An algorithm for power flow analysis in isolated hybrid energy microgrid considering DG droop model and virtual impedance control loop

Power flow analysis (PF) is an essential tool for secure and efficient operation in power systems. For isolated microgrid (IMG) with only local distributed generators (DGs), there is no slack bus that enables the microgrid to have a constant frequency. So, the bus admittance matrix (Y_bus) is not fixed. Also, IMG usually has droop-controlled DGs (DCDG) whose voltage and power are frequency-dependent. These factors make PF a challenging task for IMG that cannot be accomplished through the classic PF techniques. This paper proposes a substantial modification to the well-established Newton–Raphson PF algorithm, called (ENR), to fit the IMG. A new formulation of the Jacobian matrix is developed to accommodate the different control characteristics of DGs as well as the frequency variation. Droop control, maximum power point tracking, and constant power control are considered as DG control types with complete models. Moreover, the virtual impedance concept and its control loop are integrated into the DCDG control scheme to guarantee the stable operation regardless the microgrid X/R ratio. Further, the ENR convergence speed is improved by introducing acceleration factors for voltage angle, magnitude, and frequency. The optimal acceleration factors are determined using a modified PSO method. The ENR is applied to a 45-bus IMG with 12 renewable and dispatchable DGs based on a modified version of the IEEE 33-bus test system. Results are compared to time-domain simulations and also to recent literature. The accuracy and high speed of the ENR are verified.