**6. Conclusion**

Electrochemical batteries are becoming quite usual components for electrical engineers. One of our purposes was to provide a good understanding for such users, by the way of a short form equivalent circuit.

This equivalent circuit sums up the different steps of a simplified physical analysis. Two most important aspects may be cited:


144 Sustainable Growth and Applications in Renewable Energy Sources

Instead of using Q as a reference for the storage voltage, we use the voltage given by the optimized RC storage net. Again the plot is made for steps between constant values of the current. We can see that between curves corresponding to two given values of the current,

Fig. 19a. General Validation of diffusion/stockage and activation phenomena

Fig. 19b. Reduction of activation voltage variations by linearisation

The same points are plotted using the pseudo-voltage after exponential transform. We see that now the plot between two given values of the current, which constitutes a good

s V

s V

Electrochemical batteries are becoming quite usual components for electrical engineers. One of our purposes was to provide a good understanding for such users, by the way of a short

This equivalent circuit sums up the different steps of a simplified physical analysis. Two

**5.4 Improved storage voltage estimation** 

there remains a variation of the activation voltage.

Vin-Eo

**5.5 Effect of the non linear voltage transformation** 

*V*

validation of the non linear model.

**6. Conclusion** 

form equivalent circuit.

most important aspects may be cited:


## **6.1 Investigation of nonlinearities**

Characterization of dynamical non linear systems is quite complex. Purely phenomenological description may lead to a huge number of parameters for imperfect results.

From our physical analysis, nonlinearities are summarized by two simple elements:

