Voltage-Instability Bus Identification in Power Transmission Networks Using an Improved Strength Pareto Evolutionary Algorithm

Voltage instability remains a major operational challenge in stressed transmission networks because reactive power deficiencies and contingency events can force bus voltages outside acceptable operating limits. This paper presents an Improved Strength Pareto Evolutionary Algorithm (ISPEA) for the identification of voltage-instability buses in transmission systems under steady-state and contingency loading. A Newton–Raphson load-flow model was first used to obtain the operating point of the network. Contingency severity is represented by a 90% increase in reactive demand at load buses, after which the ISPEA ranks buses using a multi-objective fitness structure based on voltage magnitude deviation, maximum loading capacity, and generator operating constraint penalties. ISPEA runs for 200 generations with a population of 100, an archive of 100, and a Newton–Raphson convergence tolerance of 10⠻⠵ p.u. The method was evaluated on the IEEE 30-bus and Nigerian 31-bus networks using MATLAB R2023a. Under base-case conditions, the IEEE 30-bus system reaches its minimum voltage at Bus 5 (0.9360 p.u.), whereas the Nigerian 31-bus system records its lowest voltage at Bus 21 (0.9430 p.u.). After contingency loading, the number of under-voltage buses increased from 2 to 8 in the IEEE system and from 2 to 9 in the Nigerian system. ISPEA identifies Buses 5, 7, and 23 as the most critical in the IEEE 30-bus system, and Buses 5, 11, and 21 in the Nigerian 31-bus system. Compared with LVSI and VCPI screening, ISPEA yields the lowest maximum loading capacity values across all evaluated buses, confirming the superior identification of genuinely vulnerable buses for reactive power compensation siting.