An analysis of a given electrical circuit using a fractional derivative. The statespace equation was developed. The dynamics of tensions described by Kirchhoff’s laws equations. The paper used the definition of the integral derivative Caputo and CDF conformable fractional definition. An electrical circuit solution using Caputo and CDF defini- tions for rectangular with zero initial conditions was developed. The results obtained using the Caputo and CDF definitions were compared. The solutions are shown for capacitor voltages, for fractional derivative orders of 0.6, 0.8, 1. The results were compared using graphs.

This paper presents a novel approach for reactive power planning of a connected power network. Reactive power planning is nothing but the optimal usage of all reactive power sources i.e., transformer tap setting arrangements, reactive generations of generators and shunt VAR compensators installed at weak nodes. Shunt VAR compensator placement positions are determined by a FVSI (Fast Voltage Stability Index) method. Optimal setting of all reactive power reserves are determined by a GA (genetic algorithm) based optimization method. The effectiveness of the detection of the weak nodes by the FVSI method is validated by comparing the result with two other wellknown methods of weak node detection like Modal analysis and the L-index method. Finally, FVSI based allocation of VAR sources emerges as the most suitable method for reactive power planning.