Quadratic sensitivities for power system steady-state control

Sensitivity analysis is employed by a variety of power system steady-state control tools, either purely algorithmic, knowledge-based or hybrid. First-order Taylor series expansion of the power flow equations is commonly used to calculate the necessary amount of control and predict the future state of the power system, if the control were to be implemented online. This paper introduces the concept of quadratic sensitivity as an extension to the established linear sensitivity approach. Multivariate calculus and tensor algebra are used to derive an analytical expression for the three-dimensional matrix of quadratic sensitivities. Quadratic and linear sensitivities are successively used in voltage control scenarios, simulated on the IEEE 30-bus test system. A comparison between the two approaches in terms of accuracy and run-time is performed. The proposed method improves the accuracy of voltage control by roughly one order of magnitude, provided no discontinuity due to generator reactive power limiting occurs. The effects of discontinuities induced by generator reactive power limiting are also investigated. In such instances, the accuracy of voltage control may be improved by a new generator tracking method