Power transmission network distribution robust low-carbon scheduling method based on Wasserstein distance

Abstract

The invention provides a power transmission network distribution robust low-carbon scheduling method based on a Wasserstein distance. The method comprises the following steps: establishing a deterministic low-carbon economic scheduling model containing thermal power cost and carbon emission cost; constructing a wind and light output uncertainty set based on a Wasserstein distance, and converting a deterministic low-carbon economic dispatching model containing thermal power cost and carbon emission cost into a two-stage distribution robust optimization model by adopting an affine decision; simplifying the two-stage distribution robust optimization model into a new two-stage distribution robust optimization low-carbon economic dispatching model by adopting a duality theory; solving the new two-stage distribution robust optimization low-carbon economic dispatching model to obtain a power flow result; establishing a whole-network carbon emission flow model containing energy storage; obtaining whole network carbon flow distribution under a power flow result; according to the method, the randomness and extreme fluctuation of wind and light output can be more accurately and flexibly dealt with; and meanwhile, the calculation complexity is simplified, and the robustness and economy of the model are effectively balanced.

Description

Technical Field

[0001] The present invention relates to a distributed robust low-carbon dispatching method for a transmission network based on Wasserstein distance, and belongs to the technical field of power system optimization dispatching. Background Art

[0002] As the low-carbon transformation of the power system deepens, accurately addressing the uncertainty of wind and solar power output has become a key challenge for low-carbon economic dispatch models that include new energy. Existing uncertainty optimization methods mainly include stochastic optimization (SO) and robust optimization (RO). However, current uncertainty optimization methods have the following problems:

[0003] 1) Stochastic optimization SO constructs a scenario set based on historical probability distribution and relies on the distribution stability assumption. It is not adaptable enough when the probability distribution shifts, such as in extreme weather. That is, the solution efficiency depends on the number of samples, and the limited historical samples cannot cover low-probability, high-impact extreme events.

[0004] 2) Although robust optimization (RO) can handle the worst case scenario, the box-type uncertainty set it adopts often assumes that all uncertain parameters reach their boundary values ​​at the same time, ignoring the correlation and probability distribution information between uncertainty parameters, resulting in an overly conservative system. In addition, robust optimization (RO) lacks a quantification mechanism for the degree of conservatism and is usually based on a static decision structure, which cannot be dynamically adjusted according to the real-time implementation of uncertainty, further limiting its practicality. Summary of the Invention

[0005] The purpose of the present invention is to provide a robust low-carbon scheduling method for transmission network distribution based on Wasserstein distance to solve the problems in the prior art of insufficient adaptability in the case of probability distribution deviation and the need to improve the flexibility of the model.

[0006] The technical solution of the present invention is:

[0007] A distributed robust low-carbon dispatching method for transmission networks based on Wasserstein distance comprises the following steps:

[0008] S1. Establish a deterministic low-carbon economic dispatch model that includes thermal power costs and carbon emission costs;

[0009] S2. Based on the Wasserstein distance, the uncertainty set of wind and solar power output is constructed, and the deterministic low-carbon economic dispatch model containing thermal power costs and carbon emission costs is converted into a two-stage distributed robust optimization model using affine decision making.

[0010] S3. Using the duality theory, the two-stage distributed blue stick optimization model is simplified into a new two-stage distributed blue stick optimization low-carbon economic dispatch model;

[0011] S4. Solve the new two-stage distributed blue stick optimization low-carbon economic dispatch model and obtain the power flow results including branch power and output of each unit;

[0012] S5. Establish a network-wide carbon emission flow model including energy storage;

[0013] S6. Input the tidal flow result obtained in step S4 into the network-wide carbon emission flow model including energy storage in step S5 to obtain the network-wide carbon flow distribution under the tidal flow result.

[0014] Furthermore, in step S1, the objective function of the deterministic low-carbon economic dispatch model including thermal power cost and carbon emission cost is:

[0015]

[0016] In the formula, after the power generation cost is piecewise linearized into m segments, the piecewise linearized power generation cost f is obtained gen : Among them, K s Represents the slope of each section of the coal consumption function after piecewise linearization, and the coal consumption generated when the unit is started and running at minimum output Output of each unit p gen,s : Start-stop costs Among them, C g,U is the total startup cost of coal-fired unit g; C g,D is the total shutdown cost of coal-fired unit g; carbon emission cost Among them, e g is the carbon emission intensity of coal-fired unit g; f curt Cost of curtailing wind and solar power;

[0017] The constraints in the first stage include power flow constraints, energy storage operation constraints, thermal power unit operation constraints, and wind and solar curtailment constraints.

[0018] (1) Flow constraints:

[0019]

[0020] -2π≤θ≤2π (3)

[0021]

[0022] Formula (2) gives the power balance constraint, where P dis is the energy storage discharge power; P ch is the energy storage charging power; P l is the branch current; Pwind Forecast output of wind turbine; P pv Forecast output of photovoltaic units; P wcurt is the wind power curtailment; P vcurt is the abandoned optical power; P L For load;

[0023] Formula (3) gives the node phase angle constraint, θ is the node phase angle;

[0024] Formula (4) gives the branch power flow constraint, X l is the impedance of the branch; Δθ is the phase angle difference between the first and last nodes; P l,max and P l,min are the upper and lower limits of the branch power flow respectively; the branch power flow adopts the simplified DC power flow equation;

[0025] (2) Energy storage operation constraints:

[0026] B ch (t)+B dis (t)≤1 (5)

[0027]

[0028]

[0029] Equation (5) gives the energy storage charge and discharge mutual exclusion constraint, where B ch , B dis are 0-1 variables representing the energy storage charging and discharging status;

[0030] Formula (6) gives the upper and lower limit constraints of energy storage charging and discharging power, where P ch，max , P dis，max They are the upper limits of energy storage charging and discharging power respectively;

[0031] Equation (7) gives the constraints of the energy storage state of charge SOC, where η ch , η dis are energy storage charging and discharging efficiency; E is energy storage capacity; SOC max and SOC min They are the upper and lower limits of energy storage SOC; SOC initial and SOC end They are the initial and final states of energy storage SOC; SOC set is the set SOC state;

[0032] (3) Operation constraints of thermal power units:

[0033]

[0034]

[0035]

[0036]

[0037]

[0038]

[0039] Formula (8) gives the output constraint of thermal power units, where: and are the upper and lower limits of the output of thermal power unit g; u g It is a 0-1 variable indicating the start and stop status of the thermal power unit g in each period;

[0040] Formula (9) gives the start and stop time constraints of thermal power units, where T g，on and T g，off are the start-up and shutdown times of thermal power unit g; T g，on，min and T g，off，min are the minimum start-up and shutdown times of thermal power unit g;

[0041] Formula (10) gives the start-up and shutdown cost constraints of thermal power units, where H g and J g are the startup and shutdown cost coefficients of thermal power unit g, respectively;

[0042] Equation (11) gives the unit hot standby constraint, where μ is the hot standby coefficient; P L is the total load in each time period;

[0043] Formula (12) gives the unit climbing constraint, where R up，g and R down，g They are the up and down ramp rates of thermal power unit g;

[0044] Equation (13) gives the emission constraints for the start and stop of thermal power units, where SE g and SD g are the carbon emission coefficients of thermal power units starting and stopping;

[0045] (4) Constraints on curtailment of wind and solar power:

[0046] 0≤P wcurt ≤P wind (14)

[0047] 0≤P vcurt ≤P pv (15)

[0048] Equation (17) gives the wind power curtailment constraint;

[0049] Equation (18) gives the constraint on the abandoned optical power.

[0050] Furthermore, in step S1, since the constraints are all equality or inequality constraints, the first stage constraint condition is abstracted as Ax-b≤0, where x is the first stage decision variable including P dis 、P ch 、P l 、P wind 、P pv 、P wcurt 、P vcurt 、P L ,θ,SOC,P gen,g 、B ch 、B dis 、u g , belongs to the set Г; A and b are coefficient matrices. The deterministic low-carbon economic dispatch model containing thermal power cost and carbon emission cost is abstracted as follows:

[0051]

[0052] Where, f T is the cost coefficient vector corresponding to all first-stage decision variables.

[0053] Furthermore, in step S2, the wind and solar power output uncertainty set is constructed based on the Wasserstein distance, specifically,

[0054] S21, for the wind historical prediction error sample set {ξ1,ξ2,…,ξ n ,…,ξ N}, then the empirical distribution of wind and solar power output forecast error is

[0055]

[0056] Where, ξ n is the nth historical forecast error sample;

[0057] Distribute experience As an estimate of the true distribution P, when the total number of samples N approaches infinity, we have Wasserstein distance between empirical distribution and true distribution

[0058]

[0059] Where inf represents the lower bound; For the empirical distribution to the joint probability distribution of the true distribution P; ξ is the error parameter that obeys the true distribution P; ||·||1 represents the 1 norm;

[0060] S22. Empirical distribution Construct the wind and solar power output uncertainty set X with the Wasserstein sphere as the center and ε(N) as the radius:

[0061]

[0062] Where, Β Ξ is the probability distribution set that supports all data-driven support sets Ξ; ε(N) is the radius of the coverage uncertainty range, which controls the uncertainty range around the empirical distribution; when the total number of samples N approaches infinity, At this time, the sphere is reduced to a point, that is, At this point, the empirical distribution is the true distribution;

[0063] S23. Calculate the Wasserstein radius ε(N) using quantile estimation:

[0064]

[0065] In the formula, β is the confidence level, D is the coefficient, in, is the sample mean; υ is a coefficient greater than zero;

[0066] S24. After standardizing the historical forecast error sample set, the uncertainty parameter can be obtained

[0067]

[0068] Where, is the sample variance; uncertain parameters The mean and variance of are 0 and 1;

[0069] Let Θ be the uncertain parameter The uncertain set of , is:

[0070]

[0071] In the formula, the uncertain parameters for The nth element in ; d is the boundary, so solving the uncertainty set Θ that characterizes the range of wind power prediction error is equivalent to solving the boundary d;

[0072] S25, boundary d is solved by the following boundary solution formula:

[0073]

[0074] Where, d max is the upper limit of the boundary; sup represents the supremum; P std and K stdThey represent the true probability distribution and fuzzy uncertainty set of error parameters respectively; η represents the confidence of the support set;

[0075] Using duality theory to simplify the boundary solution formula is:

[0076]

[0077] Where κ is the dual variable; (·) + Represents the maximum value of 0 and the variables in brackets;

[0078] Combined with formula (24), formula (23) is simplified to:

[0079]

[0080] The boundary d is determined by the boundary solution formula of formula (25). According to step S24, the uncertainty set Θ of the original space is obtained by inverse transformation to obtain the support set Ξ:

[0081] Furthermore, in step S2, the deterministic low-carbon economic dispatch model including thermal power cost and carbon emission cost is converted into a two-stage distributed robust optimization model by using affine decision making. Specifically,

[0082] S21. Use affine decision to adjust the output:

[0083] Total wind and solar forecast error Among them, the prediction error of wind power Where, is the actual output of wind power, and the prediction error of photovoltaic in, The actual output of photovoltaic power.

[0084] Thermal power unit output adjustment, adjusted thermal power output Among them, a g represents the affine adjustment coefficient of thermal power units;

[0085] Adjustment of upper and lower limits of thermal power unit output: Adjustment of hot standby constraints for thermal power units:

[0086] Adjustment of thermal power unit climbing constraints:

[0087] Energy storage charging and discharging power adjustment: Where, and Represent the adjusted energy storage charging and discharging power respectively; a ch and a dis represent the affine adjustment coefficients for energy storage charging and discharging, respectively;

[0088] Adjustment of upper and lower limits of energy storage charging and discharging:

[0089] Energy storage charging and discharging SOC constraint adjustment: Where, represents the adjusted SOC;

[0090] Adjustment of abandoned optical power: Where, is the adjusted abandoned optical power; a vcurt is the light rejection affine adjustment coefficient;

[0091] Wind power curtailment adjustment: Where, is the adjusted abandoned optical power; a wcurt is the light rejection affine adjustment coefficient;

[0092] Adjustment of upper and lower limits of wind power curtailment:

[0093] Adjustment of upper and lower limits of discarded optical power:

[0094] Power balance constraint adjustment:

[0095] The objective function is to minimize the first-stage objective function plus the worst-case minimum adjustment cost:

[0096]

[0097] Where, represents the expectation of the minimum adjustment cost of the worst scenario in the fuzzy uncertainty set X; E P (·) is the expected function; To adjust costs;

[0098] S22. According to the constraints and objective function in step S21, the two-stage distributed robust optimization model is expressed as:

[0099]

[0100] Where, d T represents the coefficient vector corresponding to the second-stage decision variables; represents the second stage objective function; represents the second stage constraints, where E represents the coefficient matrix,

[0101] Parameter representing the second-stage error.

[0102] Furthermore, in step S3, the duality theory is used to simplify the two-stage distributed blue-robust optimization model into a new two-stage distributed blue-robust optimization low-carbon economic dispatch model, specifically,

[0103] S31. Apply duality theory to transform formula (26) to obtain:

[0104]

[0105]

[0106] Where γ is the duality coefficient; represents the i-th error sample; τ i is an auxiliary variable;

[0107] S32. Further transform formula (28) into:

[0108]

[0109] Where, and ξ represent the upper and lower limits of the error respectively; I T represents a unit vector;

[0110] S33. Combining Equations (16), (26) and (29), we can get a new two-stage distributed blue stick optimization low-carbon economic dispatch model:

[0111]

[0112] The beneficial effects of the present invention are:

[0113] This Wasserstein distance-based distributed robust low-carbon dispatch method for transmission networks utilizes Wasserstein distance-based distributed robust optimization technology to build a low-carbon economic dispatch model that incorporates wind, solar, thermal, and storage. This method combines the distributed information utilization of stochastic optimization with the worst-case considerations of robust optimization, overcoming the major shortcomings of both. This method enables the construction of a more robust low-carbon economic dispatch model that can more accurately and flexibly address the randomness and extreme fluctuations of wind and solar output. The use of an affine decision rule enables dispatch decisions to be adaptively adjusted based on real-time deviations in wind and solar output, enhancing the model's flexibility. Furthermore, the duality theory is employed to simplify computational complexity, effectively balancing the model's robustness and economic efficiency.

[0114] Second, this distributed robust low-carbon dispatch method for the transmission network based on the Wasserstein distance. This Wasserstein-based distributed robust optimization method accurately characterizes the uncertainty characteristics of wind and solar power output by constructing a fuzzy set centered on the empirical distribution. Uncertainty is quantified by combining the confidence level parameter with the Wasserstein radius. Furthermore, based on carbon emission flow theory, this invention constructs a carbon flow model to track the carbon flow distribution across the entire network, deriving the carbon potential of each node and providing a node-level reference for the carbon trading market. BRIEF DESCRIPTION OF THE DRAWINGS

[0115] Figure 1 1 is a flow chart of a robust low-carbon dispatching method for a transmission network based on Wasserstein distance according to an embodiment of the present invention;

[0116] Figure 2 Schematic diagram of wind and solar power output and error in the embodiment;

[0117] Figure 3 The output of each unit after the first stage of scheduling in the embodiment;

[0118] Figure 4 Schematic diagram of the output of each unit after two-stage split-rod scheduling in the embodiment;

[0119] Figure 5 1 is a schematic diagram comparing the carbon potential distribution of nodes in the embodiments, wherein (a) is a schematic diagram of the carbon potential distribution of nodes in Case A, and (b) is a schematic diagram of the carbon potential distribution of nodes in Case B;

[0120] Figure 6 2 is a comparative schematic diagram of the carbon flow rate distribution of the branch in the embodiment, wherein (a) is a schematic diagram of the carbon flow rate distribution of the branch of Case A, and (b) is a schematic diagram of the carbon flow rate distribution of the branch of Case B. DETAILED DESCRIPTION

[0121] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0122] The embodiment provides a method for distributed robust low-carbon dispatching of a transmission network based on Wasserstein distance, such as Figure 1 , including the following steps,

[0123] S1. Establish a deterministic low-carbon economic dispatch model that includes thermal power costs and carbon emission costs.

[0124] In step S1, the objective function of the deterministic low-carbon economic dispatch model including thermal power cost and carbon emission cost is:

[0125]

[0126] In the formula, after the power generation cost is piecewise linearized into m segments, the piecewise linearized power generation cost f is obtained gen : Among them, K s Represents the slope of each section of the coal consumption function after piecewise linearization, and the coal consumption generated when the unit is started and running at minimum output Output of each unit p gen,s : Start-stop costs Among them, C g,U is the total startup cost of coal-fired unit g; C g,D is the total shutdown cost of coal-fired unit g; carbon emission cost Among them, e g is the carbon emission intensity of coal-fired unit g; f curt The cost of curtailing wind and solar power.

[0127] In order to improve the solution efficiency of the model, the nonlinear term of power generation cost in the deterministic low-carbon economic dispatch model including thermal power cost and carbon emission cost is piecewise linearized.

[0128] The constraints in the first stage include power flow constraints, energy storage operation constraints, thermal power unit operation constraints, and wind and solar curtailment constraints.

[0129] (1) Flow constraints:

[0130]

[0131] -2π≤θ≤2π (3)

[0132]

[0133] Formula (5) gives the power balance constraint, where P dis is the energy storage discharge power; P ch is the energy storage charging power; P l is the branch current; P wind Forecast output of wind turbine; P pv Forecast output of photovoltaic units; P wcurt is the wind power curtailment; P vcurt is the abandoned optical power; P L For load;

[0134] Equation (6) gives the node phase angle constraint, θ is the node phase angle;

[0135] Formula (7) gives the branch power flow constraint, X l is the impedance of the branch; Δθ is the phase angle difference between the first and last nodes; P l,max and P l,min are the upper and lower limits of the branch power flow respectively; the branch power flow adopts the simplified DC power flow equation;

[0136] (2) Energy storage operation constraints:

[0137] B ch (t)+B dis (t)≤1 (5)

[0138]

[0139]

[0140] Equation (8) gives the energy storage charge and discharge mutual exclusion constraint, where B ch , B dis are 0-1 variables representing the energy storage charging and discharging status;

[0141] Formula (9) gives the upper and lower limit constraints of energy storage charging and discharging power, where P ch，max , P dis，max They are the upper limits of energy storage charging and discharging power respectively;

[0142] Formula (10) gives the constraint of the energy storage state of charge SOC, where η ch , η dis are energy storage charging and discharging efficiency; E is energy storage capacity; SOC max and SOC min They are the upper and lower limits of energy storage SOC; SOC initial and SOC end They are the initial and final states of energy storage SOC; SOC set is the set SOC state;

[0143] (3) Operation constraints of thermal power units:

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150] Formula (11) gives the output constraint of thermal power units, where: and are the upper and lower limits of the output of thermal power unit g; u g It is a 0-1 variable indicating the start and stop status of the thermal power unit g in each period;

[0151] Formula (12) gives the start and stop time constraints of thermal power units, where T g，on and T g，off are the start-up and shutdown times of thermal power unit g; T g，on，min and T g，off，min are the minimum start-up and shutdown times of thermal power unit g;

[0152] Formula (13) gives the start-up and shutdown cost constraints of thermal power units, where H g and J g are the startup and shutdown cost coefficients of thermal power unit g, respectively;

[0153] Equation (14) gives the unit hot standby constraint, where μ is the hot standby coefficient; P L is the total load in each time period;

[0154] Formula (15) gives the unit climbing constraint, where R up，g and R down，g They are the up and down ramp rates of thermal power unit g;

[0155] Equation (16) gives the emission constraints for the start and stop of thermal power units, where SE g and SD g are the carbon emission coefficients of thermal power units starting and stopping;

[0156] (4) Constraints on curtailment of wind and solar power:

[0157] 0≤P wcurt ≤P wind (14)

[0158] 0≤P vcurt ≤P pv (15)

[0159] Equation (17) gives the wind power curtailment constraint;

[0160] Equation (18) gives the constraint on the abandoned optical power.

[0161] In step S1, since the constraints are all equality or inequality constraints, the first stage constraint condition is abstracted as Ax-b≤0, where x is the first stage decision variable including P dis 、P ch 、P l 、P wind 、P pv 、P wcurt 、P vcurt 、P L ,θ,SOC,P gen,g 、B ch 、B dis 、u g, belongs to the set Г; A and b are coefficient matrices. The deterministic low-carbon economic dispatch model containing thermal power cost and carbon emission cost is abstracted as follows:

[0162]

[0163] Where, f T is the cost coefficient vector corresponding to all first-stage decision variables.

[0164] S2. Based on the Wasserstein distance, an uncertain set of wind and solar power output is constructed, and an affine decision is used to convert the deterministic low-carbon economic dispatch model containing thermal power costs and carbon emission costs into a two-stage distributed robust optimization model.

[0165] In step S2, the wind and solar power output uncertainty set is constructed based on the Wasserstein distance, specifically,

[0166] S21, for the wind historical prediction error sample set {ξ1,ξ2,…,ξ n ,…,ξ N}, then the empirical distribution of wind and solar power output forecast error is

[0167]

[0168] Where, ξ n is the nth historical forecast error sample;

[0169] Distribute experience As an estimate of the true distribution P, when the total number of samples N approaches infinity, we have Wasserstein distance between empirical distribution and true distribution

[0170]

[0171] Where inf represents the lower bound; For the empirical distribution to the joint probability distribution of the true distribution P; ξ is the error parameter that obeys the true distribution P; ||·||1 represents the 1 norm;

[0172] S22. Empirical distribution Construct the wind and solar power output uncertainty set X with the Wasserstein sphere as the center and ε(N) as the radius:

[0173]

[0174] Where, Β Ξis the probability distribution set that supports all data-driven support sets Ξ; ε(N) is the radius of the coverage uncertainty range, which controls the uncertainty range around the empirical distribution; when the total number of samples N approaches infinity, At this time, the sphere is reduced to a point, that is, At this point, the empirical distribution is the true distribution;

[0175] S23. Calculate the Wasserstein radius ε(N) using quantile estimation:

[0176]

[0177] In the formula, β is the confidence level, D is the coefficient, in, is the sample mean; υ is a coefficient greater than zero;

[0178] S24. After standardizing the historical forecast error sample set, the uncertainty parameter can be obtained

[0179]

[0180] Where, is the sample variance; uncertain parameters The mean and variance of are 0 and 1;

[0181] Let Θ be the uncertain parameter The uncertain set of , is:

[0182]

[0183] In the formula, the uncertain parameters for The nth element in ; d is the boundary, so solving the uncertainty set Θ that characterizes the range of wind power prediction error is equivalent to solving the boundary d;

[0184] S25, boundary d is solved by the following boundary solution formula:

[0185]

[0186] Where, d max is the upper limit of the boundary; sup represents the supremum; P std and K std They represent the true probability distribution and fuzzy uncertainty set of error parameters respectively; η represents the confidence of the support set;

[0187] Using duality theory to simplify the boundary solution formula is:

[0188]

[0189] Where κ is the dual variable; (·) + Represents the maximum value of 0 and the variables in brackets;

[0190] Combined with formula (24), formula (23) is simplified to:

[0191]

[0192] The boundary d is determined by the boundary solution formula of formula (25). According to step S24, the uncertainty set Θ of the original space is obtained by inverse transformation to obtain the support set Ξ:

[0193] In step S2, the Wasserstein distance is characterized as the distance between the empirical distribution and the true distribution, which can be understood as a transportation problem of transferring from one distribution to another with the least workload. The present invention represents the uncertainty set in the distributional robust model as a fuzzy set established by the Wasserstein distance, and controls the conservatism of the model by adjusting the Wasserstein radius. When the number of samples is sufficient, the true distribution is included in the probability distribution with a high probability. In the modeling of uncertainty in new energy output, distributional robust optimization replaces a single hypothetical distribution by constructing a fuzzy set containing multiple possible distributions. This method combines the conservatism of robust optimization and the probabilistic characteristics of stochastic optimization.

[0194] In step S2, the deterministic low-carbon economic dispatch model including thermal power cost and carbon emission cost is converted into a two-stage distributed robust optimization model using affine decision making. Specifically,

[0195] S21. Use affine decision to adjust the output:

[0196] Total wind and solar forecast error Among them, the prediction error of wind power Where, is the actual output of wind power, and the prediction error of photovoltaic in, The actual output of photovoltaic power.

[0197] Thermal power unit output adjustment, adjusted thermal power output Among them, a g represents the affine adjustment coefficient of thermal power units;

[0198] Adjustment of upper and lower limits of thermal power unit output: Adjustment of hot standby constraints for thermal power units:

[0199] Adjustment of thermal power unit climbing constraints:

[0200] Energy storage charging and discharging power adjustment: Where, and Represent the adjusted energy storage charging and discharging power respectively; a ch and a dis represent the affine adjustment coefficients for energy storage charging and discharging, respectively;

[0201] Adjustment of upper and lower limits of energy storage charging and discharging:

[0202] Energy storage charging and discharging SOC constraint adjustment: Where, represents the adjusted SOC;

[0203] Adjustment of abandoned optical power: Where, is the adjusted abandoned optical power; a vcurt is the light rejection affine adjustment coefficient;

[0204] Wind power curtailment adjustment: Where, is the adjusted abandoned optical power; a wcurt is the light rejection affine adjustment coefficient;

[0205] Adjustment of upper and lower limits of wind power curtailment:

[0206] Adjustment of upper and lower limits of discarded optical power:

[0207] Power balance constraint adjustment:

[0208] The objective function is to minimize the first-stage objective function plus the worst-case minimum adjustment cost:

[0209]

[0210] Where, represents the expectation of the minimum adjustment cost of the worst scenario in the fuzzy uncertainty set X; E P (·) is the expected function; To adjust costs;

[0211] S22. According to the constraints and objective function in step S21, the two-stage distributed robust optimization model is expressed as:

[0212]

[0213] Where, d T represents the coefficient vector corresponding to the second-stage decision variables; represents the second stage objective function; represents the second stage constraints, where E represents the coefficient matrix,

[0214] Parameter representing the second-stage error.

[0215] S3. Using the duality theory, the two-stage distributed blue stick optimization model is simplified into a new two-stage distributed blue stick optimization low-carbon economic dispatch model.

[0216] S31. Apply duality theory to transform formula (26) to obtain:

[0217]

[0218]

[0219] Where γ is the duality coefficient; represents the i-th error sample; τ i is an auxiliary variable;

[0220] S32. Further transform formula (28) into:

[0221]

[0222] Where, and ξ Represent the upper and lower limits of error respectively; I T represents a unit vector;

[0223] S33. Combining Equations (16), (26) and (29), we can get a new two-stage distributed blue stick optimization low-carbon economic dispatch model:

[0224]

[0225] In step S33, the new two-stage distributed blue-rod optimization low-carbon economic dispatch model obtained can be successfully solved by a commercial solver.

[0226] S4. Solve the new two-stage distributed blue rod optimization low-carbon economic dispatch model and obtain the power flow results including branch power and output of each unit.

[0227] In step S4, the solver cplex / gurobi is used to solve the new two-stage distributed blue stick optimization low-carbon economic dispatch model.

[0228] S5. Establish a network-wide carbon emission flow model including energy storage.

[0229] Carbon emission flow is defined as a virtual network flow representing carbon emissions attached to power flow. It is an important tool for studying the distribution characteristics and dynamic transmission patterns of carbon emissions in power systems. It aims to quantify the transmission paths of carbon emissions at nodes and branches based on power flow. The most critical carbon flow indicators include carbon flow rate, carbon flow density, and node carbon potential.

[0230] S51. Calculate the carbon flow index including carbon flow density and node carbon potential. The ratio of branch carbon flow rate to branch active power is the branch carbon flow density ρ calculation formula: Where P is the branch active power; node carbon potential e n Calculation formula: Where, I + is the set of branches where active power flows into node n; i is the branch belonging to set I + Branch; P i is the active power of branch i; ρ i is the branch carbon flow density of branch i; P G,n is the active power of the generator connected to node n; ρ G,n is the carbon emission intensity of the generator connected to node n. The node carbon potential calculation formula shows that the node carbon potential is only related to the branches flowing into the node. Therefore, when the power flow distribution is known, the node carbon potential can be calculated by determining the branch flowing into the node based on the active power flow direction. It should be noted that the carbon flow density of the branch flowing out of a node is equal to the node carbon potential.

[0231] S52. For a network with N nodes, M loads, and K generators connected, the flow results are summarized as the branch flow distribution matrix P B , unit injection matrix P G , load distribution matrix P L Considering that the node carbon potential is only affected by the inflow power, it is necessary to establish the node active flux matrix P in the carbon flow calculation. N , used to express the contribution of all injected power of the node, since P N is a diagonal matrix, the node active flux matrix P N The diagonal elements P Nnn for:

[0232]

[0233] Where p Bi is the active power of branch i, that is, the branch power flow distribution matrix P B middle element; p Gn is the generator power connected to node n, that is, the unit injection matrix P G The elements in the node can be obtained by N :

[0234] PN =diag(ξ N+K P Z ) (32)

[0235] Where, ξ N+K is a unit row vector of dimension N+K, P Z To assist in the calculation of the matrix, P Z =[P B P G ] T ;

[0236] S53. Determine the carbon emission intensity of each type of generator set according to the type of generator set connected, and obtain the generator set carbon emission intensity vector E G ; Let the node carbon potential vector be E N , the calculation formula of the node carbon potential in step S51 is derived through matrix expression as follows:

[0237]

[0238] Where, P Bjn is the branch flow from node j to node n; P Gkn The power flow injected into node n by generator k; is an N-dimensional unit row vector whose n-th element is 1;

[0239] Expanded to matrix dimensions:

[0240]

[0241] The carbon emission flow model of the entire network including energy storage is obtained from formula (34):

[0242]

[0243] The carbon potential of all nodes in the system can be obtained by formula (35).

[0244] Branch carbon flow rate matrix R B :R B =P B diag(E N )(36);

[0245] Load carbon flow rate vector R L :R L =P L E N (37);

[0246] The dynamic nature of energy storage devices' charging and discharging determines their varying carbon emission characteristics during each state. During charging, the energy storage device draws power from the grid, and the carbon flow in the energy storage accumulates with the incoming power flow. At this point, the energy storage device can be considered a load, and its carbon flow calculation is similar to that of a load.

[0247] The energy storage charging carbon potential is the carbon potential of the node, and reference is made to the node carbon potential calculation formula in step S51.

[0248] During the discharge phase from T0 to T, the carbon flow rate F is: Where F0 is the carbon flow at time T0;

[0249] During the discharge phase from T0 to T, the charge Es is: Where, E s0 is the power at time T0;

[0250] Energy storage discharge carbon potential: After converting the integral into sum, we can get

[0251] S6. Input the tidal flow result obtained in step S4 into the network-wide carbon emission flow model including energy storage in step S5 to obtain the network-wide carbon flow distribution under the tidal flow result.

[0252] This Wasserstein distance-based distributed robust low-carbon dispatch method for transmission networks utilizes Wasserstein distance-based distributed robust optimization technology to build a low-carbon economic dispatch model that incorporates wind, solar, thermal, and storage. This method combines the distributed information utilization of stochastic optimization with the worst-case considerations of robust optimization, overcoming the key drawbacks of both. This method enables the construction of a more robust low-carbon economic dispatch model that can more accurately and flexibly address the randomness and extreme fluctuations of wind and solar output. The use of an affine decision rule enables dispatch decisions to be adaptively adjusted based on real-time deviations in wind and solar output, enhancing the model's flexibility. Furthermore, the duality theory is employed to simplify computational complexity, effectively balancing the model's robustness and economic efficiency.

[0253] This distributed blue-carbon dispatch method for transmission networks based on Wasserstein distance focuses on the distributed blue-carbon low-carbon economic dispatch problem considering the uncertainty of wind and solar power output. First, a deterministic low-carbon economic dispatch model is established, and some nonlinear constraints are linearized to facilitate the solution. Secondly, the uncertainty of wind and solar power is captured based on Wasserstein fuzzy sets, and a two-stage distributed blue-carbon low-carbon economic dispatch model considering the uncertainty of wind and solar power output is constructed. Finally, in order to obtain the carbon flow distribution of the entire network, a carbon flow model is constructed based on the carbon emission flow.

[0254] This Wasserstein distance-based distributed robust low-carbon dispatch method for the transmission network accurately characterizes the uncertainty characteristics of wind and solar power output by constructing a fuzzy set centered on the empirical distribution. This Wasserstein-based distributed robust optimization method combines a confidence level parameter with the Wasserstein radius to achieve uncertainty quantification. Furthermore, based on carbon emission flow theory, this invention constructs a carbon flow model to track the carbon flow distribution across the entire network, deriving the carbon potential of each node and providing a node-level reference for the carbon trading market.

[0255] The embodiment of the Wasserstein distance-based transmission network distributed robust low-carbon scheduling method is illustrated by selecting IEEE14 nodes as an example as follows:

[0256] The IEEE14 node consists of three thermal power units, one wind turbine, one photovoltaic unit, and one battery energy storage system. The scheduling period is set to 24 hours, with a scheduling interval of 1 hour. The battery energy storage parameters are as follows: ESS capacity is 20 MWh; maximum charge and discharge power is 10 MW; initial SOC is 0.5; and charge and discharge efficiency are 95%, respectively.

[0257] In order to clearly analyze the consideration of wind and solar power output uncertainty and the carbon flow distribution of the entire network before and after taking into account the uncertainty, the case analysis is mainly divided into the following cases for comparative consideration: Case A: a low-carbon economic dispatch model without considering the uncertainty of wind and solar power output; Case B: a two-stage distributed blue-robust low-carbon economic dispatch model considering the uncertainty of wind and solar power output.

[0258] (1) Operation results analysis

[0259] The confidence level is set to 0.95. The Wasserstein sphere radius for wind power in Case B is 7107.4895 mm, and the Wasserstein sphere radius for photovoltaic power is 451.6089 mm. The various scheduling costs for the two cases are shown in Table 1.

[0260] Table 1 Operation results in different scenarios

[0261]

[0262] As can be seen from Table 1, after taking into account the uncertainty of wind and solar power, the operating cost decreases due to the stable output of thermal power, but since the adjustment cost is taken into account, the total cost is higher, indicating that after taking into account the uncertain influence of wind and solar power, the scheduling of the present invention is more robust.

[0263] (2)Output analysis

[0264] Figure 2 In the middle, the blue and yellow bands are errors, combined with Figure 2The wind and solar power output and error analysis shows that renewable energy not only has obvious time complementarity, with wind power peaking at 18-22 hours at night and photovoltaic power concentrated in the 12-15 hour period, but also exhibits a significant uncertainty range in the high output range. Therefore, the present invention introduces distributed blue bars to cope with the above-mentioned wind and solar power fluctuations and enhance the robustness of the system.

[0265] Figure 3 The output of Case A unit is as follows: Figure 4 This is the output of the Case B unit. Figure 3 and Figure 4 From the unit output results, we can find that in Case A, which does not consider the uncertainty of wind and solar power output, the system scheduling shows traditional optimization characteristics: Thermal Power 1 and Thermal Power 2, as base load units, maintain relatively stable output levels, the system prioritizes the consumption of renewable energy such as wind power and photovoltaic power, and the energy storage system is mainly charged during the low-load periods of 1-4 hours and 14-16 hours, and discharged during the peak load periods of 10-13 hours and 17-22 hours, reflecting the typical peak shaving and valley filling characteristics.

[0266] In contrast, Case B, a distributed blue-rod model that takes into account the uncertainty of wind and solar output, shows a more cautious and flexible scheduling strategy. First, in terms of energy storage scheduling, the charging and discharging mode is more dynamic and is no longer limited to a simple intraday cycle. Instead, it is fine-tuned according to the real-time needs of the system, especially in the 5-8h and 19-22h periods, showing more reasonable charging and discharging decisions. Second, in terms of unit combination, the output distribution of thermal power units is more balanced, effectively responding to Figure 2 The uncertainty range of wind and solar output is shown in Figure 2. This shift in dispatch mode reflects that the system is placing greater emphasis on operational robustness and flexibility after considering uncertainty, avoiding system risks that may arise from over-reliance on fluctuating resources.

[0267] (3) Carbon flow analysis

[0268] Figure 5 The difference in the spatial and temporal distribution of the node carbon potential under the two scenarios is clearly shown. Figure 5 In Case A (a), the overall system node carbon potential is high, with a distinct high carbon potential band forming around nodes 1, 2, and 9, reaching a maximum carbon potential of nearly 230 tCO₂ / MWh. This uneven carbon potential distribution also exhibits significant fluctuations over time, becoming more pronounced during the 18-24 hour high-load period.

[0269] After introducing uncertainty considerations, Figure 5The carbon potential distribution of the nodes in Case B shown in (b) shows significant improvement. First, the overall carbon potential level is significantly reduced, the scope of the high carbon potential area is greatly reduced, and the maximum carbon potential of the system is reduced to about 190tCO2 / MWh. Secondly, the carbon potential is more balanced in spatial distribution, the carbon potential difference between nodes is reduced, and the original high carbon potential concentration area is effectively alleviated. In addition, the volatility of carbon potential in the time dimension is also significantly reduced, indicating that the system can manage carbon emissions more stably and avoid excessive concentration of carbon emissions in specific periods. This improvement directly reflects the advantages of distributed robust optimization in the rationality of resource allocation. Further comparison Figure 6 The branch carbon flow rate distribution in Figure 6 In Case A shown in (a), the carbon flow is mainly concentrated on a few key routes, such as branches 2-3 and 18-21. This unbalanced carbon flow distribution not only increases the carbon emission pressure in some areas of the system, but may also lead to regional imbalances in the carbon trading market.

[0270] In contrast, Figure 6 In Case B (b), the branch carbon flow distribution is more dispersed and balanced, with a significant decrease in high-carbon flow branches and a significant reduction in the peak carbon flow rate. Especially during high-load periods, the spatial distribution of carbon flow is more uniform, and the differences in carbon flow between branches are reduced. This balanced carbon flow distribution demonstrates that distributional robust optimization, after accounting for uncertainty, can achieve a more reasonable carbon emissions allocation and provide a fairer basis for inter-regional carbon emissions trading.

[0271] In summary, while traditional deterministic scheduling models maximize the utilization of renewable energy, they underestimate the impact of uncertainty in wind and solar output, resulting in uneven distribution of carbon emissions in both spatial and temporal dimensions and a high overall carbon emission intensity. The distributed robust optimization framework based on Wasserstein distance proposed in this paper achieves more robust resource allocation and carbon emission management while ensuring system reliability by scientifically considering the probabilistic distribution characteristics of wind and solar output.

[0272] (4) Comparison with other uncertain optimization algorithms

[0273] The confidence level is set to 0.95. To verify the superiority of the method proposed in this invention, the Wasserstein distance-based robust optimization proposed in this invention is compared with traditional robust optimization and stochastic optimization (SO) in terms of solution efficiency and cost under different sample numbers. The solution efficiency results are shown in Table 2:

[0274] Table 2 Comparison of solution efficiency of each algorithm under different sample numbers

[0275] algorithm 1000 samples(s) 3000 samples(s) 7000 samples(s) 10,000 samples(s) SO 16.41 57.48 187.41 378.63 RO 1.03 1.67 2.64 4.80 DRO 7.67 10.13 13.21 15.35

[0276] From the perspective of solution efficiency, the data in Table 2 shows that as the sample size increases from 1000 to 10000, the calculation time of SO increases linearly, climbing sharply from 16.41 seconds to 378.63 seconds, an increase of up to 23 times, and the solution burden is relatively large. RO maintains a high computational efficiency at all sample sizes, increasing from 1.03 seconds to only 4.80 seconds. This is because RO does not consider probability distribution information and only focuses on the uncertainty set. When the sample size is expanded by 10 times, the solution time of the DRO algorithm of the present invention only increases by about 2 times. This feature is due to the fact that the Wasserstein distance used in the present invention only searches for boundaries through historical data, and the solution will not become more complicated as the number of samples increases. At the same time, the duality theory and affine decision rule effectively simplify the computational complexity.

[0277] The cost results are shown in Table 3:

[0278] Table 3 Comparison of cost results of each algorithm under different sample numbers

[0279] algorithm 1000 samples (yuan) 3000 samples (yuan) 7000 samples (yuan) 10,000 samples (yuan) SO 1569458 1569458 1569423 1569423 RO 2488503 2488503 2488503 2488503 DRO 1991630 1902436 1797304 1663667

[0280] From an economic perspective, Table 3 shows that the cost of RO remains basically unchanged under all sample sizes. This phenomenon directly verifies the basic principle that the RO method does not rely on sample distribution information and only optimizes based on the worst case of the uncertainty set. It also reflects its inherent over-conservatism. The cost of the SO method also shows a high degree of stability. This is because SO is based on scenario optimization and its core algorithm does not change with the sample size, but this low cost cannot provide a safety guarantee for unknown scenarios. The DRO of the present invention shows a significant downward trend in system operating costs as the sample size increases. This feature essentially reflects that the DRO method can effectively utilize the distribution information in the sample to optimize the decision boundary. The richer the sample, the more accurate the characterization of the true distribution, and the more accurate the conservativeness of the decision, thereby avoiding unnecessary economic losses. This result verifies the significant advantages of the present invention in balancing system safety and economy.

[0281] Combining the analysis of Tables 2 and 3, it can be seen that the distributionally robust optimization method based on Wasserstein distance proposed in the present invention avoids the excessive conservatism of RO and the insufficient computational efficiency of SO while maintaining moderate computational complexity; more importantly, as the data sample size increases, the method exhibits significant data-driven characteristics, can automatically adjust the degree of decision conservatism, and continuously optimize economic efficiency without affecting safety, providing practical scheduling decision support for power systems with a high proportion of renewable energy.

[0282] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A robust low-carbon dispatching method for transmission network distribution based on Wasserstein distance, characterized by: The following steps are included: S1. Establish a deterministic low-carbon economic dispatch model that includes thermal power costs and carbon emission costs; S2. Based on the Wasserstein distance, the uncertainty set of wind and solar power output is constructed, and the deterministic low-carbon economic dispatch model containing thermal power costs and carbon emission costs is converted into a two-stage distributed robust optimization model using affine decision making. S3. Using the duality theory, the two-stage distributed blue stick optimization model is simplified into a new two-stage distributed blue stick optimization low-carbon economic dispatch model; S4. Solve the new two-stage distributed blue stick optimization low-carbon economic dispatch model and obtain the power flow results including branch power and output of each unit; S5. Establish a network-wide carbon emission flow model including energy storage; S6. Input the tidal flow result obtained in step S4 into the network-wide carbon emission flow model including energy storage in step S5 to obtain the network-wide carbon flow distribution under the tidal flow result.

2. The Wasserstein distance-based robust low-carbon dispatching method for transmission network distribution according to claim 1, characterized in that: In step S1, the objective function of the deterministic low-carbon economic dispatch model including thermal power cost and carbon emission cost is: In the formula, after the power generation cost is piecewise linearized into m segments, the piecewise linearized power generation cost f is obtained gen : Among them, K s Represents the slope of each section of the coal consumption function after piecewise linearization, and the coal consumption generated when the unit is started and running at minimum output Output of each unit p gen,s : Start-stop costs Among them, C g,U is the total startup cost of coal-fired unit g; C g,D is the total shutdown cost of coal-fired unit g; carbon emission cost Among them, e g is the carbon emission intensity of coal-fired unit g; f curt Cost of curtailing wind and solar power; The constraints in the first stage include power flow constraints, energy storage operation constraints, thermal power unit operation constraints, and wind and solar curtailment constraints. (1) Power flow constraints: -2π≤θ≤2π (3) Formula (2) gives the power balance constraint, where P dis is the energy storage discharge power; P ch is the energy storage charging power; P l is the branch current; P wind Forecast output of wind turbine; P pv Forecast output of photovoltaic units; P wcurt is the wind power curtailment; P vcurt is the abandoned optical power; P L For load; Formula (3) gives the node phase angle constraint, θ is the node phase angle; Formula (4) gives the branch power flow constraint, X l is the impedance of the branch; Δθ is the phase angle difference between the first and last nodes; P l,max and P l,min are the upper and lower limits of the branch power flow respectively; the branch power flow adopts the simplified DC power flow equation; (2) Energy storage operation constraints: B ch (t)+B dis (t)≤1 (5) Equation (5) gives the energy storage charge and discharge mutual exclusion constraint, where B ch , B dis are 0-1 variables representing the energy storage charging and discharging status; Formula (6) gives the upper and lower limit constraints of energy storage charging and discharging power, where P ch，max , P dis，max They are the upper limits of energy storage charging and discharging power respectively; Equation (7) gives the constraints of the energy storage state of charge SOC, where η ch , η dis are energy storage charging and discharging efficiency; E is energy storage capacity; SOC max and SOC min They are the upper and lower limits of energy storage SOC; SOC initial and SOC end They are the initial and final states of energy storage SOC; SOC set is the set SOC state; (3) Operation constraints of thermal power units: Formula (8) gives the output constraint of thermal power units, where: and are the upper and lower limits of the output of thermal power unit g; u g It is a 0-1 variable indicating the start and stop status of thermal power unit g in each period; Formula (9) gives the start and stop time constraints of thermal power units, where T g，on and T g，off are the start-up and shutdown times of thermal power unit g; T g，on，min and T g，off，min are the minimum start-up and shutdown times of thermal power unit g; Formula (10) gives the start-up and shutdown cost constraints of thermal power units, where H g and J g are the startup and shutdown cost coefficients of thermal power unit g, respectively; Equation (11) gives the unit hot standby constraint, where μ is the hot standby coefficient; P L is the total load in each time period; Formula (12) gives the unit climbing constraint, where R up，g and R down，g They are the up and down ramp rates of thermal power unit g; Equation (13) gives the emission constraints for the start and stop of thermal power units, where SE g and SD g are the carbon emission coefficients of thermal power units starting and stopping; (4) Constraints on curtailment of wind and solar power: 0≤P wcurt ≤P wind (14) 0≤P vcurt ≤P pv (15) Equation (17) gives the wind power curtailment constraint; Equation (18) gives the constraint on the abandoned optical power.

3. The Wasserstein distance-based robust low-carbon dispatching method for transmission network distribution according to claim 2, characterized in that: In step S1, since the constraints are all equality or inequality constraints, the first stage constraint condition is abstracted as Ax-b≤0, where x is the first stage decision variable including P dis 、P ch 、P l 、P wind 、P pv 、P wcurt 、P vcurt 、P L ,θ,SOC,P gen,g 、B ch 、B dis 、u g , belongs to the set Г; A and b are coefficient matrices. The deterministic low-carbon economic dispatch model containing thermal power cost and carbon emission cost is abstracted as follows: Where, f T is the cost coefficient vector corresponding to all first-stage decision variables.

4. The Wasserstein distance-based robust low-carbon dispatching method for transmission network distribution according to claim 2, characterized in that: In step S2, the wind and solar power output uncertainty set is constructed based on the Wasserstein distance, specifically, S21, for the wind historical prediction error sample set {ξ1,ξ2,…,ξ n ,…,ξ N }, then the empirical distribution of wind and solar power output forecast error is Where, ξ n is the nth historical forecast error sample; Distribute experience As an estimate of the true distribution P, when the total number of samples N approaches infinity, we have Wasserstein distance between empirical distribution and true distribution Where inf represents the lower bound; For the empirical distribution to the joint probability distribution of the true distribution P; ξ is the error parameter that obeys the true distribution P; ||·||1 represents the 1 norm; S22. Empirical distribution Construct the wind and solar power output uncertainty set X with the Wasserstein sphere as the center and ε(N) as the radius: Where, Β Ξ is the probability distribution set that supports all data-driven support sets Ξ; ε(N) is the radius of the coverage uncertainty range, which controls the uncertainty range around the empirical distribution; when the total number of samples N approaches infinity, At this time, the sphere is reduced to a point, that is, At this point, the empirical distribution is the true distribution; S23. Calculate the Wasserstein radius ε(N) using quantile estimation: In the formula, β is the confidence level, D is the coefficient, in, is the sample mean; υ is a coefficient greater than zero; S24. After standardizing the historical forecast error sample set, the uncertainty parameter can be obtained Where, is the sample variance; uncertain parameters The mean and variance of are 0 and 1; Let Θ be the uncertain parameter The uncertain set of , is: In the formula, the uncertain parameters for The nth element in ; d is the boundary, so solving the uncertainty set Θ that characterizes the range of wind power prediction error is equivalent to solving the boundary d; S25, boundary d is solved by the following boundary solution formula: Where, d max is the upper limit of the boundary; sup represents the supremum; P std and K std They represent the true probability distribution and fuzzy uncertainty set of error parameters respectively; η represents the confidence of the support set; Using duality theory to simplify the boundary solution formula is: Where κ is the dual variable; (·) + Represents the maximum value of 0 and the variables in brackets; Combined with formula (24), formula (23) is simplified to: The boundary d is determined by the boundary solution formula of formula (25). According to step S24, the uncertainty set Θ of the original space is obtained by inverse transformation to obtain the support set Ξ:

5. The Wasserstein distance-based robust low-carbon dispatching method for transmission network distribution according to claim 3, characterized in that: In step S2, the deterministic low-carbon economic dispatch model including thermal power cost and carbon emission cost is converted into a two-stage distributed robust optimization model using affine decision making. Specifically, S21. Use affine decision to adjust the output: Total wind and solar forecast error Among them, the prediction error of wind power Where, is the actual output of wind power, and the prediction error of photovoltaic in, The actual output of photovoltaic power. Thermal power unit output adjustment, adjusted thermal power output Among them, a g represents the affine adjustment coefficient of thermal power units; Adjustment of upper and lower limits of thermal power unit output: Adjustment of hot standby constraints for thermal power units: Adjustment of thermal power unit climbing constraints: Energy storage charging and discharging power adjustment: Where, and Represent the adjusted energy storage charging and discharging power respectively; a ch and a dis represent the affine adjustment coefficients for energy storage charging and discharging, respectively; Adjustment of upper and lower limits of energy storage charging and discharging: Energy storage charging and discharging SOC constraint adjustment: Where, represents the adjusted SOC; Adjustment of abandoned optical power: Where, is the adjusted abandoned optical power; a vcurt is the light rejection affine adjustment coefficient; Wind power curtailment adjustment: Where, is the adjusted abandoned optical power; a wcurt is the light rejection affine adjustment coefficient; Adjustment of upper and lower limits of wind power curtailment: Adjustment of upper and lower limits of abandoned optical power: Power balance constraint adjustment: The objective function is to minimize the first-stage objective function plus the worst-case minimum adjustment cost: Where, represents the expectation of the minimum adjustment cost of the worst scenario in the fuzzy uncertainty set X; E P (·) is the expected function; To adjust costs; S22. According to the constraints and objective function in step S21, the two-stage distributed robust optimization model is expressed as: Where, d T represents the coefficient vector corresponding to the second-stage decision variables; represents the second stage objective function; represents the second stage constraints, where E represents the coefficient matrix, Parameter representing the second-stage error.

6. The Wasserstein distance-based robust low-carbon dispatching method for transmission network distribution according to claim 5, characterized in that: In step S3, the duality theory is used to simplify the two-stage distributed blue stick optimization model into a new two-stage distributed blue stick optimization low-carbon economic dispatch model, specifically, S31. Apply duality theory to transform formula (26) to obtain: Where γ is the duality coefficient; represents the i-th error sample; τ i is an auxiliary variable; S32. Further transform formula (28) into: Where, and ξ Represent the upper and lower limits of error respectively; I T represents a unit vector; S33. Combining Equations (16), (26) and (29), we can get a new two-stage distributed blue stick optimization low-carbon economic dispatch model:

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