A Mathematical Model of Hybrid Microgrid With Pole Placement Controller Using State Feedback For Stability Improvement

Abstract: This paper presents the development of a mathematical model of a converter state space model for a hybrid microgrid. The hybrid model combines the models of components such as DC-Converters, DC-AC converters, and their individual controllers, as well as loads. The input to the converter is considered a constant DC voltage, assumed to originate from distributed generations like solar, battery storage, or fuel-cells. The converter output is connected to a DC line through an LCL filter. The controller circuitry is designed to regulate the voltage, current, and power from the converter. Sensors are strategically placed to measure the currents, voltages, and power, and calculate the reference pulse signal using PWM for the switch. Similarly, the DC-AC converter is modeled. In the state space domain the converter models is used to design overall microgrid system. A single DC converter has six states and two inputs, with all states as outputs. A single DC-AC converter has thirteen states and three inputs, with all states as outputs. Three such converters of each type are considered to develop the DC microgrid and AC microgrid, which are then combined using mathematical analysis to model a hybrid microgrid. For the hybrid microgrid development, network and load models were also included. Eigenvalue analysis has been conducted to study the small signal stability of the considered system. The complete state space model of the hybrid microgrid has been programmed, and a pole-placement controller has been designed to enhance the stability of the system.