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In the existing literatures, modal analysis for steady-state voltage stability is based on the reduced Jacobian matrix, i.e. active power equations are eliminated, and reactive power equations of the constant power/voltage buses (PV buses) are ignored in the polar coordinate expression, which is actually designed for voltage controllability, but questionable for voltage stability.In this article, power outputs of the rotating machines are newly decomposed to the steady-state and dynamic components, with the latter proportional to derivative of the rotor flux. Therefore, neither the active nor the reactive power equations of the rotating machines may be eliminated or ignored in the Jacobian matrix. Only the static buses with constant load impedance should be eliminated. Numerical results show that elimination of active power equations or ignorance of reactive power equations of the rotating machines will yield optimistic stability margins, while including power equations of static load buses yields pessimistic stability margin. It is also find that more static load component yields larger stability margin.

Configuration of Jacobian Matrix in Steady-State Voltage Stability Analysis Based on Rotor Flux Dynamics of Rotating Machines