Pilot Buses Selection Based on Reduced Jacobian Matrix Nivine Abou Daher 1, 2 , Imad Mougharbel 1 , Maarouf Saad 3 , Hadi Y. Kanaan 2 and Dalal Asber 4 1 Electrical Department, Faculty of Engineering, Lebanese University, Hadath, Lebanon 2 Electrical and Mechanical Department, Saint-Joseph University, Faculty of Engineering, Mar Roukoz, Lebanon 3 Electrical Engineering Department, Ecole de Technologie Supérieure, Montreal, Canada 4 Research Institute of Hydro-Quebec, Power Systems and Mathematics, Varennes, Canada ndaher89@hotmail.com, imadmoug@ul.edu.lb, maarouf.saad@etsmtl.ca, hadi.kanaan@usj.edu.lb, Asber.Dalal@ireq.ca Abstract—The non-supervised insertion of renewable energy sources into electric power networks causes fluctuations that may lead to voltage instability. The simple and coordinated secondary voltage control systems are used to avoid this instability. To obtain maximum regulation performance with optimized number of controllers, an appropriate selection of pilot buses is suggested. In this paper new algorithm is proposed to select optimal pilot buses. This method is based on the singular decomposition of the reduced Jacobian matrix with the voltage security margin index. To evaluate the efficiency of this algorithm, a comparison with the Bifurcation, Clustering with Node-Partitioning Around Medoids and the Hybrid algorithms is proposed. The simulation results show that the proposed algorithm gives optimal pilot buses according to the selection criteria (explained later in the paper). Keywords—Renewable energy; Pilot buses selection; Secondary Voltage Control; Power Network Stability. I. INTRODUCTION The significant and non-supervised insertion of renewable energy sources into electric power networks causes fluctuations that may have impact on voltage stability. The secondary voltage control and the coordinated secondary voltage control provide network stability by performing the control on some selected buses called pilot buses. Pilot buses are the buses giving an accurate indication about the voltage profile picture of the whole network. The appropriate selection of pilot buses minimizes the number of controllers and maximizes the regulation performance when the network is subjected to fluctuations. The selection of the optimal set of pilot buses should consider the observability, the controllability and the robustness against disturbances and against initialization. A comparative study was performed on sixteen different algorithms used for this purpose [12]. This comparison shows that all of them have a weakness in at least one comparative criterion [12]. The algorithms based on the minimization of electrical distance and of short circuit capacity give week controllability on pilot buses [1-3]. The pilot buses selection based on voltage variation makes control loses robustness [4]. In [5] the Partitioning Around Medoid (PAM) gives non controllable and non-robust against initialization pilot buses, and the Clustering With Node-Partitioning Around Medoids (CWN-PAM) improves the controllability. In [6-8] many meta- heuristic algorithms are used to minimize a linear objective function. The annealing algorithm [6, 7] gives non controllable and non-robust pilot buses. The controllability is enhanced using greedy, local search, and genetic algorithms [7, 8] and the robustness is enhanced using extended greedy, extended local and global search algorithms [7]. The bifurcation algorithm [9] and the hybrid algorithm [10] applied after the non-linear modeling of power network give robustness problems of pilot buses against disturbances. This problem is improved in [11] using the immune algorithm without improving the robustness against initialization. In order to enhance controllability and robustness against initialization, the hybrid algorithm based on local search and global search algorithms is proposed in [12]. The local search algorithm improves the controllability and the global search algorithm improves the robustness against initialization. All pilot buses selection algorithms are achieved along two steps: power network modeling and optimization of an objective function. The power network modeling is classified into three categories: simple rule modeling, linear approach and non-linear approach. The robustness against disturbances depends on the modeling of the electric power network. The optimization algorithm applied after the simple rule modeling of power network ensures pilot buses robustness against disturbances, since it gives non-robust pilot buses after the linear and non-linear modeling. The hybrid algorithm proposed in [12] is applied after a simple rule modeling based on electric power system; therefore the robustness against disturbances is not considered. In order to eliminate the power network modeling dependency and to improve the robustness against disturbances, we propose in this work the pilot buses selection based on the singular decomposition of the reduced Jacobian matrix with the voltage security margin index. This work is organized as follows. The second section describes the proposed pilot buses selection algorithm. The third section presents a comparison study with existing techniques. Also the Clustering with Node-Partitioning Around Medoids, the Bifurcation and the Hybrid algorithms are described. The fourth section describes the simulation results performed on the standard network IEEE 39 bus system. Finally the fifth section concludes this work. II. PROPOSED ALGORITHM The robustness of pilot buses against disturbances depends on the power network modeling. In order to eliminate this dependency we propose the algorithm based on the singular