Optimal flow for general multi-carrier energy systems,including load flow equations

Abstract

Optimization is an
important tool for the operation of an energy system. Multi-carrier energy
systems (MESs) have recently become more important. Load ow (LF) equations are used
within optimization to determine if physical network limits are violated. The
way these LF equations are included in the optimal ow (OF) problem, influences
the solvability of the OF problem and the convergence of the optimization
algorithms. This paper considers two ways to include the LF equations within
the OF problem for general MESs. In the first formulation, optimization is over
the combined control and system-state variables, with the LF equations included
explicitly as equality constraints. In the second formulation, optimization is
over the control variables only. The system-state variables are solved from the
LF equations in a separate subsystem, given the control variables. Hence, the LF
equations are included only implicitly in the second formulation. The two
formulations are compared theoretically. The effect of the two formulations on
the solvability of the OF problem is illustrated by optimizing two MESs. Both
formulation I and formulation II result in a solvable OF problem. For the two
example MESs, the optimization algorithms require significantly fewer
iterations with formulation II than with formulation I. For formulation II, the
direct and the adjoint approach can be used to determine the required
derivatives within the optimization algorithms. Scaling is needed to solve the
OF problem for MESs. Both matrix scaling and per unit scaling can be used, but they
are not equivalent.