Although fossil fuels consumption may causes to rapid economic growth, but due to related pollutants and its consequences, the world has suffered from climate changes. Moreover, fossil fuel resources such as petroleum, gas, coal and uranium are being exhausted rapidly in the last decades. Therefore, seeking an appropriate as well as low-cost alternative for the above-mentioned energy carriers is one of the most important research topics. Regarding this situation, the utilization of renewable energy sources especially solar and wind energies is very important. In this study, the social welfare is maximized and optimal trajectory of solar and wind energy substitution is derived by using an optimal control approach. The model is solved empirically by genetic algorithm using MATLAB software. The results show that assuming social discount rate of 5% and no reduction in solar and wind energy conversion cost during next years, transition from fossil energy to solar and wind energy must occur in 2089 while assuming a 50 % reduction in solar and wind energy conversion cost in every 10 years period, this transition must take place in 2032.

Keywords: Optimal Control Theory, Endogenous Substitution, Wind Energy, Solar Energy, Social Discount Rate.

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