This paper presents a comprehensive three-bus equivalent circuit model of three-phase step voltage regulators. The proposed model can be efficiently integrated in the Z-bus power flow method and can accurately simulate any configuration of step voltage regulators. In contrast to the conventional step voltage regulator models that include the tap variables inside the YBUS matrix of the network, the proposed model simulates them in the form of current sources, outside the YBUS matrix. As a result, the re-factorization of the YBUS matrix is avoided after every tap change reducing significantly the computational burden of the power flow. Furthermore, possible convergence issues caused by the low impedance of step voltage regulators are addressed by introducing fictitious impedances, without, however, affecting the accuracy of the model. The results of the proposed step voltage regulator model are compared against well-known commercial softwares such as Simulink and OpenDSS using the IEEE 4-Bus and an 8-Bus network. According to the simulations, the proposed model outputs almost identical results with Simulink and OpenDSS confirming its high accuracy. Furthermore, the proposed 3-bus equivalent model is compared against a recently published conventional step voltage regulator model in the IEEE 8500-Node test feeder. Simulation results indicate that the proposed step voltage regulator model produces as accurate results as the conventional one, while its computation time is significantly lower. More specifically, in the large IEEE 8500-node network consisting of four SVRs, the proposed model can reduce the computation time of power flow around one minute for every tap variation. Therefore, the proposed step voltage regulator model can constitute an efficient simulation tool in applications where subsequent tap variations are required.
The secondary control is applied in islanded Microgrids (MGs), after the primary control, in order to restore the buses voltage and frequency to specified values. The existing power flow methods can accurately calculate the power flow for droop-controlled islanded MGs, but in many cases, they cannot calculate the steady-state solution of the MG after the action of secondary controllers. The main challenge in the steady-state modelling of the secondary layer lies in that the secondary controllers consist of integral parts, which can integrate functions with different integral histories, and therefore, under certain circumstances, can imply inaccurate power sharing between the distributed generation units (DGs). This phenomenon is most pronounced under communication failures, as will be shown in the simulations. In this way, this paper proposes a power flow method for calculating, accurately, the steady-state solution of hierarchically controlled islanded AC MGs, including droop-based primary control and secondary control. The paper includes four main features: a) generalized implementation in several communication strategies e.g., centralized, decentralized, consensus, distributed averaging, b) precise simulation of communication links and integral parts of secondary controllers, c) low computation time, and d) accurate 4-wire network representation. Simulations were executed to validate the proposed method against Simulink and to highlight the importance of an accurate modelling of secondary control in the power flow method for islanded MGs