Voltage security enhancement using energy based sensitivities

An energy based security measure is used to define vulnerability to voltage instability, and a method of security enhancement by examining the sensitivity of the security margin to various control actions is proposed. The use of the energy function in systems with significant line losses is reviewed, and the analytic expressions for first-order total derivatives with respect to relevant control parameters are derived. Computational properties, such as the sparsity of various vector and matrix quantities, are examined. Numerical examples of security enhancement based on these sensitivities are computed for a thirty bus example system. Potential application of this approach within a security constrained optimal power flow is also discussed