Electricity-carbon dispersion collaborative optimization operation method considering source side uncertainty

Abstract

The invention relates to the technical field of collaborative optimization operation of a power system, in particular to an electricity-carbon dispersion collaborative optimization operation method considering source side uncertainty, which comprises the following steps of: coping with fluctuation of wind and light energy in day-ahead scheduling based on a DRO model of a data-driven probability density Wasserstein distance; establishing an uncertainty scheduling model of the source side of the electricity-carbon cooperative system; establishing a DRO day-ahead scheduling model of the multi-zone power system by combining the DRO uncertainty model; the DRO day-ahead scheduling model is converted into a single-layer linear programming model through out-of-sample approximation and constraint dual conversion; and designing a power system electricity-carbon point-to-point transaction distributed coordinated optimization architecture containing grid security constraints, and solving the single-layer linear programming model by adopting an ADMM under a dynamic penalty factor updating strategy to obtain a coordinated operation scheme. According to the method, the data privacy of the multi-zone power system is protected on the premise of ensuring the calculation accuracy, and meanwhile, the solving speed is remarkably increased.

Description

Technical Field

[0001] The present invention relates to the technical field of coordinated optimization operation of power systems, and in particular to a method for decentralized coordinated optimization operation of electricity and carbon taking into account source-side uncertainty. Background Art

[0002] With the increase of controllable equipment in each region and the continuous expansion of the power grid, the regional distribution network (DN) has gradually formed an organizational form of distributed collaborative operation of multiple subsystems. The decentralized and collaborative multi-regional power grid also provides more optimization solutions for the safe-economic-low-carbon operation of the new power system based on the characteristics of energy interaction and backup sharing. In addition, the carbon emission trading (CET) market mechanism, as an important policy tool to promote green and low-carbon development, plays an important role in dealing with the safety-economy-low-carbon triangle under the "dual carbon" goal. In 2021, the power industry was included in the national carbon market for the first time; the "Interim Regulations on the Administration of Carbon Emission Trading" implemented on May 1, 2024, for the first time in the form of administrative regulations, clarified the CET system with quota allocation and trading as the core. The multi-regional power system has gradually participated in the national carbon market transactions, and the establishment of a fair, effective, scientific and standardized multi-regional power system CET mechanism has become an issue worthy of in-depth study.

[0003] In recent years, the electricity-carbon market has been interactively linked, and electricity trading and CET have been coordinated and connected. Multi-region power systems can participate in centralized or distributed trading of electricity and carbon emission rights. Compared with centralized trading, electricity-carbon distributed peer-to-peer (P2P) trading can achieve decentralized computing, while improving trading flexibility and protecting the privacy of subject data. At present, the research on electricity-carbon P2P trading in power systems mainly focuses on the design of effective and secure trading algorithms and the risk assessment of uncertain trading.

[0004] On the one hand, the smooth conduct of electricity-carbon P2P transactions in the power system requires the support of effective and secure trading algorithms to ensure fair profits, privacy protection and physical feasibility of trading plans for trading entities. Existing studies mainly use theories such as game theory, auction mechanism and alternating direction method of multipliers (ADMM) to design electricity-carbon P2P trading algorithms. However, game theory is difficult to consider the complex network security constraints of the power system, and it is necessary to design a two-layer iterative algorithm to ensure the security and feasibility of the trading scheme, which restricts the improvement of computational efficiency; while auction theory often requires the pre-set identities of the main buyers and sellers, reducing transaction flexibility. Distributed ADMM calculates the P2P transaction price and quantity based on the goal of maximizing total social welfare, while realizing price discovery and privacy protection functions. In existing studies, consensus-based adaptive step-size ADMM is used to solve the electricity-carbon P2P trading problem, but the grid transmission security constraints and carbon emissions caused by purchased electricity are not considered. A safer and more effective electricity-carbon P2P trading ADMM needs further research.

[0005] On the other hand, there are a lot of uncertain factors in the power system, such as renewable energy output, which will seriously affect the effectiveness of trading plans and the safety of system operation. Existing studies on electricity-carbon P2P trading that take uncertainty assessment into account mainly use stochastic optimization (SO), robust optimization (RO) or distributionally robust optimization (DRO) algorithms to model uncertainty, but the chance-constrained SO method requires the probability distribution of uncertain variables to be preset, and it takes a long time to solve in multiple scenarios; the RO algorithm often makes the trading results too conservative, which is not conducive to stimulating the vitality of the electricity-carbon market. The DRO algorithm adopted in existing studies combines the advantages of SO and RO, reducing the conservatism of decisions while not relying on accurate probability distribution predictions; but the original DRO model has a complex structure and most of them require two-stage iterative solutions. The traditional affine approximation strategy parameters increase exponentially with the increase of uncertainty variables and optimization variables, and it is difficult to select appropriate parameters. In recent years, the DRO simplification method based on out-of-sample approximation and constraint dual transformation has begun to attract attention. This method provides a coupled constraint linearization method, which converts the DRO model into a single-stage linear problem that can be handled by the solver without introducing additional parameters. It has good performance in terms of solution time and accuracy. Summary of the invention

[0006] The present invention aims at the uncertainty risks, price discovery and privacy protection issues faced by the electricity-carbon coordinated operation and scheduling of the power system, and provides an electricity-carbon decentralized coordinated optimization operation method taking into account the uncertainty on the source side.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] A method for decentralized coordinated optimization of electricity and carbon taking into account source-side uncertainty, comprising:

[0009] The DRO model based on the data-driven probability density Wasserstein distance can cope with the volatility of wind and solar energy in day-ahead scheduling, and establish an uncertainty scheduling model on the source side of the electricity-carbon synergy system;

[0010] Combined with the DRO uncertainty model, a DRO day-ahead dispatch model for multi-region power systems is established;

[0011] The DRO day-ahead scheduling model is transformed into a single-level linear programming model through out-of-sample approximation and constraint dual transformation;

[0012] Considering the decentralized coordinated operation strategy of electricity-carbon in multi-region power systems, a distributed coordinated optimization architecture of electricity-carbon point-to-point transactions in power systems with grid security constraints is designed. The ADMM under the dynamic penalty factor update strategy is used to solve the single-layer linear programming model to obtain a coordinated operation plan.

[0013] As an optimal technical solution, in the DRO uncertainty model, the distribution system operator DSO uniformly participates in market transactions and conducts energy management and point-to-point transactions with power and electricity-carbon. The optimal scheduling of DRO is carried out based on the day-ahead forecast and the local historical wind and solar output curve, specifically to solve the following optimization problem:

[0014]

[0015] Where: ρ is an auxiliary variable; is the historical sample mean; The historical output data of wind and solar power of the sth item in the distribution network; The true distribution Distribution with experience The distance between is the Wasserstein sphere radius corresponding to the historical data and predicted output distribution; is the Wasserstein metric confidence level of the renewable energy output distribution in the distribution network n; The number of samples for renewable energy output data.

[0016] As a preferred technical solution, the distribution fuzzy uncertainty set in the method is defined as a Wasserstein ball with the empirical distribution as the center and the Wasserstein distance as the radius;

[0017] The empirical distribution of renewable energy output data is shown as follows:

[0018]

[0019] Wasserstein distance d w The average transfer cost is used to measure the distance between two distributions. The true distribution Distribution with experience The distance between is expressed as:

[0020]

[0021] Where: () is the Dirac measure; is the sample data of renewable energy in distribution network n; The marginal distribution is The joint probability distribution of .

[0022] As a preferred technical solution, the DRO uncertainty model is combined to establish a multi-region power system DRO day-ahead dispatch model, which is as follows:

[0023] The DSO day-ahead dispatch in the secondary carbon market further considers the impact of power flow in the distribution network and P2P transactions, and its distributed robust objective function is:

[0024]

[0025] Where: U n,t and are the random variables and optimization variables for day-ahead dispatch of the distribution network in the secondary carbon market; C carbon ,sec and C trade They are the end-to-end transaction costs of carbon and electricity in the secondary carbon market; is the excess carbon emissions of the distribution network during the contract period n; and are the CEA price and quantity traded from distribution network n to distribution network m, and For the price and quantity of electricity traded; n,i,t and θ n,ij,t are the voltage value of node i in the distribution network and the phase angle difference of branch ij at time t; N n is the set of nodes in the distribution network n.

[0026] As a preferred technical solution, the constraints of the multi-region power system DRO day-ahead dispatch model include:

[0027] Electricity-carbon P2P trading constraints: In the secondary carbon market, DSO conducts free trading of quotas within the region, and excess carbon emissions must be traded with trading entities outside the region at the primary carbon market price to ensure that the compliance requirements of the carbon market are met; after conducting end-to-end trading of carbon quotas within the region, the excess carbon emissions of distribution network n are:

[0028]

[0029] The constraints on DSO’s participation in end-to-end electricity trading are:

[0030]

[0031] Where: and are the maximum end-to-end transaction values ​​of carbon and electricity per unit time between distribution networks n and m, respectively;

[0032] Distribution network flow constraints:

[0033] P n,ij,t =g n,ij (v n,i,t -v n,j,t )-b n,ij θ n,ij,t

[0034] Q n,ij,t =-b n,ij (v n,i,t -v n,j,t )-g n,ij θ n,ij,t

[0035]

[0036] Where: P n,ij,t and Q n,ij,t are respectively the active and reactive power of branch ij in distribution network n at time t; g n,ij and b n,ij are the conductance and susceptance values ​​of the nth branch ij of the distribution network respectively; and They are the upper and lower limits of the voltage of the n nodes in the distribution network respectively; and They are the upper and lower limits of the node phase angle respectively;

[0037] Power generation equipment and power purchase constraints: In the multi-region power system dispatch, in addition to distributed generators and power grid purchase power, the consumption of wind and solar renewable energy is constrained by the day-ahead forecast output;

[0038] ES equipment constraints: The ES equipment modeling adopts a linear robust structure. When there are no other discrete variables in the optimization problem, the actual state of charge of the ES under the non-convex complementary constraint is between the relaxed SOC curve with relaxed complementary constraints and the simplified SOC curve considering the net charge of the ES. The linear robust model meets the physical feasibility of the ES scheduling results by cutting the feasible search domain of the charge and discharge power.

[0039] The relaxation SOC curve is:

[0040]

[0041] The simplified SOC curve is:

[0042]

[0043] Where: and are the SOC state and the relaxed simplified SOC state of the distribution network n at time t, respectively; η c and η d are the charging and discharging efficiency of ES equipment; E SOC,max and P ES,max They are SOC state and upper limit of charge and discharge power respectively;

[0044] Carbon emission constraints: Carbon capture equipment output meets constraints:

[0045]

[0046] Where: and are the carbon emissions of DG equipment and the carbon capture of CCS equipment; e emi,DG is the carbon emission coefficient converted from DG power generation; η ele The power consumption rate of carbon capture for CCS equipment; is the maximum power of the CCS equipment in the distribution network n at time t;

[0047] The total carbon emissions of distribution network n are:

[0048]

[0049] Where: Carbon emissions from purchasing electricity for distribution networks; emi,grid The carbon emission coefficient is calculated for purchased electricity.

[0050] As a preferred technical solution, in the ES device constraint, further, on the premise of satisfying the ES power constraint, starting point constraints and boundary constraints are imposed on the relaxed SOC curve and the relaxed SOC curve:

[0051]

[0052] The boundary constraints are as follows:

[0053]

[0054] As a preferred technical solution, the DRO day-ahead scheduling model is converted into a single-layer linear programming model as follows:

[0055] The random variables in the expression of random variables contained in the DRO problem of the power system DRO day-ahead dispatch model are replaced with sample means by out-of-sample approximation, and the coupling constraints of decision variables and random variables are simplified. The worst-case expected value of the DRO model will be consistent with the optimal value of the finite-dimensional convex problem considering the behavior of the power system in the carbon market.

[0056] Based on the dual transformation method, the max-min two-layer problem in the finite-dimensional convex problem after the model simplification is transformed into a single-layer linear model according to the dual theorem.

[0057] As a preferred technical solution, the finite dimensional convex problem is specifically as follows:

[0058]

[0059] Where: and C pen,sec They are the uncertain optimization variables and the wind and solar power abandonment costs after out-of-sample approximation processing; and They are the data of the s-th wind power and photovoltaic output curves of distribution network n at time t; and are the prediction deviations of the s-th wind and solar power output data of distribution network n at time t;

[0060] The single-layer linear model transformed based on the dual transformation method is specifically:

[0061]

[0062] Where: C pen,sec,dual is the cost of wind and solar power abandonment after dual conversion; and are the dual multipliers of the constraints respectively.

[0063] As a preferred technical solution, the ADMM distributed computing multi-area power system day-ahead transaction dispatching strategy using the dynamic penalty factor update strategy is as follows:

[0064] Introducing auxiliary variables Replace the constraint formula of DSO participating in end-to-end electricity trading with the following formula to solve the equivalent problem with two-block structure:

[0065]

[0066] After introducing the auxiliary variable constraint, the augmented Lagrangian function L of the day-ahead dispatching target of the distribution network under end-to-end transactions is n for:

[0067]

[0068] Where: and are the auxiliary variables and the set of dual variables with two-block structural equivalence problems, respectively; and are the ADMM dual multipliers of carbon and electricity P2P processes, respectively, CEA and φ trade are ADMM penalty factors respectively.

[0069] As a preferred technical solution, the ADMM iteration process under the dynamic penalty factor update strategy is as follows:

[0070] Optimization variable update: In the k+1th update, each distribution network uses the auxiliary variable set obtained from the existing k iterations With the dual variable set Solve the optimization problem and update the optimization variable set

[0071]

[0072] Auxiliary variable update: Auxiliary variable set The update solution to the optimization problem is as follows:

[0073]

[0074] The auxiliary variable update problem is decomposed into two sub-problems, and the auxiliary variable k+1th iteration formula is obtained from the KKT equivalent conditions of the sub-problems:

[0075]

[0076]

[0077] Dual variable update: The dual multiplier update strategy of ADMM is used. The k+1th update strategy of the dual variable set is:

[0078]

[0079] Iterative convergence judgment and dynamic factor update: The convergence criteria of the ADMM problem include the primal residual and the dual residual. When both convergence parameters are less than fixed limits, the solution is judged to have converged.

[0080] Compared with the prior art, the present invention has the following beneficial effects:

[0081] The method proposed in the present invention processes the uncertainty of renewable energy output of power system based on the Wasserstein distributed robust model, transforms the day-ahead double-layer scheduling problem of multi-region power system into a single-layer linear problem by using out-of-sample approximation, constraint dual transformation and other methods, and further adopts the alternating direction multiplier method under the dynamic penalty factor update strategy to construct a decentralized optimization architecture of peer-to-peer (P2P) trading of electricity and carbon quota, and uses a solver to solve it.

[0082] 1) Under the decentralized collaborative framework of electricity-carbon P2P trading, each system establishes a distributed robust day-ahead scheduling model based on Wasserstein distance to cope with the uncertainty of renewable energy output. The double-layer max-min problem is transformed into a single-layer linear programming model through out-of-sample approximation and constraint duality transformation, which can be solved using a solver.

[0083] 2) Considering the electricity-carbon coordinated operation strategy of multi-region power systems, a distributed coordination optimization architecture of electricity-carbon P2P transactions in power systems with grid security constraints is designed, a distributed transaction pricing mechanism is established, and ADMM solution is adopted under the dynamic penalty factor update strategy. The algorithm protects the privacy of multi-region power system data while ensuring the accuracy of calculation, and significantly improves the solution speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 This is a flow chart of the electricity-carbon decentralized collaborative optimization operation method taking into account source-side uncertainty of the present invention;

[0085] Figure 2 This is a schematic diagram of the electricity-carbon decentralized synergistic optimization operation model of the present invention. DETAILED DESCRIPTION

[0086] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0087] Example 1

[0088] In view of the uncertainty risks, price discovery and privacy protection issues faced by the coordinated operation and dispatch of electricity and carbon in power systems, the present invention proposes an electricity-carbon decentralized coordinated optimization operation method that takes into account the uncertainty on the source side. The uncertainty of the output of new energy in the power system is processed based on the Wasserstein distributed robust model. The day-ahead double-layer dispatching problem of the multi-region power system is converted into a single-layer linear problem by using methods such as out-of-sample approximation and constrained dual transformation. The alternating direction multiplier method under the dynamic penalty factor update strategy is further used to construct a decentralized optimization architecture for peer-to-peer (P2P) transactions of electricity and carbon quotas, and the architecture is solved by a solver. The present invention uses out-of-sample approximation and constrained dual transformation to simplify the DRO distributed robust optimization (DRO), and converts the DRO model into a single-stage linear problem that can be processed by the solver without introducing additional parameters, with good performance in terms of solution time and accuracy. Figure 1 As shown, the steps of the method proposed by the present invention include:

[0089] S1: In order to solve the uncertainty modeling problem on the source side of the electricity-carbon synergistic system, a DRO model based on the data-driven probability density Wasserstein distance is adopted to deal with the volatility of wind and solar energy in day-ahead scheduling. An uncertainty scheduling model is established based on local historical data to deal with energy fluctuation risks and improve the reliability of grid operation.

[0090] S2: Combined with the DRO uncertainty model, a DRO day-ahead dispatch model for multi-region power systems is established. The double-layer max-min problem is transformed into a single-layer linear programming model through out-of-sample approximation and constraint duality transformation, which can be solved using a solver.

[0091] S3: Considering the decentralized coordinated operation strategy of electricity-carbon in multi-region power systems, a distributed coordination optimization architecture of electricity-carbon P2P transactions in power systems with grid security constraints is designed, a distributed transaction pricing mechanism is established, and the ADMM solution is adopted under the dynamic penalty factor update strategy.

[0092] Specifically, in step S1, a DRO model based on data-driven probability density Wasserstein distance is adopted to deal with the volatility of wind and solar energy in day-ahead scheduling, and an uncertainty scheduling model is established based on local historical data.

[0093] Multi-region power systems aggregate distributed resources such as distributed generators (DG), carbon capture and storage (CCS), photovoltaics (PV), wind turbines (WT), and electric storage (ES), and the distribution system operator (DSO) uniformly participates in market transactions and performs energy management. Since it is difficult to directly use the carbon resources captured by CCS equipment in the power system, the present invention assumes that the captured carbon dioxide is not suitable for the CET market, and focuses on the CEA day-ahead spot trading of the power system. In addition, in order to further support the construction of distributed energy and flexible resource consumption in new power systems and improve the utilization efficiency of the power grid, DSO also participates in power P2P transactions and performs day-ahead scheduling based on economic and carbon emission conditions.

[0094] In this process, DSO carries out the optimal DRO dispatch according to the day-ahead forecast and the local historical wind and solar output curve. The present invention adopts a DRO model based on the data-driven probability density Wasserstein distance to deal with the volatility of wind and solar energy in day-ahead dispatch.

[0095] Wasserstein distance d w The average transfer cost is used to measure the "distance" between two distributions. The distribution fuzzy uncertainty set can be defined as a Wasserstein ball with the empirical distribution as the center and the Wasserstein distance as the radius, covering all possible probability distributions with a certain confidence level. After obtaining the local renewable energy output data RE∈[PV,WT], the empirical distribution can be obtained

[0096]

[0097] Where: The historical output data of wind and solar power of the sth grid n; () is the Dirac measure.

[0098] Since DSO can obtain the uncertainty set of renewable energy generation through the power upper and lower bounds of historical power generation data, When 1-norm is used as the transfer cost, the true distribution Distribution with experience The distance between is written as:

[0099]

[0100] Where: is the sample data of renewable energy RE in distribution network n; The marginal distribution is The joint probability distribution of .

[0101] Based on the Wasserstein metric, we can define a renewable energy power distribution similar to the empirical distribution, which falls within The Wasserstein distance is the radius of the sphere, that is:

[0102]

[0103] According to the conditional probability formula (4), the calculation of the Wasserstein sphere radius formula (6) corresponding to the historical data and the predicted output distribution can be transformed into the optimization problem formula (5) and solved with the help of the "Fmincon" function in the MATLAB toolbox.

[0104]

[0105] Where: is the Wasserstein metric confidence level of the renewable energy output distribution in the distribution network n; is a constant, obtained by the optimization problem (5); ρ is an auxiliary variable; is the historical sample mean.

[0106] The uncertainty dispatch strategy based on local historical data will provide support for coping with energy fluctuation risks and improving the reliability of grid operation, and will be more in line with the actual energy management needs of DSO.

[0107] In step S2, a DRO day-ahead dispatch model for a multi-region power system is established in combination with the DRO uncertainty model. The double-layer max-min problem is transformed into a single-layer linear programming model through out-of-sample approximation and constraint duality transformation, which can be solved using a solver.

[0108] In addition to the uncertainty of wind and solar power, the DSO day-ahead dispatch in the secondary carbon market further considers the impact of power flow in the distribution network and P2P transactions. Its distributed robust objective function is:

[0109]

[0110] Where: U n,t and are the random variables and optimization variables for day-ahead dispatch of the distribution network in the secondary carbon market; C carbon ,sec and C trade They are the end-to-end transaction costs of carbon and electricity in the secondary carbon market; is the excess carbon emissions of the distribution network during the contract period n; and are the CEA price and quantity traded from distribution network n to distribution network m, and is the price and quantity of electricity traded, a positive value indicates buying, a negative value indicates selling; v n,i,t and θ n,ij,t are the voltage value of node i in the distribution network and the phase angle difference of branch ij at time t; N n is the set of nodes in the distribution network n.

[0111] The constraints of the DRO optimal dispatch problem in the power system also include:

[0112] 1) Constraints on electricity-carbon P2P trading

[0113] In the secondary carbon market, DSOs can freely trade quotas within the region, and excess carbon emissions must be traded with trading entities outside the region at the primary carbon market price to ensure that the compliance requirements of the carbon market are met. After conducting P2P of carbon quotas within the region, the excess carbon emissions of each distribution network n are:

[0114]

[0115] In addition, DSO also participates in electricity P2P transactions, with the following constraints:

[0116]

[0117]

[0118] Where: and They are the maximum values ​​of carbon and electricity P2P transactions per unit time between distribution networks n and m respectively.

[0119] 2) Distribution network flow constraints

[0120] The present invention adopts a linear model based on first-order Taylor series expansion to describe the power flow in the power system:

[0121] P n,ij,t =g n,ij (v n,i,t -v n,j,t )-b n,ij θ n,ij,t (15)

[0122] Q n,ij,t =-b n,ij (v n,i,t -v n,j,t )-g n,ij θ n,ij,t (16)

[0123]

[0124] Where: P n,ij,t and Q n,ij,t are respectively the active and reactive power of branch ij in distribution network n at time t; g n,ij and b n,ij are the conductance and susceptance values ​​of the nth branch ij of the distribution network respectively; and They are the upper and lower limits of the voltage of the n nodes in the distribution network respectively; and are the upper and lower limits of the node phase angle respectively.

[0125] 3) Power generation equipment and power purchase constraints

[0126] In the multi-region power system dispatch, in addition to the DG and power grid purchase power, the consumption of wind and solar renewable energy is constrained by the day-ahead forecast output:

[0127]

[0128] Where: It is the upper limit of DG output power in distribution network n.

[0129] 4) ES device constraints

[0130] ES equipment modeling adopts a linear robust structure. When there are no other discrete variables in the optimization problem, the actual state of charge (SOC) of the ES under the non-convex complementary constraint is between the relaxed SOC curve (23) with relaxed complementary constraints and the simplified SOC curve (24) considering the net charge of the ES. Furthermore, under the premise of satisfying the ES power constraints (28)-(30), the starting point constraints (25) and boundary constraints (26), (27) can be imposed on the two curves to relax the non-convex complementary conditions in the ES model, at the cost of slightly improving the conservatism of the scheduling results, to ensure that the ES scheduling plan after linear relaxation is physically feasible, thereby maintaining the continuous convexity of the optimal scheduling problem. The ES linear robust model is written as:

[0131]

[0132]

[0133] Where: and are the SOC state and the relaxed simplified SOC state of the distribution network n at time t, respectively; η c and η d are the charging and discharging efficiency of ES equipment; E SOC,max and P ES,max They are SOC state and upper limit of charge and discharge power respectively.

[0134] Equations (23)-(27) constrain the SOC range of ES devices, and equations (28)-(30) limit the upper limit of ES power. The linear robust model meets the physical feasibility of ES scheduling results by cutting the feasible search domain of charging and discharging power.

[0135] 5) Carbon emissions constraints

[0136] CCS equipment further reduces gas emissions caused by DG output through carbon capture and storage. In the power system, the output of CCS equipment meets constraints (31)-(34).

[0137]

[0138] Where: and are the carbon emissions of DG equipment and the carbon capture of CCS equipment; e emi,DG is the carbon emission coefficient converted from DG power generation; η ele The power consumption rate of carbon capture for CCS equipment; is the maximum power of the CCS equipment in distribution network n at time t.

[0139] Therefore, the total carbon emissions of distribution network n are:

[0140]

[0141] Where: Carbon emissions from purchasing electricity for distribution networks; emi,grid The carbon emission coefficient is calculated for purchased electricity.

[0142] After the random variables in the expressions (37), (39), and (40) of the DRO problem (7)-(9) are replaced with sample means out of sample, and the coupling constraint (39) between the decision variables and the random variables is simplified, the worst-case expected value of the DRO model (7)-(9) will be consistent with the optimal value of the finite-dimensional convex problem (37)-(41) considering the behavior of the power system in the carbon market:

[0143]

[0144] Formula (6), Formula (10) to Formula (36) (41)

[0145] Where: and c pen,sec They are the uncertain optimization variables and the wind and solar power abandonment costs after out-of-sample approximation processing; and They are the data of the s-th wind power and photovoltaic output curves of distribution network n at time t; and They are respectively the prediction deviations of the s-th wind and solar power output data of distribution network n at time t.

[0146] Based on the dual transformation method, the max-min double-layer problem in model (37) can be transformed into a single-layer linear model according to the dual theorem:

[0147]

[0148] Formula (6), Formula (10) to Formula (36) (47)

[0149] Where: C pen,sec,dual is the cost of wind and solar power abandonment after dual conversion; and are the dual multipliers of constraint (40) respectively. After dual transformation, the DRO scheduling of each distribution network is reconstructed into a single-layer linear problem (42)-(47), which can be directly processed by commercial solvers such as Gurobi.

[0150] In step S3, the decentralized coordinated operation strategy of electricity and carbon in multi-region power systems is considered, a distributed coordinated optimization architecture of electricity and carbon P2P transactions in power systems with grid security constraints is designed, a distributed transaction pricing mechanism is established, and the ADMM solution is adopted under the dynamic penalty factor update strategy.

[0151] The P2P activities between power systems are distributed bilateral free trading processes. In order to protect the privacy information such as historical data and grid constraints of each distribution network, the present invention adopts the ADMM distributed computing multi-area power system day-ahead trading scheduling strategy with dynamic update of penalty factors.

[0152] In the optimization problem (42)-(47), after out-of-sample approximation and dual transformation, the scheduling model presents a multi-block linear structure, and the convergence of the algorithm cannot be guaranteed. In order to solve the convergence problem of ADMM, an auxiliary variable is introduced Replace constraint (13) with (48) and (49), and replace constraint (14) with (50) and (51), and solve the equivalent problem with a two-block structure.

[0153]

[0154] After introducing the auxiliary variable constraint, the augmented Lagrangian function L of the day-ahead dispatching target of the distribution network under P2P trading is n for:

[0155]

[0156] Where: and are auxiliary variables, the dual variable set of formula (48) and formula (50) respectively; and are the ADMM dual multipliers of carbon and electricity P2P processes, respectively, CEA and φ trade are ADMM penalty factors respectively.

[0157] The optimization problem (52)-(54) can be split for each distribution network, and the ADMM iterative process under the dynamic penalty factor update strategy is as follows, which can realize the solution of distributed energy management strategy.

[0158] Step 1: Optimize variable updates

[0159] In the k+1th update, each distribution network uses the auxiliary variable set obtained from the existing k iterations With the dual variable set Solve the optimization problem (55) and update the optimization variable set

[0160]

[0161] Step 2: Auxiliary variable update

[0162] Auxiliary variable set The update solves the optimization problem:

[0163]

[0164] because Associating only with paired transaction variables, the auxiliary variable updating problem (56) can be decomposed into two sub-problems (57) and (58).

[0165]

[0166] Therefore, the KKT equivalent conditions of problems (57) and (58) can be used to obtain the auxiliary variable k+1th iteration formula:

[0167]

[0168] Step 3: Dual variable update

[0169] The dual multiplier update strategy of ADMM and the k+1th update strategy of the dual variable set are:

[0170]

[0171] Step 4: Iteration convergence determination and dynamic factor update

[0172] The convergence criterion of the ADMM problem consists of the primal residual (62) and the dual residual (63). When both convergence parameters are less than fixed limits, the solution is judged to have converged.

[0173]

[0174] Compared with the traditional ADMM algorithm, the dynamic penalty factor update strategy adaptively adjusts the penalty term step size φ={φ CEA ,φ trade}, reduce the impact of inappropriate initial step size on convergence and speed up the calculation process. k+1 Much larger than the dual residual s k+1 , the strategy chooses to increase the step size to punish the violation of the original feasibility by the distribution network optimization in step 1, and vice versa.

[0175]

[0176] Where: μ in ,μ de ,κ are parameters greater than 1, representing the step size increase factor, decrease factor and the threshold for starting to update the residual ratio.

[0177] Therefore, the optimization problem (38) can be iteratively updated by the four steps shown in (55)-(64) to optimize the variables, auxiliary variables, dual variables and penalty factors, and realize the decentralized collaborative energy management of multi-region power systems in the secondary carbon market, while completing market price discovery and protecting the transaction privacy of the power system. Since the DRO scheduling in the distribution network can be reconstructed as a linear programming problem, the global convergence of the 2-block ADMM in the present invention can be guaranteed.

[0178] Example 2

[0179] As a second aspect of the present invention, the present application also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned electric-carbon decentralized collaborative optimization operation method taking into account the uncertainty of the source side. In addition to the above-mentioned processor, memory and interface, any device with data processing capability in which the device in the embodiment is located may also include other hardware according to the actual function of the device with data processing capability, which will not be described in detail.

[0180] Example 3

[0181] As a third aspect of the present invention, the present application also provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implements the above-mentioned electric-carbon decentralized collaborative optimization operation method taking into account source-side uncertainty. The computer-readable storage medium may be an internal storage unit of any device with data processing capabilities described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium may also be an external storage device, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), an SD card, a flash card (Flash Card), etc. equipped on the device. Furthermore, the computer-readable storage medium may also include both an internal storage unit and an external storage device of any device with data processing capabilities. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capabilities, and may also be used to temporarily store data that has been output or is to be output.

[0182] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for decentralized electricity-carbon coordinated optimization operation taking into account source-side uncertainty, characterized in that the steps include: The DRO model based on the data-driven probability density Wasserstein distance can cope with the volatility of wind and solar energy in day-ahead scheduling, and establish an uncertainty scheduling model on the source side of the electricity-carbon synergy system; Combined with the DRO uncertainty model, a DRO day-ahead dispatch model for multi-region power systems is established; The DRO day-ahead scheduling model is transformed into a single-level linear programming model through out-of-sample approximation and constraint dual transformation; Considering the decentralized coordinated operation strategy of electricity-carbon in multi-region power systems, a distributed coordinated optimization architecture of electricity-carbon point-to-point transactions in power systems with grid security constraints is designed. The ADMM under the dynamic penalty factor update strategy is used to solve the single-layer linear programming model to obtain a coordinated operation plan.

2. The method for decentralized electricity-carbon coordinated optimization operation taking into account source-side uncertainty according to claim 1, characterized in that: In the DRO uncertainty model, the distribution system operator DSO participates in market transactions and conducts energy management and point-to-point transactions with power and carbon. The optimal DRO dispatch is carried out based on the day-ahead forecast and the local historical wind and solar output curve. Specifically, the following optimization problem is solved: Where: ρ is an auxiliary variable; is the historical sample mean; The historical output data of wind and solar power in the distribution network nth item; d w (F n RE ,F n RE,pre ) is the true distribution F n RE With the empirical distribution F n RE,pre The distance between is the Wasserstein sphere radius corresponding to the historical data and predicted output distribution; is the Wasserstein metric confidence level of the renewable energy output distribution in the distribution network n; The number of samples for renewable energy output data.

3. The method for decentralized electricity-carbon coordinated optimization operation taking into account source-side uncertainty according to claim 2, characterized in that: In the method, the distribution fuzzy uncertainty set is defined as a Wasserstein ball with the empirical distribution as the center and the Wasserstein distance as the radius; The empirical distribution of renewable energy output data is shown as follows: Wasserstein distance d w The average transfer cost is used to measure the distance between the two distributions. The true distribution F n RE With the empirical distribution F n RE,pre The distance between is expressed as: Where: () is the Dirac measure; P n RE,pre is the sample data of renewable energy in distribution network n; The marginal distribution is F n RE ,F n RE,pre The joint probability distribution of .

4. The method for decentralized electricity-carbon coordinated optimization operation taking into account source-side uncertainty according to claim 1, characterized in that: The DRO uncertainty model is combined to establish a multi-region power system DRO day-ahead dispatch model, which is as follows: The DSO day-ahead dispatch in the secondary carbon market further considers the impact of power flow in the distribution network and P2P transactions, and its distributed robust objective function is: Where: U n,t and are the random variables and optimization variables for day-ahead dispatch of the distribution network in the secondary carbon market; C carbon,sec and C trade They are the end-to-end transaction costs of carbon and electricity in the secondary carbon market; is the excess carbon emissions of the distribution network during the contract period n; and are the CEA price and quantity traded from distribution network n to distribution network m, and For the price and quantity of electricity traded; n,i,t and θ n,ij,t are the voltage value of node i in the distribution network and the phase angle difference of branch ij at time t; N n is the set of nodes in the distribution network n.

5. The method for decentralized electricity-carbon coordinated optimization operation taking into account source-side uncertainty according to claim 4, characterized in that: The constraints of the multi-region power system DRO day-ahead dispatch model include: Electricity-carbon P2P trading constraints: In the secondary carbon market, DSO conducts free trading of quotas within the region, and excess carbon emissions must be traded with trading entities outside the region at the primary carbon market price to ensure that the compliance requirements of the carbon market are met; after conducting end-to-end trading of carbon quotas within the region, the excess carbon emissions of distribution network n are: The constraints on DSO’s participation in end-to-end electricity trading are: Where: and are the maximum end-to-end transaction values ​​of carbon and electricity per unit time between distribution networks n and m, respectively; Distribution network flow constraints: P n,ij,t =g n,ij (v n,i,t -v n,j,t )-b n,ij θ n,ij,t Q n,ij,t =-b n,ij (v n,i,t -v n,j,t )-g n,ij θ n,ij,t Where: P n,ij,t and Q n,ij,t are respectively the active and reactive power of branch ij in distribution network n at time t; g n,ij and b n,ij are the conductance and susceptance values ​​of the nth branch ij of the distribution network respectively; and They are the upper and lower limits of the voltage of the n nodes in the distribution network respectively; and They are the upper and lower limits of the node phase angle respectively; Power generation equipment and power purchase constraints: In the multi-region power system dispatch, in addition to distributed generators and power grid purchase power, the consumption of wind and solar renewable energy is constrained by the day-ahead forecast output; ES equipment constraints: The ES equipment modeling adopts a linear robust structure. When there are no other discrete variables in the optimization problem, the actual state of charge of the ES under the non-convex complementary constraint is between the relaxed SOC curve with relaxed complementary constraints and the simplified SOC curve considering the net charge of the ES. The linear robust model meets the physical feasibility of the ES scheduling results by cutting the feasible search domain of the charge and discharge power. The relaxation SOC curve is: The simplified SOC curve is: Where: and are the SOC state and the relaxed and simplified SOC state of distribution network n at time t respectively; η c and η d are the charging and discharging efficiency of ES equipment; E SOC,max and P ES,max They are SOC state and upper limit of charge and discharge power respectively; Carbon emission constraints: Carbon capture equipment output meets constraints: Where: and are the carbon emissions of DG equipment and the carbon capture of CCS equipment; e emi,DG is the carbon emission coefficient converted from DG power generation; η ele The power consumption rate of carbon capture for CCS equipment; is the maximum power of the CCS equipment in the distribution network n at time t; The total carbon emissions of distribution network n are: Where: Carbon emissions from purchasing electricity for distribution networks; emi,grid The carbon emission coefficient is calculated for purchased electricity.

6. The method for decentralized electricity-carbon coordinated optimization operation taking into account source-side uncertainty according to claim 5, characterized in that: In the ES device constraints, under the premise of satisfying the ES power constraints, starting point constraints and boundary constraints are imposed on the relaxed SOC curve and the relaxed SOC curve: The boundary constraints are as follows:

7. The method for decentralized electricity-carbon coordinated optimization operation taking into account source-side uncertainty according to claim 1, characterized in that: The conversion of the DRO day-ahead scheduling model into a single-layer linear programming model is specifically as follows: The random variables in the expression of random variables contained in the DRO problem of the power system DRO day-ahead dispatch model are replaced with sample means by out-of-sample approximation, and the coupling constraints of decision variables and random variables are simplified. The worst-case expected value of the DRO model will be consistent with the optimal value of the finite-dimensional convex problem considering the behavior of the power system in the carbon market. Based on the dual transformation method, the max-min two-layer problem in the finite-dimensional convex problem after the model simplification is transformed into a single-layer linear model according to the dual theorem.

8. The method for decentralized electricity-carbon coordinated optimization operation taking into account source-side uncertainty according to claim 7, characterized in that: The finite dimensional convex problem is specifically as follows: Where: and C pen,sec They are the uncertain optimization variables and the wind and solar power abandonment costs after out-of-sample approximation processing; and They are the data of the s-th wind power and photovoltaic output curves of distribution network n at time t; and are the prediction deviations of the s-th wind and solar power output data of distribution network n at time t; The single-layer linear model transformed based on the dual transformation method is specifically: Where: C pen,sec,dual is the cost of wind and solar power abandonment after dual conversion; and are the dual multipliers of the constraints respectively.

9. The method for decentralized electricity-carbon coordinated optimization operation taking into account source-side uncertainty according to claim 1, characterized in that: The ADMM distributed computing multi-area power system day-ahead transaction dispatching strategy using the dynamic penalty factor update strategy is as follows: Introducing auxiliary variables Replace the constraint formula of DSO participating in end-to-end electricity trading with the following formula to solve the equivalent problem with two-block structure: After introducing the auxiliary variable constraint, the augmented Lagrangian function L of the day-ahead dispatching target of the distribution network under end-to-end transactions is n for: Where: and are the auxiliary variables and the set of dual variables with two-block structural equivalence problems, respectively; and are the ADMM dual multipliers of carbon and electricity P2P processes, respectively, CEA and φ trade are ADMM penalty factors respectively.

10. The method for decentralized electricity-carbon coordinated optimization operation taking into account source-side uncertainty according to claim 9, characterized in that: The ADMM iteration process under the dynamic penalty factor update strategy is as follows: Optimization variable update: In the k+1th update, each distribution network uses the auxiliary variable set obtained from the existing k iterations With the dual variable set Solve the optimization problem and update the optimization variable set Auxiliary variable update: Auxiliary variable set The update solution to the optimization problem is as follows: The auxiliary variable update problem is decomposed into two sub-problems, and the auxiliary variable k+1th iteration formula is obtained from the KKT equivalent conditions of the sub-problems: Dual variable update: The dual multiplier update strategy of ADMM is used. The k+1th update strategy of the dual variable set is: Iterative convergence judgment and dynamic factor update: The convergence criteria of the ADMM problem include the primal residual and the dual residual. When both convergence parameters are less than fixed limits, the solution is judged to have converged.

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