New formulations of the ‘energy hub’ model to address operational constraints

Abstract

We present new formulations of the ‘energy hub’ model and evaluate their performance. The energy hub model consists of a mixed-integer linear programming problem that balances energy demand and supply between multiple energy carriers by determining the optimal conversion and storage schedule within certain constraints. The new formulations extend the model to account for performance constraints concerning system efficiencies, storage losses and operating limits. Each formulation allows a more accurate representation of real plant performance to be included in the optimisation, giving more accurate optimised schedules and carbon emissions totals.The first major innovation is a means of limiting the number of state changes (startups or shutdowns). This is achieved by specifying a minimum time for which the plant must operate once it is running. The second innovation is the use of stepwise approximations of efficiency curves, thus allowing part-load behaviour to be accurately simulated using a linear model. The third innovation adds a storage loss term that is a percentage of the current amount stored, rather than a fixed value.The new formulations are demonstrated in an example case, where the impact on the optimal schedule is observed. They are also analysed for each week of the heating season, and their impact on the time taken to find the optimal solution is also discussed. Overall changes in the predicted carbon emissions of up to 22% were found, highlighting the importance of accurate plant representation in energy hub models.