The probabilistic and reliable connected power dominating set problems

Abstract

As a variation of minimum dominating set problem, the power dominating set problem is proposed to achieve the complete observation of a power system by placing the smallest number of PMUs. Under different contingencies consisting line outages or PMU losses, the reliability of observation for each bus should be guaranteed to ensure the security and robustness of the power system. Thus, the probabilistic power dominating set (PPDS) problem is proposed in this paper. Given a pre-specified reliability level for each bus in the power system to be observed and known distribution of random events, an integer programming formulation, with consideration of zero-injection property, is presented for the PPDS problem. Additionally, the reliable connected power dominating set problem is studied to meet two requirements, including the connectivity of the PMU subgraph and the reliability of the connectivity of this subgraph. Numerical experiments based on several IEEE test cases are performed to find the best deployment of PMUs satisfying different requirements.

Mathematical Models for the Single-Channel and Multi-Channel PMU Allocation Problem and Their Solution Algorithms

“…Thus, each PMU enables it to make better line capability observation with PMU measurements [56,58,60,61,64]. As a result, the installation of single-line PMUs could be a standard practice interpreted as a minimum edge covering problem [28][29][30][31]61].…”

“…So, the node set covering problem interprets the above strategy in graph theory [28][29][30][31]. In practice, it can be used primarily in industries such as utility companies to construct a modern grid with the capability of optimal "branch" placement of PMUs [61].…”

“…This work proposes an OPP-based model considering the limited number of channels per PMU device using extended ILP models initially presented in [56][57][58] and [60] where a set cover problem is introduced [28][29][30][31]. The suggested optimization models have been solved by BBA, heuristic algorithms, and nonlinear algorithms.…”

“…Graphs are useful models for many problems considered in combinatorial optimization [28][29][30][31]. Let G = (V, E) be a graph depicting a power transmission system, where a vertex depicts a power network node and an edge is a connectivity line by which two graph vertices are joined [28][29][30][31].…”

“…The pioneering work is to address the OPP-based model on optimization [28][29][30][31][32] using a zero-one integer linear programming (ILP) model, and some interesting research works have been published in the OPP domain in the recent past [33][34][35][36].…”