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. 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: •
Thermal units, which include
nuclear ones, that burn some sort of fuel to produce electricity. They are subject to numerous complex technical constraints, among which we mention
minimum up/down time,
ramp up/down rate,
modulation/stability (a unit cannot change its production level too many times), and
start-up/shut-down ramp rate (when starting/stopping, a unit must follow a specific power curve which may depend on how long the plant has been offline/online). Therefore, optimizing even a single unit is in principle already a complex problem which requires specific techniques. •
Hydro units, that generate energy by harvesting
water potential energy, are often organized into systems of connected reservoirs called
hydro valleys. Because water released by an upstream reservoir reaches the downstream one (after some time), and therefore becomes available to generate energy there, decisions on the optimal production must be taken for all units simultaneously, which makes the problem rather difficult even if no (or little) thermal production is involved, even more so if the complete electrical system is considered. Hydro units may include
pumped-storage units, where energy can be spent to pump water uphill. This is the only current technology capable of storing enough (potential) energy to be significant at the typical level of the UC problem. Hydro units are subject to complex technical constraints. The amount of energy generated by turbining some amount of water is not constant, but it depends on the
water head which in turn depends on previous decisions. The relationship is nonlinear and nonconvex, making the problem particularly difficult to solve. • Renewable generation units, such as
wind farms,
solar plants,
run-of-river hydro units (without a dedicated reservoir, and therefore whose production is dictated by the flowing water), and
geothermal units. Most of these cannot be
modulated, and several are also
intermittent, i.e., their production is difficult to accurately forecast well in advance. In UC, these units do not really correspond to decisions, since they cannot be influenced. Rather, their production is considered fixed and added to that of the other sources. The substantial increase of intermittent renewable generation in recent years has significantly increased uncertainty in the
net load (demand minus production that cannot be modulated), which has challenged the traditional view that the
forecasted load in UC is accurate enough. whereby some of the lines of the grid can be dynamically opened and closed across the
time horizon. Incorporating this feature in the UC problem makes it difficult to solve even with the DC approximation, even more so with the full AC model. == Uncertainty in unit commitment problems ==