**A MILP Optimization Method for Building Seasonal Energy Storage: A Case Study for a Reversible Solid Oxide Cell and Hydrogen Storage System**

#### **Oscar Lindholm 1,\* , Robert Weiss <sup>1</sup> , Ala Hasan <sup>1</sup> , Frank Pettersson <sup>2</sup> and Jari Shemeikka <sup>1</sup>**


Received: 10 June 2020; Accepted: 3 July 2020; Published: 9 July 2020

**Abstract:** A new method for the optimization of seasonal energy storage is presented and applied in a case study. The optimization method uses an interval halving approach to solve computationally demanding mixed integer linear programming (MILP) problems with both integer and non-integer operation variables (variables that vary from time step to time step in during energy storage system operation). The seasonal energy storage in the case study uses a reversible solid oxide cell (RSOC) to convert electricity generated by solar photovoltaic (PV) panels into hydrogen gas and to convert hydrogen gas back to electricity while also generating some heat. Both the case study results and the optimization method accuracy are examined and discussed in the paper. In the case study, the operation of the RSOC and hydrogen storage system is compared with the operation of a reference system without energy storage. The results of the study show that installing an RSOC and hydrogen storage system could increase the utilization of onsite renewable energy generation significantly. Overall, the optimization method presents a relatively accurate solution to the case study optimization problem and a sensibility analysis shows a clear and logical pattern.

**Keywords:** energy storage; hydrogen; power-to-gas; reversible solid oxide cell; optimization; mixed integer linear programming; MILP
