Before new renewable generators can be connected to the electricity network, it is necessary to carefully evaluate the impact they will have. Firm connection agreements are based on snapshot assessments of the worst-case situation of maximum generation and minimum demand, which restrict renewable capacities despite infrequent occurrence. This work describes how time series of several renewable generation technologies together with demand can be applied to examine the opportunities and challenges offered by non-firm generation connections. It applies optimal power flow to extract maximum energy from available renewable resources while using curtailment of generation to maintain the network within thermal and voltage limits. By way of a case study of potential wind, wave and tidal current development in the Orkney Islands, Scotland, the analysis provides estimates for the degree of curtailment and consequent economic impact a renewable generator operating under non-firm connection may experience. The methods described provide a first-level analysis that could facilitate appraisal of non-firm connections at the planning stage by estimating the consequences of concurrent generation and demand as well as the frequency and duration of necessary curtailments.