Unit Commitment Method Based on Branch and Bound Internal Induction

Abstract

This invention discloses a unit commitment method based on branch-and-bound internal induction, comprising the following steps: 1) establishing a power system unit commitment model; 2) constructing a system congestion sensitivity assessment index; 3) establishing a small-scale integer programming model; and 4) determining the unit commitment method using a branch-and-bound approach. By using branch-and-bound internal induction, this invention avoids optimality loss caused by model modifications and further improves the calculation speed of the UC.

Description

Technical Field

[0001] The present invention relates to the field of power systems and automation thereof, and in particular to a unit combination method based on branch and bound internal induction. Background Art

[0002] Unit Commitment (UC) in a power system is the process of developing the most economical and efficient short-term unit generation plan while satisfying the system's operational constraints, transmission constraints, and generator technical limitations. As the first step in day-ahead power market transactions, UC formulates generator start-up and shutdown plans through market bidding and unified optimization. This provides the prerequisite information and decision-making basis for subsequent economic dispatch, safety verification, and other steps, and serves as the foundation for optimal energy trading and electricity price settlement. However, due to the large scale, strong integer non-convexity, and high line congestion of UC in actual projects, the computational efficiency of commercial solvers is insufficient to match the relatively narrow day-ahead market clearing window.

[0003] Existing UC acceleration algorithms primarily achieve acceleration through external modifications to the model, including heuristic and deterministic methods. Heuristic methods achieve acceleration by massively reducing integer variables, but struggle to guarantee optimality. Deterministic methods, such as active constraint identification and constraint tightening, guarantee optimality but offer limited improvement in acceleration. Summary of the Invention

[0004] The present invention aims to provide a unit commitment method based on branch and bound internal induction, comprising the following steps:

[0005] 1) Establish a power system unit combination model.

[0006] The objective function of the power system unit combination model is as follows:

[0007]

[0008] In the formula, the integer variable x g,t Indicates the startup status of the g-th unit at time t. b,t represents the slack variable. M represents the penalty factor. The constant U g represents the startup cost of the g-th unit. g,t represents the real-time output of the g-th unit at time t. g,t ) indicates the output p g,t The operating cost of the next g-th unit. gather gather They represent time period, total number of units and total number of lines respectively. b represents line.

[0009] The constraints of the power system unit combination model are as follows:

[0010]

[0011]

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018] In the formula, the integer variable y g,t 、z g,t They represent the running status and shutdown status of the g-th unit at time t respectively. g,t -1, z g,t-1 They represent the operating status and shutdown status of the g-th unit at time t-1 respectively. d,t Represents the load data at time t. PTDF g,b PTDF d,b Denotes the power transfer distribution factor. F b Indicates the transmission capacity of the bth line. P g Indicates the upper and lower limits of the output of the g-th unit. Indicates the minimum start and stop time of the g-th unit. Indicates the ramp rate of the g-th unit. Indicates the start and stop rate of the g-th unit. Indicates load.

[0019] 2) Construct a system blocking sensitivity evaluation index.

[0020] The steps to construct a system blocking sensitivity evaluation index include:

[0021] 2.1) Determine the blocking sensitivity evaluation index to be optimized b,t ,Right now:

[0022]

[0023] Where UB represents the upper bound and LB represents the lower bound. represents the upper bound of the slack variable. represents the lower bound of the slack variable.

[0024] 2.2) The congestion sensitivity evaluation index to be optimized based on the short-term unit power generation planning model b,t Optimize and obtain the blocking sensitivity evaluation index, namely:

[0025]

[0026] Where, O g It represents the blocking sensitivity evaluation index of the g-th unit.

[0027] 3) Establish a small-scale integer programming model.

[0028] The steps to build a small-scale integer programming model include:

[0029] 3.1) Establishing a small-scale optimization space Right now:

[0030]

[0031] Where, Represents the integer variable x g,t , integer variable y g,t , integer variable z g,t Collection. Collection i g,t Represents an integer variable, i = x, y, z.

[0032] Create a collection The method is as follows: calculate the blocking sensitivity evaluation index of each unit in the power system, and sort all units in descending order according to the blocking sensitivity evaluation index to obtain the unit set Assemble the crew The first N units in the middle write collection N is the preset number of units.

[0033] 3.2) Establish a small-scale integer programming model, namely:

[0034]

[0035] In the formula, the set is the upper bound of an integer variable.

[0036] 4) Use the branch and bound method to determine the unit combination method.

[0037] In the process of determining the unit combination mode by the branch and bound method, whenever the upper and lower bounds change, a small-scale integer programming model is solved to obtain the integer variable i g,t The feasible solution of in After solving, determine the feasible solution ub in Less than Is it true? If so, update the upper bound of the integer variable

[0038] It is worth noting that the present invention first analyzes the system congestion sensitivity, analyzes the influence relationship between unit output and line flow based on the power system DC power flow equation, and constructs a system congestion sensitivity evaluation index based on solving upper and lower bound information.

[0039] Then, a small-scale integer programming model is constructed. Based on the system congestion sensitivity evaluation index, some key units with the greatest sensitivity to system congestion are selected. Based on the upper bound information, a small-scale integer programming induction model with state relaxation only for key units is constructed.

[0040] Secondly, induced branch-and-bound pruning. Based on the rapid solution of the small-scale integer programming induced model, a better feasible solution is obtained to update the current upper bound of the branch-and-bound algorithm, thereby accelerating the branch-and-bound pruning process and reducing the node exploration space.

[0041] Finally, through the commercial solver CPLEX, an actual test system in a province in China verifies that the present invention can accelerate UC solution.

[0042] The technical effects of this invention are undeniable. By leveraging system congestion information and upper and lower bound information to construct and solve a small-scale integer programming model, the present invention implements internal induction of the branch-and-bound algorithm in existing commercial solvers, accelerating the solution of unit commitments. Specifically, the present invention involves system congestion sensitivity analysis, small-scale integer programming model building, and branch-and-bound induction. By employing branch-and-bound internal induction, the present invention avoids the loss of optimality caused by model modifications and further improves the computational speed of the UC. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Flow chart of the method. DETAILED DESCRIPTION

[0044] The present invention will be further described below with reference to the following examples, but it should not be understood that the scope of the present invention is limited to the following examples. Without departing from the above technical ideas of the present invention, various substitutions and modifications can be made according to common technical knowledge and customary means in the art, and all should be included in the scope of protection of the present invention.

[0045] Example 1:

[0046] See also Figure 1 , a unit commitment method based on internal induction of branch and bound, including the following steps:

[0047] 1) Establish a power system unit combination model.

[0048] The objective function of the power system unit combination model is as follows:

[0049]

[0050] In the formula, the integer variable x g,t Indicates the startup status of the g-th unit at time t. b,t represents the slack variable. M represents the penalty factor. The constant U g represents the startup cost of the g-th unit. g,t represents the real-time output of the g-th unit at time t. g,t ) indicates the output p g,t The operating cost of the next g-th unit. gather gather They represent time period, total number of units and total number of lines respectively. b represents line.

[0051] The constraints of the power system unit combination model are as follows:

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] In the formula, the integer variable y g,t 、z g,t They represent the running status and shutdown status of the g-th unit at time t respectively. g,t -1, z g,t-1 They represent the operating status and shutdown status of the g-th unit at time t-1 respectively. d,t Represents the load data at time t. PTDF g,b PTDF d,b Denotes the power transfer distribution factor. F b Indicates the transmission capacity of the bth line. P g Indicates the upper and lower limits of the output of the g-th unit. Indicates the minimum start and stop time of the g-th unit. Indicates the ramp rate of the g-th unit. Indicates the start and stop rate of the g-th unit. Indicates load.

[0061] 2) Construct a system blocking sensitivity evaluation index.

[0062] The steps to construct a system blocking sensitivity evaluation index include:

[0063] 2.1) Determine the blocking sensitivity evaluation index to be optimized b,t ,Right now:

[0064]

[0065] Where UB represents the upper bound and LB represents the lower bound. represents the upper bound of the slack variable. represents the lower bound of the slack variable.

[0066] 2.2) The congestion sensitivity evaluation index to be optimized based on the short-term unit power generation planning model b,t Optimize and obtain the blocking sensitivity evaluation index, namely:

[0067]

[0068] Where, O g It represents the blocking sensitivity evaluation index of the g-th unit.

[0069] 3) Establish a small-scale integer programming model.

[0070] The steps to build a small-scale integer programming model include:

[0071] 3.1) Establishing a small-scale optimization space Right now:

[0072]

[0073] Where, Represents the integer variable x g,t , integer variable y g,t , integer variable z g,t Collection. Collection i g,t Represents an integer variable, i = x, y, z.

[0074] Create a collection The method is as follows: calculate the blocking sensitivity evaluation index of each unit in the power system, and sort all units in descending order according to the blocking sensitivity evaluation index to obtain the unit set Assemble the crew The first N units in the middle write collection N is the preset number of units.

[0075] 3.2) Establish a small-scale integer programming model, namely:

[0076]

[0077] In the formula, the set is the upper bound of an integer variable.

[0078] 4) Use the branch and bound method to determine the unit combination method.

[0079] In the process of determining the unit combination mode by the branch and bound method, whenever the upper and lower bounds change, a small-scale integer programming model is solved to obtain the integer variable i g,t The feasible solution of in After solving, determine the feasible solution ub in Less than Is it true? If so, update the upper bound of the integer variable

[0080] Example 2:

[0081] The unit commitment method based on branch and bound internal induction includes the following steps:

[0082] 1) Analyze system blocking sensitivity

[0083] 1.1) Establishing the UC Model

[0084] UC is to formulate the most economical and effective short-term unit power generation plan while meeting the system's operating constraints, transmission constraints, and generator unit technical constraints. Therefore, the model is established as follows:

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094] The integer variable x g,t ,y g,t ,z g,t They represent the startup state, operation state and shutdown state of the g-th unit respectively, and are related to each other through logical constraints (4)-(5). g,t Indicates the real-time output of the g-th unit. According to the actual needs of the project, a slack variable s is added to the line flow limit. b,t , and is penalized by the penalty factor M in the objective function. The constant U g represents the startup cost of the g-th unit, D d,t Represents load data, PTDF g,b ,PTDF d,b represents the power transfer distribution factor, F b represents the transmission capacity of the bth line, P g Indicates the upper and lower limits of the output of the g-th unit, Indicates the minimum start and stop time of the g-th unit, Represent the ramp rate and start-stop rate of the g-th unit respectively. They represent time period, unit, line and load respectively.

[0095] 1.2) Constructing system blocking sensitivity evaluation indicators

[0096] According to the above UC model, the objective function consists of two parts: the unit cost and the system line flow over-limit cost. Due to the large penalty factor M, the objective function is more affected by the system congestion. Therefore, compared with the feasible solution obtained in the current solution process (i.e., the upper bound of the branch and bound algorithm), the optimal solution requires further releasing the system congestion and reducing the slack variable s. b,t .

[0097] On the other hand, since the lower bound of the branch-and-bound algorithm is obtained by relaxing the integer variable constraint (5), the objective function of the lower bound is smaller than the optimal solution. The distance between the upper and lower bounds measures the convergence direction of the branch-and-bound algorithm. The optimal solution will be obtained in the process of solving the problem from the upper bound to the lower bound. Therefore, a system blocking index based on the information of solving the upper and lower bounds is constructed. The blocking amount to be optimized is measured as follows:

[0098]

[0099] Where UB represents the upper bound and LB represents the lower bound.

[0100] According to the line flow constraint (3), the influence of the output of different units on the system's optimized blocking amount is determined by the power transfer distribution factor. Therefore, the system blocking sensitivity evaluation index is constructed as follows:

[0101]

[0102] 2) Construct a small-scale integer programming model

[0103] According to the system blocking sensitivity evaluation index, some key units have a greater impact on the system blocking line. Therefore, N key units with greater sensitivity are selected. Relax its running state variables to construct a small-scale optimization space:

[0104]

[0105] in represents the set of all integer variables,

[0106] Then, the induced constraints are added to the original UC model to construct a small-scale integer programming model:

[0107]

[0108] in The hot start based on the upper bound can ensure the feasibility of the small-scale model. In order to reduce the extra time consumed in solving the small-scale integer programming model, N must be kept small enough.

[0109] 3) Induced branch and bound pruning

[0110] By solving the above small-scale integer programming model, a new feasible solution is quickly obtained. in . in Compared with the upper bound, if they are equal, no processing is done. If ub in If the value is less than the upper bound, the upper bound of the branch and bound algorithm is updated. Since nodes outside the upper bound do not need to be explored during the branch and bound solution process, quickly updating the upper bound can induce the branch and bound pruning process, reduce the exploration of unnecessary nodes, and thus speed up the convergence time of the algorithm.

[0111] Since the upper and lower bound information changes dynamically during the branch and bound solution process, the algorithm for constructing and solving the small-scale integer programming model is embedded in the branch and bound algorithm. Whenever the upper and lower bound information changes, the method proposed in the present invention is called, thereby accelerating the UC solution.

[0112] The present invention avoids the optimality loss caused by modifying the model through the branch-and-bound internal induction method, and further improves the calculation speed of UC.

[0113] Example 3:

[0114] The verification test of the unit commitment method based on branch and bound internal induction is as follows:

[0115] This embodiment verifies the effectiveness of the present invention through an actual test case in a province of China. In this case, there are 320 units, 62 lines, and 96 time periods. The penalty factor in the UC model is set to 10 8 The number of critical units was set to 10, the integer programming convergence target was 1%, and the solution time limit for the small-scale integer programming model was 15 seconds. The comparison algorithms were: the commercial CPLEX solver with default settings and the commercial CPLEX solver using the proposed method. The solution time comparison results for each algorithm are shown in Table 1.

[0116] Simulation results show that the solution time using CPLEX ranges from 69.42 seconds to 3920.88 seconds, while the solution time improvement using the present invention ranges from 1.14 to 4.97 times, with an average improvement of 2.35 times. Taking 900 seconds (the time limit for day-ahead market clearing in UC calculations) as the standard, the test cases can be divided into 6 simple cases (1-6), 2 medium cases (7-8), and 2 difficult cases (9-10). In the simple cases, both CPLEX and the present invention can solve within the time limit, and the present invention has a shorter solution time; in the medium cases, CPLEX cannot solve within the time limit, while the present invention can solve within the time limit; in the difficult cases, both CPLEX and the present invention cannot solve within the time limit, but the present invention accelerates the solution process, which is more conducive to the subsequent adjustment link in the day-ahead market.

[0117] Table 1 Comparison of the improvement effects of the present invention in actual test examples in a certain province in China

[0118]

[0119] In summary, the present invention proposes a branch-and-bound internal induction method for accelerating unit commitment. This method utilizes system congestion information and upper and lower bounds to analyze the impact sensitivity of units. Key units with high sensitivity are selected to construct and solve a small-scale integer programming model. This method implements branch-and-bound internal induction based on existing commercial solvers, accelerating the solution of unit commitment while ensuring optimality. Case studies demonstrate that the present invention is more conducive to the needs of power system unit commitment calculations.

Claims

1. A unit commitment method based on branch-and-bound internal induction, characterized in that: The following steps are involved: 1) Establish a power system unit combination model; 2) Constructing system blocking sensitivity evaluation indicators; 3) Establish a small-scale integer programming model; 4) Use the branch and bound method to determine the unit combination method; The objective function of the power system unit combination model is as follows: In the formula, the integer variable x g,t Indicates the startup status of the g-th unit at time t; s b,t represents the slack variable; M represents the penalty factor; the constant U g represents the startup cost of the g-th unit; the continuous variable p g,t represents the real-time output of the g-th unit at time t; f(p g,t ) indicates the output p g,t The operating cost of the next g-th unit; set gather gather They represent time period, total number of units and total number of lines respectively; b represents line; The constraints of the power system unit combination model are as follows: In the formula, the integer variable y g,t 、z g,t They represent the running status and shutdown status of the g-th unit at time t respectively; y g,t-1 、z g,t-1 They represent the operating status and shutdown status of the g-th unit at time t-1 respectively; D d,t Represents the load data at time t; PTDF g,b PTDT d,b represents the power transfer distribution factor; F b represents the transmission capacity of the bth line; 、 P g Indicates the upper and lower limits of the output of the g-th unit; Indicates the minimum start and stop time of the g-th unit; Indicates the ramp rate of the g-th unit; represents the start and stop rate of the g-th unit; the set Indicates load; The steps to construct a system blocking sensitivity evaluation index include: 2.1) Determine the blocking sensitivity evaluation index to be optimized b,t ,Right now: Where UB represents the upper bound and LB represents the lower bound; represents the upper bound of the slack variable; represents the lower bound of the slack variable; 2.2) The congestion sensitivity evaluation index to be optimized based on the short-term unit power generation planning model b,t Optimize and obtain the blocking sensitivity evaluation index, namely: Where, O g represents the blocking sensitivity evaluation index of the g-th unit; The steps to build a small-scale integer programming model include: 3.1) Establishing a small-scale optimization space Right now: Where, Represents the integer variable x g,t , integer variable y g,t , integer variable z g,t collection of i g,t Represents an integer variable, i = x, y, z; 3.2) Establish a small-scale integer programming model, namely: In the formula, the set is the upper bound of an integer variable.

2. The unit commitment method based on branch and bound internal induction according to claim 1, characterized in that: Create a collection The method is as follows: calculate the blocking sensitivity evaluation index of each unit in the power system, and sort all units in descending order according to the blocking sensitivity evaluation index to obtain the unit set Assemble the crew The first N units in the middle write collection In the middle; N is the preset number of units.

3. The unit commitment method based on branch and bound internal induction according to claim 1, characterized in that: In the process of determining the unit combination mode by the branch and bound method, whenever the upper and lower bounds change, a small-scale integer programming model is solved to obtain the integer variable i g,t The feasible solution of in ; After solving, determine the feasible solution ub in Less than Is it true? If so, update the upper bound of the integer variable

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