Evaluating SOCP for AC Optimal Power Flow in Stressed Power System Conditions

Abstract

The Optimal Power Flow is essential for ensuring the reliable and cost-effective operation in modern power systems. However, solving the AC Optimal Power Flow problem is difficult because it is highly non-convex and computationally demanding, particularly when the power system operates under stressed conditions. Convex relaxation methods, such as Second-Order Cone Programming, have been widely used to obtain faster solutions, although their accuracy can be reduced in meshed transmission networks. This paper evaluates the performance of the strengthened SOCP-III relaxation for solving AC-OPF problems under stressed loading conditions. The study is carried out using the IEEE 30, 57 and 118 bus test systems respectively. Where the system load is gradually increased to represent different levels of operating stress. The obtained solutions are compared with the results of conventional AC-OPF to assess the effectiveness of the approach. The evaluation focuses on generation cost and computational efficiency. In addition, the approach preserves acceptable voltage profiles even at higher loading levels. These findings demonstrate that SOCP-III provides a good balance between computational speed and solution accuracy. The method is using increasing load conditions (100%–125%) especially suitable for real-time and large-scale power system optimization.