Battery sizing Suppose you are offgrid running on a 24V PV s

Battery sizing. Suppose you are off-grid running on a 24V PV system at a site with 6 hours of peak sun or 6 kWh/m2 in one day. You have a load of two DC motors consuming 0.1 kW each. Motor 1 runs all day and motor 2 runs 4 h twice per day. Size the batteries assuming 95% availability and 80% discharge allowance. Specify a 24V battery bank for the following two options. Compare number of batteries needed and cost. a. 12 V and 80Ah (20h rate) batteries at $150 each b. 6 V and 220 Ah (20h rate) batteries at $240 each

Solution

Load is two DC motor of Power rating 0.1 kW each.

Energy Consumed by total load per day is E = 0.1*24 + 0.1*8 = 3.2 kWH / day

Given peak sun at given location is 6 kWh/m² , We came to know that 1 kW PV system able to generate 6 kWh of energy under ideal conditions .

We need to size PV system base on energy required per day and to charge batteries

Ideal Size of PV system is P = 3.2*1/6 = 0.533 kW;

Energy consumed by load during peak sun is Epl = 0.1*6 + 0.1*4 = 1 kWh and 2.2 kWh energy need to be stored by battery. Considering battery availability and discharge total energy stored by battery is

Eb = 2.2/(0.8*0.95) = 2.894 kWh /day

PV system size required to generate energy of Epv = 2.894+1 = 3.894 kWh and

size is Ppv = 3.894*1/6 = 0.649 kW

Battergy Size required and Cost

1) 12 V and 80 Ah (20 rate) , cost = $150 each

Energy need to stored is 2.894 kWh and Each battery stores Eeb = 12*80 = 960 Wh = 0.96 kWh

No.of Batteires required is N = 2.894/0.96 = 3 batteries , but required system voltage is 24 V , we need take 4 batteries

Cost of batteries is C = $150*4 = $600;

Two batteries connected in series and two such string are required.

2) 6 V , 220 Ah and Cost = $240 each

Energy need to stored is 2.894 kWh and Each battery stores Eeb = 6*220 = 1320 Wh = 1.32 kWh

No.of Batteires required is N = 2.894/1.32 = 2.19 batteries , but required system voltage is 24 V , we need take 4 batteries

Cost of batteries is C = $240*4 = $960;

All batteries connected in series