A bi-linear optimization model for collaborative energy management in smart grid

This paper addresses the residential energy cost optimization problem in smart grid. More precisely, it proposes an approximate optimization model and evaluates its performance with an exact model. Previously, we developed an exact model which considers energy trading between the households in the microgrid. In the proposed approach, all households determine the microgrid energy price and quantity in collaboration with others. The complexity of the model was further increased when the unfair cost distribution problem among the households was addressed. The final model is a multi-objective non-convex Mixed Integer Non-Linear Programming (MINLP) problem. Its complexity is NP-hard which means that using the resulting solution is not practical because the solution times increase exponentially according to the increase in the problem size. To tackle this issue, this paper proposes an approximate model by using bi-linear optimization to reduce the computational complexity. The bilinear model breaks down the MINLP model into multiple Mixed Integer Linear Programming (MILP) modules and iteratively solves these modules until it meets the terminating criterion. Results show that solution times of the bi-linear model are very low compared to the exact model. Moreover, 97% of the solutions generated by the bi-linear model are optimal solutions. The proposed model maintains Pareto optimality which means that no households will be worse off to improve the cost of others. The final solution minimizes the total cost of the households in the microgrid.