Reliable design optimization for industrial hybrid energy systems with uncertain sustainable energy

More and more attention has been paid to the industrial hybrid energy systems which comprise fossil energy and renewable energy for achieving carbon neutrality. Wherein, the uncertainty of renewable energy, fluctuation of energy requirement from process units, and failure rate of energy conversion devices have significant effects on the reliability of industrial hybrid energy systems and thus restrict the application and promotion. How to simultaneously address these issues for realizing the reliable design of industrial hybrid energy systems has been a matter of great concern and challenge. Hence, a systematic reliable design optimization method is presented in this study to tackle these challenges. In this study, the two-stage stochastic programming method is implemented to conduct the uncertain optimization in dealing with the uncertainty of renewable energy and fluctuation of energy requirement, while a mixed stand-by redundancy allocation problem is proposed for simultaneously enhancing the reliability and minimizing the number of stand-by devices. A multi-objective mixed integer nonlinear programming framework using reliability and total annual cost as the dual objectives is then formulated and applied to a refinery site for the reliable design optimization of the industrial hybrid energy system. According to the solution results, compared to the minimum total annual cost scheme without stand-by redundancy, the maximum reliability of the industrial hybrid energy system can reach 0.9878 using the stand-by redundancy strategy. As a result, the reliability can be significantly enhanced by 44%, with only a 5% increment of the total annual cost. Moreover, a Pareto frontier under multi-objective optimization is constructed, and the optimization schemes at the Pareto frontier can realize the trade-off between reliability and the total annual cost of the industrial hybrid energy system. Subsequently, a reliability-gain index is proposed to further evaluate the trade-off schemes and thus guide the choice of appropriate design schemes.