Leaky storage model for optimal multi-service allocation of thermostatic loads

Collectively, thermostatically controlled loads (TCLs) offer significant potential for short-term demand response. This intrinsic flexibility can be used to provide various ancillary services or to carry out energy arbitrage. This study introduces an aggregate description of the flexibility of a heterogeneous TCL as a leaky storage unit, with associated constraints that are derived from the TCL device parameters and quality of service requirements. In association with a suitable TCL control strategy this enables a straightforward embedding of TCL dynamics in optimisation frameworks. The tools developed are applied to the problem of determining an optimal multi-service portfolio for TCLs. A linear optimisation model is constructed for the optimal simultaneous allocation of frequency services and energy arbitrage. In a case study, optimal service allocations are computed for eight representative classes of cold appliances and the results are validated using simulations of individual refrigerators. Finally, it is demonstrated that clustering of appliances with similar capabilities can significantly enhance the flexibility available to the system.