This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON POWER SYSTEMS 1 Dynamic Optimization Based Reactive Power Planning to Mitigate Slow Voltage Recovery and Short Term Voltage Instability Magesh Paramasivam, Student Member, IEEE, Ahmed Salloum, Member, IEEE, Venkataramana Ajjarapu, Fellow, IEEE, Vijay Vittal, Fellow, IEEE, Navin B. Bhatt, Fellow, IEEE, and Shanshan Liu, Member, IEEE Abstract—Short term voltage stability poses a significant threat to system stability and reliability. This paper applies dynamic VAr injection to ensure short term voltage stability following a large disturbance in a power system with high concentration of induction motor loads. Decelerating and stalling of induction motor loads is considered to be the major cause of fault induced delayed voltage recovery (FIDVR) and short term voltage sta- bility. If system dynamics are not taken into account properly, the proposed control solution may be an expensive over design or an under design that is not capable of eliminating FIDVR problems completely. In this work, the optimal amount and locations for installing dynamic reactive resources are found by control vector parameterization (CVP), a dynamic optimization approach. The efficiency and effectiveness of this approach is improved by uti- lizing results from trajectory sensitivity analysis, singular value decomposition and linear programming optimization. Dynamic optimization based on CVP approach is tested in an IEEE 162-bus system and a realistic large scale utility power system. Index Terms—Dynamic optimization, nonlinear programming, power system dynamics, power system planning, reactive power, SVC. NOMENCLATURE J Performance measure for optimal control. F, G Differential and algebraic equations of dynamic system. x, u, p State variables, control variables and parameters of optimal control problem. y Decision variables in NLP problem. Manuscript received August 03, 2012; revised December 25, 2012, April 20, 2013, and June 04, 2013; accepted June 10, 2013. This material is based upon work supported by the Electric Power Research Institute (EPRI). Paper no. TPWRS-00907-2012. M. Paramasivam and V. Ajjarapu are with the Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011 USA (e-mail: mageshp@iastate.edu; vajjarap@iastate.edu). A. Salloum and V. Vittal are with the School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287 USA (e-mail: asalloum@asu.edu; vijay.vittal@asu.edu). N. B. Bhatt and S. Liu are with Electric Power Research Institute (EPRI), Loveland, OH 874214 USA (e-mail: nbhatt@epri.com; sliu@epri.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2013.2271260 Number of state variables, control variables and parameters. Number of decision variables and nonlinear constraints. Initial and final time of optimal control problem. Maximum susceptance of SVC at bus . Integer decision variables, location chosen for SVC installation if value equals 1. Bus cost coefficient in NLP optimization. Change in voltage at bus for a reactive power injection at bus . Trajectory sensitivity index for reactive power injection at bus . Total number of time instants. Total number of buses in the system. Weighting factor to designate the importance of time instant , . Weighting factor to designate the importance of bus , . SVD Singular value decomposition. SVD sensitivity matrix at time . Column of SVD output matrix at time . Column of SVD input matrix at time . th singular value of SVD matrix at time . Nominal voltage at bus . Fault clearing time. First instant of time when the voltage crosses 70% of its nominal value. Time instants where the voltage crosses 0.7 p.u. Voltage dip at bus , th occurence. Starting time of voltage dip. End time of voltage dip. U.S. Government work not protected by U.S. copyright.