University of South Wales Master of Sciences Thesis

 
Standalone hybrid generation system for the remote area of Thar, Pakistan
 
 
 
Rechargeable batteries have standard electric potential, which is the potential difference between the 
cathode and anode [6, 17]. A simplified equivalent circuit of a battery at its steady state is given in 
[11] and is shown below (Figure 2-20) working as a voltage source with an internal resistance. 
Fig. 2.20 Equivalent circuit of a battery 
Assuming that the open circuit voltage and resistance when the battery was fully charged are E0 and 
R0, then the open circuit voltage and internal resistance at any time when battery is discharging can be 
given as [11]: 
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The open circuit voltage decreases and the internal resistance increases with the Ah discharge, Qd. 
The constants K1 and K2 are found from curve-fitting test data [11]. The internal resistance is a 
function of SOC, battery capacity and operating temperature. With higher battery capacity, the 
electrodes will be larger and the internal resistance will be lower [11]. Figure 2-21 shows simple 
circuit model of the simplified electric circuit with the conducting resistance, Rohm included. 
Fig. 2.21 General electric circuit model for a rechargeable battery [11] 
The simple electric circuit model shown above includes an internal resistance, Ri, conductor 
resistance, Rohm and a standard cell potential E0. Applying the maximum power transfer theory, the 
peak power, delivered from the battery in the above model is: 
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Since Ei and Ri depend on SOC, the maximum power that can be delivered to the load by the battery 
also depends on SOC. The efficiency at any SOC can also be derived into the following form where it 
depends on SOC [11]. 
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