Power system alternating current power flow solving method based on binary neighborhood dynamic expansion

Abstract

The invention discloses a power system alternating current power flow solving method based on binary neighborhood dynamic expansion. Based on a binary expansion theory, establishing a binary neighborhood dynamic expansion method for alternating current power flow; establishing an alternating current power flow power system optimization scheduling model based on binary neighborhood dynamic expansion; and solving the alternating current power flow power system optimization scheduling model based on binary neighborhood dynamic expansion to obtain an alternating current power flow power system optimization operation scheme. The method is used for solving the solving difficulty caused by the bicontinuous variable product, and the solvable performance of the problem can be effectively improved; a mathematical model of alternating current power flow is improved, the convergence speed is high, and the average error of a calculation result is far lower than that of other traditional algorithms; the model provided by the invention does not need iterative calculation to generate a result, and can be suitable for dispatching calculation of a larger-scale power system. And the extensibility is excellent.

Description

Technical Field

[0001] The present invention relates to a method for solving AC power flow in a power system, and more particularly to a method for solving AC power flow in a power system based on dynamic expansion of binary neighborhoods. Background Art

[0002] The safe and economical operation of the power system is one of the guarantees for my country's rapid development. The optimization goal is usually to minimize the system operation cost while meeting the power system's power flow constraints and safety constraints. With the opening of the power market and the high proportion of renewable energy access, the operation of the power system has become increasingly complex, which requires the power grid to calculate the power flow more quickly and accurately.

[0003] At present, the power grid uses a DC power flow model, which can quickly solve the power flow by directly constraining the amplitude of the node voltage and ignoring the reactive power in the branch. However, the power generation plan formulated often deviates greatly from the actual situation. Compared with the former, the AC power flow model considers the changes in node voltage and the distribution of active and reactive power in the branch. The power flow results calculated by it are more realistic and more reliable. However, from a mathematical point of view, AC power flow optimization is described as a non-convex nonlinear mathematical programming problem, which is extremely difficult to solve. Therefore, it is of great significance to study more efficient solutions for power system optimization and dispatching, which needs further research and improvement. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a method for solving AC power flow in an electric power system based on dynamic expansion of a binary neighborhood, which can effectively improve the solvability of the problem in order to overcome the deficiencies of the prior art.

[0005] The technical solution adopted by the present invention is: a method for solving AC power flow of power system based on dynamic expansion of binary neighborhood, comprising the following steps:

[0006] 1) Based on binary expansion theory, a binary neighborhood dynamic expansion method is established for AC power flow, including;

[0007] (1.1) Establish a binary neighborhood dynamic expansion method for the product of linear continuous variables; including;

[0008] (1.1.a) The product of linear continuous variables is expressed as:

[0009]

[0010] Where ζ is the product of any two linear continuous variables, and ζ = x·y; x and y are both linear continuous variables, and the variable boundary conditions are stable, and the value range is x∈[x l ,x u ],y∈[yl ,y u ]; the superscripts u and l represent the constant upper and lower bounds of a linear continuous variable; z n is the nth variable in the sequence of 0-1 integer variables, with z n =0or1; represents the unit interval after the variable y is discretized, is the distance between two discrete points; K is a scale parameter of 0-1 integer variable, y is 2 K variable z n Complete discretization;

[0011] (1.1.b) Dynamically expand the binary neighborhood of the newly added extended 0-1 integer variable;

[0012] Modify the linearization constraints and expand them into:

[0013]

[0014] Among them, ξ=χ·γ, χ and γ are both linear continuous variables, the variable boundary conditions are stable, and χ∈[χ l ,x u ],γ∈[γ l ,γ u ],ε m is the mth variable in the continuous variable sequence whose value is in [0,1];

[0015] (1.2) Apply the binary neighborhood dynamic expansion method to the product of linear continuous variables in the AC power flow model, including:

[0016] The linear continuous variable product v in the linear continuous variable product formula in the AC power flow model i v j Use ψ ij It is expressed as follows:

[0017]

[0018] Among them, P ij , Q ij is the active and reactive power on branch i→j, b ij , g ij are the susceptance and conductance on branch i→j respectively; i and j are nodes in the power grid, v i 、v j is the voltage amplitude of nodes i and j, θ i ,θ j is the voltage phase angle of nodes i and j; N is a point set, including all power generation and load nodes; E is a line set, including all interconnected edges of nodes in the system, i.e., transmission lines; ψ ijis the voltage amplitude v of the nodes on both sides of branch i→j i 、v j The product of ψ ij =v i ·v j ;

[0019]

[0020] Among them, v i 、v j There are upper and lower bounds, v i 、v j ∈[v l ,v u ]; w jk After the product is expanded, the kth intermediate variable after the jth node is discretized has w jk =v i ·ε jk , ε jk is the kth continuous variable between [0, 1] after the jth node is discretized; Represents the variable v j The unit interval of is:

[0021]

[0022] 2) Establish an AC power flow system optimization dispatch model based on binary neighborhood dynamic expansion, including:

[0023] (2.1) Taking economy as the goal, the objective function of the AC power flow system optimization dispatching model based on binary neighborhood dynamic expansion is established:

[0024] minfc=Cg+Clost

[0025] Among them, fc is the operating cost of the AC power flow system, Cg is the power generation cost of the thermal power unit, and Clost is the line loss cost of the entire network;

[0026] (2.2) Establishing constraint conditions for an AC power flow power system optimization dispatch model based on binary neighborhood dynamic expansion, wherein the constraint conditions include AC power flow constraints embedded in binary neighborhood dynamic expansion, unit constraints, and safety constraints;

[0027] 3) Solving the AC power flow system optimization dispatching model based on binary neighborhood dynamic expansion to obtain the AC power flow system optimization operation plan.

[0028] The method for solving power system AC power flow based on binary neighborhood dynamic expansion of the present invention has the following advantages:

[0029] 1. The present invention proposes a binary neighborhood dynamic expansion algorithm to solve the difficulties caused by the product of two continuous variables, which can effectively improve the solvability of the problem;

[0030] 2. The present invention improves the mathematical model of AC power flow, has a fast convergence speed, and compared with the Newton-Ray method for calculating the nonlinear AC power flow model, the average error of the calculation result is much lower than other traditional algorithms;

[0031] 3. The model proposed in this invention does not require iterative calculation to generate results, and can be applied to larger-scale power system dispatch calculations. It also has excellent scalability, and its application in various special scenarios, such as multi-energy complementarity or section limits, can be further explored in the future, which has certain theoretical and practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a schematic diagram of the binary neighborhood dynamic expansion method described in the present invention;

[0033] Figure 2 This is a topological diagram of the IEEE39 node standard calculation example of the present invention;

[0034] Figure 3 It is a schematic diagram of the deviation of the voltage amplitude of each node after the power flow calculation of the example of the present invention. DETAILED DESCRIPTION

[0035] The following is a detailed description of the method for solving AC power flow in a power system based on dynamic expansion of binary neighborhoods of the present invention in conjunction with the embodiments and drawings.

[0036] A method for solving AC power flow in an electric power system based on dynamic expansion of a binary neighborhood according to the present invention comprises the following steps:

[0037] 1) Based on the binary expansion theory, a binary neighborhood dynamic expansion method is established for AC power flow, such as Figure 1 Shown, including

[0038] (1.1) Establish a binary neighborhood dynamic expansion method for the product of linear continuous variables; including;

[0039] (a) Express the product of linear continuous variables as:

[0040]

[0041] Where ζ is the product of any two linear continuous variables, and ζ = x·y; x and y are both linear continuous variables, and the variable boundary conditions are stable, and the value range is x∈[x l ,x u ],y∈[y l ,y u]; the superscripts u and l represent the constant upper and lower bounds of a linear continuous variable; z n is the nth variable in the sequence of 0-1 integer variables, with z n =0or1; represents the unit interval after the variable y is discretized, is the distance between two discrete points; K is a scale parameter of 0-1 integer variable, y is 2 K variable z n Complete discretization;

[0042] (b) Dynamically expand the binary neighborhood of the newly added extended 0-1 integer variable;

[0043] Modify the linearization constraints and expand them into:

[0044]

[0045] Among them, ξ=χ·γ, χ and γ are both linear continuous variables, the variable boundary conditions are stable, and χ∈[χ l ,χu],γ∈[γ l ,γu],ε m is the mth variable in the continuous variable sequence whose value is in [0,1];

[0046] (1.2) Apply the binary neighborhood dynamic expansion method to the product of linear continuous variables in the AC power flow model, including:

[0047] The linear continuous variable product v in the linear continuous variable product formula in the AC power flow model i v j Use ψ ij It is expressed as follows:

[0048]

[0049] Among them, P ij , Q ij is the active and reactive power on branch i→j, b ij , g ij are the susceptance and conductance on branch i→j respectively; i and j are nodes in the power grid, v i 、v j is the voltage amplitude of nodes i and j, θ i ,θ j is the voltage phase angle of nodes i and j; N is a point set, including all power generation and load nodes; E is a line set, including all interconnected edges of nodes in the system, i.e., transmission lines; ψ ij is the voltage amplitude v of the nodes on both sides of branch i→j i 、v j The product of ψij =v i ·v j ;

[0050]

[0051] Among them, v i 、v j There are upper and lower bounds, v i 、v j ∈[v l ,v u ]; w jk After the product is expanded, the kth intermediate variable after the jth node is discretized has w jk =v i ·ε jk , ε jk is the kth continuous variable between [0, 1] after node j is discretized; Represents the variable v j The unit interval is

[0052]

[0053] The variable ψ ij Make the following constraints:

[0054]

[0055]

[0056] Among them, w jk After the product is expanded, the kth intermediate variable after the jth node is discretized has w jk =v i ·ε jk , ε jk is the kth continuous variable between [0, 1] after the jth node is discretized; By v j Modify the value range, that is To simplify the constraint equation, v j Transformed into a linear continuous variable starting from 0 to avoid adding unnecessary constants in the constraints.

[0057] The variable ψ ij And the corresponding constraint proof derivation process is as follows:

[0058] Let ω = βα p , ω is an intermediate variable with no practical significance, β is an arbitrary continuous variable, α p is the pth variable in the sequence of continuous variables whose values ​​are in [0,1]. The superscripts u and l represent the upper and lower bounds of the constant value of the variable, respectively. To prove that the deduction is valid, we need to discuss each case separately.

[0059] Case 1: If 0≤α p <1, it is easy to get ω-M·β≤0, M is a large constant. In order to make the envelope as tight as possible, M=ω u =β u , then ω≤β u α p , and ω≤β;

[0060] Case 2: If α p =1, then ω = β, split the equal sign; for case 2a: ω ≥ β, that is, β-ω-M (1-α p )<0, still take M=β u , we can get β-ω-β u (1-α p )<0; For case 2b: ω≤β, β-ω-M(1-α p )≥0; still take M=β u , we can get β-ω-β u (1-α p )≥0; if α p = 1, then ω ≥ β and ω ≤ β, which can ensure the constraint, but due to β-ω-M(1-α p The ω≤β constraint derived from )≥0 repeats the conclusion of Case 1 and is no longer reflected in the constraint group.

[0061] 2) Establish an AC power flow system optimization dispatch model based on binary neighborhood dynamic expansion, including:

[0062] (2.1) Taking economy as the goal, the objective function of the AC power flow system optimization dispatching model based on binary neighborhood dynamic expansion is established:

[0063] minfc=Cg+Clost

[0064] Among them, fc is the operating cost of the AC power flow system, Cg is the power generation cost of the thermal power unit, and Clost is the line loss cost of the entire network;

[0065] The power generation cost of the thermal power unit described in (a) is:

[0066]

[0067] Among them, C g is the power generation cost of thermal power units in the grid; P g is the active output of the g-th device; G is a point set, including all the generator sets in the system; a, b, c are the economic parameters of coal consumption of thermal power units. In the project, piecewise linearization is used to transform this part from mixed integer programming to mixed integer linear programming to improve the solution efficiency;

[0068] The line loss cost of the entire network described in (b) is:

[0069]

[0070] Among them, C lost is the heat loss cost of the whole network; l ij is the square value of the current on branch i→j; r ij is the resistance value of branch i→j, and E is the line set, which includes all the interconnected edges of each node in the system, that is, the transmission lines.

[0071] (2.2) Establishing constraint conditions for the AC power flow power system optimization dispatch model based on binary neighborhood dynamic expansion, wherein the constraint conditions include AC power flow constraints, unit constraints, and safety constraints embedded in the binary neighborhood dynamic expansion; wherein,

[0072] The AC power flow constraint embedded in the binary neighborhood dynamic expansion described in (a) is expressed as follows:

[0073]

[0074]

[0075] Among them, P ij , Q ij is the active and reactive power on branch i→j, b ij , g ij are the susceptance and conductance of branch i→j respectively; i and j are nodes in the power grid; v i 、v j is the voltage amplitude of nodes i and j; v i 、v j There are upper and lower bounds, v i 、v j ∈[v l ,v u ];ψ ij is the voltage amplitude v of the nodes on both sides of branch i→j i 、v j The product of ψ ij =v i ·v j θ i ,θ j is the voltage phase angle of nodes i and j; N is a point set, including all power generation and load nodes; E is a line set, including all interconnected edges of nodes in the system, that is, transmission lines; superscripts u and l represent the upper and lower bounds of the constant of linear continuous variables respectively; w jk After the product is expanded, the kth intermediate variable after the jth node is discretized has w jk =vi ·ε jk , ε jk is the kth continuous variable between [0, 1] after the jth node is discretized; Represents the variable v j The unit interval is Is

[0076] v j Modify the value range,

[0077] (b) The crew constraints mentioned in the preceding paragraph include:

[0078] The upper and lower bounds of the unit output are as follows:

[0079] P g.min ≤P g ≤P g.max ,

[0080] Q g.min ≤Q g ≤Q g.max ,g∈G

[0081] Among them, P g , Q g are the active and reactive outputs of the g-th unit respectively; P g.max , P g.min are the upper and lower bounds of the active power output of the g-th unit respectively; Q g.max , Q g.min are the upper and lower bounds of reactive power output of the g-th unit, respectively, and G is a point set including all generators in the system;

[0082] The unit standby constraints are as follows:

[0083] ∑ g∈G (P g.max -P g )≥ρ∑ i∈N P d

[0084] Among them, ρ is the system hot standby parameter; P d is the load of the ith node;

[0085] (c) The safety constraints described herein include:

[0086] The node voltage constraints are as follows:

[0087] v l ≤v i ≤v u

[0088] The upper and lower bounds of the phase angle are as follows:

[0089]

[0090] The thermal constraints of the branch power flow are as follows:

[0091]

[0092] The upper and lower bounds of branch current are as follows:

[0093] l ij.min ≤l ij ≤l ij.max

[0094] in, is the maximum allowable phase difference between the node voltages on both sides of branch i→j; t ij is the thermal limit of branch i→j; l ij is the square value of the current on branch i→j; l ij.min , l ij.max are the upper and lower bounds of the square value of the current on branch i→j.

[0095] 3) Solving the AC power flow system optimization dispatching model based on binary neighborhood dynamic expansion to obtain the AC power flow system optimization operation plan.

[0096] The following are specific examples

[0097] Examples:

[0098] Taking the IEEE39 node standard example as the simulation scenario, the topological structure diagram is as follows: Figure 2 As shown. A comparative analysis is conducted through simulation with other methods. The details of the method are as follows:

[0099] Method 1: DC power flow calculation method (DCPF) of power system;

[0100] Method 2: AC power flow calculation method based on quadratic convex relaxation (QC-ACPF);

[0101] Method 3: Power system AC power flow solution method based on binary neighborhood dynamic expansion (BE-ACPF).

[0102] To illustrate the accuracy of the proposed method, the power flow calculation results obtained by PYPOWER are taken as the assumed accurate reference value, denoted as PY-ACPF, and compared with this value after the corresponding calculation results are obtained by other algorithms. The accuracy of the relevant power flow quantity is described as the relative error with PY-ACPF, that is, the smaller the deviation with PY-ACPF, the more accurate it is. The correctness of the proposed power flow model is illustrated by comparing several existing power flow algorithms, and the average deviation of the power flow calculation results is expressed as It indicates that x is the corresponding variable.

[0103] Table 1 shows the average deviation of each variable after the flow calculation

[0104] Table 1

[0105]

[0106]

[0107] in, is the average deviation of the voltage amplitude and phase angle of nodes in the network; is the average deviation of active and reactive power of branch power flow in the network. Analysis of the results in Table 1 shows that the DCPF algorithm constrains the voltage value and approximates the reactive power flow, resulting in inaccurate calculation results. The average deviation between the active power of the branch and the precise value calculated by PY-ACPF even reaches 10.62%. However, due to the defect of continuous use of M-envelope by the QC-ACPF algorithm, the calculated results also have partial deviations. It can be seen from the table that the average deviations of the node parameters of the QC-ACPF algorithm are 0.23% and 0.1379deg respectively, and the average deviations of the branch power flow are relatively small, which are 0.81% and 3.12% respectively.

[0108] The BE-ACPF algorithm is an improved and optimized algorithm based on the QC-ACPF algorithm. It avoids the continuous use of M-envelope for approximation within the algorithm, but uses a more accurate binary neighborhood dynamic expansion to linearize the node parameters. The final simulation results show that the calculation results of the power system AC power flow solution method based on the binary neighborhood dynamic expansion of the present invention are closest to the results calculated by the nonlinear algorithm. The voltage amplitude per unit value of each node is constrained between 0.94 and 1.06, meeting the 6% voltage fluctuation limit of the IEEE39 example. The average node voltage deviation is about 1 / 10 of the QC-ACPF algorithm, and the average branch active power deviation and reactive power deviation are 0.59% and 0.56% respectively. It can be seen that the power flow results calculated by the BE-ACPF algorithm are more accurate than those of the QC-ACPF algorithm.

[0109] Figure 3 1 is a schematic diagram of the deviation of the voltage amplitude of each node after the power flow calculation of the embodiment of the present invention;

[0110] from Figure 3It can be seen that the voltage results of each node are consistent with the AC power flow results calculated by the nonlinear method. A small deviation occurs at node 34, where the voltage amplitude deviates from the accurate result by 0.047%. This deviation mainly comes from the algorithm itself. When the power flow passing through the branch is large, the difference between the lowest limit value obtained by the algorithm using the M-envelope and the actual value will widen. Although this deviation cannot be avoided, since only one M-envelope is used for approximation, the deviation is still within an acceptable range.

Claims

1. A method for solving AC power flow in power system based on dynamic expansion of binary neighborhood, characterized in that: The steps include: 1) Based on the binary expansion theory, a binary neighborhood dynamic expansion method is established for AC power flow; include; (1.1) Establish a binary neighborhood dynamic expansion method for the product of linear continuous variables; include; (1.1.a) The product of linear continuous variables is expressed as: Where ζ is the product of any two linear continuous variables, and ζ = x·y; x and y are both linear continuous variables, and the variable boundary conditions are stable, and the value range is x∈[x l ,x u ],y∈[y l ,y u ]; the superscripts u and l represent the constant upper and lower bounds of a linear continuous variable; z n is the nth variable in the sequence of 0-1 integer variables, with z n =0or1; represents the unit interval after the variable y is discretized, is the distance between two discrete points; K is a scale parameter of 0-1 integer variable, y is 2 K variable z n Complete discretization; (1.1.b) Dynamically expand the binary neighborhood of the newly added extended 0-1 integer variable; Modify the linearization constraints and expand them into: Among them, ξ=χ·γ, χ and γ are both linear continuous variables, the variable boundary conditions are stable, and χ∈[χ l ,x u ],γ∈[γ l ,γ u ],ε m is the mth variable in the continuous variable sequence whose value is in [0,1]; (1.2) Apply the binary neighborhood dynamic expansion method to the product of linear continuous variables in the AC power flow model, including: The linear continuous variable product v in the linear continuous variable product formula in the AC power flow model i v j Use ψ ij It is expressed as follows: Among them, P ij , Q ij is the active and reactive power on branch i→j, b ij , g ij are the susceptance and conductance on branch i→j respectively; i and j are nodes in the power grid, v i 、v j is the voltage amplitude of nodes i and j, θ i ,θ j is the voltage phase angle of nodes i and j; N is a point set, including all power generation and load nodes; E is a line set, including all interconnected edges of nodes in the system, i.e., transmission lines; ψ ij is the voltage amplitude v of the nodes on both sides of branch i→j i 、v j The product of ψ ij =v i ·v j ; Among them, v i 、v j There are upper and lower bounds, v i 、v j ∈[v l ,v u ]; w jk After the product is expanded, the kth intermediate variable after the jth node is discretized has w jk =v i ·ε jk , ε jk is the kth continuous variable between [0, 1] after the jth node is discretized; Represents the variable v j The unit interval of is: 2) Establish an AC power flow system optimization dispatch model based on binary neighborhood dynamic expansion, including: (2.1) Taking economy as the goal, the objective function of the AC power flow system optimization dispatching model based on binary neighborhood dynamic expansion is established: minfc=Cg+Clost Among them, fc is the operating cost of the AC power flow system, Cg is the power generation cost of the thermal power unit, and Clost is the line loss cost of the entire network; (2.2) Establishing constraint conditions for an AC power flow power system optimization dispatch model based on binary neighborhood dynamic expansion, wherein the constraint conditions include AC power flow constraints, unit constraints, and safety constraints embedded in the binary neighborhood dynamic expansion; 3) Solving the AC power flow system optimization dispatching model based on binary neighborhood dynamic expansion to obtain the AC power flow system optimization operation plan.

2. The method for solving AC power flow in power system based on dynamic expansion of binary neighborhood according to claim 1 is characterized in that: Step 1) In step (1.2), the variable ψ ij Make the following constraints: w jk ≤(v u -v l )·ε jk Among them, w jk After the product is expanded, the kth intermediate variable after the jth node is discretized has w jk =v i ·ε jk , ε jk is the kth continuous variable between [0, 1] after the jth node is discretized; By v j Modify the value range, that is To simplify the constraint equation, v j Transformed into a linear continuous variable starting from 0 to avoid adding unnecessary constants in the constraints.

3. The method for solving AC power flow in power system based on dynamic expansion of binary neighborhood according to claim 2 is characterized in that: The variable ψ ij And the corresponding constraint proof derivation process is as follows: Let ω = βα p , ω is an intermediate variable with no practical significance, β is an arbitrary continuous variable, α p is the pth variable in the sequence of continuous variables whose values ​​are in [0,1]. The superscripts u and l represent the upper and lower bounds of the constant value of the variable, respectively. To prove that the deduction is valid, we need to discuss each case separately. Case 1: If 0≤α p <1, it is easy to get ω-M·β≤0, M is a large constant. In order to make the envelope as tight as possible, M=ω u =β u , then ω≤β u α p , and ω≤β; Case 2: If α p =1, then ω = β, split the equal sign; for case 2a: ω ≥ β, that is, β-ω-M (1-α p )<0, still take M=β u , we can get β-ω-β u (1-α p )<0; For case 2b: ω≤β, β-ω-M(1-α p )≥0; still take M=β u , we can get β-ω-β u (1-α p )≥0; if α p = 1, then ω ≥ β and ω ≤ β, which can ensure the constraint, but due to β-ω-M(1-α p The ω≤β constraint derived from )≥0 repeats the conclusion of Case 1 and is no longer reflected in the constraint group.

4. The method for solving AC power flow in power system based on dynamic expansion of binary neighborhood according to claim 1 is characterized in that: Step 2) In step (2.1): The power generation cost of the thermal power unit is: Among them, C g is the power generation cost of thermal power units in the grid; P g is the active output of the g-th device; G is a point set, including all the generator sets in the system; a, b, c are the economic parameters of coal consumption of thermal power units. In the project, piecewise linearization is used to transform this part from mixed integer programming to mixed integer linear programming to improve the solution efficiency; The line loss cost of the entire network is: Among them, C lost is the heat loss cost of the whole network; l ij is the square value of the current on branch i→j; r ij is the resistance value of branch i→j, and E is the line set, which includes all the interconnected edges of each node in the system, that is, the transmission lines.

5. The method for solving AC power flow in power system based on dynamic expansion of binary neighborhood according to claim 1, characterized in that: Step 2) In step (2.2): The AC power flow constraint embedded in the binary neighborhood dynamic expansion described in (a) is expressed as follows: Among them, P ij , Q ij is the active and reactive power on branch i→j, b ij , g ij are the susceptance and conductance of branch i→j respectively; i and j are nodes in the power grid; v i 、v j is the voltage amplitude of nodes i and j; v i 、v j There are upper and lower bounds, v i 、v j ∈[v l ,v u ];ψ ij is the voltage amplitude v of the nodes on both sides of branch i→j i 、v j The product of ψ ij =v i ·v j θ i ,θ j is the voltage phase angle of nodes i and j; N is a point set, including all power generation and load nodes; E is a line set, including all interconnected edges of nodes in the system, that is, transmission lines; superscripts u and l represent the upper and lower bounds of the constant of linear continuous variables respectively; w jk After the product is expanded, the kth intermediate variable after the jth node is discretized has w jk =v i ·ε jk , ε jk is the kth continuous variable between [0, 1] after the jth node is discretized; Represents the variable v j The unit interval is By v j Modify the value range, (b) The crew constraints mentioned in the preceding paragraph include: The upper and lower bounds of the unit output are as follows: P g.min ≤P g ≤P g.max , Q g.min ≤Q g ≤Q g.max ,g∈G Among them, P g , Q g are the active and reactive outputs of the g-th unit respectively; P g.max , P g.min are the upper and lower bounds of the active power output of the g-th unit respectively; Q g.max , Q g.min are the upper and lower bounds of reactive power output of the g-th unit, respectively, and G is a point set including all generators in the system; The unit standby constraints are as follows: ∑ g∈G (P g.max -P g )≥ρ∑ i∈N P d Among them, ρ is the system hot standby parameter; P d is the load of the ith node; (c) The safety constraints described herein include: The node voltage constraints are as follows: in l ≤in i ≤in u The upper and lower bounds of the phase angle are as follows: The thermal constraints of the branch power flow are as follows: The upper and lower bounds of branch current are as follows: l ij.min ≤l ij ≤l ij.max in, is the maximum allowable phase difference between the node voltages on both sides of branch i→j; t ij is the thermal limit of branch i→j; l ij is the square value of the current on branch i→j; l ij.min , l ij.max are the upper and lower bounds of the square value of the current on branch i→j.

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