Post-Contingency Loading Margin through Plane Change in the Continuation Power Flow

This paper introduces a parameterization technique to obtain complete P-V curves for electrical power systems under various conditions, including contingencies (N-1, N-1 severe, and N-2) as well as normal operating conditions N-0 (pre-contingency). The distinct feature of this methodology lies in the utilization of the new (θ k , V k ) plane for constructing the P-V curve. In this new framework, the solution trajectory exhibits a linear characteristic in the vicinity of the maximum loading point (MLP), effectively mitigating any numerical challenges. Another crucial aspect is the point denoted as the center of the set of lines, point O (λ 0 , V k 0 ). This point can be adjusted along the ordinate axis, further enhancing the method’s ability to achieve a smoother ‘flat start’. The ‘flat start’ approach employed in the proposed methodology enables the determination of the loading margin for any system subjected to both simple and severe contingencies. Additionally, it facilitates the use of larger steps in acquiring complete P-V curves with a reduced number of iterations. A procedure presented is to not update the Jacobian matrix at each iteration but only when the system undergoes significant changes. This technique reduced the CPU Ratio by 29.74% in obtaining the P-V curve for all scenarios.