IEEE JOURNAL ON EMERGING AND SELECTED TOPICS IN CIRCUITS AND SYSTEMS, VOL. 7, NO. 2, JUNE 2017 295 Mixed Integer Second Order Cone Relaxation With Dynamic Simulation for Proper Power System Islanding Operations Tao Ding, Member, IEEE, Kai Sun, Senior Member, IEEE, Qingrun Yang, Abdul Wahab Khan, and Zhaohong Bie, Senior Member, IEEE Abstract— Power system islanding operation acts as an impor- tant attractive corrective measure that is widely studied. However, a proper splitting strategy for the islanding operation should satisfy both steady-state and transient stability constraints. As a result, an ac power flow-based optimization model with dynamic simulation is proposed to obtain a proper splitting strategy. Specifically, the method includes two steps: 1) optimization of a splitting strategy satisfying the steady-state constraints and 2) transient stability evaluation of the strategy by dynamic simulation. Furthermore, the optimization and evaluation steps are iterated until finding a splitting strategy that satisfies both the steady-state constraints and the transient stability constraints. Finally, the effectiveness of the proposed method is verified on the WSCC 9-bus and the IEEE RTS 24-bus test systems. Index Terms—System islanding, splitting strategy, partition problem, mixed integer second order cone programming. NOMENCLATURE Indices k Islands ij Branches i Buses Sets V Set of buses E Set of branches {Gen} Set of generators { Load } Set of load demands { REF } Set of reference buses Manuscript received September 15, 2016; revised December 4, 2016 and February 13, 2017; accepted April 17, 2017. Date of publication May 25, 2017; date of current version June 10, 2017. This work was supported in part by the National Key Research and Development Program of China under Grant 2016YFB0901904, in part by the National Natural Science Foundation of China under Grant 51607137, in part by the China Postdoctoral Science Foundation under Grant 2015M580847, in part by the Natural Science Basis Research Plan in Shaanxi Province of China under Grant 2016JQ5015, in part by the Project of State Key Laboratory of Electrical Insulation, and in part by the Power Equipment in Xi’an Jiaotong University under Grant EIPE16301. This paper was recommended by Guest Editor C.-C. Chu. (Corresponding author: Tao Ding.) T. Ding, Q. Yang, A. W. Khan, and Z. Bie are with the State Key Laboratory of Electrical Insulation and Power Equipment, School of Elec- trical Engineering, Xi’an Jiaotong University, Xi’an 710049, China (e-mail: tding15@mail.xjtu.edu.cn). K. Sun is with the Department of Electrical Engineering and Computer Science, The University of Tennessee, Knoxville, TN 37996 USA (e-mail: kaisun@utk.edu). 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/JETCAS.2017.2700201 Parameters P 0 L ,i The active load at bus i under normal condition Q 0 L ,i The reactive load at bus i under normal condition g ij The series conductance of the branch ij b ij The series susceptance of the branch ij r ij The resistance of transmission line ij x ij The reactance of transmission line ij b sh,ij The charging capacitance of transmission line ij N p The number of islands |V | The numbers of vertices |E | The numbers of edges I max ij The maximum current magnitude value of branch ij P max g,i / P min g,i The maximum/minimum active power output of generator i Q max g,i / Q min g,i The maximum/minimum reactive power output of generator i S max g,i The maximum capacity of generator i U max i /U min i The maximum/minimum voltage magnitude of bus i M A large number (e.g., 10 6 ) Decision Variables x i,k Binary variable: x i,k = 1 means that vertex i belongs to island k ; otherwise, x i,k = 0 y ij Binary variable: y ij = 0 means branch ij belongs to the cut set and will be switched; otherwise, y ij = 1 z ij ,k Binary variable denoting the bilinear x i,k x j ,k : If both x i,k = 1 and x j ,k = 1, z ij ,k = 1; otherwise, z ij ,k = 0 α i The load factor of bus i P g,i The active power output of generator i Q g,i The reactive power output of generator i U i The voltage magnitude of bus i θ ij The voltage angle difference between bus i and j (i.e., θ i - θ j ) P ij The active power flow of branch ij Q ij The reactive power flow of branch ij I ij The current magnitude of branch ij 2156-3357 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.