Unit commitment problem in electrical power production

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 match the energy demand at minimum cost or maximize revenues from energy 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:

Because the relevant details of the electrical system greatly vary worldwide, there are many variants of the UC problem, which are often very difficult to solve. This is also so 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, or are even entirely devoted to its solution.

There are many different UC problems, as the electrical system is structured and governed differently across the world. Common elements are:

The decisions that have to be taken usually comprise:

While the above features are usually present, there are many combinations and many different cases. Among these we mention:

The objectives of UC depend on the aims of the actor for which it is solved. For a MO, this is basically to minimize energy production costs while satisfying the demand; reliability and emissions are usually treated as constraints. In a free-market regime, the aim is rather to maximize energy production profits, i.e., the difference between revenues (due to selling energy) and costs (due to producing it). If the GenCo is a price maker, i.e., it has sufficient size to influence market prices, it may in principle perform strategic bidding in order to improve its profits. This means bidding its production at high cost so as to raise market prices, losing market share but retaining some because, essentially, there is not enough generation capacity. For some regions this may be due to the fact that there is not enough grid network capacity to import energy from nearby regions with available generation capacity. While the electrical markets are highly regulated in order to, among other things, rule out such behavior, large producers can still benefit from simultaneously optimizing the bids of all their units to take into account their combined effect on market prices. On the contrary, price takers can simply optimize each generator independently, as, not having a significant impact on prices, the corresponding decisions are not correlated.

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