1. Introduction
The security-constrained unit commitment (SCUC) considering uncertain factors has become the most significant and hottest research topic in the power market, given large-scale wind power access [
1,
2,
3]. The uncertain SCUC model has always been considered as a high-dimensional, strongly random, nonlinear NP-hard problem due to the integration of uncertain factors, discrete variables, and safety constraints, including power flow calculations [
4,
5,
6]. Therefore, it is difficult to solve the problem accurately and efficiently. Currently, the problem of solving accurately and efficiently has become a key technical bottleneck in the field of SCUC decision-making [
7]. Thus, it is of great theoretical and practical significance to research a more efficient method for solving the uncertain SCUC models.
In recent years, the idea of combining the benders decomposition method with a mature mixed integer programming algorithm has gradually become the mainstream solution of the SCUC problem [
8,
9,
10]. The method first decouples the SCUC model and then solves the decoupled subproblems by utilizing a mixed integer programming algorithm. Benders decomposition method achieves good results in solving the deterministic SCUC model. The difficulty of solving the SCUC model is reduced by decoupling the complex constraints into independent optimization subproblems in the benders decomposition method. However, the effect is not obvious for the problem of scene explosion in SCUC solution caused by the uncertainties. Therefore, its advantages are not obvious when this method is used to solve the uncertain SCUC problem. The constrained order optimization (COO) algorithm [
11] was introduced first for the problem of SCUC solving in [
12], and a solution of the uncertain SCUC was proposed based on the COO algorithm. From the perspective of the solution space, the feasible region scale of the SCUC model is reduced by constructing the COO rough model. On the basis of the COO rough model, a COO accurate model is constructed to find a good enough solution for the SCUC problem. Compared with the traditional benders decomposition method, the efficiency of the COO algorithm is enhanced to nearly 10 times [
12]. Based on the existing researches, the COO algorithm has been proven to be an effective method to solve uncertain SCUC problems rapidly. Although the traditional COO algorithm reduces the scale of the feasible region from the perspective of solution space, elimination and discrimination of the redundant information in the model itself are neglected. Therefore, the traditional COO algorithm can still be improved in terms of the solving efficiency, as described below.
1) When the SCUC model is solved by the traditional COO algorithm, the COO rough model should be constructed first, and then it is used to screen out the feasible solution space for the start–stop state of all units. However, there are many units in large-scale power systems, so the solving efficiency of the COO rough model is not high. The maximum load usually reaches 70% or higher of the installed capacity in the real large power grids, which means some units are always on or off during the scheduling period. Actually, there is no need to consider these constant units during the solving process. Consequently, if the constant units are identified first in the COO rough model, the efficiency of the COO algorithm will be improved. The problem of discrete variable identification has been studied. A linear screening model was constructed to identify the constant units in [
13]. The constant units were identified through the priority method in [
14,
15]. In reference [
16], the constant units are identified according to the relationship between the calculated active power output value and the identification rate parameter value. On the whole, the existing methods of the SCUC discrete variable identification are mainly based on the physical model driver idea, that is, constructing a complex mathematical model based on physical principles. However, it is difficult to construct an accurate mathematical model, and the identification results in the existing methods often have the problems of strong subjectivity and low accuracy. In fact, a large amount of structured historical data can be accumulated once the SCUC decision-making scheme is utilized in real power systems. In the long run, the accumulated historical SCUC decision-making scheme also has a guiding significance for the identification of the constant units. Therefore, the idea based on a data-driven method is a feasible way to address the problems of low accuracy and low objectivity of the discrete variable identification strategy.
2) Checking and computing network security constraints are one of the most computationally intensive tasks in solving SCUC problems. The strategy of checking all lines one by one was adopted in the COO accurate model in reference [
11]. This strategy will have a serious impact on the computational efficiency of the COO algorithm as the number of nodes and checked lines increases sharply with the expansion of the power grid scale. Reference [
17] showed that only a few of the network security constraints are effective that play a role in limiting the feasible region. Furthermore, a fast identification strategy for the invalid security constraints was also proposed. The method in [
17] reduces the invalid security constraints by more than 85% without affecting the calculation accuracy of the model. Thus, the identification strategy for the invalid security constraints can reduce the redundancy of the SCUC model. If this method can be introduced in the COO accurate model, the computational efficiency of the COO algorithm will be improved greatly.
In summary, a data-driven discrete variable identification strategy for the SCUC model is proposed in this paper. This strategy and the invalid security constraint identification strategy are used to improve the traditional COO algorithm [
12]. Finally, an improved COO algorithm for uncertain SCUC problem solving is proposed. This study is following three steps: construct a COO rough model with the discrete variable identification, construct an accurate COO model with the invalid safety constraint identification, solve the two models separately. The results based on IEEE 118-bus show that the redundancy of the uncertain SCUC model can be reduced effectively, and the computational efficiency can be further improved for the proposed improved strategy.
The main contributions in this study are as follows.
(1) A data-driven strategy of the SCUC discrete variable identification is proposed, and a COO rough model is constructed based on this strategy.
(2) A COO accurate model is constructed based on an identification strategy of the invalid security constraints.
(3) An improved COO algorithm suitable for the problem of SCUC solving is proposed based on the discrete variable identification strategy and the invalid security constraints identification strategy.
The rest of this paper is organized as follows. The SCUC model considering the uncertainty of wind power output is constructed in
Section 2. An overall framework for an improved COO algorithm is proposed in
Section 3. An improved strategy for the COO algorithm is proposed in
Section 4. The simulation analysis is shown in
Section 5. Finally, the conclusions are provided in
Section 6.
3. An Overall Framework for the Improved COO Algorithm
The COO [
6,
11,
12] is an efficient algorithm suitable for the SCUC model solution, and its main idea is as follows. A COO rough model is constructed first. The solution number in the solution space is reduced greatly by quickly prescreening the solution space. In addition, the feasible solutions in the solution space are preliminarily sorted, and the selected set is formed based on the certain strategy. Then, a COO accurate model is constructed to sort the solutions further in the selected set to obtain the optimal solution.
The SCUC model itself is a mixed integer programming problem with relatively independent decision variables. Therefore, the COO rough models and the COO accurate models for the discrete decision variables
UGit and continuous decision variables
PGit are constructed in the COO algorithm, respectively. In addition, the following improvements are made on the basis of the traditional COO algorithm [
12].
(1) The discrete variable identification strategy is added to the COO rough model. First, the data-driven discrete variable identification strategy is used to identify the constant units, and then, the COO rough model is adopted to solve the remaining units. Its purpose is to reduce the dimensions of the variables used in the COO rough model and to improve its computational efficiency.
(2) The identification strategy of the invalid security constraints is added to the COO accurate model, eliminating the invalid security constraints, and reducing the number of network security constraints that need to be checked for the COO accurate model. It can also reduce the complexity of solving the COO accurate model.
The overall idea of the improved COO algorithm is shown in
Figure 1. As shown in
Figure 1, the improved COO algorithm consists of three main steps as follows.
Step 1. First, the SCUC discrete variable identification model for the start–stop state of the units is constructed based on the deep learning idea, and the constant units are identified in discrete variable space. Then, the initial feasible region of the start–stop state (
UGit) is formed by eliminating the constant units. Moreover, the SCUC model is decoupled, and the variable
UGit is taken to construct a COO rough model with its related constraints and start–stop cost. The initial feasible region of the start–stop state of the units is prescreened, and the feasible region
ΘN is obtained. Select
N feasible solutions from feasible region
ΘN according to a uniform distribution to form a characterization set
Ω. The number of
N is closely related to the size of the solution space. Reference [
19] showed that the number of
N is generally 1000, as the solution space is less than 10
8.
Step 2.
Z solutions are selected further from the characterization set
Ω as the selected set
S based on the Horse Race method [
11,
20]. In set
S, it must be guaranteed that at least
α% of the probability contains
k good enough solutions. The specific selection rule of the Horse Race method is as follows.
Firstly, the COO rough model is utilized to evaluate and sort the solutions in the characterization set
Ω, and the order performance curve (OPC) is formed. Secondly, the type of OPC curve generated is determined based on the standard OPC curve. Thirdly, the optimization parameter in equation (6) [
20] is determined according to the type of the OPC, and the value of
Z is obtained. Finally, the previous
Z solutions are selected from the sorted characterization set
Ω to form the selected set
S. The
Z solution model is as follows.
The meanings of all the symbols in (16) are shown in [
20].
Step 3. The identification model of the invalid security constraints is constructed first to eliminate the invalid security constraints. Second, the minimum total cost of units is taken as an objective function. Then, a COO accurate model of continuous variable PGit is constructed under the condition of considering the constraints related to the active power output. Solving the unit output scheme and operation cost corresponding to the unit start–stop state in selected set S. Finally, the COO accurate model is employed to sort the set S to obtain the optimal solution.
6. Conclusions
An improved COO algorithm for solving the SCUC problem was proposed in this paper. The SCUC problem was solved rapidly and effectively considering the uncertainty of wind power output. Simulations based on the IEEE 118-bus example were executed. First, the data-driven discrete variable identification strategy was incorporated into the COO rough model, and then, the invalid security constraints identification strategy was incorporated into the COO accurate model. Finally, the improved COO algorithm combined the discrete variable identification with the invalid security constraint identification to make the uncertain SCUC decision. The conclusions are as follows.
(1) A deep learning model based on LSTM was constructed, and then a data-driven SCUC discrete variable identification strategy was proposed. This strategy was applicated to the COO rough model. The proposed improvement strategy can enhance the computational efficiency greatly of the rough COO model under the premise of ensuring the solution accuracy.
(2) The invalid security constraints identification strategy can identify more than 90% of the invalid security constraints in a short period of time. The strategy introduced to the COO accurate model can effectively reduce the computational redundancy of the COO accurate model and improve its computational efficiency.
(3) The data-driven SCUC discrete variable identification strategy and the invalid security constraint identification strategy were introduced based on the COO algorithm. These strategies effectively improved the compactness and the overall efficiency of the COO algorithm. Compared with the traditional COO, the accuracy and efficiency of the proposed method were improved by nearly 1.13 times and 5 times, respectively.
On the whole, the actual situation, which is common in the SCUC problem, was considered in the method of this paper. By reducing the complexity of the solution space and the model, the purpose of improving the accuracy and efficiency of the solution was achieved.