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

Optimization is an important tool for the operation of energy system. Multi-carrier systems (MESs) have recently become more important. Load flow (LF) equations are used within optimization to determine if physical network limits violated. Due nonlinearities, solvability OF problem and convergence algorithms influenced by how LF included in optimal (OF) problem. In addition, scaling greatly influences practical problems. This paper considers two ways include general MESs. formulation I, over combined control state variables, with explicitly as equality constraints. II, variables only. The solved from a separate subsystem, given variables. Hence, only implicitly II. formulations compared qualitatively, theoretical perspective based on numerical experiments. Both I II result solvable Formulation easier implement efficient terms CPU time. However, ensures feasibility can be combination dedicated load solvers. matrix per unit solve problem, but they not equivalent. • Optimal multi-carrier Comparison subsystem. Adjoint direct approach