Adaptive Soft Computing Synergistic Paradigms for VSC Based FACTS Damping Controls Since their inception, damping of Low Frequency Oscillations (LFOs) has been a critical issue in electric power systems. Voltage Source Converter (VSC) based Flexible AC Transmission Systems (FACTS) have a renowned capability for rapid regulation of various network quantities, thus being a serious candidate for future power system control and smart grids. VSC based FACTS have built in capability of absorbing or delivering reactive power. FACTS controllers when equipped with efficient supplementary damping control combat LFOs. Although, a large research investment in efficient damping control for FACTS and advancement in the field of Artificial Intelligence (AI) has led to more robust controls. Even then, there is a growing realization that the contribution to damping performance enhancement should be more rigorously addressed for different tradeoffs, such as complexity and control effort smoothness. This dissertation puts forth the claim that efficient damping control strategy to improve application quality in terms of damping performance, control effort smoothness and execution time is essential for a high performance FACTS supplementary control. This work is a design paradigm shift from conventional Takagi Sugeno Kang (TSK) based control to advanced control based on hybrid Soft Computing (SC) techniques. SC techniques are the most lucrative choice to supplementary damping control design for their optimal performance delivery in critical applications with low complexity and high precision. The direct focus of this research is to exploit the potential of hybrid SC paradigms, obtained from diversified domains such as signal processing (Fourier and wavelets), applied mathematics (Bsplines and polynomials) and AI (neural and fuzzy), to name a few. A modular approach for optimization of overall Multiple Input Single Output (MISO) TSK structure to speculate optimal combination of antecedent and consequent parts has been proposed. The contributions of this framework are the ixdamping performance improvement with smooth control effort and improved convergence speed. The work, proposed in this thesis, has further been extended to Multiple Input Multiple Output (MIMO) structure. The parameters of controller are updated online, using gradient descent based backpropagation algorithm, to avoid offline training overhead. These synergistic paradigms are later used with indirect Multiple Input Single Output (MISO) and MIMO control to ruminate optimal control schemes. The convergence analysis based on Lyapunov stability criteria has been used to ensure the stability of control scheme and to derive an upper bound on the learning rates. In case of MIMO control, convergence is guaranteed using Adaptive Learning Rates (ALRs). These schemes are applied successively to Single Machine Infinite Bus System (SMIB) with single FACTS, multimachine system with single FACTS and multimachine system with multitype FACTS controllers. The proposed control schemes have been tested for different contingencies and various operating conditions. Finally, the qualitative behavior of all the control paradigms has been quantified using different performance indices that support the nonlinear time domain simulation results. The statistics also support the claim that an ideal performance of a supplementary damping control demands a perfect match between antecedent and consequent part of the NeuroFuzzy network. The frequency domain analysis using Wigner-Ville Distribution (WVD) has also been carried out to analyze the frequency spectra of control effort for smoothness validation. The proposed hybrid control paradigms give better performance in transient and steady-state regions.