Phasor measurement units (PMUs) are preferred for installation at weak buses in a power network. Therefore, the weak buses need to be located and the strategic locations of PMUs identified to ensure network observability. Thus, the primary aim of this work is to identify the placements of the maximum number of PMUs installed at the weak buses in the electrical network. The voltage collapse proximity indicator, line stability index, fast voltage stability index, and a new voltage stability indicator utilizing load flow measurement are used to determine the weak buses. A novel deterministic methodology based on a binary-integer linear programming model is then proposed to determine the optimal locations of PMUs. The effect of a single PMU outage considering the weak buses is also demonstrated. The effectiveness of the developed approach is tested and validated on the standard IEEE 14-, 118-, 300-, and New England 39-bus systems. The obtained results are also compared to those using different weak bus methodologies.

This paper introduces an underdetermined nonlinear programming model where the equality constraints are fewer than the design variables defined on a compact set for the solution of the optimal Phasor Measurement Unit (PMU) placement. The minimization model is efficiently solved by a recursive quadratic programming (RQP) method. The focus of this work is on applying an RQP to attempt to find guaranteed global minima. The proposed minimization model is conducted on IEEE systems. For all simulation runs, the RQP converges superlinearly towards optimality in a finite number of iterations without to be rejected the full step-length. The simulation results indicate that the RQP finds out the minimal number and the optimal locations of PMUs to make the power system wholly observable.

Power system instability primarily results from the deviation of the frequency from its predefined rated value. This deviation causes voltage collapse, which further leads to sudden blackouts of the power system network. It is often triggered by a lack of reactive capacity. The solution to the reactive capacity problem can be obtained in two stages. In the first stage, the vulnerable buses, also known as ‘weak buses’, where voltage failure might occur are identified, and the Var compensating devices are mounted at those locations. The proposed approach utilizes three simple vulnerable bus detection methods: the fast voltage stability index, line stability index, and voltage collapse proximity index (VCPI). In the second stage, various optimization algorithms are implemented to determine the optimal setting of Var sources, such as particle swarm optimization, differential evolution, the whale optimization algorithm, the grasshopper optimization algorithm, the salp swarm algorithm, grey wolf optimization, and oppositional grey wolf optimization (OGWO). The results indicate that the best approach to poor bus recognition is the VCPI, and the OGWO technique provides a much less expensive system than other optimization strategies used for problems of optimal reactive power planning.