Optimum policy for integration of renewable energy sources into the power generation system

In this paper we propose a dynamic model representing the temporal evolution of the levels of power generation (installed capacity) from two competing sources. These are renewable and conventional (fossil) sources. The percentage penetration rates of renewable and nonrenewable sources are considered as control or decision variables. We introduce an objective functional based on energy demand, production of pollution associated with usage of fossil fuels, and the cost of their systematic substitution by renewable sources. Pontryagin minimum principle is used to determine optimal control policy through minimizing energy generation from fossil fuels while meeting the energy demand as closely as possible through gradual replacement of nonrenewable sources by renewable ones. For different choices of plan periods, optimal generation path along with the corresponding control policies are presented. These results demonstrate that modern control theory can be used effectively to formulate optimal socio-economic policies.