Equivalent Circuit Formulation for Solving AC Optimal Power Flow

Improving Voltage Profile of the Nigerian Power Grid

“…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].…”

“…(3) A common technique to solve for (2) and (3) in the optimization solvers is to use barrier methods [9]. Barrier methods utilize functions that constrain the slack variable to be within the bounds by making the system infeasible if the slack violates the limits.…”

“…This problem as described above is a non-convex quadratic programming problem and is solved in our approach using Newton's method [9] to obtain a local optimum solution. In order to avoid the "non-useful solutions" due to non-convexity of the problem, we make use of limiting and homotopy methods [13] to ensure that the local optimum solution is obtained such that physical nature of the grid is maintained while pushing the solution towards the high voltage solution.…”

“…This corresponds to the diode region where the voltage at the diode terminal is able to conduct high diode currents. Using the circuit-based optimization power flow formulation [9] in our prototype tool SUGAR (Simulation with Unified Grid Analyses and Renewables) [13]- [14] , we are able to introduce these diode circuits to enforce the bus voltage and generator reactive power limits by minimizing the diode currents.…”

“…In Section II of this paper, we discuss the previously proposed circuit theoretic framework for steady-state analysis of power grid [13] including adjoint circuits [9] that are used for general optimization analyses of the grid. Section III extends the existing framework with the inclusion of mathematical constraints that model the optimization circuits to enforce the limits for grid node voltages and generator reactive power limits.…”