Transmission and distribution system cooperative scheduling method considering decision dependence uncertainty

Abstract

The invention discloses a transmission and distribution system cooperative scheduling method considering decision dependence uncertainty, and relates to the field of power system operation optimization, and the method comprises the steps: 1, respectively building system determinacy optimization scheduling models with the minimum operation cost of a power transmission system and a power distribution system as a target; step 2, in combination with probability information of new energy output and load power of the transmission and distribution systems, obtaining equivalent value probability distribution of transmission and distribution coupling nodes through a convolution algorithm, and constructing a probability distribution set capable of representing boundary coupling variable decision dependence uncertainty between the transmission and distribution systems based on multiple discrete scenes; 3, the probability distribution set rewrites the transmission and distribution system certainty optimization scheduling model into a two-stage distribution robust optimization scheduling model; and step 4, adopting an integrated improved alternating direction multiplier method and a distributed solution algorithm listed in a constraint generation algorithm, and combining a solver Gurobi to realize distributed solution of the robust optimization model, so that the calculation speed is accelerated while the solution optimality is ensured.

Description

Technical Field

[0001] This invention relates to the field of power system optimization scheduling, specifically a method for coordinated scheduling of transmission and distribution systems that takes into account the uncertainty of decision-dependent processes. Background Technology

[0002] In recent years, the integration of distributed power sources and energy storage facilities into distribution systems has led to more flexible and dynamic operation, and increasingly close interaction between transmission and distribution systems. Traditional top-down dispatching models often result in insufficient coordination between generation and consumption plans between transmission and distribution systems, making it difficult to guarantee a flexible balance between the two. Furthermore, with the large-scale integration of centralized renewable energy, distributed renewable energy, and flexible loads into the power system, transmission and distribution systems exhibit strong uncertainties. In a transmission-distribution independent dispatching model, the transmission system determines coupling variables, while the distribution system uses these coupling variables as boundary conditions to determine its own dispatching scheme. However, in a transmission-distribution coordinated dispatching model, transmission and distribution systems can interact with each other based on their own resource conditions, significantly enhancing their interdependence. Since the boundary variables provided by the transmission and distribution systems are unknown to each other and directly influenced by their respective dispatching decisions, these boundary variables exhibit uncertainty, known as decision-dependent uncertainty. Current research often neglects this issue, focusing instead on the impact of decision-independent uncertainty factors on the optimized operation of transmission and distribution systems. However, if the actual operating conditions deviate from the assumptions upon which the dispatching plan is based, the dispatching plan may fail to be effectively executed, thereby affecting power supply reliability. Therefore, the coordinated optimization scheduling of the transmission and distribution system is of great significance to the economic and safe operation of the entire system. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and provide a collaborative scheduling method for a transmission and distribution system that takes into account the uncertainty of decision-dependent factors.

[0004] The object of the present invention is achieved through the following technical solutions:

[0005] A method for coordinated scheduling of a transportation and distribution system that takes into account decision-dependent uncertainty includes the following steps:

[0006] Step 1: Establish deterministic optimization scheduling models for the transmission system and the distribution system respectively, with the goal of minimizing the operating costs of the two systems. The tie lines between the two systems are considered as consistency constraints and included in the scheduling models.

[0007] Step 2: Combining the probability information of the new energy output and load power of each transmission and distribution system, the equivalent value probability distribution of the transmission and distribution coupling nodes is obtained through the convolution algorithm. Based on multiple discrete scenarios, a set of probability distributions that can characterize the decision dependence uncertainty of the boundary coupling variables between transmission and distribution systems is constructed.

[0008] Step 3: Based on the probability distribution set of uncertain factors, the deterministic optimal scheduling model of the transmission and distribution system is rewritten into a two-stage sub-Bruker optimal scheduling model.

[0009] Step four involves using an integrated and improved Alternating Directional Multiplier Method (ADMM) and List Constraint Generation Algorithm (CCG) distributed solution algorithm, combined with the solver Gurobi, to achieve distributed solution of the two-stage sub-Bruker optimization model, thereby accelerating the computation speed while ensuring optimal solution.

[0010] Furthermore, the power transmission system includes centralized new energy generating units and thermal power units; the power distribution system includes distributed new energy generating units, controllable distributed power sources, and energy storage systems.

[0011] Furthermore, the objective function of the power transmission system scheduling model in step one is to minimize the total operating cost, including the start-up and shutdown of thermal power units, fuel costs, and the costs of curtailment and load shedding of new energy sources.

[0012] The objective function of the power transmission system is:

[0013] ;

[0014] ;

[0015] ;

[0016] ;

[0017] ;

[0018] ;

[0019] Where s and u are respectively related to the set of nodes Ω of the power transmission system. T，bus Thermal power unit set Ω G For the index number; C T , C G C T，u C T，ls and C T，pc These are, respectively, the operating cost of the power transmission system, the imbalance cost, the fuel cost of thermal power units in the power transmission system, the start-up and shutdown cost of the units, and the cost of load shedding and power curtailment; c lc c pc These are the unit prices for cost items; a u , b u c u These are the fuel cost coefficients for thermal power units; For the output of thermal power unit u; κ t，uLet P be the start-up and shutdown status of the u-th generating unit at time t; c1 and c0 are the start-up and shutdown costs of the thermal power unit, respectively; P T，lc P T，pc These refer to the load shedding and power abandonment of the power transmission system, respectively. This is an auxiliary function for the quadratic term of the operating cost of thermal power unit u.

[0020] Furthermore, the objective function of the power distribution system scheduling model in step one aims to minimize the operating cost of the power distribution system, including the operating cost of distributed controllable power sources, the operating cost of energy storage systems, and the cost of load shedding and renewable energy curtailment.

[0021] The objective function of the power distribution system is:

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] Where k, i, d, and b are respectively related to the set of nodes Ω of the power distribution system. D，bus , power distribution system collection Ω D Controllable distributed power source set Ω DG and energy storage system collection Ω B For the index number; C D C loss , C DG C cyc C ls and C pc These include the operating costs of the power distribution system, imbalance costs and fuel costs of controllable power sources, operating costs of the energy storage system, and costs of load shedding and power curtailment. , , and These are the unit cost of distributed controllable power output, the unit cost of energy storage cycle life, and the unit cost of renewable energy curtailment and load shedding, respectively. Provide power for distributed power sources; , These represent the discharge / charge amounts of energy storage device b at node k during time period t. Let t be the energy storage system capacity during time period t; These represent the amount of abandoned renewable energy and the amount of unloaded power in the power distribution system.

[0027] Furthermore, the power transmission system operation constraints mentioned in step one include thermal power unit output constraints, thermal power unit ramping constraints, thermal power unit start-up and shutdown constraints, power transmission network power flow constraints, centralized new energy unit output constraints, and curtailment and load shedding limit constraints.

[0028] The relevant constraints for the thermal power units are as follows:

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] ;

[0034] ;

[0035] in, This represents the power output boundary of the thermal power unit, and subsequent... These represent the upper and lower boundaries of the variable, respectively; r u，t is the start-up and shutdown variable for thermal power units; TS and TO are the minimum shutdown / start-up times for conventional units, respectively. , These represent the uphill / downhill ramp rates of thermal power unit u, respectively.

[0036] The power flow constraints of the power transmission network are as follows:

[0037] ;

[0038] ;

[0039] Among them, G l-s Describe the impact of power changes at node s on line l; P s，t , These represent the power supply and load values ​​of the nodes, respectively. This is an identifier for the power transmission system supplying power to the distribution network. This is an identifier sent back from the power distribution system to the power transmission system;

[0040] The output constraint of the centralized new energy unit is:

[0041] ;

[0042] ;

[0043] The load shedding and power abandonment constraints are as follows:

[0044] ;

[0045] .

[0046] Furthermore, the power distribution system operation constraints mentioned in step one include distributed controllable power source output constraints, energy storage system operation constraints, power distribution network power flow constraints, distributed new energy unit output constraints, and curtailment and load shedding limit constraints.

[0047] The output constraint of the distributed controllable power source is:

[0048] ;

[0049] The operating constraints of the energy storage system are:

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] ;

[0055] in, , These represent the charging and discharging states of the energy storage device; η cha η dis These are the charging and discharging rates of the energy storage device;

[0056] The power flow constraints of the distribution network are:

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] ;

[0062] Among them, P i，kj Q i，kj These are the active power and reactive power on the branch line, respectively. , ρnode and ρbranch are the squares of the node voltage and the branch current, respectively; g and b are the conductance and susceptance at the tie point, respectively; r ij xij These are the resistance and reactance of the branch circuit, respectively.

[0063] The output constraint of the distributed new energy units is:

[0064] ;

[0065] ;

[0066] The load shedding and power curtailment constraints of the power distribution system are as follows:

[0067] ;

[0068] .

[0069] Furthermore, in step one, each tie line coupled between the transmission and distribution systems must satisfy the requirement that power supply equals power consumption, while also having a certain transmission margin to provide available capacity for mutual assistance between the transmission and distribution systems.

[0070] The aforementioned connection line constraints are:

[0071] ;

[0072] ;

[0073] ;

[0074] in, , These represent the power transmitted through the tie lines in the power transmission and distribution system; , These represent the transmission margins for different transmission directions.

[0075] Furthermore, the set of uncertainties for decision dependence of boundary coupled variables based on multiple discrete scenarios mentioned in step two is as follows:

[0076] ;

[0077] ;

[0078] ;

[0079] ;

[0080] ;

[0081] ;

[0082] ;

[0083] Among them, φD，net 、φ D，r and φ D，l These represent the probability distributions of the net load power of the power distribution system, the processing power of the new energy units, and the power load; ⨂ represents the convolution operation; P D，EL This represents the probability that the equivalent load falls within the integral region under ideal conditions. To account for the probability that the equivalent load of decision-dependent uncertainty falls within the integral region; This represents the actual output of all controllable power sources in the power distribution system at time t. p represents the maximum output of all controllable power sources in the power distribution system at time t. s The true probability of a random scene within a probability distribution set; Let θ1 be the reference probability of the random scenario; N be the number of samples of the random variable; S be the number of scenarios in the probability distribution set; θ1, θ2 are the reference probabilities of the random scenario. ∞ These represent the confidence levels satisfied by the probability distributions in the 1-norm and ∞-norm, respectively. It is a set of probability distributions.

[0084] Furthermore, the two-stage distributed bar optimization scheduling model for the transportation and distribution system based on multiple discrete scenarios described in step three is as follows:

[0085] The two-stage distributed bar scheduling model of the power transmission system is as follows:

[0086] ;

[0087] ;

[0088] ;

[0089] ;

[0090] ;

[0091] ;

[0092] ;

[0093] ;

[0094] Where c and d are the coefficient matrices of the objective functions of the first and second stages in the power transmission system scheduling model, respectively; AD, K, F, G, I u K and are the coefficient matrices of the variables under the corresponding constraints; B, D, E, R, and H are constant column vectors; Ax tran ≤b represents the constraint related to the first stage; Dy tran ≤d defines the inequality constraints related to the second-stage variables; By tran=r represents the equality constraints related to the second-stage variables in the model; Fx tran +Gy tran ≤e represents the association constraint between the decision variables in the two stages; For each time period, the output and load power of renewable energy are the predicted values; ||Kx tran ||≤h T x tran The SOC constraint is introduced into the model to handle the nonlinear terms in the thermal power operating cost function;

[0095] The two-stage distributed bar scheduling model for the power distribution system is as follows:

[0096] ;

[0097] ;

[0098] ;

[0099] ;

[0100] ;

[0101] ;

[0102] ;

[0103] ;

[0104] Where c and d are the coefficient matrices of the objective functions of the first and second stages in the power distribution system dispatch model, respectively; A, D, K, F, G, I, and K are the coefficient matrices of the variables under the corresponding constraints; B, D, E, R, and H are constant column vectors; Ax dist ≤b represents the constraint related to the first stage; Dy dist ≤d defines the inequality constraints related to the second-stage variables; By dist =r represents the equality constraints related to the second-stage variables in the model; Fx dist +Gy dist ≤e represents the association constraint between the decision variables in the two stages; For each time period, the output and load power of renewable energy are the predicted values; ||Ky dist ||≤h T y dist The SOC constraint is introduced into the model to handle the power flow nonlinearity.

[0105] Furthermore, the distributed solution algorithm described in step four integrates the improved Alternating Direction Multiplier Method (ADMM) and the List Constraint Generation Algorithm (CCG), and combines it with the Gurobi solver for the two-stage distributed bar optimization model. The distributed solution process achieved through ADMM is as follows:

[0106] Step 1: Based on the ADMM algorithm, a consensus variable regarding the range of boundary variables is introduced, rewriting the transmission and distribution system scheduling model as a dual problem; the two-stage DRO scheduling models for the transmission and distribution systems in the nth iteration are as follows:

[0107] ;

[0108] ;

[0109] in, These represent the power when the power transmission and distribution system is used as an equivalent power source; The power requirements of the transmission and distribution system as equivalent loads are respectively; EL，t , z ES，t These are the consensus variables representing the upper and lower ranges of the boundary variables in each iteration; λ tran and λ dist These are the Lagrange multipliers related to the transmission and distribution system interconnections; ρ is the penalty coefficient related to the decision variables; and n is the number of iterations.

[0110] Step 2: Consistency of key parameters of the transmission and distribution system is achieved by updating the Lagrange multipliers using the current boundary information. The multiplier update criterion related to tie-line power is as follows:

[0111] ;

[0112] The update criterion for consensus variables is:

[0113] ;

[0114] Step 3: The algorithm stops converging when the iterative convergence accuracy of the transmission and distribution system satisfies the following formula:

[0115] ;

[0116] ;

[0117] ;

[0118] in, Let R be the verification function; and S be the original residual and the dual residual, respectively.

[0119] Furthermore, the distributed solution algorithm described in step four integrates the improved Alternating Direction Multiplier Method (ADMM) and the List Constraint Generation Algorithm (CCG), and combines it with the Gurobi solver to solve the two-stage sub-Bruker optimization model in a distributed manner. The process of solving the sub-Bruker model through CCG is as follows:

[0120] Step 1, the compact form of the two-stage sub-Bruker model for dual decomposition using ADMM is as follows:

[0121] ;

[0122] Where x and y are the decision variables for the first and second stages of the scheduling model, respectively:

[0123] ;

[0124] Step 2: Decompose the three-level optimization problem of min-max-min in Step 1 into main and sub-problems and iterate them alternately. The main and sub-problems are as follows:

[0125] ;

[0126] ;

[0127] Step 3: Input the result of solving the main problem into the subproblem for verification, add constraints to the main problem in the subproblem, and solve iteratively; when the iteration reaches the convergence accuracy, the final scheduling result is obtained.

[0128] Furthermore, the integrated improved Alternating Direction Multiplier Method (ADMM) and List Constraint Generation Algorithm (CCG) distributed solution algorithm described in step four, combined with the Gurobi solver for the two-stage distributed bar optimization model, specifically involves:

[0129] First, during the DRO model solution phase, the binary variables solved by the CCG algorithm in the main problem are fixed, and the ADMM algorithm is only applied to terms containing coupled variables, considering the updates of their Lagrange multipliers and tie-line coupled variables. Then, the distribution system scheduling results are transmitted to the transmission system to correct the consensus variables that depend on decision uncertainty. Next, {x} is verified by solving subproblems, and the C&CG iterative process is completed by adding cuts to the main problem. Finally, the scheduling results are output until the ADMM algorithm and the C&CG algorithm satisfy the convergence conditions.

[0130] The beneficial effects of this invention are:

[0131] (1) By fully considering the collaborative relationship between the transmission and distribution systems, this invention constructs a set of decision-dependent uncertainties based on multiple discrete scenarios through the source-load probability information of the transmission and distribution systems, which refines the collaborative scheduling process of the transmission and distribution systems, making the scheduling model fit the actual engineering and effectively improving the computational accuracy of distributed optimization.

[0132] (2) The distributed method integrating ADMM and CCG algorithms described in this invention can effectively improve the solution speed of the transportation and distribution coordination model, reduce the computation time, and improve the efficiency of scheduling plan formulation. Attached Figure Description

[0133] Figure 1 This is a schematic diagram of the dispatching process of the distribution system of the present invention;

[0134] Figure 2 This is a schematic diagram illustrating the importance of load nodes in this invention;

[0135] Figure 3 This is a schematic diagram illustrating the principle of the equivalent imbalance cumulative effect of the present invention. Figure 4 The flowchart for the distributed solution of ADMM-CCG transportation and distribution coordinated scheduling is shown below. Detailed Implementation

[0136] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the following description.

[0137] like Figure 1 As shown, a collaborative scheduling method for a power transmission and distribution system that takes into account the uncertainty of decision-dependent processes is provided, comprising the following steps:

[0138] Step 1: Establish deterministic optimization scheduling models for the transmission system and the distribution system respectively, with the goal of minimizing the operating costs of the two systems. The tie lines between the two systems are considered as consistency constraints and included in the scheduling models.

[0139] Step 2: Combining the probability information of the new energy output and load power of each transmission and distribution system, the equivalent value probability distribution of the transmission and distribution coupling nodes is obtained through the convolution algorithm. Based on multiple discrete scenarios, a set of probability distributions that can characterize the decision dependence uncertainty of the boundary coupling variables between transmission and distribution systems is constructed.

[0140] Step 3: Based on the probability distribution set of uncertain factors, the deterministic optimal scheduling model of the transmission and distribution system is rewritten into a two-stage sub-Bruker optimal scheduling model.

[0141] Step four involves using an integrated and improved Alternating Directional Multiplier Method (ADMM) and List Constraint Generation Algorithm (CCG) distributed solution algorithm, combined with the solver Gurobi, to achieve distributed solution of the two-stage sub-Bruker optimization model, thereby accelerating the computation speed while ensuring optimal solution.

[0142] The power transmission system mentioned in step one contains centralized new energy generating units and thermal power units; the power distribution system contains distributed new energy generating units, controllable distributed power sources, and energy storage systems.

[0143] The objective function of the power transmission system scheduling model in Step 1 is to minimize the total operating cost, including the start-up and shutdown of thermal power units, fuel costs, and the costs of curtailment and load shedding of renewable energy. The objective function is:

[0144] ;

[0145] ;

[0146] ;

[0147] ;

[0148] ;

[0149] ;

[0150] Where s and u are respectively related to the set of nodes Ω of the power transmission system. T，bus Thermal power unit set Ω G For the index number; C T , C G C T，u C T，ls and C T，pc These are the operating costs of the power transmission system, imbalance costs, and fuel costs, start-up and shutdown costs, load shedding costs, and curtailment costs of thermal power units within the power transmission system; c lc c pc These are the unit prices for cost items; a u b u c u These are the fuel cost coefficients for thermal power units; For the output of thermal power unit u; κ t，u Let P be the start-up and shutdown status of the u-th generating unit at time t; c1 and c0 are the start-up and shutdown costs of the thermal power unit, respectively; P T，lc P T，pc These refer to the load shedding and power abandonment of the power transmission system, respectively. This is an auxiliary function for the quadratic term of the operating cost of thermal power unit u.

[0151] The objective function of the power distribution system scheduling model in Step 1 aims to minimize the operating cost of the power distribution system, including the operating costs of distributed controllable power sources, energy storage systems, load shedding, and renewable energy curtailment. The objective function is as follows:

[0152] ;

[0153] ;

[0154] ;

[0155] ;

[0156] Where k, i, d, and b are respectively related to the set of nodes Ω of the power distribution system. D，bus , power distribution system collection Ω D Controllable distributed power source set Ω DG and energy storage system collection Ω B For the index number; C DG C cyc C D，ls and C D，pc These are the fuel cost of controllable power sources in the power distribution system, the operating cost of the energy storage system, and the cost of load shedding and power curtailment, respectively, with c being the unit cost of each item. Provide power for distributed power sources; , These represent the discharge / charge amounts of energy storage device b at node k during time period t. Let t be the energy storage system capacity during time period t.

[0157] The power transmission system operation constraints in step one include thermal power unit output constraints, thermal power unit ramping constraints, thermal power unit start-up and shutdown constraints, power transmission network power flow constraints, centralized new energy unit output constraints, and curtailment and load shedding limits.

[0158] The relevant constraints for the thermal power units are as follows:

[0159] ;

[0160] ;

[0161] ;

[0162] ;

[0163] ;

[0164] ;

[0165] in, This represents the power output boundary of the thermal power unit, and subsequent... These represent the upper and lower boundaries of the variable, respectively; r u，t is the start-up and shutdown variable for thermal power units; TS and TO are the minimum shutdown / start-up times for conventional units, respectively. , These represent the uphill / downhill ramp rates of thermal power unit u, respectively.

[0166] The power flow constraints of the power transmission network are as follows:

[0167] ;

[0168] ;

[0169] Among them, G l-s Describe the impact of power changes at node s on line l; P s，t , These represent the power supply and load values ​​of the nodes, respectively. This is an identifier for the power transmission system supplying power to the distribution network. It is a marker for the power distribution system to send back to the power transmission system.

[0170] The output constraint of the centralized new energy unit is:

[0171] ;

[0172] ;

[0173] The load shedding and power abandonment constraints are as follows:

[0174] ;

[0175] ;

[0176] The power distribution system operation constraints mentioned in step one include distributed controllable power source output constraints, energy storage system operation constraints, power distribution network power flow constraints, distributed new energy unit output constraints, and curtailment and load shedding limit constraints.

[0177] The output constraint of the distributed controllable power source is:

[0178] ;

[0179] The operating constraints of the energy storage system are:

[0180] ;

[0181] ;

[0182] ;

[0183] ;

[0184] ;

[0185] in, , These represent the charging and discharging states of the energy storage device; η cha η dis These represent the charge and discharge rates of the energy storage device.

[0186] The power flow constraints of the distribution network are:

[0187] ;

[0188] ;

[0189] ;

[0190] ;

[0191] ;

[0192] Among them, P i，kj Q i，kj These are the active power and reactive power on the branch line, respectively. , ρn represents the square of the node voltage and the square of the branch current, respectively; g and b represent the conductance and susceptance at the tie point, respectively; rn ij x ij These are the resistance and reactance of the branch circuit, respectively.

[0193] The output constraint of the distributed new energy units is:

[0194] ;

[0195] ;

[0196] The load shedding and power curtailment constraints of the power distribution system are as follows:

[0197] ;

[0198] ;

[0199] The constraints for the interconnection lines between the transmission and distribution systems in step one are as follows:

[0200] like Figure 2As shown, to ensure power supply reliability, power transmission and distribution systems often transmit power through multiple tie lines, meaning there are multiple coupling variables between the systems. Therefore, the coupling constraints of the power transmission and distribution system proposed in this embodiment consider two aspects: 1) Each tie line between the transmission and distribution systems must satisfy the condition that power supply equals power consumption; 2) In addition to the transmission capacity constraints of the tie lines themselves, a certain transmission margin must be reserved to provide available capacity for mutual support between the transmission and distribution systems, while preventing system instability or failure due to tie line overload, ensuring sufficient adjustment space in the event of emergencies. Specifically:

[0201] ;

[0202] ;

[0203] ;

[0204] in, , These represent the power transmitted through the tie lines in the power transmission and distribution system; , These represent the transmission margins for different transmission directions.

[0205] The set of uncertainties for decision dependence of boundary coupled variables based on multiple discrete scenarios in step two is as follows:

[0206] like Figure 3 As shown, assuming the predicted values ​​of renewable energy output and load power in the distribution system are independently distributed, the net load probability density function is the convolution of the two. Electricity demand only arises in the distribution system when the net load is positive and exceeds the maximum available generating capacity of the controllable power source. In other words, the probability information of electricity demand can be represented by integrating the net load probability density function over the region where the controllable power source's supply capacity is insufficient. Region a represents the probability distribution of the minimum equivalent load of the distribution system. However, due to the influence of distributed controllable power sources, the equivalent load also possesses probability information from region b. Therefore, this invention utilizes these two parts to jointly represent the set of probability distributions of boundary variables. Specifically, unlike previous uncertainties, in the first stage of transmission system scheduling optimization, the boundary variables considered are obtained through optimization rather than being pre-set. Specifically:

[0207] ;

[0208] ;

[0209] ;

[0210] ;

[0211] ;

[0212] ;

[0213] ;

[0214] Where, φ D，net 、φ D，r and φ D，l These represent the probability distributions of the net load power of the power distribution system, the processing power of the new energy units, and the power load; ⨂ represents the convolution operation; P D，EL This represents the probability that the equivalent load falls within the integral region under ideal conditions. To account for the probability that the equivalent load of decision-dependent uncertainty falls within the integral region; This represents the actual output of all controllable power sources in the power distribution system at time t. p represents the maximum output of all controllable power sources in the power distribution system at time t. s The true probability of a random scene within a probability distribution set; Let θ1 be the reference probability of the random scenario; N be the number of samples of the random variable; S be the number of scenarios in the probability distribution set; θ1, θ2 are the reference probabilities of the random scenario. ∞ These represent the confidence levels satisfied by the probability distributions in the 1-norm and ∞-norm, respectively. It is a set of probability distributions.

[0215] The two-stage distributed bar optimization scheduling model for the transportation and distribution system based on multiple discrete scenarios in step three is as follows:

[0216] The two-stage distributed bar scheduling model of the power transmission system is as follows:

[0217]

[0218]

[0219]

[0220]

[0221]

[0222]

[0223]

[0224]

[0225] Where c and d are the coefficient matrices of the objective functions of the first and second stages in the power transmission system scheduling model, respectively; A, D, K, F, G, I u K and are the coefficient matrices of the variables under the corresponding constraints; B, D, E, R and H are constant column vectors; Axtran ≤b represents the constraint related to the first stage; Dy tran ≤d defines the inequality constraints related to the second-stage variables; By tran =r represents the equality constraints related to the second-stage variables in the model; Fx tran +Gy tran ≤e represents the association constraint between the decision variables in the two stages; For each time period, the output and load power of renewable energy are the predicted values; ||Kx tran ||≤h T x tran The SOC constraint is introduced into the model to handle the nonlinear terms in the thermal power operating cost function.

[0226] The two-stage distributed bar scheduling model for the power distribution system is as follows:

[0227] ;

[0228] ;

[0229] ;

[0230] ;

[0231] ;

[0232] ;

[0233] ;

[0234] ;

[0235] Where c and d are the coefficient matrices of the objective functions of the first and second stages in the power distribution system dispatch model, respectively; A, D, K, F, G, I u K and are the coefficient matrices of the variables under the corresponding constraints; B, D, E, R, and H are constant column vectors; Ax dist ≤b represents the constraint related to the first stage; Dy dist ≤d defines the inequality constraints related to the second-stage variables; By dist =r represents the equality constraints related to the second-stage variables in the model; Fx dist +Gy dist ≤e represents the association constraint between the decision variables in the two stages; For each time period, the output and load power of renewable energy are the predicted values; ||Ky dist ||≤h T y distThe SOC constraint is introduced into the model to handle the power flow nonlinearity.

[0236] The distributed solution algorithm in step four integrates the improved Alternating Direction Multiplier Method (ADMM) and the List Constraint Generation Algorithm (CCG). The process of implementing distributed solution through ADMM is as follows:

[0237] Step 1: Based on the ADMM algorithm, a consensus variable regarding the range of boundary variables is introduced, rewriting the transmission and distribution system scheduling model as a dual problem. The two-stage DRO scheduling models for the transmission and distribution systems in the nth iteration are as follows:

[0238] ;

[0239] ;

[0240] in, These represent the power when the power transmission and distribution system is used as an equivalent power source; The power requirements of the transmission and distribution system as equivalent loads are respectively; EL，t , z ES，t These are the consensus variables representing the upper and lower ranges of the boundary variables in each iteration; λ tran and λ dist ρ represents the Lagrange multiplier associated with the transmission and distribution system connection lines; n represents the penalty coefficient associated with the decision variables; and n represents the number of iterations.

[0241] Step 2: Consistency of key parameters of the power transmission and distribution system is achieved by updating the Lagrange multipliers using the current boundary information. The multiplier update criterion related to tie-line power is as follows:

[0242] ;

[0243] The update criterion for consensus variables is:

[0244] ;

[0245] Step 3: When the iterative convergence accuracy of the transmission and distribution system satisfies the following formula, the algorithm stops converging:

[0246] ;

[0247] ;

[0248] ;

[0249] in, Let R be the verification function; and S be the original residual and the dual residual, respectively.

[0250] The process of solving the sub-Bruker model using CCG is as follows:

[0251] Step 1, the compact form of the two-stage sub-Bruker model for dual decomposition using ADMM is as follows:

[0252] ;

[0253] Where x and y are the decision variables for the first and second stages of the scheduling model, respectively:

[0254] ;

[0255] Step 2: Decompose the three-level optimization problem of min-max-min in Step 1 into main and sub-problems and iterate them alternately. The main and sub-problems are as follows:

[0256] ;

[0257] ;

[0258] Step 3: Input the result obtained from solving the main problem into the subproblem for verification. Add constraints to the main problem from the subproblem and solve iteratively. Obtain the final scheduling result when the iteration reaches convergence accuracy.

[0259] Step four describes the use of a distributed solution algorithm that integrates the improved Alternating Direction Multiplier Method (ADMM) and the List Constraint Generation Algorithm (CCG), combined with the Gurobi solver for a distributed solution of the two-stage sub-Bruker optimization model. Specifically:

[0260] like Figure 4 As shown, firstly, in the DRO model solution phase, the binary variables solved by the CCG algorithm in the main problem are fixed, and the ADMM algorithm only operates on terms containing coupled variables, considering the updates of their Lagrange multipliers and tie-line coupled variables; then, the distribution system scheduling results are transmitted to the transmission system to correct the consensus variables that depend on decision uncertainty; furthermore, {x} is verified by solving subproblems, and the C&CG iteration process is completed by adding cuts to the main problem; finally, the scheduling results are output until the ADMM algorithm and the C&CG algorithm satisfy the convergence conditions.

[0261] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A method for coordinated scheduling of a transportation and distribution system that takes into account decision-dependent uncertainty, characterized in that, Includes the following steps: Step 1: Establish deterministic optimization scheduling models for the transmission system and the distribution system respectively, with the goal of minimizing the operating costs of the two systems. The tie lines between the two systems are considered as consistency constraints and included in the scheduling models. Step 2: Combining the probability information of the new energy output and load power of each transmission and distribution system, the equivalent value probability distribution of the transmission and distribution coupling nodes is obtained through the convolution algorithm. Based on multiple discrete scenarios, a set of probability distributions that can characterize the decision dependence uncertainty of the boundary coupling variables between transmission and distribution systems is constructed. Step 3: Based on the probability distribution set of uncertain factors, the deterministic optimal scheduling model of the transmission and distribution system is rewritten into a two-stage sub-Bruker optimal scheduling model. Step four involves employing an integrated and improved distributed solution algorithm combining the alternating direction multiplier method and the list constraint generation algorithm, along with the solver Gurobi, to achieve distributed solution of the two-stage sub-Bruker optimization model. This approach ensures optimal solution while accelerating computation.

2. The method for coordinated scheduling of a transmission and distribution system considering decision-dependent uncertainty as described in claim 1, characterized in that, The power transmission system includes centralized new energy generating units and thermal power units; the power distribution system includes distributed new energy generating units, controllable distributed power sources, and energy storage systems.

3. The method for coordinated scheduling of a transmission and distribution system considering decision-dependent uncertainty according to claim 1, characterized in that, The objective function of the power transmission system scheduling model in step one is to minimize the total operating cost, including the start-up and shutdown of thermal power units, fuel costs, and the costs of curtailment and load shedding of new energy sources. The objective function of the power transmission system is: ； ； ； ； ； ； Where s and u are the index numbers of the power transmission system node set ΩT, bus, and thermal power unit set ΩG, respectively; CT, CG, CT,u, CT,ls and CT,pc are respectively the operating cost of the power transmission system, the imbalance cost, the fuel cost of thermal power units in the power transmission system, the start-up and shutdown cost of the units, and the cost of load shedding and power curtailment; clc and cpc are respectively the unit prices of the cost items; au, bu and cu are respectively the fuel cost coefficients of thermal power units; Let u be the output of the thermal power unit; κt, u be the start-up and shutdown status of the u-th unit at time t; c1, c0 be the start-up and shutdown costs of the thermal power unit; PT, lc, PT, pc be the load shedding and power curtailment of the power transmission system, respectively. This is an auxiliary function for the quadratic term of the operating cost of thermal power unit u.

4. The method for coordinated scheduling of a transmission and distribution system considering decision-dependent uncertainty according to claim 1, characterized in that, The objective function of the power distribution system scheduling model in step one aims to minimize the operating cost of the power distribution system, including the operating cost of distributed controllable power sources, the operating cost of energy storage systems, and the cost of load shedding and renewable energy curtailment. The objective function of the power distribution system is: ； ； ； ； Where k, i, d, and b are the index numbers of the distribution system node set ΩD, bus, distribution system set ΩD, controllable distributed power source set ΩDG, and energy storage system set ΩB, respectively; CD, Closs, CDG, Ccyc, Cls, and Cpc are the distribution system operating cost, imbalance cost, controllable power source fuel cost, energy storage system operating cost, load shedding cost, and power curtailment cost, respectively. , , and These are the unit cost of distributed controllable power output, the unit cost of energy storage cycle life, and the unit cost of renewable energy curtailment and load shedding, respectively. Provide power for distributed power sources; , These represent the discharge / charge amounts of energy storage device b at node k during time period t. Let t be the energy storage system capacity during time period t; These represent the amount of abandoned renewable energy and the amount of unloaded power in the power distribution system.

5. The method for coordinated scheduling of a transmission and distribution system considering decision-dependent uncertainty according to claim 1, characterized in that, The power transmission system operation constraints mentioned in step one include thermal power unit output constraints, thermal power unit ramping constraints, thermal power unit start-up and shutdown constraints, power transmission network power flow constraints, centralized new energy unit output constraints, and curtailment and load shedding limit constraints. The relevant constraints for the thermal power units are as follows: ； ； ； ； ； ； in, This represents the power output boundary of the thermal power unit, and subsequent... , , represent the upper and lower boundaries of the variables; ru, t are the start-up and shutdown variables of the thermal power unit; TS, TO are the minimum shutdown / start-up times of the conventional unit, respectively; , These represent the uphill / downhill ramp rates of thermal power unit u, respectively. The power flow constraints of the power transmission network are as follows: ； ； Where Gl-s describes the impact of power changes at node s on line l; Ps,t, These represent the power supply and load values ​​of the nodes, respectively. This is an identifier for the power transmission system supplying power to the distribution network. This is an identifier sent back from the power distribution system to the power transmission system; The output constraint of the centralized new energy unit is: ； ； The load shedding and power abandonment constraints are as follows: ； 。 6. The method for coordinated scheduling of a transmission and distribution system considering decision-dependent uncertainty according to claim 1, characterized in that, The power distribution system operation constraints mentioned in step one include distributed controllable power source output constraints, energy storage system operation constraints, power distribution network power flow constraints, distributed new energy unit output constraints, and curtailment and load shedding limit constraints. The output constraint of the distributed controllable power source is: ； The operating constraints of the energy storage system are: ； ； ； ； ； in, , ηcha and ηdis are the charge and discharge states of the energy storage device, respectively; ηcha and ηdis are the charge and discharge rates of the energy storage device, respectively. The power flow constraints of the distribution network are: ； ； ； ； ； Where Pi, kj, Qi, and kj are the active power and reactive power on the branch, respectively. , α is the square of the node voltage and the square of the branch current, respectively; g and b are the conductance and susceptance of the tie line landing point, respectively; rij and xij are the resistance and reactance of the branch, respectively. The output constraint of the distributed new energy units is: ； ； The load shedding and power curtailment constraints of the power distribution system are as follows: ； 。 7. The method for coordinated scheduling of a transmission and distribution system considering decision-dependent uncertainty according to claim 1, characterized in that, In step one, each tie line between the transmission and distribution systems must ensure that the power supply equals the power consumption, while also leaving a certain transmission margin to provide available capacity for mutual assistance between the transmission and distribution systems. The aforementioned connection line constraints are: ； ； ； in, , These represent the power transmitted through the tie lines in the power transmission and distribution system; , These represent the transmission margins for different transmission directions.

8. The method for coordinated scheduling of a transmission and distribution system considering decision-dependent uncertainty according to claim 1, characterized in that, The set of uncertainties for decision dependence of boundary coupled variables based on multiple discrete scenarios mentioned in step two is as follows: ； ； ； ； ； ； ； Where φD,net, φD,r and φD,l are the probability distributions of the net load power of the power distribution system, the processing power of the new energy units and the power load, respectively; ⨂ is the convolution operation; PD,EL is the probability that the equivalent load falls in the integration region under ideal conditions; To account for the probability that the equivalent load of decision-dependent uncertainty falls within the integral region; This represents the actual output of all controllable power sources in the power distribution system at time t. t represents the maximum output of all controllable power sources in the power distribution system at time t; ps represents the true probability of a random scenario within a probability distribution set. θ1 represents the reference probability of the random scenario; N represents the number of samples of the random variable; S represents the number of scenarios in the probability distribution set; θ1 and θ∞ represent the confidence levels satisfied by the probability distributions on the 1-norm and ∞-norm, respectively. It is a set of probability distributions.

9. A method for coordinated scheduling of a transmission and distribution system considering decision-dependent uncertainty according to claim 1, characterized in that, The two-stage distributed bar optimization scheduling model for the transportation and distribution system based on multiple discrete scenarios described in step three is as follows: The two-stage distributed bar scheduling model of the power transmission system is as follows: ； ； ； ； ； Where c and d are the coefficient matrices of the objective functions of the first and second stages in the power transmission system scheduling model, respectively; AD, K, F, G, Iu, and K are the coefficient matrices of the variables under the corresponding constraints; B, D, E, R, and H are constant column vectors; Axtran≤b is the constraint related to the first stage; Dytran≤d defines the inequality constraints related to the variables of the second stage; Bytran=r is the equality constraint related to the variables of the second stage in the model; Fxtran+Gytran≤e is the association constraint between the decision variables of the two stages; For each time period, the output and load power of renewable energy are the predicted values; ||Kxtran||≤hTxtran is the SOC constraint introduced in the model to handle the nonlinear terms in the thermal power operating cost function; The two-stage distributed bar scheduling model for the power distribution system is as follows: ； ； ； ； ； ； ； ； Where c and d are the coefficient matrices of the objective functions of the first and second stages in the power distribution system dispatch model, respectively; A, D, K, F, G, and Iu, K are the coefficient matrices of the variables under the corresponding constraints; B, D, E, R, and H are constant column vectors; Axdist≤b is the constraint related to the first stage; Dydist≤d defines the inequality constraint related to the variables of the second stage; Bydist=r is the equality constraint related to the variables of the second stage in the model; Fxdist+Gydist≤e is the association constraint between the decision variables of the two stages; The output and load power of renewable energy are the predicted values ​​for each time period; ||Kydist||≤hTydist is the SOC constraint introduced in the model to handle the power flow nonlinearity.

10. A method for coordinated scheduling of a transmission and distribution system considering decision-dependent uncertainty according to claim 1, characterized in that, The distributed solution algorithm described in step four integrates the improved alternating direction multiplier method and the column constraint generation algorithm. It also combines the Gurobi solver for the two-stage distributed bar optimization model. The distributed solution process implemented through the ADMM algorithm is as follows: Step 1: Based on the ADMM algorithm, a consensus variable regarding the range of boundary variables is introduced, rewriting the transmission and distribution system scheduling model as a dual problem; the two-stage DRO scheduling models for the transmission and distribution systems in the nth iteration are as follows: ； ； in, These represent the power when the power transmission and distribution system is used as an equivalent power source; λtransmission, λdistribution represent the power demand when the transmission and distribution system is used as an equivalent load, respectively; zEL,t, zES,t represent the consensus variables of the upper and lower ranges of the boundary variables in each iteration; λtran and λdist represent the Lagrange multipliers related to the transmission and distribution system tie lines, respectively; ρ is the penalty coefficient related to the decision variables; n is the number of iterations. Step 2: Consistency of key parameters of the power transmission and distribution system is achieved by updating the Lagrange multipliers using the current boundary information. The multiplier update criterion related to tie-line power is as follows: ； The update criterion for consensus variables is: ； Step 3: When the iterative convergence accuracy of the transmission and distribution system satisfies the following formula, the algorithm stops converging: ； ； ； in, Let R be the verification function; and S be the original residual and the dual residual, respectively.

11. A method for coordinated scheduling of a transmission and distribution system considering decision-dependent uncertainty according to claim 1, characterized in that, The distributed solution algorithm described in step four integrates an improved alternating direction multiplier method and a list constraint generation algorithm. It also combines the Gurobi solver for a two-stage distributed Brull bar optimization model. The process of solving the Brull bar model using the CCG algorithm is as follows: Step 1, the compact form of the two-stage sub-Bruker model for dual decomposition using ADMM is as follows: ； Where x and y are the decision variables for the first and second stages of the scheduling model, respectively: ； Step 2: Decompose the three-level optimization problem of min-max-min in Step 1 into main and sub-problems and iterate them alternately. The main and sub-problems are as follows: ； ； Step 3: Input the result of solving the main problem into the subproblem for verification, add constraints to the main problem in the subproblem, and solve iteratively; when the iteration reaches the convergence accuracy, the final scheduling result is obtained.

12. The method for coordinated scheduling of a transmission and distribution system considering decision-dependent uncertainty according to claim 1, characterized in that, The integrated and improved alternating direction multiplier method and the distributed solution algorithm based on the constraint generation algorithm described in step four, combined with the Gurobi solver for the two-stage distributed Bruker optimization model, are specifically as follows: First, during the DRO model solution phase, the binary variables solved by the CCG algorithm in the main problem are fixed, and the ADMM algorithm is only applied to terms containing coupled variables, considering the updates of its Lagrange multipliers and tie-line coupled variables. The distribution system scheduling results are transmitted to the transmission system to correct the consensus variables that depend on the uncertainty of decision-making. {x} is verified by solving subproblems, and the C&CG iterative process is completed by adding cuts to the main problem. Finally, the scheduling results are output until the ADMM algorithm and the CCG algorithm meet the convergence conditions.

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