Optimisation of Multi-Energy System Operation with Convex Efficiency Representation at Partial Loading

The optimal operation of multi-energy systems (MES) that supply a demand formed by different energy vectors can be determined based on a given objective function with the relevant constraints. An efficient approach formulated in the literature defines an optimisation model with linear constraints considering constant efficiency or constant coefficient of performance (
COP
) of the individual equipment. This paper extends this optimisation model by considering non-linear convex expressions of the equipment efficiencies and
COP
s. The optimisation with linear constraints is solved in an iterative way, by updating the efficiencies and
COP
s at each iteration until the convergence criterion is satisfied. The results of this approach are shown for a MES that supplies electricity, heat and cooling demand in representative cases for winter and summer periods. The relevant aspects are the possibility of determining more realistic operation costs, higher than the operation costs found with constant efficiencies when the efficiency of the equipment varies in a monotonic way. Conversely, with non-monotonic variations (e.g., for the
COP
, when the MES serves a cooling demand), the operation costs do not increase in all cases. Finding more realistic operation costs becomes crucial in MES applications with increasing electricity and gas prices, with higher correlations occurring at high price levels. Finally, a novel graphical method is presented to indicate the MES contributions equipment in serving electricity, heat and cooling demand, also showing the upward and downward flexibility due to energy shifting in the MES.