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.
Elements of unit commitment problems There are many different UC problems, as the electrical system is structured and governed differently across the world. Common elements are:
A time horizon along which the decisions have to be made, sampled at a finite number of time instants. This is usually one or two days, up to a week, where instants are usually hours or half-hours; less frequently, 15 or 5 minutes. Hence, time instants are typically between 24 and around 2000. A set of generating units with the corresponding energy production cost and/or emission curves, and (complex) technical constraints. A representation of the significant part of the grid network. A (forecasted) load profile to be satisfied, i.e., the net amount of energy to be delivered to each node of the grid network at each time instant. Possibly, a set of reliability constraints ensuring that demand will be satisfied even if some unforeseen events occur. Possibly, financial and/or regulatory conditions (energy revenues, market operation constraints, financial instruments, ...). The decisions that have to be taken usually comprise:
commitment decisions: whether a unit is producing energy at any time instant; production decisions: how much energy a unit is producing at any time instant; network decisions: how much energy is flowing (and in which direction) on each branch of the transmission and/or distribution grid at any given time instant. While the above features are usually present, there are many combinations and many different cases. Among these we mention:
whether the units and the grid are all handled by a Monopolistic Operator (MO), or a separate Transmission System Operator (TSO) manages the grid providing fair and not discriminatory access to generating companies (GenCos) that compete to satisfy the production on the (or, most often, several interconnected) energy market(s); the different kinds of energy production units, such as thermal/nuclear ones, hydro-electric ones, and renewable sources (wind, solar, ...); which units can be modulated, i.e., their produced energy can be decided by the operator (albeit subject to the technical constraints of the unit), as opposed to it being entirely dictated by external factors such as weather conditions; the level of detail at which the working of the electrical grid must be considered, ranging from basically ignoring it to considering the possibility of dynamically opening (interrupting) a line in order to optimally change the energy routing on the grid.
Management objectives 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.
Types of production units In the context of UC, generating units are usually classified as:
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