Research On Existence And Stability For The Powerflow Of DC Microgrid

Microgrids are playing an increasingly essential role in power systems.Compared with AC microgrids,DC microgrids have advantages such as high transmission efficiency,high reliability,and greater flexibility.Moreover,DC microgrids are better suited for connecting renewable energy sources such as photovoltaics and energy storage batteries.Loads in DC microgrids are mainly connected to power systems through converters directly,hence loads can be equivalent to constant power loads(CPLs).The nonlinearity of constant power load and the fluctuation of renewable energy can easily lead to the instability of the system.First of all,the increase of CPLs is easy to cause the DC microgrid to lose its equilibrium due to transmission losses(the power-flow equation of the system has no feasible solution),thus leading to voltage collapse,that is,the instability of static voltage.The power-flow equation of the system is a strongly coupled nonlinear equation,so how to derive its solvability conditions is a big challenge.Secondly,the negative impedance characteristic of CPLs easily makes the Jacobian matrix of the system appear positive real part characteristic roots,which leads to the instability of the system.At the same time,the fluctuation of renewable energy is likely to cause frequent changes of the equilibrium of the system,resulting in the uncertainty of the Jacobian matrix,which makes the stability analysis difficult.Finally,large disturbances such as fluctuation of renewable energy and system’ faults can easily lead to a sharp drop in system voltage,resulting in transient voltage instability.In addition,the traditional large signal stability analysis method based on quadratic energy function requires a large amount of calculation,has a complex solution process,and has no analytical conditions,so it is difficult to apply to the DC microgrid systems containing renewable energy with strong randomness.In general,this paper mainly studies the existence of power-flow solution,small signal stability and large-signal stability of DC microgrids.The main contributions and innovations of this paper are as follows:(1)Aiming at the existence problem of power-flow solution of DC microgrids,this paper derives analytical solvability sufficient conditions of the power-flow equation based on fixed point theorem.Firstly,the powerflow equation of the system is transformed into a fixed point form of mapping.Thus,this scientific problem is transformed into the existence of a fixed point.Secondly,three solvability conditions are proposed based on Brouwer’s fixed point method by constructing a self-mapping.The proposed solvability condition can help prevent the occurrence of voltage breakdown of the system.Compared with the existing related results,the solvability condition of the power-flow equation obtained in this paper are less conservative.In order to solve the power-flow equation,an iterative algorithm based on Banach’s fixed point theorem is proposed and the convergence condition of the algorithm is dedrived.Finally,the research methods of the existence of the power-flow solution and the convergence of the power-flow algorithm propsed in this paper are extended to the AC system,and the sufficient solvability condition of decoupled reactive power-flow equation of the AC system is obtained.(2)Regarding the small signal stability problem of DC microgrids,this paper dedrives the analytic conditions for the robust stability of the system.Firstly,a DC microgrid system model with pure resistive lines is established in this paper.By analyzing the eigenvalues of the system’s Jacobian matrix,a robust stability condition is derived.Secondly,a DC microgrid model considering the line inductance and the fluctuation of renewable energy is established.The stability of the high-voltage equilibrium and low-voltage equlibria of the system is analyzed,and the analytical stability conditions for local robust stability of the high-voltage equilibrium of the system are derived.The proposed robust stability conditions provide theoretical support for the correct operation of the system when large-scale renewable generators are integrated into the microgrids.(3)Regarding the large signal stability problem of the DC microgrid,based on the Brayton-Moser mixed potential function theory,this paper proposes the condition that the equilibrium of the system is the local minimum of the mixed potential function,that is,the equilibrium of the system is astable equilibrium.First of all,this paper emphasizes several key points which are often misunderstood in the previous application of Brayton-Moser mixed potential function theory,which provides a correct idea for the correct application of the Brayton-Moser mixed potential function theory in the large signal stability analysis.Secondly,this paper proves that all the low voltage equilibria in the system are unstable,only the high voltage equilibrium may be stable.Based on the inherent properties of the high voltage equilibrium,the conditions for the stability of the high voltage equilibrium are derived.When the proposed stability conditions are satisfied,the high voltge equilibrium of the system is the local minimum of the constructed mixed potential function(MPF).Finally,based on the closet unstable equilibrium,this paper estimates the attraction region of the high-voltage equilibrium to ensure that when the initial point belongs to the attraction region,the high-voltage equilibrium of the system is stable.