Optimal multistage schedualing of PMU: an ILP approach

Indian Inst. of Technol., Mumbai
IEEE Transactions on Power Delivery (Impact Factor: 1.73). 11/2008; 23(4):1812 - 1820. DOI: 10.1109/TPWRD.2008.919046
Source: IEEE Xplore


This paper addresses various aspects of optimal phasor measurement unit (PMU) placement problem. We propose a procedure for multistaging of PMU placement in a given time horizon using an integer linear programming (ILP) framework. Hitherto, modeling of zero injection constraints had been a challenge due to the intrinsic nonlinearity associated with it. We show that zero injection constraints can also be modeled as linear constraints in an ILP framework. Minimum PMU placement problem has multiple solutions. We propose two indices, viz, BOI and SORI, to further rank these multiple solutions, where BOI is bus observability index giving a measure of number of PMUs observing a given bus and SORI is system observability redundancy index giving sum of all BOI for a system. Results on IEEE 118 bus system have been presented. Results indicate that: (1) optimal phasing of PMUs can be computed efficiently; (2) proposed method of modeling zero injection constraints improve computational performance; and (3) BOI and SORI help in improving the quality of PMU placement.

Download full-text


Available from: Rajeev Gajbhiye, Apr 30, 2013
150 Reads
  • Source
    • "This method is complex because of the non-linear formulation, and it also may not reach the optimum solution for larger case studies. Also, in [5] [6] [7] [8], linear programming has been used for this placement but they did not consider contingencies (PMU loss and line outage) at the same time. "
    [Show abstract] [Hide abstract]
    ABSTRACT: A multi-objective optimal phasor measurement unit placement model using integer linear programming is presented in this article. The proposed model simultaneously optimizes two objectives, i.e., minimization of phasor measurement unit numbers and maximization of measurement redundancy. To calculate the redundancy criteria, the single-line outage and the phasor measurement unit loss are considered simultaneously. A linear formulation is presented for both objective functions. Also herein, to address conflicting attributes and identify Pareto optimal solutions of the multi-objective optimal phasor measurement unit placement problem, a new multi-objective mathematical programming method is proposed. Finally, a new index, i.e., minimum distance to utopia point, is implemented to select the most preferred solution among the available Pareto front based options on the goal to achieve judicious decision makers. Two test systems, i.e., a modified 9-bus and an IEEE 118-bus test systems, are used to illustrate the effectiveness of the proposed framework.
    Electric Power Components and Systems 10/2015; 43(17). DOI:10.1080/15325008.2015.1068886 · 0.66 Impact Factor
  • Source
    • "A dominating set (or an externally stable set) in a graph G is a set of vertices that dominates every vertex u in G in the following sense : Either u is included in the dominating set or is adjacent to one or more vertices in the dominating set [32]. Hence, minimum OPP problem maps to smallest dominating set problem on the graph [13]. It is assumed that the PMU has enough channels to measure the voltage phasor at the associated bus and the current phasors of all the lines emanating from that bus [10]. "
  • Source
    • "Considering that: the start-up times of the controllable loads are naturally discrete variables, the energy prices are discrete known values, generation and load powers easily can be discretized, the day-ahead scheduling procedure should be fast and simple, then, the optimization problem can be formulated in ILP theory using binary variables [21]. "
    [Show abstract] [Hide abstract]
    ABSTRACT: Microgrids include distributed energy resources, controllable loads, and storage devices, and they can be classified into AC and DC types, depending on the characteristics of the supply voltage. In this paper, an optimal control strategy for a DC microgrid is proposed, and the strategy is aimed at minimizing the daily total energy costs. The DC micro grid can include non-dispatchable generation units (such as photovoltaic power generation) and dispatchable generation units, energy storage systems (batteries), and controllable/not controllable loads. The control strategy is based on a two-step procedure, i.e., (1) the implementation of one day-ahead scheduling and (2) a very short-time predictive control. The day-ahead scheduling is formulated using integer linear programming methodology and is aimed at achieving the optimal scheduling of controllable loads. The very short-time predictive control is based on the solution of a non-linear, multi-period, optimization problem and is aimed at achieving the real-time optimal charging/discharging profile of storage powers and the real-time optimal profile of powers of dispatchable generators thereby minimizing the cost of total daily energy. For both procedures, optimization models were formulated and solved, including technical constraints that guaranteed an adequate lifetime of the storage system. Case studies relative to a DC microgrid obtained by a modification of the actual structure of the electrical power plant of an Italian industrial facility were investigated in order to show the feasibility and the effectiveness of the proposed approach.
    International Journal of Electrical Power & Energy Systems 05/2015; 67:25-38. DOI:10.1016/j.ijepes.2014.11.003 · 3.43 Impact Factor
Show more