electrical problem

The unit commitment problem (UC) in electrical power production is a large family of mathematical optimization problems where the production of a set of electrical generators is coordinated in order to achieve some common target, usually either matching the energy demand at minimum cost or maximizing revenue from electricity production. This is necessary because it is difficult to store electrical energy on a scale comparable with normal consumption; hence, each (substantial) variation in the consumption must be matched by a corresponding variation of the production.
Coordinating generation units is a difficult task for a number of reasons:

the number of units can be large (hundreds or thousands);
there are several types of units, with significantly different energy production costs and constraints about how power can be produced;
generation is distributed across a vast geographical area (e.g., a country), and therefore the response of the electrical grid, itself a highly complex system, has to be taken into account: even if the production levels of all units are known, checking whether the load can be sustained and what the losses are requires highly complex power flow computations.
Because the relevant details of the electrical system vary greatly worldwide, there are many variants of the UC problem, which are often very difficult to solve. This is also because, since some units require quite a long time (many hours) to start up or shut down, the decisions need be taken well in advance (usually, the day before), which implies that these problems have to be solved within tight time limits (several minutes to a few hours). UC is therefore one of the fundamental problems in power system management and simulation. It has been studied for many years, and still is one of the most significant energy optimization problems. Recent surveys on the subject count many hundreds of scientific articles devoted to the problem. Furthermore, several commercial products comprise specific modules for solving UC, such as MAON and PLEXOS, or are even entirely devoted to its solution.

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