Lead acid battery equivalent circuit

The function describing the frequency dependence of such an impedance element is equivalent to that of diffusion in Eq. (28), bnt the meaning of the parameters must be redefined as Rd = Rm, Rp = Ret, Cd = Cdi, and Cp = Cad- A complete equivalent circuit of the lead acid battery will involve serially connected elements described in previous paragraphs for the electrolyte and anode and cathode, with the addition of series resistance and inductance. 

FIGURE 9.3 Equivalent circuit model of the lead-acid battery by Abolhassani et al. (From Abolhassani Monfared, N. et al.. Journal of Power Sources 158, 932-935, 2006.)... 

The Thevenin equivalent circuit is the simplest combination, since it is the association of an ideal voltage source and a resistor connected in series. This is a much more realistic way of modeling a lead-acid battery. Indeed, the resistor illustrates the voltage drop due to the current passing through the components of the battery. In the case of LABs, this instantaneous voltage drop mainly results from the low electrical conductivity of electrolyte and is proportional to the current. But, such a simple combination does not account for the polarization of the electrodes happening later on, when the battery is operated. 

FIGURE 9.11 Equivalent circuit model of a LAB by Appelbaum and Weiss. (From Appelbaum, J., and Weiss, R., An electrical model of the lead-acid battery. In Proc. Int. Telecommunications Energy Conf., pp. 304-307. Washington, DC, 1982.)... 

Typical dimensions for the /5-alumina electrolyte tube are 380 mm long, with an outer diameter of 28 mm, and a wall thickness of 1.5 mm. A typical battery for automotive power might contain 980 of such cells (20 modules each of 49 cells) and have an open-circuit voltage of lOOV. Capacity exceeds. 50 kWh. The cells operate at an optimum temperature of 300-350°C (to ensure that the sodium polysulfides remain molten and that the /5-alumina solid electrolyte has an adequate Na" " ion conductivity). This means that the cells must be thermally insulated to reduce wasteful loss of heat atjd to maintain the electrodes molten even when not in operation. Such a system is about one-fifth of the weight of an equivalent lead-acid traction battery and has a similar life ( 1000 cycles). 

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