Abstract
Security-constrained unit commitment (SCUC) has been extensively studied as a key decision-making tool to determine optimal power generation schedules in the operation of electricity market. With the development of emerging power grids, fruitful research results on SCUC have been obtained. Therefore, it is essential to review current work and propose future directions for SCUC to meet the needs of developing power systems. In this paper, the basic mathematical model of the standard SCUC is summarized, and the characteristics and application scopes of common solution algorithms are presented. Customized models focusing on diverse mathematical properties are then categorized and the corresponding solving methodologies are discussed. Finally, research trends in the field are prospected based on a summary of the state-of-the-art and latest studies. It is hoped that this paper can be a useful reference to support theoretical research and practical applications of SCUC in the future.
AS a critical decision-making tool for power system operations and as a theoretical basis for day-ahead electricity markets, independent system operators (ISOs) execute unit commitment (UC) to determine the optimal commitment and dispatch of thermal generation units at minimal operation cost, subject to prevailing unit and system constraints [
Several review papers related to SCUC have been published. Reference [
Based on the state of the art of SCUC, this paper conducts a comprehensive summary of the modeling approaches and solution algorithms according to practical needs and then prospects future research trends. This paper can act as a reference for researchers and engineers interested in theoretical research and practical application of SCUC.
The remainder of this paper is organized as follows. Section II presents the mathematical model of the standard SCUC and summarizes the characteristics and application scopes of common solution algorithms. The modeling and solution methodologies of SCUC with diverse mathematical properties are reviewed in Section III. Section IV prospects the research trends of SCUC based on the latest achievements. Finally, conclusions are drawn in Section V.
The objective of the standard SCUC model is to minimize the total cost during a particular scheduling cycle subject to various physical constraints [
(1) |
where is the overall operation cost; T is the number of time periods; is the number of thermal units; is the on/off status of unit i at time t, which equals 0 when unit i is off, and 1 otherwise; is the active power output of unit i at time t; and , , and are the generation cost, start-up cost, and shut-down cost of unit i at time t, respectively.
1) Generation power limits. The unit output is limited by the minimum technical output. In addition, the sum of the output and spinning reserve is also restricted by its capacity [
(2) |
where and are the minimum and maximum power limits of unit i, respectively; and is the spinning reserve of unit i at time t.
2) The minimum on/off time constraints. The frequent start-up/shut-down of a generator over a short period can induce excessive tear and wear, which should be avoided [
(3) |
where and are the on and off time counters of unit i at time t, respectively; and and are the minimum on and off time requirements of unit i, respectively.
3) Ramping rate constraints. The power adjustment ranges of generators per unit time are constrained by the maximum ramping up/down capability [
(4) |
where and are the ramping up and down limits of unit i, respectively.
In particular, for units that can provide ancillary services, the spinning and operation reserve capabilities should be constrained [
(5) |
where is the maximum sustained ramping rate of unit i; is the operation reserve of unit i at time t; and is the quick-start capacity of unit i.
1) System power balance constraint. The total output of operating units must meet the system load demand and is expressed as:
(6) |
where is the system load forecasting value; and is the total losses.
2) Reserve requirements. To cope with unforeseen conditions such as generator outages and/or load fluctuations, sufficient spinning and operation reserves should be considered [
(7) |
where and are the system spinning and operation reserve requirements at time t, respectively.
3) Network security constraints. To maintain secure operation, power flows of transmission lines cannot exceed their limits [
(8) |
where is the capacity limit of line l under line outage contingency c; is the line outage distribution factor; , , , and are the power transfer distribution factors; D is the number of load nodes; is the load of node d at time t; and C is the set of contingencies.
The standard SCUC model can be formulated as a mixed-integer non-linear programming (MINLP) problem. The common solving algorithms include heuristic, mathematical optimization (DP, BBA, LR, BD, OA, OO, C&CG), and intelligent optimization algorithms. The advantages and disadvantages of these algorithms are summarized in
The heuristic algorithm is one of the earliest algorithms employed to solve the SCUC. The most common heuristic algorithms are the local search method [
The mathematical optimization algorithm solves SCUC problems by leveraging analytical methods and the properties of the model. As the physical meaning of this process is clear, mathematical optimization algorithms have been widely applied to SCUC problems including the dynamic programming (DP) [
DP is used to solve multi-stage optimization problems. The main idea is to phase solution seeking to compress the feasible space. However, this requires that the problem satisfy the basic premise of the optimality theorem; otherwise, the global optimality cannot be guaranteed. In addition, the “curse of dimensionality” may incur with the increasing number of generation units. In practice, DP is typically utilized in combination with the priority list algorithm [
The main idea of BBA is to solve a series of relaxation problems of the original problem along the branch-and-bound tree and to update the upper and lower bounds of the objective function iteratively. In essence, BBA uses different searching strategies to find the optimal solution and improves the searching efficiency through reasonable branch-and-bound actions. The number of subproblems, however, increases sharply, leading to a considerable reduction in computational efficiency with the expansion of power systems [
LR is widely used in solving SCUC problems. Its main strategy is to convert the inequality constraints as penalty terms into the objective function. Then, based on the duality principle, it decouples the UC problem into a series of subproblems. LR is flexible in application and overcomes the obstacle of dimensionality but is easily affected by the initial value and Lagrangian multiplier update strategies, which may cause oscillations in the iterative process [
To reduce the solving complexity, the BD decouples the SCUC model into a master problem and several subproblems, which coordinate through Benders cuts iteratively. Currently, the BD, which has been employed in SCUC problems extensively, is one of the most effective algorithms to address the complicated constraints in SCUC [
As a decomposition strategy to solve MINLP, the OA involves solving an alternating sequence of primal and relaxed mixed-integer linear programming (MILP) problems. A sequence of valid lower and upper bounds on the global optimum are generated, which offers a theoretical guarantee of convergence to the global optimum in a finite number of iterations. Different from the BD, the OA and its variants are based on the use of optimal primal information [
In the solving process of OO, a rough model with a relatively simple structure is used to screen the feasible space rapidly, obtaining the selected set. Then, the suboptimal solution that satisfies the practical needs is identified through the accurate model through complicated calculation that renders higher accuracy [
C&CG has been widely applied to solve two-stage optimization problems, where the column generation step adds new decision variables of the second stage to the master problem, and the constraint generation step adds the cutting planes. As new variables are introduced in each iteration, the dimensionality of the solution space increases significantly [
Unlike mathematical optimization algorithms based on model analysis, intelligent optimization algorithms seek the optimal solution directly through a multi-point random migration strategy. They include two core steps: an evaluation method and a migration strategy. The first evaluates the performance of the results generated in the current stage and determines the direction of the next stage. The second uses a fixed strategy to promote the algorithm convergence with an optimal direction. As the lesser requirement on model information and multi-point optimization, intelligent optimization algorithms offer better application and faster calculation. Therefore, they are widely applied in solving SCUC. Researchers usually seek inspiration for migration strategies from nature or human social behavior. Depending on the different migration strategies, intelligent optimization algorithms include the genetic algorithm [
In general, uncertainty and instability exist in the solving process of intelligent optimization algorithms. The algorithms may also rapidly converge to suboptimal solutions restricted by migration strategies. To enhance calculation efficiency, some intelligent optimization algorithms have been used in a hybrid manner. These include the chaotic particle swarm optimization [
With the increasing complexity of power systems, standard SCUC model usually cannot satisfy practical engineering needs. Accordingly, many researchers have made efforts to improve the mathematical models in terms of the objective function, complicated constraints, or a combination of the two. Based on the mathematical models from particular applications, we categorize them into SCUC models with multiple objectives, with uncertainties, with additional variables, with complicated constraints, as well as with multiple areas and timescales.
With the transformation of energy infrastructures and increasing environmental concerns, the standard SCUC model with minimal economic cost as the optimization objective may not be sufficient. To this end, many efforts have been made to study SCUC with multiple objectives [
The SCUC with multiple objectives can be commonly expressed as:
(9) |
where is the
In addition to the economic cost, the SCUC with multi-objectives usually includes pollutant emission and social welfare. Specifically, the objective function for minimizing pollutant emission can be expressed as [
(10) |
where is the overall pollutant emission; is the number of pollutant types, including CO2, SO2, and NO2; and , , and are the coefficients of pollutants.
The objective function of social welfare is [
(11) |
where is the social welfare function; is the gross earnings of utility with the implemented electricity price; and is the number of buses.
For SCUC with multiple objectives, the solution is to transform the multi-objective problem into a single-objective one. The corresponding methodologies include the weighted sum method, fuzzy optimization algorithm, and Pareto optimization.
The main idea of the weighted sum method is to endow individual objectives with weights, converting the multi-objective problem into a single-objective one. A primary issue is to determine the weights of individual objectives. According to the setting strategies, weighted sum method can be categorized into subjective [
The fuzzy optimization algorithm commonly normalizes each subobjective first and then establishes the corresponding membership function by using a real number between 0 and 1 to indicate the membership degree. It then sums the membership functions of individual subobjectives to convert the multi-objective problem to a single-objective one [
The common idea of the Pareto optimization is to guarantee the optimality for at least one objective without exacerbating others [
The large-scale penetration of intermittent renewable energy such as wind power and photovoltaic power produces numerous uncertainties in power systems [
When a single type of uncertainty is considered in an SCUC problem, the general model mainly includes stochastic and robust SCUC according to whether the probabilistic distribution of uncertain parameters is known.
If the probability distribution of uncertainty has been assumed, the SCUC with uncertainty can be formulated as a stochastic SCUC:
(12) |
where is the expected total operation cost of generation units under the assumed distribution ; is a random variable that obeys the distribution ; is the
If the probability distribution of uncertainty is not given, the SCUC model with uncertainties can be formulated as a robust SCUC model:
(13) |
where is the uncertainty interval of parameter ; is the
In general, these stochastic and robust SCUC models are regarded as two-stage optimization problems. In other words, the commitment solution is solved in the first stage with the aim of minimizing the operation cost of traditional units. In the second stage, the initial decisions are checked and generation dispatches are further determined to satisfy the uncertainty realizations in real time [
Overall, these two-stage SCUC models cannot rigorously consider the situations in which uncertainty realizations are reviewed gradually and decisions are made at each time step along the scheduling horizon with all uncertainty realization information available up to the current time point. Accordingly, some researchers have proposed multi-stage optimization models that can make decisions dynamically by leveraging uncertainty information over time. The operation costs can be reduced by the more accurate interaction between decision-making and uncertainty in the multi-stage stochastic model. However, as the numbers of stages and decisions within each stage increase dramatically, the multi-stage models are harder to solve. The multi-stage model can be transformed into a two-stage problem to obtain the solution. Advanced decomposition algorithms have also been developed to accelerate the solving process [
In addition, there are various uncertainty factors in practical power systems [
Currently, the common solution methodologies to solve SCUC models with uncertainties include the scenario-based approach (SBA), chance-constrained optimization (CCO), RO, and information-gap decision theory (IGDT).
The main idea of the SBA is to generate a set of scenarios for simulating the possible conditions of uncertain factors. With the two-stage model, the sampling method is used to generate multiple independent scenarios based on the presumed probabilistic distribution functions. With the multi-stage model, a scenario tree with random paths is generated based on the dynamic stochastic process. However, many scenarios are needed to formulate the uncertainties (up to a point precisely), which complicates the solving process [
CCO is another technique for handling stochastic problems, where constraints can be violated by a specified small level of probability [
RO seeks the optimal solution in a worst-case scenario in which the uncertain factors have the greatest impact on system economics and/or reliability and then seeks the corresponding optimal solution [
IGDT constructs the robust model hedging risk and the chance model pursuing risk benefits by estimating the impact of uncertainties on the specified goals. The obtained robust and chance results can provide decision guidance for system operators. It does not require probability distribution functions of uncertainties and is suitable for the cases with numerous uncertainties or lacking uncertainty information [
The aforementioned solution methodologies for SCUC models with uncertainties are compared in
With the rapid development of smart grids, system operators can leverage flexible demand-side resources along with supply-side dispatching. In this regard, some researchers have attempted to plug demand response (DR) resources into the SCUC model as additional variables [
As a potential demand-side response resource, ILs may reduce the system operation cost effectively by load shedding during peak or system fault periods. In addition, regarding the output fluctuation of intermittent resources, they could also be applied to balance system loads and to optimize the configuration of system resources. Therefore, the general objective function of SCUC model with IL is [
(14) |
where is the compensation expense of IL j at time t; is the number of ILs; is the demand level of ILs; and is the state of IL j at time t, which equals 1 when the IL participates in scheduling, and 0 otherwise.
In addition to the prevailing constraints, the constraints such as the minimum interrupted time and maximum continuous invocation time [
As an efficient resource to mitigate the fluctuation and uncertainty of intermittent energy, ESSs can be embedded into SCUC models. The operation cost of ESSs should be considered in the SCUC model, and the specific function is [
(15) |
where is the number of dispatchable ESSs; and are the coefficients of charging and discharging expenses, respectively; and and are the charging power and discharging power of ESS n at time t, respectively.
Similar to the ESS, an electric vehicle (EV) can operate as load under charging state and inject power to the system by vehicle-to-grid (V2G). As a result, some studies have embedded EVs into the SCUC model [
Researchers have also proposed SCUC models with complicated constraints. These mainly include SCUC models with transmission switching, with AC constraints, and with frequency constraints.
The high penetration of wind power and EVs in day-ahead electricity markets usually causes disturbances to power systems. In addition, abnormal changes of power flows and line losses under extreme conditions may increase the system operation costs. Accordingly, transmission switching is typically adopted to maintain secure operations. Therefore, the constraints of transmission switching have been introduced into SCUC models [
The objective function of the SCUC model with transmission switching remains the same as that of the standard SCUC model. The additional constraints are formulated as [
(16) |
where is the active power limit of line k; is the state of line k at time t, which equals 0 when line k is switched off without active power; and is the active power of line k at time t.
To maintain system voltage stability, the voltage phase angle constraint before closing lines should also be considered as [
(17) |
where is the phase angle of line k at time t; is the maximum stable phase angle difference of line k; and is a large positive constant.
As the DC power flow model can be solved directly without iterative calculation, it is always adopted to formulate the network security constraints in SCUC models [
Because of strong non-linearity, the AC power flow model must be solved using an iterative calculation. The computational complexity also increases sharply with the increase in grid scale. The SCUC model itself is a non-convex problem, and the introduction of AC constraints in the SCUC model will considerably complicate the solution and may result in non-convergence [
1) Introduce network loss factor or voltage index into the DC power flow model [
2) Introduce an AC power flow model but linearize it in the solving process [
3) Directly introduce AC power flow constraints into the SCUC model without simplifications [
For power systems with high penetration of renewable energy sources, because of the low inertia and limited reserve capacity of renewable energy sources, the frequency is likely to exceed the limit when disturbances occur, leading to a frequency collapse of the entire system [
The existing SCUC models that consider frequency constraints mainly focus on steady-state [
Based on the dispersed locations of generation resources and the solving timescale, some researchers have also concentrated on the modeling and solutions of SCUC models with multiple areas and timescales.
To tackle the problems of uneven energy distribution and power-supply/demand balance, inter-regional electricity interconnection has become a major choice for system operators [
With superior dispatching centers as participants, the centralized decision-making strategy is a vertical decision-making, multi-level coordination, and level-by-level refinement process. This strategy is implemented to break information blocking between multiple areas and to further realize optimal allocation of resources in a larger scope. Based on different operation modes of power systems, we categorize the centralized decision-making strategy into two types: regional-provincial grid coordination and transmission-distribution system coordination.
For the regional-provincial grid coordination, we take the coordinated dispatching of regional-provincial grid as an example, which can be described as a bi-level optimization problem. Its decision framework can be illustrated by

Fig. 1 Framework of regional-provincial grid coordination.
In
For the transmission-distribution system coordination, in market-oriented power systems, ISOs derive the day-ahead generation scheme through market clearing, where the distribution systems are usually directly simplified as loads. With the rapid deployment of distributed generators (DGs), the distribution network has changed from the fixed load form with unidirectional power flow to a new network pattern with bidirectional power flows between power supply and demand. In this context, as simplifying distribution systems as fixed load fails to reflect the internal operation features of distribution systems, the corresponding SCUC model may lead to problems such as over-voltage and transmission line congestion. Therefore, some researchers have embedded distribution systems with DGs into the SCUC problem, where a bi-level optimization-based transmission-distribution system coordination was established in [
To cope with the issue of computational efficiency, in [
With the expansion of the scale of interconnected power systems, for the centralized decision-making strategy, it is difficult to obtain global information of large-scale power systems without compromising the information privacy among interconnected areas. As a result, the generation resources of interconnected regional power grids cannot be optimally scheduled. Accordingly, studies have been conducted that utilized decentralized decision-making strategies to calculate SCUC decisions [
Without the participation of superior dispatching centers, the decentralized decision-making strategy could maximize the overall economic benefit of interconnected power systems by adjusting the tie-line power flows through neighbors’ information. The general framework of decentralized decision-making strategy is shown in

Fig. 2 Framework of decentralized decision-making strategy.
The common solutions of decentralized decision-making strategies include the alternating direction method of multipliers (ADMM) and synchronous alternating direction method of multipliers (SADMM). ADMM solves a convex optimization problem by decomposing it into several smaller subproblems that can be easily handled. It can guarantee the independent autonomy of each subsystem and information privacy simultaneously [
SCUC models use 1 hour as a basic time step size to calculate day-ahead schedules. However, with the increasing deployment of intermittent energy and flexible loads, some researchers have strategically adopted different time resolutions for the SCUC calculation. The main types include adaptive timescale, intraday multi-timescale, and long-term multi-timescale SCUC models.
The decision step size is generally fixed at 1 hour or 30 min in most day-ahead SCUC models. Therefore, these models may fail to accurately capture the random fluctuations of load or intermittent power at a finer time resolution. Therefore, shortening the time step size is a possible means of improving decision accuracy. However, this would increase the computational burden considerably. To this end, [
Currently, the forecasting accuracy of intermittent energy increases gradually with a finer time resolution. In addition, the response characteristics of loads vary under different timescales [

Fig. 3 Intraday multi-timescale SCUC model.
The intraday multi-timescale SCUC model first must make day-ahead decisions based on day-ahead load forecasting. Then, based on continual updated forecasting, it derives intraday and real-time schemes to allocate flexible load resources and intermittent energy reasonably.
Start-up processes of thermal generators, particularly those with large capacities, may require considerable time with multiple steps, thereby limiting the economics and operability of the day-ahead SCUC [

Fig. 4 Long-term multi-timescale SCUC model.
Compared with standard SCUC models, the optimization periods as well as the decision variables and constraints of long-term multi-timescale SCUC models are multiplied. In addition, the critical factors affecting the calculation efficiency are the coupling relationships among constraints such as the minimum start-up/shut-down time constraints. Regarding the processing of time coupled constraints, existing studies have utilized cutting plane methods to adjust the constraint-variable relationship of valid inequalities [
To handle the problems of environmental pollution and to promote the sustainable development of clean energy, integrated operations of multiple energy systems such as power, natural gas, and heating are currently being considered. Indeed, integrated energy systems (IESs) with multiple supplying resources, loads, and coupled energy forms have been established to improve energy efficiency [
Due to their fast response, low pollution, and high energy efficiency, gas turbines have had rapid growth in recent years as connecting hubs between power and natural gas systems. In addition, with the extensive application of power-to-gas (P2G) technology, energy begins to flow bidirectionally between power and natural gas systems. Taking gas turbines and P2G devices as coupling nodes, power and natural gas systems are tightly coupled into a highly dependent IES at both the physical and information levels. For this type of system, in addition to the standard SCUC model for power systems, the constraints of natural gas pipeline networks and related characteristics should be considered. Therefore, a new SCUC framework has been developed [
Some similarities exist between models of natural gas and power systems. The energy sources are limited by upper/lower boundaries, and the energy transmission is limited by the physical characteristics of lines or pipelines. However, the operation characteristics and energy transmission speeds of these models are different, which present new and significant challenges.
Existing studies have presented two main strategies in the SCUC modeling of power-gas systems: sequential optimization [
In terms of solution approaches, the main challenge is the non-linearity of the natural gas pipeline constraints. In this regard, the latest studies have mostly focused on refining the static models, despite their required simplification in the solving process. Specifically, non-linear constraints such as the flow equations of natural gas are usually linearized or relaxed. Under the assumption that pipeline gas flow direction is known, [
However, several challenging issues remain that must be further studied. First, influenced by the price fluctuation and supply shortage of natural gas, natural gas systems face certain uncertainties. In addition, because of the different response speeds of power and natural gas systems, the influence mechanisms and response characteristics of their uncertainty factors are also different. How to construct an SCUC model that can comprehensively consider the uncertainties of these two systems must be resolved [
The heat loss of conventional thermal power units in the generation process usually leads to lower energy utilization [
Regarding the SCUC for heat-power systems, because of the slow dynamics of the heating, the heterogeneous time step in the SCUC modeling is a major issue that deserves attention. In this regard, the studies employing a variable timescale to establish the model have been conducted [
Limited by the “heat-led” mode, the outputs of combined heating and power units must be adjusted based on the dynamic changes of heating loads [
As an optimization problem, the studies on SCUC have consistently encountered the trade-offs between decision accuracy and computational efficiency. The pursuit of more accurate SCUC decisions requires a more refined model [
Compact modeling is recognized as an effective means of improving the solving efficiencies of SCUC [
By the Buckets effect, optimal SCUC decisions are commonly described by a small portion of constraints [
The on/off statuses of certain units remain unchanged throughout a scheduling day. Thus, eliminating these integer variables can effectively compress the solution space and facilitate calculation efficiency [
The efficient algorithm is an important theoretical guarantee for refining SCUC models. With the development of parallel computing technology, [
Reference [
Conventionally, the main idea behind an SCUC is first to establish the corresponding models according to engineering needs, introduce various mathematical methods to process or simplify them, and finally study the applicable solving algorithms. The entire modeling and solving processes are based on rigorous logical deductions and supported by mathematical theories. These are referred to as physical-model-driven SCUC (PMD-SCUC) [
In recent years, with the rapid development of artificial intelligence technologies and their wide applications in various fields of power systems [
Some studies have conducted the applications of artificial intelligence in SCUC problems. Long short-term memory was previously introduced in [
As one of the latest research directions in this field, the following problems remain in DD-SCUC that must be solved. ① Neural network training generally requires data with a fixed structure. By contrast, in the long-term development of power systems, the dynamic changes of generation resources and grid structures lead to non-stationary data samples. To solve this issue, [
With the continual changes in energy structures and the rapid development of emerging technologies, SCUC problems present new challenges and opportunities. This study reviewed the major research findings of the studies on SCUC and discussed future research trends. The basic mathematical model of the standard SCUC was first summarized, and the characteristics and application scopes of common solutions were then presented. SCUC models from different research focuses were next classified in terms of their mathematical properties. These SCUC models included those with multi-objectives, uncertainties, additional variables, complicated constraints, and those designed for multiple areas and multiple timescales. The corresponding solution ideas were then generalized. Finally, the research trends of SCUC were prospected based on a survey of the state-of-the-art and latest research achievements. The trends mainly include the challenges posed to SCUC by the interconnection of power and other energy systems, the new contributions toward trade-off between decision accuracy and computational efficiency throughout SCUC research, and the potential opportunities for SCUC presented by the rapid development of artificial intelligence.
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