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

Abstract

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 (θk, Vk) 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 (λ0, Vk0). 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.

Estimation of Total Real and Reactive Power Losses in Electrical Power Systems via Artificial Neural Network

“…For the IEEE 14-bus system, 213 samples were utilized, while for the IEEE 30-bus system, 184 samples were used, and for the IEEE 57-bus system, 202 samples were employed, resulting in a total of 599 samples. These samples were acquired according to the parameterization continuation power flow (PCPF) method described in [2,11] and were used for training and validation of ANN. Each sample is composed of five pieces of data: three input data for the ANN, which include the loading factor (λ) and the real and reactive powers generated at the slack bus (P g slack and Q g slack ), and two output data representing the loss total real (Pa) and reactive (Pr) power of the system.…”

“…It is crucial to identify this point, as it marks the transition between the region of stability and the region of instability of the system. However, accurately obtaining this point can be challenging due to the singularity of the Jacobian matrix, requiring the use of parameterization techniques for its determination [11]. These additional techniques can significantly increase the computational cost of the process.…”