A new unbalanced three-phase governor power flow formulation based on the current injections method

•A new unbalanced three-phase governor power flow formulation.•Both synchronous generators and droop-based distributed generators modeling.•Allows the evaluation of the system frequency due to active power unbalance.•The losses are distributed among the generating units in a more realistic way.•From this formulation any bus of the system can be the system reference bus. This paper presents a new unbalanced three-phase governor power flow formulation using the three-phase current injection equations (TCIM) expressed as a function of voltages expressed in rectangular coordinates. The proposed technique considers the representation of the primary frequency regulation for synchronous generators, as well as, voltage and frequency regulation in a droop-based control for distributed generation units (DGs). The static response of the generation governor, droop control equations and an equation to define the network reference angle for a given value are incorporated into the modeling. As the system is unbalanced, an internal additional bus, having balanced voltages, was created for each synchronous generator. As a consequence, two additional equations were included to keep internal voltages balanced. The inclusion of new equations results in an augmented formulation which is then linearized and solved using the Newton–Raphson method, in which the original structure of the Jacobian matrix from the current injections method is preserved. The proposed formulation allows the distribution of the active losses among the generating units as well as the determination of the frequency deviation due to variations, either in the total amount of generation or in the total system load. Any bus (load or generation bus) of the system can be chosen as the system reference bus. The results obtained using the unbalanced three-phase 6-bus test system were validated using the well known RTDS (real time digital simulator). The 25-bus islanded test system was also used in the simulations with the inclusion of synchronous generation (SG) units to demonstrate the effectiveness of the proposed methodology.