A sliding mode controller for SSSC to delay Hopf bifurcation in a differential-algebraic power system model

A novel sliding mode controller (SMC) is proposed for static synchronous series capacitors (SSSCs) to delay Hopf bifurcation (HBF) in a differential-algebraic power system model. The proposed controller consists of an equivalent control term and a switching term. The major drawback of SMC approach, viz., the undesired chattering is eliminated by introducing a continuously changing switching term instead of the conventional switching function. The effectiveness of the controller is demonstrated in a bifurcation perspective. Steady state bifurcation diagrams are constructed by the application of an algorithm based on continuation method for the entire Jacobian matrix of structure preserving power system model. From the bifurcation diagram, existence of HBF is identified with the help of eigen value analysis. Occurrence of HBF is confirmed through computation of HBF index. The effectiveness of the proposed SMC over the conventional PI controller for SSSC in delaying HBF and maintaining load voltage constant for higher reactive power loading is illustrated for a 3 machine, 9-bus system.