This paper presents a model to optimise the operation of a small-scale, grid-connected, hybrid power plant with and without demand response of the associated load. The model minimises the full cost of supplying electricity from a combination of solar photovoltaic, battery storage, a natural gas fuelled reciprocating engine generator and network delivered electricity, while satisfying several technical and environmental constraints. This includes the use of demand response, historical local solar irradiance and demand traces, constraints on solar photovoltaic, battery and engine performance, full electricity and natural gas tariffs, and the option to participate in the wholesale electricity market. The model is first applied to a school in Victoria, Australia as a case study. It is found that the optimal hybrid plant configuration depends strongly on the choice of greenhouse gas abatement target, electricity and natural gas tariffs, particularly tariffs with demand charges and the option to export electricity to the network grid. The school can also benefit from demand response, where savings result not only from the avoided network delivered electricity cost but also avoided hybrid plant capital investment and operation. Importantly, whilst demand response impacts the hybrid plant configuration it does not displace the optimality of hybrid power plants in distribution networks.