Affine Optimal Energy Flow Calculation Method for Electrical Interconnection Systems Based on Compact Convex Envelope

Abstract

This invention relates to an affine optimal energy flow calculation method for an electrical interconnection system based on a compact convex envoy, comprising the following steps: Step S1: Constructing a deterministic optimal energy flow model for the electrical-gas interconnection system; Step S2: Constructing a mixed-integer linear programming model from the deterministic optimal energy flow model based on the convex envoy; Step S3: Characterizing uncertain wind power in an affine form based on the mixed-integer linear programming model, constructing an affine optimal energy flow model for the electrical-gas interconnection system; Step S4: Transforming the affine optimal energy flow model for the electrical-gas interconnection system into a deterministic multi-objective optimization problem based on affine arithmetic theory; Step S5: Solving the multi-objective optimization problem using the compact convex envoy method to obtain the affine optimal energy flow. This invention ensures the feasibility of the optimal solution and has high computational efficiency.

Description

Technical Field

[0001] This invention relates to the field of electrical interconnection system control, and more specifically to an affine optimal energy flow calculation method for electrical interconnection systems based on a compact convex hull. Background Technology

[0002] Under the dual pressures of energy demand and environmental pollution, the contradiction between traditional energy utilization patterns and sustainable development is becoming increasingly prominent. The introduction of integrated energy systems is an effective way to solve this problem. Integrated electricity-gas systems (IEGS) are an important component of integrated energy systems. In recent years, the rapid development of gas turbines and power-to-gas technology has led to close coupling between electricity and natural gas systems, while also increasing the difficulty of coordinated operation of IEGS. The optimal energy flow problem of IEGS, as one of the key issues in the optimized operation of IEGS, has received widespread attention. However, optimal energy flow is not only a nonlinear programming problem but also a nonconvex programming problem, making it extremely difficult to solve. Therefore, it is necessary to study an efficient and accurate method for calculating optimal energy flow. Furthermore, with the growth of wind power installed capacity, its volatility and intermittency have a significant impact on IEGS. Therefore, it is necessary to study the impact of wind power uncertainty and research methods for optimal energy flow under uncertainty. Summary of the Invention

[0003] In view of this, the purpose of this invention is to provide an affine optimal energy flow calculation method for electrical interconnection systems based on a compact convex hull, in order to solve the above-mentioned problems.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A method for calculating affine optimal energy flow in an electrical interconnection system based on a compact convex hull includes the following steps:

[0006] Step S1: Construct a deterministic optimal energy flow model for the electro-pneumatic interconnected system;

[0007] Step S2: Based on the convex envelope, the deterministic optimal energy flow model is convexly reconstructed into a mixed-integer linear programming model;

[0008] Step S3: Based on the mixed-integer linear programming model, the uncertain wind power is represented as an affine form.

[0009] Construct an affine optimal energy flow model for an electro-pneumatic interconnected system;

[0010] Step S4: Based on affine arithmetic theory, the affine optimal energy flow model of the electro-pneumatic interconnection system is transformed into a deterministic multi-objective optimization problem;

[0011] Step S5: Solve the multi-objective optimization problem based on the compact convex hull method to obtain the affine optimal energy flux.

[0012] Furthermore, the objective function of the deterministic optimal energy flow model of the electro-pneumatic interconnection system is expressed as follows:

[0013]

[0014] Where: Ω G Ω W and Ω P2G This refers to a collection of coal-fired power units, gas sources, and electro-gas conversion equipment; α i and β i c is the cost coefficient for coal-fired unit i; w,m and c P2G,i P represents the cost coefficient of the gas source m and the electro-gas conversion equipment i; G,i and P P2G,i F represents the active power output of coal-fired unit i and power-to-gas conversion equipment i, respectively; W,m This indicates the gas production rate of gas source m.

[0015] Furthermore, the constraints of the deterministic optimal energy flow model of the electro-pneumatic interconnection system include:

[0016] ① Power system constraints

[0017] Power system constraints include DC power flow equations (2), nodal power balance equations (3), coal-fired unit output constraints (4), gas-fired unit output constraints (5), power-to-gas conversion equipment output constraints (6), wind power output constraints (7), and line transmission power constraints (8), which are as follows:

[0018] P ij =B ij (θ i -θ j (2)

[0019]

[0020] 0≤P WA,i ≤P W,i (7)

[0021]

[0022] Where: Ω i Let P be the set of tail nodes with node i as the first node; ij B ij and θ i Let P be the transmission power, mutual susceptance, and phase angle of line ij, respectively; G,i P GT,i P P2G,i and PL,i These represent the output of coal-fired unit i, gas-fired unit i, and power-to-gas conversion equipment i, respectively, and the electrical load of node i; P WA,i and P W,i These represent the actual and predicted wind power output of wind farm i, respectively. These are the upper and lower limits of output for coal-fired unit i and gas-fired unit i, respectively; The maximum conversion power of the electro-gas conversion device i; This represents the upper limit of the allowed transmission power for line ij;

[0023] ② Natural gas system constraints

[0024] The constraints of the natural gas system include the natural gas flow equation (9), node flow balance constraints (10), gas source flow constraints (11), node pressure constraints (12), pipeline flow constraints (13), compressor station flow constraints (14), and compressor station pressurization constraints (15), which are as follows:

[0025]

[0026] Where: Ω m Let F be the set of first nodes whose tail node is m; mn C mn and p m Let F be the flow rate of pipe mn, the pipe constant, and the square air pressure at node m; W,m F P2G,m F GT,m and F L,i These represent the gas production at gas source m, the gas production at the power-to-gas conversion equipment at node m, the gas consumption at node m by the gas turbine unit, and the natural gas load at node m, respectively; F C,m p m,s and p m,d These are the flow rate, inlet pressure, and outlet pressure of compressor station m, respectively. These are the upper and lower limits of the flow output of the gas source m, respectively; These are the upper and lower pressure limits for node m, respectively; Let mn be the upper limit of the flow rate in pipe mn; This represents the upper limit of the flow rate at compressor station m. These are the upper and lower limits of the compression ratio for compressor station m, respectively.

[0027] ③ Coupling device constraints

[0028] The power system and the natural gas system are coupled through power-to-gas equipment and gas turbine units, and their coupling constraints are as follows:

[0029]

[0030] In the formula: η GT,i η P2 G,i The efficiencies of the gas turbine unit and the electro-gas conversion equipment, respectively; H g This refers to the calorific value of natural gas.

[0031] Furthermore, step S2 specifically includes:

[0032] The nonconvexity of the natural gas flow equation (9) comes from the absolute value and the quadratic term. Introducing 0-1 variables transforms (9) into (18)-(20) equivalently:

[0033]

[0034] In the formula, ξ mn These are 0-1 variables, representing the direction of natural gas flow in the pipeline;

[0035] Introducing new auxiliary variables and Equation (20) is transformed into (21)-(25):

[0036]

[0037] The quadratic term in equation (21) can be further approximated by the McCormick convex hull, and then by a set of linear inequalities as shown in (26)-(28):

[0038]

[0039] Based on the above convexity treatment, the deterministic optimal energy flow model is transformed into a mixed-integer linear programming model, whose compact form is expressed as follows:

[0040]

[0041] In the formula: x and y represent vectors of continuous variables and 0-1 variables, respectively; A and b represent coefficient matrices with respect to equality constraints; c and d represent coefficient matrices with respect to the objective function; G1, G2, and h represent coefficient matrices with respect to inequality constraints.

[0042] Furthermore, step S3 specifically includes:

[0043] The affine form of an uncertain wind power output is as follows:

[0044]

[0045] In the formula: Let P be the affine form corresponding to the uncertain wind power of wind farm i; W,i,0 ε w,i and P W,i These are the predicted center value of the power of wind farm i, the noise element, and the corresponding noise element coefficient, respectively.

[0046] Based on (29) and (30), the affine optimal energy flow model is expressed as follows:

[0047]

[0048] In the formula: A continuous variable vector in affine form; and It is the coefficient matrix in affine form.

[0049] Furthermore, step S4 specifically includes:

[0050] The equality constraints, inequality constraints, and affine form of the objective function in the affine optimal energy flow model (31) are defined as follows:

[0051] 1) Definition of equality constraints

[0052] Affine form equality constraints are defined as having equal central values ​​and noise element coefficients on both sides of the equation and having the same noise element.

[0053]

[0054] In the formula: x0 and x s They are respectively The center value and the noise element coefficient corresponding to the s-th noise element; b0 and b s They are respectively The center value and noise element coefficient; n is the number of noise elements;

[0055] 2) Definition of Inequality Constraints

[0056] Following interval theory, affine inequality constraints can be defined as follows:

[0057]

[0058] In the formula: h0 and h s They are respectively The center value and noise element coefficient;

[0059] 3) Definition of the objective function

[0060] The objective function for the affine optimal energy flux can be expressed as follows:

[0061]

[0062] (34) It can be equivalently transformed into a deterministic multi-objective optimization problem:

[0063]

[0064] Based on the above definition, and by introducing optimization weights, the affine optimal energy flow problem (31) of the electro-pneumatic interconnected system can be expressed as the following deterministic optimization problem:

[0065]

[0066] In the formula: w represents the multi-objective optimization weight.

[0067] Furthermore, the specific solution steps for step S5 are as follows:

[0068] 1) Initialization: Set the convergence threshold δ and the maximum number of iterations r. max and decreasing sequence {a r Set the iteration count r = 1;

[0069] 2) Solve the affine optimal energy flow problem (36) to obtain And based on equation (37) Transform into interval form

[0070]

[0071] 3) Update the upper and lower boundaries of the convex hull:

[0072]

[0073] 4) Calculate the relaxation gap and its upper and lower bounds according to equations (40)-(41). If G mn >-δ and Output the affine optimal energy flow calculation results; if r ≥ r max If the iteration fails, exit; otherwise, proceed to step 2); update r = r + 1

[0074]

[0075] Compared with the prior art, the present invention has the following advantages:

[0076] This invention utilizes convex hulls to reconstruct a deterministic optimal energy flow model into a mixed-integer linear programming problem, overcoming the conservatism problem caused by nonlinear affine operations. Furthermore, the constructed affine optimal energy flow model can track the correlations between uncertain variables, avoiding the interval expansion problem of interval arithmetic, and reducing conservatism while ensuring completeness. Simultaneously, this method can quantify the impact of uncertain factors on IEGS, revealing the propagation trajectory of uncertain factors. Moreover, this method guarantees the feasibility of the optimal solution and has high computational efficiency. Attached Figure Description

[0077] Figure 1 This is one embodiment of the present invention. A schematic diagram of the convex hull;

[0078] Figure 2 This is a flowchart of the method of the present invention. Detailed Implementation

[0079] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0080] Please refer to Figure 2 This invention provides an affine optimal energy flow calculation method for an electrical interconnection system based on a compact convex hull, comprising the following steps:

[0081] Step S1: Construct a deterministic optimal energy flow model for the electro-pneumatic interconnected system;

[0082] Step S2: Based on the convex envelope, the deterministic optimal energy flow model is convexly reconstructed into a mixed-integer linear programming model;

[0083] Step S3: Based on the mixed integer linear programming model, the uncertain wind power is represented as an affine form, and an affine optimal energy flow model of the electric-gas interconnection system is constructed.

[0084] Step S4: Based on affine arithmetic theory, the affine optimal energy flow model of the electro-pneumatic interconnection system is transformed into a deterministic multi-objective optimization problem;

[0085] Step S5: Solve the multi-objective optimization problem based on the compact convex hull method to obtain the affine optimal energy flux.

[0086] In this embodiment, the objective function of the deterministic optimal energy flow model for the electro-pneumatic interconnected system is expressed as follows:

[0087]

[0088] Where: Ω G Ω W and Ω P2G This refers to a collection of coal-fired power units, gas sources, and electro-gas conversion equipment; α i and β i c is the cost coefficient for coal-fired unit i; w,m and c P2G,i P represents the cost coefficient of the gas source m and the electro-gas conversion equipment i; G,i and P P2G,i F represents the active power output of coal-fired unit i and power-to-gas conversion equipment i, respectively; W,m This indicates the gas production rate of gas source m.

[0089] In this embodiment, the constraints of the deterministic optimal energy flow model of the electro-pneumatic interconnected system include:

[0090] ① Power system constraints

[0091] Power system constraints include DC power flow equations (2), nodal power balance equations (3), coal-fired unit output constraints (4), gas-fired unit output constraints (5), power-to-gas conversion equipment output constraints (6), wind power output constraints (7), and line transmission power constraints (8), which are as follows:

[0092] P ij =B ij (θ i -θ j (2)

[0093]

[0094] 0≤P WA,i ≤P W,i (7)

[0095]

[0096] Where: Ω i Let P be the set of tail nodes with node i as the first node; ij B ij and θ i Let P be the transmission power, mutual susceptance, and phase angle of line ij, respectively; G,i P GT,i P P2G,i and P L,i These represent the output of coal-fired unit i, gas-fired unit i, and power-to-gas conversion equipment i, respectively, and the electrical load of node i; P WA,i and P W,i These represent the actual and predicted wind power output of wind farm i, respectively. These are the upper and lower limits of output for coal-fired unit i and gas-fired unit i, respectively; The maximum conversion power of the electro-gas conversion device i; This represents the upper limit of the allowed transmission power for line ij;

[0097] ② Natural gas system constraints

[0098] The constraints of the natural gas system include the natural gas flow equation (9), node flow balance constraints (10), gas source flow constraints (11), node pressure constraints (12), pipeline flow constraints (13), compressor station flow constraints (14), and compressor station pressurization constraints (15), which are as follows:

[0099]

[0100] Where: Ω m Let F be the set of first nodes whose tail node is m; mn C mn and p mLet F be the flow rate of pipe mn, the pipe constant, and the square air pressure at node m; W,m F P2G,m F GT,m and F L,i These represent the gas production at gas source m, the gas production at the power-to-gas conversion equipment at node m, the gas consumption at node m by the gas turbine unit, and the natural gas load at node m, respectively; F C,m p m,s and p m,d These are the flow rate, inlet pressure, and outlet pressure of compressor station m, respectively. These are the upper and lower limits of the flow output of the gas source m, respectively; These are the upper and lower pressure limits for node m, respectively; Let mn be the upper limit of the flow rate in pipe mn; This represents the upper limit of the flow rate at compressor station m. These are the upper and lower limits of the compression ratio for compressor station m, respectively.

[0101] ③ Coupling device constraints

[0102] The power system and the natural gas system are coupled through power-to-gas equipment and gas turbine units, and their coupling constraints are as follows:

[0103]

[0104] In the formula: η GT,i η P2 G ,i The efficiencies of the gas turbine unit and the electro-gas conversion equipment, respectively; H g This refers to the calorific value of natural gas.

[0105] In this embodiment, step S2 specifically includes:

[0106] The nonconvexity of the natural gas flow equation (9) comes from the absolute value and the quadratic term. Introducing 0-1 variables transforms (9) into (18)-(20) equivalently:

[0107]

[0108] In the formula, ξ mn These are 0-1 variables, representing the direction of natural gas flow in the pipeline;

[0109] Introducing new auxiliary variables and Equation (20) is transformed into (21)-(25):

[0110]

[0111] The quadratic term in equation (21) can be further approximated by the McCormick convex hull, and then by a set of linear inequalities as shown in (26)-(28):

[0112]

[0113] Based on the above convexity treatment, the deterministic optimal energy flow model is transformed into a mixed-integer linear programming model, whose compact form is expressed as follows:

[0114]

[0115] In the formula: x and y represent vectors of continuous variables and 0-1 variables, respectively; A and b represent coefficient matrices with respect to equality constraints; c and d represent coefficient matrices with respect to the objective function; G1, G2, and h represent coefficient matrices with respect to inequality constraints.

[0116] In this embodiment, step S3 specifically includes:

[0117] The affine form of an uncertain wind power output is as follows:

[0118]

[0119] In the formula: Let P be the affine form corresponding to the uncertain wind power of wind farm i; W,i,0 ε w,i and P W,i These are the predicted center value of the power of wind farm i, the noise element, and the corresponding noise element coefficient, respectively.

[0120] Based on (29) and (30), the affine optimal energy flow model is expressed as follows:

[0121]

[0122] In the formula: A continuous variable vector in affine form; and It is the coefficient matrix in affine form.

[0123] Since the deterministic optimal energy flow problem (29) is a mixed-integer programming problem, the affine optimal energy flow model (31) does not involve nonlinear affine operations. To solve the affine optimal energy flow problem, the equality constraints, inequality constraints, and affine form of the objective function in (31) can be defined as follows:

[0124] The equality constraints, inequality constraints, and affine form of the objective function in the affine optimal energy flow model (31) are defined as follows:

[0125] 1) Definition of equality constraints

[0126] Affine form equality constraints are defined as having equal central values ​​and noise element coefficients on both sides of the equation and having the same noise element.

[0127]

[0128] In the formula: x0 and x s They are respectively The center value and the noise element coefficient corresponding to the s-th noise element; b0 and b s They are respectively The center value and noise element coefficient; n is the number of noise elements;

[0129] 2) Definition of Inequality Constraints

[0130] Following interval theory, affine inequality constraints can be defined as follows:

[0131]

[0132] In the formula: h0 and h s They are respectively The center value and noise element coefficient;

[0133] 3) Definition of the objective function

[0134] The objective function for the affine optimal energy flux can be expressed as follows:

[0135]

[0136] (34) It can be equivalently transformed into a deterministic multi-objective optimization problem:

[0137]

[0138] Based on the above definition, and by introducing optimization weights, the affine optimal energy flow problem (31) of the electro-pneumatic interconnected system can be expressed as the following deterministic optimization problem:

[0139]

[0140] In the formula: w represents the multi-objective optimization weight.

[0141] In this embodiment, step S5, the specific solution steps are as follows:

[0142] 1) Initialization: Set the convergence threshold δ and the maximum number of iterations r. max and decreasing sequence {a r Set the iteration count r = 1;

[0143] 2) Solve the affine optimal energy flow problem (36) to obtain And based on equation (37) Transform into interval form

[0144]

[0145] 3) Update the upper and lower boundaries of the convex hull:

[0146]

[0147] 4) Calculate the relaxation gap and its upper and lower bounds according to equations (40)-(41). If G mn >-δ and Output the affine optimal energy flow calculation results; if r ≥ r max If the iteration fails, exit; otherwise, proceed to step 2); update r = r + 1

[0148]

[0149] The above description is only a preferred embodiment of the present invention. All equivalent changes and modifications made within the scope of the claims of the present invention should be included in the scope of the present invention.

Claims

1. A method for calculating affine optimal energy flow in an electrical interconnection system based on a compact convex hull, characterized in that, Includes the following steps: Step S1: Construct a deterministic optimal energy flow model for the electro-pneumatic interconnected system; Step S2: Based on the convex envelope, the deterministic optimal energy flow model is convexly reconstructed into a mixed-integer linear programming model; Step S3: Based on the mixed integer linear programming model, the uncertain wind power is represented as an affine form, and an affine optimal energy flow model of the electric-gas interconnection system is constructed. Step S4: Based on affine arithmetic theory, the affine optimal energy flow model of the electro-pneumatic interconnection system is transformed into a deterministic multi-objective optimization problem; Step S5: Solve the multi-objective optimization problem based on the compact convex hull method to obtain the affine optimal energy flux; The objective function of the deterministic optimal energy flow model for the electro-pneumatic interconnected system is expressed as follows: Where: Ω G Ω W and Ω P2G This refers to a collection of coal-fired power units, gas sources, and electro-gas conversion equipment; α i and β i c is the cost coefficient for coal-fired unit i; w,m and c P2G,i This represents the cost coefficient of the gas source m and the electro-gas conversion equipment i; P G,i and P P2G,i F represents the active power output of coal-fired unit i and power-to-gas conversion equipment i, respectively; W,m This indicates the gas production rate of gas source m; Step S2 specifically involves: The nonconvexity of the natural gas flow equation comes from the absolute value and the quadratic term. Introducing 0-1 variables transforms the natural gas flow equation into (18)-(20): In the formula, ξ mn These are 0-1 variables, representing the direction of natural gas flow in the pipeline; Introducing new auxiliary variables and Equation (20) is transformed into (21)-(25): The quadratic term in equation (21) can be further approximated by the McCormick convex hull, and then by a set of linear inequalities as shown in (26)-(28): The deterministic optimal energy flow model is transformed into a mixed-integer linear programming model, which is expressed in a compact form as follows: In the formula: x and y represent vectors of continuous variables and 0-1 variables, respectively; A and b represent coefficient matrices with respect to equality constraints; c and d represent coefficient matrices with respect to the objective function; G1, G2, and h represent coefficient matrices with respect to inequality constraints; Step S3 specifically involves: The affine form of an uncertain wind power output is as follows: In the formula: Let P be the affine form corresponding to the uncertain wind power of wind farm i; W,i,0 ε w,i and P W,i These are the predicted center value of the power of wind farm i, the noise element, and the corresponding noise element coefficient, respectively. Based on (29) and (30), the affine optimal energy flow model is expressed as follows: In the formula: A continuous variable vector in affine form; and It is the coefficient matrix in affine form.

2. The affine optimal energy flow calculation method for electrical interconnection systems based on compact convex enveloping as described in claim 1, characterized in that, The constraints of the deterministic optimal energy flow model of the electro-pneumatic interconnected system include: ① Power system constraints Power system constraints include DC power flow equations (2), nodal power balance equations (3), coal-fired unit output constraints (4), gas-fired unit output constraints (5), power-to-gas conversion equipment output constraints (6), wind power output constraints (7), and line transmission power constraints (8), which are as follows: P ij =B ij (i i -θ j ) (2) 0≤P WA,i ≤P W,i (7) Where: Ω i Let P be the set of tail nodes with node i as the first node; ij B ij and θ i Let P be the transmission power, mutual susceptance, and phase angle of line ij, respectively; G,i P GT,i P P2G,i and P L,i These represent the output of coal-fired unit i, gas-fired unit i, and power-to-gas conversion equipment i, respectively, and the electrical load of node i; P WA,i and P W,i These represent the actual and predicted wind power output of wind farm i, respectively. These are the upper and lower limits of output for coal-fired unit i and gas-fired unit i, respectively; The maximum conversion power of the electro-gas conversion device i; This represents the upper limit of the allowed transmission power for line ij; ② Natural gas system constraints The constraints of the natural gas system include the natural gas flow equation (9), node flow balance constraints (10), gas source flow constraints (11), node pressure constraints (12), pipeline flow constraints (13), compressor station flow constraints (14), and compressor station pressurization constraints (15), which are as follows: Where: Ω m Let F be the set of first nodes whose tail node is m; mn C mn and p m Let F be the flow rate of pipe mn, the pipe constant, and the square air pressure at node m; W,m F P2G,m F GT,m and F L,i These represent the gas production at gas source m, the gas production at the power-to-gas conversion equipment at node m, the gas consumption at node m by the gas turbine unit, and the natural gas load at node m, respectively; F C,m p m,s and p m,d These are the flow rate, inlet pressure, and outlet pressure of compressor station m, respectively. These are the upper and lower limits of the flow output of the gas source m, respectively; These are the upper and lower pressure limits for node m, respectively; Let mn be the upper limit of the flow rate in pipe mn; This represents the upper limit of the flow rate at compressor station m. These are the upper and lower limits of the compression ratio for compressor station m, respectively. ③ Coupling device constraints The power system and the natural gas system are coupled through power-to-gas equipment and gas turbine units, and their coupling constraints are as follows: In the formula: η GT,i η P2G,i The efficiencies of the gas turbine unit and the electro-gas conversion equipment, respectively; H g This refers to the calorific value of natural gas.

3. The affine optimal energy flow calculation method for electrical interconnection systems based on compact convex enveloping as described in claim 1, characterized in that, Step S4 specifically involves: The equality constraints, inequality constraints, and affine form of the objective function in the affine optimal energy flow model (31) are defined as follows: 1) Definition of equality constraints Affine form equality constraints are defined as having equal central values ​​and noise element coefficients on both sides of the equation and having the same noise element. In the formula: x0 and x s They are respectively The center value and the noise element coefficient corresponding to the s-th noise element; b0 and b s They are respectively The center value and noise element coefficient; n is the number of noise elements; 2) Definition of Inequality Constraints Following interval theory, affine inequality constraints can be defined as follows: In the formula: h0 and h s They are respectively The center value and noise element coefficient; 3) Definition of the objective function The objective function for the affine optimal energy flux can be expressed as follows: Furthermore, (34) can be equivalently transformed into a deterministic multi-objective optimization problem: Based on the above definition, and by introducing optimization weights, the affine optimal energy flow problem (31) of the electro-pneumatic interconnected system can be expressed as the following deterministic optimization problem: stAx0=b0 In the formula: w represents the multi-objective optimization weight.

4. The affine optimal energy flow calculation method for electrical interconnection systems based on compact convex enveloping as described in claim 1, characterized in that, The specific solution steps for step S5 are as follows: 1) Initialization: Set the convergence threshold δ and the maximum number of iterations r. max and decreasing sequence {a r Set the iteration count r = 1; 2) Solve the affine optimal energy flow problem (36) to obtain And based on equation (37) Transform into interval form 3) Update the upper and lower boundaries of the convex hull: 4) Calculate the relaxation gap and its upper and lower boundaries according to equations (40)-(41). If G mn >-δ and Output the affine optimal energy flow calculation results; if r ≥ r max If the iteration fails, exit; otherwise, proceed to step 2); update r = r + 1

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