Mixed-integer linear programming models and algorithms for generation and transmission expansion planning of power systems

With the increasing penetration of renewable generating units, especially in remote areas not well connected with load demand, there are growing interests to co-optimize generation and transmission expansion planning (GTEP) in power systems. Due to the volatility in renewable generation, a planner needs to include the operating decisions into the planning model to guarantee feasibility. However, solving the GTEP problem with hourly operating decisions throughout the planning horizon is computationally intractable. Therefore, we propose several spatial and temporal simplifications to the problem. Built on the generation expansion planning (GEP) formulation of Lara et al. (2018), we propose a mixed-integer linear programming formulation for the GTEP problem. Three different formulations, i.e., a big-M formulation, a hull formulation, and an alternative big-M formulation, are reported for transmission expansion. We theoretically compare the tightness of the LP relaxations of the three formulations. The proposed MILP GTEP model typically involves millions or tens of millions of variables, which makes the model not directly solvable by the commercial solvers. To address this computational challenge, we propose a nested Benders decomposition algorithm and a tailored Benders decomposition algorithm that exploit the structure of the GTEP problem. Using a case study from Electric Reliability Council of Texas (ERCOT), we are able to show that the proposed tailored Benders decomposition outperforms the nested Benders decomposition. The coordination in the optimal generation and transmission expansion decisions from the ERCOT study implies that there is an additional value in solving GEP and TEP simultaneously.