝐷𝐷 = 𝐼_ŋ𝑀𝑆𝐷

Equation 5

Where; ŋM is the module derate factor, which represents energy losses from the module due to accumulation of dust, mismatch between modules and degradation over time.

𝐼𝑆𝐷 = (𝐼𝐷) max Equation 6

Where; (ID)max corresponds to the largest current at the design month and selected tilt angle refers to the tilt at selected design current = βs

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𝐼𝐷(1−12)= _𝐻𝐸𝑐(𝐴ℎ)

𝑝𝑝(1−12) Equation 7

Where: Hps(1-12) represents the monthly average of the peak sun hours per day for the

months of January to December at a particular tilt angle (β), Ec(Ah) refers to the Corrected Ampere-hour load calculated using Equation 8.

𝐸𝑐(𝐴ℎ)= 𝐸_ŋ𝑤ŋ𝑏𝑑(𝐴ℎ) Equation 8

Where; ŋw and ŋb represents wire and battery efficiency respectively. Ed(Ah) is the Ampere-hour load calculated from Equation 9

𝐸𝑑(𝐴ℎ)=∑ 𝑁𝑖𝐼𝑖𝑉𝑖𝐻𝑖

𝑛 𝑖=1

ŋ𝑝𝑐𝑒𝑉𝑛𝑝𝑎

Equation 9

Where; Ni is the number of ith residential load,

Ii, and Vi refers to the current and voltage respectively that is drawn by the ith loads, Hi is the daily duty cycle of the ith load,

Vnsv and ŋpce represents the nominal voltage of the system and the power conversion efficiency.

The number of parallel PV modules in the array is obtained using Equation 10.

𝑀𝑝=𝐼_𝐼𝐷𝐷

𝑟 Equation 10

Where; Ir is the module rated current (A).

The number of modules in series in the array is given by Equation 11.

𝑀𝑝=𝑉𝑛𝑏𝑎_𝑉𝑥𝐵𝑝 𝑥 1.2

𝑀,𝑇𝑇𝑎𝑇 Equation 11

Where; VM,Tmax is the highest temperature voltage of the module. The total number of module is calculated using Equation 12

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𝑀𝑇 =𝑀𝑝𝑥𝑀𝑝

Equation 12

2.8.2 Battery storage

According to Wenham, Green & Watt (1994), the storage capacity of a PV system battery bank (BSC) is calculated taking into consideration the battery efficiency, efficiency of the inverter, depth of discharge of the battery and the system autonomy (number of cloudy days). The formula for the determination of the battery size is shown in Equation 13.

𝐵𝑆𝐶 = _ŋ 𝑁𝑐𝑥𝐿𝑒𝑒

𝐵𝑥𝐷𝑑𝑥ŋ𝑖 Equation 13

Where; Dd is the maximum depth of discharge of the battery and Nc refers to the system autonomy (continuous number of cloudy days).

Bhuiyan and Asgar (2003) designed the battery bank using the following equations (Equation 14, Equation 15 and Equation 16):

𝐵𝑟𝑐 =_{(𝐷𝑃𝐷}𝐸𝑐(𝐴ℎ₎)𝑥𝐷𝑝

𝑇𝑎𝑇𝑥ŋ𝑇 Equation 14

Where; Ds represents the battery autonomy while (DOD)maxand ŋT represents the maximum battery depth of discharge and temperature correction factor respectively. The batteries in parallel is obtained using Equation 15

𝐵𝑝=_𝐵𝐵𝑟𝑐

𝑆𝐶 Equation 15

Where; Bsc represents the selected battery capacity. The batteries in series is given by Equation 16

𝐵𝑝 =_𝑉𝑉𝑛𝑝𝑎

𝑛𝑏𝑎 Equation 16

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The total battery in the battery bank is given by Equation 17 𝐵𝑇 =𝐵𝑝𝑥𝐵𝑝

Equation 17

2.8.3 Controller Specification

The function of the charge controller in a system is to ensure safe charging of the battery and consequently eliminating the risk of having the batteries over charged. The controller must have the capacity to handle the maximum current generated by the PV array and its voltage compatible with the nominal voltage of the system. Hence this device must be selected carefully to ensure that it is able to carry the generated current by the array. The size of the charge controller (Scc) is given by Equation 18.

𝑆𝑐𝑐=𝐴𝐴𝐴𝐴𝐴𝑐𝑐𝐴𝐴𝑐𝑐𝑐𝑥 1.25

Equation 18

The array current is multiplied by a factor of 1.25 so as to give flexibility to the charge controller to accommodate high current generated by the PV array during period of high irradiance (Sandia National Laboratories, 1995).

2.8.4 Determination of inverter size

There is need for an inverter to convert the generated dc current into ac current so as to power the ac loads in the building. The inverter should be selected in such a way that it must be able to handle the maximum expected ac power loads (Abdul & Anjum, 2015). Hence, it is recommended for the selected inverter to be 20% higher than the total rated power of the required ac loads.