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Load flow calculation for droop‐controlled islanded microgrids based on direct Newton–Raphson method with step size optimisation

Load flow calculation for droop-controlled islanded microgrids (IMGs) is different from that of transmission or distribution systems due to the absence of slack bus and the variation of frequency. Meanwhile considering the common three-phase imbalance condition in low-voltage systems, a load flow algorithm based on the direct Newton–Raphson (NR) method with step size optimisation for both three-phase balanced and unbalanced droop-controlled IMGs is proposed in this study. First, the steady-state models for balanced and unbalanced droop-controlled IMGs are established based on their operational mechanisms. Then taking frequency as one of the unknowns, the non-linear load flow equations are solved iteratively by the NR method. Generally, iterative load flow algorithms are faced with challenges of convergence performance, especially for unbalanced systems. To tackle this problem, a step-size-optimisation scheme is employed to improve the convergence performance for three-phase unbalanced IMGs. In each iteration, a multiplier is deduced from the sum of higher-order terms of Taylor expansion of the load flow equations. Then the step size is optimised by the multiplier, which can help smooth the iterative process and obtain the solutions. The proposed method is performed on several balanced and unbalanced IMGs. Numerical results demonstrate the correctness and effectiveness of the proposed algorithm.