# HyungSeon Oh Receives Award from Consortium for Electric Reliability Technology Solutions Assistant Professor HyungSeoh Oh has received an award for his project "“Towards An Efficient AC Optimal Power Flow & Global Optimizer Solutions" from the Consortium for Electric Reliability Technology Solutions (CERTS).

The objective of this project is to develop an algorithm that can used to find an optimizer for solving a nonlinear AC optimal power flow (AC OPF) problem in near real time.  AC OPF is the most detailed model available for finding an optimal operation point for a power system. As it is represented in the polar coordinate system, AC OPF is highly nonlinear, and, therefore, it can be impractical to find an algebraic solution to the problem. It is well known that a global solution to an OPF problem can be found by rank relaxation if the rank of (= vvT where v is the control variable) equals 1. Due to the symmetry of the power flow equations, this condition extends to cases in which the rank is 2. There was a claim that assigning arbitrarily generated values to a transformer makes the rank less than or equal to 2. When a solution is extracted from the solution to the relaxed problem in which the rank of W is above 2, the extracted solution typically violates certain constraints such as voltage limits, which makes it an infeasible solution to the original OPF problem. The solution in the conventional approach clearly violates the voltage constraints specified for the problem in, for example, MATPOWER OPF calculations.

It is believed that due to this nonlinearity the calculation effectively yields a numerical solution when an iterative method is used to solve the problem. The method involves the reevaluation and the inverse of the matrix, which needs to solve Ax = b for x over many iterations. An efficient way to solve Ax = b for x is to factorize A and solve the linear equation with the factors. The factorization number for determining 15-minute dispatches over 30 years is about 11 million. The number further increases if multiple scenarios must be considered in the stochastic optimization framework to accommodate variable energy resources or contingencies in the optimization problem, such as security-constrained optimal power flow (SCOPF). If the OPF is formulated in the Cartesian coordinate system, most elements in A are constant, i.e., need not be updated at every iteration since they depend only on the transmission network of interest. Because the transmission network is not often modified, the computation cost of solving Ax = b through factorization would be reduced if the elements were stored and reused.

This approach provides an important advantage because it involves only one major computation for each topology by storing and reusing elements of the A matrix. Given this advantage, it is natural to extend the approach to the challenge of solving a unit commitment problem, because the transmission topology is in general invariant for a day-ahead market.