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 *W *(= *vv* 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.