A mathematical programming/economic equilibrium model for the quantitative analysis of the stability of Japan’s energy system

Japan’s energy supply-demand system is fully dependent on the import of primary energy resources from foreign countries. So the availability of primary energy, including crude oil and coal, is a very important factor for the stability of the present energy system. In order to measure the energy system’s stability under an uncertain future availability of energy resources, a mathematical programming/economic equilibrium model was built, based upon linear programming techniques. In the model analysis uncertain future availability of primary energy resources is expressed as random variables with a given probability distribution, and the economic equilibrium point is obtained by iterative convergent computation. From the present numerical results an optimal energy supply-demand structure is known with equilibrium prices of primary energy resources at the future target year, and obtained supply stability and instability probabilities of the present energy system. Furthermore, applicability of decomposition techniques to the energy model analysis and necessary and sufficient conditions for the stability of the present energy system are discussed.