Robust Power Flow and Three-Phase Power Flow Analyses

Abstract

Robust simulation is essential for reliable operation and planning of transmission and distribution power grids. At present, disparate methods exist for steady-state analysis of the transmission (power flow) and distribution power grid (threephase power flow). Due to the non-linear nature of the problem, it is difficult for alternating current (AC) power flow and threephase power flow analyses to ensure convergence to the correct physical solution, particularly from arbitrary initial conditions, or when evaluating a change (e.g. contingency) in the grid. In this paper, we describe our equivalent circuit formulation approach with current and voltage variables that models both the positive sequence network of the transmission grid and three-phase network of the distribution grid without loss of generality. The proposed circuit models and formalism enable the extension and application of circuit simulation techniques to solve for the steadystate solution with excellent robustness of convergence. Examples for positive sequence transmission and three-phase distribution systems, including actual 75k+ nodes Eastern Interconnection transmission test cases and 8k+ nodes taxonomy distribution test cases, are solved from arbitrary initial guesses to demonstrate the efficacy of our approach.

Implicitly Modeling Frequency Control within Power Flow

“…Using the circuit heuristics, we are able to solve large and complex power systems robustly [17]. We further extend these properties to frequency dependent proposed formulation as shown in Figure 3.…”

Improving Voltage Profile of the Nigerian Power Grid

“…One of the circuit simulation methods limits the Newton-Raphson (NR) step to avoid leading the solution to a space that may cause divergence or oscillations. In [13], we demonstrated that damping the step size of each element based on the physical properties results in better convergence of the solver. While limiting the NR step can improve convergence, limiting by itself does not guarantee that the solution represents a physically stable dispatch.…”

“…Current-voltage (I-V) based formulations have been explored in the past for performing power flow and three-phase power flow analyses [13]- [16]. Amongst these approaches, a recently introduced equivalent circuit approach [13] maps the different network models of the grid (e.g. PV, PQ, etc.)…”

“…While limiting the NR step can improve convergence, limiting by itself does not guarantee that the solution represents a physically stable dispatch. In order to lead the NR to a meaningful solution (high voltage magnitude and angular stable), we introduced a homotopy method [13], "Tx stepping", that sequentially solves a series of sub-problems with the use of a homotopy factor. The Tx-stepping method first solves a trivial problem and uses the solution to iteratively solve a series of sub-problems that eventually is equivalent to the original problem.…”

“…In order to solve the problem given by (1) using the equivalent circuit approach [9], the necessary first-order optimality conditions given by the KKT conditions are mapped onto a set of equivalent circuits. These circuits are represented by a set of power flow circuits that can be derived following the methodology in [13] and a set of adjoint circuits that can be derived following the methodology in [9]. The solution of this net aggregated circuit (power flow circuits + adjoint circuits) then corresponds to an optimal solution of the optimization problem assuming the hold of the second-order sufficient conditions and is obtained by using the circuit simulation techniques described in [9], [17].…”