Zero forcing and power domination for graph products

The power domination number arose from the monitoring of electrical networks, and methods for its determination have the associated application. The zero forcing number arose in the study of maximum nullity among symmetric matrices described by a graph (and also in control of quantum systems and in graph search algorithms). There has been considerable effort devoted to the determination of the power domination number, the zero forcing number, and maximum nullity for specific families of graphs. In this paper we exploit the natural relationship between power domination and zero forcing to obtain results for the power domination number of tensor products and the zero forcing number of lexicographic products of graphs. In addition, we establish a general lower bound for the power domination number of a graph based on the maximum nullity of the matrices described by the graph. We also establish results for the zero forcing number and maximum nullity of tensor products and Cartesian products of certain graphs

Solving the multistage PMU placement problem by integer programming and equivalent network design model

Recently, phasor measurement units (PMUs) are becoming widely used to measure the electrical waves on a power grid to determine the health of the system. Because of high expense for PMUs, it is important to place minimized number of PMUs on power grids without losing the function of maintaining system observability. In practice, with a budget limitation at each time point, the PMUs are placed in a multistage framework spanning in a long-term period, and the proposed multistage PMU placement problem is to find the placement strategies. Within each stage for some time point, the PMUs should be placed to maximize the observability and the complete observability should be ensured in the planned last stage. In this paper, the multistage PMU placement problem is formulated by a mixed integer program (MIP) with consideration of the zero-injection bus property in power systems. To improve the computational efficiency, another MIP, based on the equivalent network flow model for the PMU placement problem, is proposed. Numerical experiments on several test cases are performed to compare the two MIPs.12 month embargo; published online: 13 June 2018This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]