A Homotopy-Based Approach to Solve the Power Flow Problem in Islanded Microgrid with Droop-Controlled Distributed Generation Units

Abstract

This paper proposes a homotopy-based approach to solve the power flow problem (PFP) in islanded microgrid networks with droop-controlled distributed generation (DG) units. The technique is based on modifying an “easy” problem solution that evolves with the computation of intermediate results to the PFP solution of interest. These intermediate results require the solution of nonlinear equations through Newton–Raphson (NR) method. In favor of convergence, the intermediate solutions are close to each other, strengthening the convergence qualities of the technique for the solution of interest. The DG units are modeled with operational power limits and three types of droop-control strategies, while the loads are both magnitude voltage- and frequency-dependent. To evaluate the method performance, simulations are performed considering the proposed and classical NR methods, both departing from a flat start estimation. Tests are carried out in three test systems. Different load and DG unit scenarios are implemented for a 6-, 38-, and 69-bus test system. A base case is studied for all systems, while for the two larger models, a loading factor is used to simulate the load augmenting up to the maximum value. The results demonstrated that for the largest-size model system, only the homotopy-based approach could solve the PFP for stringent requirements such as the diversification of the load profile and hard loading operation point.

Steady‐state operating points of islanded virtual synchronous machine microgrid

“…( ) 35) and (36), then ( 28) and ( 32) are, respectively, obtained. Also, if K = 0 qi in (37), then E E = ci .…”

“…Guaranteed convergence PSO with Gaussian mutation was proposed in Esmaeli et al 34 However, the performance of metaheuristic techniques depends on the selection of parameters. Homotopy-based method to provide solution to load flow of droop-controlled IM is presented in Lima-Silva et al 36 The droop bus models discussed in the last paragraph are only valid for DGs that incorporate droop control schemes and cannot provide complete SSOPs of the SVI-VISMA model especially when in its natural state. SVI-VISMA in its natural state does not implement a governor and hence does not actuate a primary frequency control but nevertheless, an external droop controller can be added.…”

Numerical Solution of the Steady-State Network Flow Equations for a Nonideal Gas

“…There are subtle but crucial differences from homotopic continuation methods [9]- [11] which are constructive and postulate a trajectory connecting the solution of a known problem to the solution of the nonlinear system of interest. Homotopic continuation is mainly used as a numerical algorithm [12], [13], but theoretical assertions require that the system satisfy very stringent hypotheses that are verifiable only in rare cases [14] where the system has some special structure. In contrast, assertions of existence following degree theory and homotopy invariance as used here, require weaker assumptions (such as allowing the Jacobian to be singular at a solution).…”