4. Reduction Techniques for TEP Problems

One of the most common representations of the TEP problem is a mixed-integer linear programming (MILP) problem, in which operation costs are modeled by linear variables, and investment decisions are represented by integer variables. The large size of the TEP problem, together with the lumpiness of investment decisions, makes the problem very hard to solve. To cope with this issue, techniques to represent the TEP problem in a compact way, i.e., reduction techniques, can lessen the size of the problem and make it easier to solve. The TEP problem can be reduced in three dimensions: the power grid representation (spatial dimension), the operating point representation (temporal representation), and the number of candidate grid elements to consider. An interesting methodology to reduce the TEP problem in each of its three dimensions is to guide the reduction using the information from the solution of a more tractable version of the problem. The first step consists in solving a linear relaxation of the TEP problem. Then, we make use of the information associated with this approximate solution to formulate the TEP problem in a compact way for each dimension. This chapter introduces three efficient reduction techniques, one reduction technique for each problem dimension, that are based on this linear relaxation.

This chapter is organized as follows. Section 4.1 presents a methodology to reduce the size of the temporal representation of the TEP problem, also called snapshot selection method. Section 4.2 presents a methodology to reduce the size of the spatial representation of the problem, also called network reduction method. Section 4.3 introduces a methodology to identify promising candidate grid elements, also called search-space reduction method. Finally, Sect. 4.4 concludes.