Feasible Power-Flow Solution Analysis of DC Microgrid Considering Distributed Generations Under MPPT Control

Abstract

For a DC microgrid with constant power loads (CPLs), the existence of a feasible power-flow solution, which is usually difficult to analyze, is a necessary condition for the correct operation of systems. In this paper, the solvability of power-flow equation of DC microgrid with CPLs is analyzed, where a majority of distributed generations (DGs) are under MPPT control while other DGs are under droop control. At first, this paper builds a power-flow mathematical model of the DC microgrid. Secondly, three solvability conditions are proposed with the first one being applied to ensure the power-flow equation has a solution, while the other two applying to ensure the solution within the given voltage deviation. The first analytical condition ( <xref ref-type="theorem" rid="theorem2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Theorem 2</xref> ) is obtained by applying Brouwer fixed-point theorem. Compared with the existing results, this obtained sufficient condition is less conservative. Furthermore, the other two sufficient solvability conditions ( <xref ref-type="theorem" rid="theorem3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Theorems 3</xref> and <xref ref-type="theorem" rid="theorem4" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</xref> ) can guarantee the equilibrium not only exists, but also the voltage deviation is within an acceptable range. Finally, case studies verify the correctness of the proposed theorems. The obtained conditions provide a guidance for establishing a dependable DC microgrid.