Electricity systems require a real-time balance between generation and demand for electricity. In the past, changing the output of larger generators has been the primary means of achieving this balance, but more recently, smaller distributed energy resources (DERs) are becoming a contributor. As electricity generation becomes more intermittent due to the uptake of renewables, the task of balancing the electricity system is becoming more challenging. As such, there will be a greater need for DERs for grid balancing in future. DERs may be delivered via aggregators for this purpose, where several individual resources are grouped to be traded in contracts with a System Operator (SO). This paper presents a novel framework for DERs aggregators to determine by optimisation the capacity of a generating unit to contract with the SO, using mixed integer non-linear programming (MINLP). Results show the site revenue increases between 6.2% and 29.8% compared to the heuristic approach previously employed. Sensitivity analysis is performed to assess the impact of temporal resolution of demand characterisation on results, showing that increased resolution improves accuracy significantly, and reduces the estimate of capacity that the site should contract with the aggregator.