Linear programming techniques for developing an optimal electrical system including high-voltage direct-current transmission and storage

The planning and design of an electric power system, including high-voltage direct-current transmission, is a complex optimization problem. The optimization must integrate and model the engineering requirements and limitations of the generation, while simultaneously balancing the system electric load at all times. The problem is made more difficult with the introduction of variable generators, such as wind and solar photovoltaics. In the present paper, we introduce two comprehensive linear programming techniques to solve these problems. Linear programming is intentionally chosen to keep the problems tractable in terms of time and computational resources. The first is an optimization that minimizes the deviation from the electric load requirements. The procedure includes variable generators, conventional generators, transmission, and storage, along with their most salient engineering requirements. In addition, the optimization includes some basic electric power system requirements. The second optimization is one that minimizes the overall system costs per annum while taking into consideration all the aspects of the first optimization. We discuss the benefits and disadvantages of the proposed approaches. We show that the cost optimization, although computationally more expensive, is superior in terms of optimizing a real-world electric power system. The present paper shows that linear programming techniques can represent an electrical power system from a high-level without undue complication brought on by moving to mixed integer or nonlinear programming. In addition, the optimizations can be implemented in the future in planning tools.