Power Flow Calculation in Power Systems Using the P-Q Decomposition Method

The P-Q decomposition method is an efficient and practical algorithm for power flow calculation in power systems, particularly well-suited for analyzing large-scale electrical networks. By reasonably simplifying the Newton-Raphson method, this approach decomposes the Jacobian matrix into two submatrices (P and Q), significantly reducing computational complexity. In power flow calculations, the core concept of the P-Q decomposition method leverages two key characteristics of power systems: active power is primarily related to voltage phase angles, while reactive power is mainly associated with voltage magnitudes. Based on these characteristics, the algorithm decomposes the problem into two independent parts—active power iteration and reactive power iteration—which are solved alternately until convergence is achieved. During implementation, the first step involves constructing the system's admittance matrix and initializing the voltage magnitudes and phase angles at each node. The algorithm then iteratively updates the mismatches in active and reactive power, gradually correcting the voltage phase angles and magnitudes. Each iteration checks whether the power mismatches meet the convergence criteria; if satisfied, the final results are output; otherwise, iterations continue. For learners, understanding the P-Q decomposition method requires grasping both its physical significance and mathematical derivation. While referencing existing code can quickly yield calculation results, implementing the algorithm personally provides deeper insights into key components such as matrix construction, iterative control, and convergence criteria. It is recommended to start with simple test systems to progressively validate the algorithm's correctness and convergence behavior. The method's advantages include fast computation speed and low memory usage, making it particularly suitable for online analysis of large-scale power systems. However, when dealing with ill-conditioned systems or heavily loaded lines, it may be necessary to incorporate other improvement strategies to ensure convergence.