Читать книгу Mathematical Programming for Power Systems Operation - Alejandro Garcés Ruiz - Страница 25

Phase balancing is a combinatorial problem that consists of phase swapping of the loads and generators to reduce power loss. Despite being a classic problem, it is still relevant since the unbalance is a common phenomenon in microgrids, especially when single-phase photovoltaic units are included. Because it is a combinatorial problem, phase balancing requires heuristic algorithms with high computational effort. However, it is possible to generate simplified instances of the problem, as presented in Chapter 13.

Each three-phase node has six possible configurations as depicted in Figure 1.6. The problem consists of defining the phase in which each load or generator is connected in order to reduce the grid’s total losses. Therefore, the problem is combinatorial since there are 6ⁿ possible configurations, where n is the number of three-phase nodes. The problem is nontrivial even in small networks; for example, a microgrid with 10 nodes will have 6 × 10⁷ possible configurations.

Figure 1.6 Set of possible configurations in a three-phase node.

Phase-balancing problems appear in many applications such as aircraft electric systems [4], and in power distribution grids with high penetration of electric vehicles [5]. Due to its combinatorial nature, the problem necessitates the use of heuristics [6], and meta-heuristics [7] as well as expert systems [8]. Modern approaches include the uncertainty associated to the load and generator [9].