Application of Graph Theory in Stability Analysis of Meshed Microgrids
نویسندگان
چکیده
This paper studies microgrids where loads are supplied by parallel connected inverters controlled by decentralized active power/voltage frequency and reactive power/voltage magnitude droop control laws. The implementation of droop control laws for sharing of power between inverters has been known to present stability problems particularly for large values of active power/voltage frequency droop control gains. Stability analysis of the microgrid requires a mathematical formulation of the interaction between the inverters due to their droop control laws. However, a simple and elegant mathematical model resulting in a conclusive proof of stability has been found to be lacking in reported literature. In this paper, a state dynamical model has been derived by combining active power flow equations with the active power/voltage frequency droop control laws. Using an analogy between the model matrix and connected graphs, a proof of stability of the microgrid has been stated as a theorem. The paper further examines the limitations of the proof and the difference between the results of the proof and reported practical results.
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