Unique Symbolic Factorization for Fast Contingency Analysis Using Full Newton–Raphson Method

Abstract

Contingency analysis plays an important role in assessing the static security of a network. Its purpose is to check whether a system can operate safely when some elements are out of service. In a real-time application, the computational time required to perform the calculation is paramount for operators to take immediate actions to prevent cascading outages. Therefore, the numerical performance of the contingency analysis is the main focus of this current research. In power flow calculation, when solving the network equations with a sparse matrix solver, most of the time is spent factorizing the Jacobian matrix. In terms of computation time, the symbolic factorization is the costliest operation in the LU (Lower-upper) factorization process. This paper proposes a novel method to perform the calculation with only one symbolic factorization using a full Newton–Raphson-based generic formulation and modular approach (GFMA). The symbolic factorization retained can be used during the iterations of any power flow contingency scenario. A computer study demonstrates that reusing the same symbolic factorization greatly reduces computation time and improves numerical performance. Power system security assessment under N-1 and N-2 contingency conditions is performed for the IEEE standard 54-bus and 108-bus to evaluate the numerical performance of the proposed method. A comparison with the conventional power flow method shows that the time required for the analysis is shortened considerably, with a minimum gain of 228%. The comparative analysis demonstrates that the proposed solution has better numerical performance for large-scale networks.

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

“…Lastly, [9] presents an alternative methodology for shunt reactive power compensation allocation, aiming to reduce total reactive power losses, improve voltage profiles, and increase the loading margin. In the literature, several studies have been conducted on contingency analysis [10][11][12][13]. It is known that obtaining all possible contingencies of the system is impractical, so the idea is to have a fast method that simulates as many contingencies as possible.…”

“…An efficient method for selecting multiple contingencies using genetic algorithms with high accuracy is presented in [11]. Ref [12] focuses on computational efficiency in contingency analysis, proposing a novel approach that significantly reduces computation time by reusing symbolic factorization, yielding impressive results in power system security assessment. In [13], a method via artificial neural networks was proposed to obtain the complete P-V curves of electrical power systems subjected to double contingencies (N-2).…”