A distributed energy transaction and operation integration method under a power distribution network constraint

Abstract

This invention discloses an integrated method for distributed energy trading and operation under distribution network constraints, belonging to the field of energy trading in the electricity market. The method first establishes an integrated distributed trading and operation model based on the Vickrey-Clarke-Groves mechanism under distribution network constraints; then, it proposes a distributed zero-sum settlement method that can effectively quantify the costs of distributed energy trading and operation and maintenance services; and it proposes a distributed solution algorithm based on the alternating multiplier method to solve the convex optimization problem of constructing distributed energy trading under distribution network constraints. This method directly incorporates distribution network constraints into the distributed trading process in a distributed manner, trading flexibility services used to ensure the safe operation of the distribution network along with energy in the distributed market. It eliminates the need for a trusted third-party institution to maintain the distribution network operation, effectively reducing overall energy costs while supporting the safe operation of the distribution network.

Description

Technical Field

[0001] This invention relates to an integrated method for distributed energy trading and operation under the constraints of a power distribution network, belonging to the field of energy trading in the electricity market. Background Technology

[0002] With the rapid development of distributed renewable energy sources such as rooftop solar PV, smart home control terminals, and energy storage devices, users are being given a more flexible role in the power distribution system. The large-scale integration of distributed renewable energy makes distributed trading among small-scale users possible. However, ensuring the safe operation of the power distribution network while organizing distributed trading remains a challenging research problem. Considering the flexibility of demand-side resources, distributed markets have the ability to maintain the safe operation of the power distribution network system without relying on a trusted third party. Distributed trading problems considering network constraints are usually modeled as an OPF problem aiming to maximize global social welfare, neglecting the user's own utility maximization needs. Traditional posterior models cannot leverage the flexibility of demand-side resources through distributed trading to support power distribution network operation; therefore, it is necessary to research an integrated model that can coordinate user interests with power distribution network operation requirements. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies, the purpose of this invention is to propose an integrated method for distributed energy trading and operation under the constraints of power distribution networks.

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

[0005] An integrated method for distributed energy trading and operation under distribution network constraints is proposed. First, an integrated distributed trading model based on the Vickrey-Clarke-Groves (VCG) mechanism is established under distribution network constraints. Based on this, to address the asymmetry of distributed payments in the VCG model, a zero-sum symmetric distributed settlement method is proposed that can effectively quantify the costs of distributed energy trading and operation and maintenance services. Finally, to solve the convex optimization problem of distributed energy trading construction under distribution network constraints, a distributed solution algorithm based on the alternating multiplier method is proposed.

[0006] The specific steps are as follows:

[0007] (1) Distributed transaction and operation integration model based on VCG mechanism under distribution network constraints

[0008] Users participating in distributed transactions are prosumer-consumption users who simultaneously possess flexible loads and rooftop solar power, and their load model is subject to the following constraints:

[0009]

[0010]

[0011] In the formula, E represents the electrical load of user c during the time period τ; c This represents the total basic energy requirement of users throughout the entire trading period; and These represent the upper and lower bound power constraints of the user load, respectively.

[0012] The user's original electricity demand based on their electricity consumption habits is expressed as Deviations between user adjustments to electricity usage schedules and original user needs can cause user discomfort. Here, a penalty for quadratic deviation is used to define the user's discomfort cost, specifically expressed as:

[0013]

[0014] In the formula, α c This represents the user's willingness to adjust their electricity demand.

[0015] Since the deficits and surpluses in distributed transactions are balanced by the upper-level power grid using retail or grid connection prices, the corresponding balancing costs are defined as the balancing costs shared by distributed users. The rules for allocating distributed transaction balancing costs among users follow the principle of proportional allocation based on transaction volume, specifically expressed as follows:

[0016]

[0017] In the formula, This represents a group of electricity buyers. Represents the set of electricity retailers; the allocation ratio coefficient η c，τ Represents users participating in distributed transactions The allocation ratio of the total energy trading volume; the overall energy balance cost can be expressed as:

[0018]

[0019] In the formula, and These represent the retail electricity price at which a user purchases electricity from the upstream power grid and the on-grid electricity price at which a user sells the electricity they generate to the upstream power grid, respectively. P represents the total inelastic load that directly trades with the upstream power grid during the time period τ under node i; 0，τ This represents the net power injected from the root node into the upper-level power grid;

[0020] apportionment ratio coefficient η c，τ Specifically, the proportion of trading volume is expressed as follows:

[0021]

[0022] In the formula, This represents the energy injected by user C into the distribution network; This represents the total balancing energy required by the distributed market; This represents the total energy transaction volume in the distributed market.

[0023] Therefore, the utility of users participating in distributed transactions comprises two parts: the discomfort costs caused by load adjustment and the energy cost savings from participating in distributed transactions, which can be specifically expressed as:

[0024]

[0025] In the formula, This represents a distributed transaction payment from user c to user m during time period τ. This represents a distributed transaction payment from user m to user c during time period τ. Clearly, distributed payments for users within a single transaction period must satisfy complementary constraints.

[0026] The problem with the integrated distributed transaction and operation model is to maximize the overall utility while meeting the operational safety constraints of the distribution network. The value of user c's participation in distributed transactions is defined as a negative energy cost. The utility of a user participating in a distributed transaction is their value minus the total payment of the distributed transaction. This represents the theoretical total payoff of a user to all other users in the market, according to the VCG mechanism. Incorporating complementary constraints... We can deduce that total utility equals the user's total value function. Therefore, the objective function of the integrated distributed transaction and operation model includes discomfort costs and distributed transaction balancing costs, specifically:

[0027]

[0028] Its constraints include power distribution network security constraints, namely active power balance constraints, reactive power balance constraints, voltage boundary constraints, current boundary constraints, voltage drop constraints, and user electricity demand constraints.

[0029] (2) Zero-sum symmetric distributed settlement method

[0030] The value of user c participating in distributed transactions is defined as a negative energy cost, specifically expressed as:

[0031]

[0032] The user's distributed transaction volume and total transaction payment can be obtained through the following rules:

[0033] a) The distributed transaction volume of users is the optimal solution that maximizes the total value of all users, specifically:

[0034]

[0035] b) The total payment for a user's distributed transaction is the increase in the total value of other users when the user exits the distributed transaction, specifically:

[0036]

[0037]

[0038]

[0039] In the formula, This represents the total value when user c leaves the distributed trading market and other users choose the optimal electricity consumption. This represents the optimal electricity consumption for user m when user c exits the distributed trading market. The value of what is below.

[0040] c) Define the utility of a user participating in a distributed transaction as their value minus the total payment of the distributed transaction, specifically:

[0041]

[0042] In the formula, This represents the theoretical total payment from a user to all other users in the market according to the VCG mechanism. d) Due to the near-zero-sum condition for payment and settlement problems in distributed transactions without distribution network constraints. Both are true; the actual payment from user c to user m can be specifically represented as:

[0043]

[0044] In the formula Furthermore, distributed payment satisfies the symmetric complementarity constraint.

[0045] e) When the distribution network constraints are valid, for the payment and settlement problem of distributed transactions, the constraints for any user c are as follows: If this holds true, then the user's utility under actual payment is greater than the utility under theoretical payment. This satisfies the interests of rational individual users participating in the market; therefore, when the distribution network constraints are effective, the actual payment from user c to user m can also be specifically expressed as:

[0046]

[0047] (3) A distributed solution algorithm based on the shared form of the alternating multiplier method

[0048] Solving the distributed transaction and operation integrated model under the constraints of the aforementioned power distribution network typically requires a central system operator with access to all user and node information. The collection of large amounts of user and node data poses challenges to communication and data security. Therefore, this paper designs a distributed solution algorithm based on the shared alternating multiplier method. Distributed computation is completed through limited information exchange between adjacent nodes and users to ensure user privacy and data security.

[0049] a) Use Representing user variables The objective function, The function representing the node variables represents the overall balancing cost, thus the distributed transaction problem under the security constraints of a single-time distribution network can be specifically represented as:

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056] In the formula, Represents user variable x c The copy variable z at the node c The constant difference; This represents the flexible load upper and lower bound constraints for producer and consumer users; z i The variables representing distribution network nodes include node active power injection, reactive power injection, node voltage, line current from the node to the mother node, line active power, and line reactive power. Indicates the constraints of the distribution network; y (j)i The variable z representing node i i The variable is copied at the adjacent node j; This represents the branch power flow equality constraint; x c -z c +c c =0 and z i -y (i)j =0 represents the consistency constraints for node variables and user variables, respectively.

[0057] b) The augmented Lagrangian function of the extended distributed transaction problem under the security constraints of the single-time distribution network described above can be specifically expressed as:

[0058]

[0059] In the formula, π c and μ (i)j They represent the equality constraints x respectively c -z c +c c =0 and z i -y (i)j =0 extended augmented Lagrange multipliers; ζ1>0 and ζ2>0 denote penalty factors.

[0060] The steps of the alternating multiplier method iterative algorithm in each iteration can be represented as:

[0061]

[0062]

[0063]

[0064]

[0065]

[0066] In the formula, It represents the active power balance, reactive power balance, and voltage drop equation constraints of the distribution network.

[0067] For z i The variable update problem can be represented as:

[0068]

[0069]

[0070] Use ν i The above z represents i The augmented Lagrange multipliers for the variable update problem are then expressed as:

[0071]

[0072] In order to x c Using node z during variable update i Use variables to replace the user-side z i Variable, node z i Treating the variable as a fixed quantity, for the above z i Solving the variable optimization problem yields the following:

[0073]

[0074] In the formula, This represents the total number of users connected to node i; z i x i c i , π i These represent user variable z. c x c c c , π c The sum at node i.

[0075] Substituting the above equation into the Lagrange multiplier π c The update steps can be obtained That is, all users under the same node i All variables are the same.

[0076] c) The specific steps of the shared-form alternating multiplier iterative algorithm are as follows:

[0077]

[0078]

[0079]

[0080]

[0081]

[0082] In the formula, This represents the total number of users connected to node i; z i x i c i , π i These represent user variable z. c x c c c , π c The sum at node i.

[0083] The beneficial effects of this invention are as follows:

[0084] The method of this invention directly incorporates distribution network constraints into the distributed trading process in a distributed manner, and trades the flexibility services used to ensure the safe operation of the distribution network together with energy in the distributed market. There is no need for a trusted third-party institution to maintain the operation of the distribution network, which can effectively reduce the overall energy cost while supporting the safe operation of the distribution network. Attached Figure Description

[0085] Figure 1 A structural diagram of a distributed transaction and operation integrated model;

[0086] Figure 2The flowchart shows the distributed solution algorithm for the integrated distributed transaction and operation model. Detailed Implementation

[0087] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0088] An integrated method for distributed energy trading and operation under distribution network constraints is proposed. First, an integrated distributed trading model based on the Vickrey-Clarke-Groves (VCG) mechanism is established under distribution network constraints. Based on this, to address the asymmetry of distributed payments in the VCG model, a zero-sum symmetric distributed settlement method is proposed that can effectively quantify the costs of distributed energy trading and operation and maintenance services. Finally, to solve the convex optimization problem of distributed energy trading construction under distribution network constraints, a distributed solution algorithm based on the alternating multiplier method is proposed.

[0089] The specific steps are as follows:

[0090] (4) Integrated Distributed Trading and Operation Model Based on VCG Mechanism under Distribution Network Constraints

[0091] Users participating in distributed transactions are prosumer-consumption users who simultaneously possess flexible loads and rooftop solar power, and their load model is subject to the following constraints:

[0092]

[0093]

[0094] In the formula, E represents the electrical load of user c during the time period τ; c This represents the total basic energy requirement of users throughout the entire trading period; and These represent the upper and lower bound power constraints of the user load, respectively.

[0095] The user's original electricity demand based on their electricity consumption habits is expressed as Deviations between user adjustments to electricity usage schedules and original user needs can cause user discomfort. Here, a penalty for quadratic deviation is used to define the user's discomfort cost, specifically expressed as:

[0096]

[0097] In the formula, α c This represents the user's willingness to adjust their electricity demand.

[0098] Since the deficits and surpluses in distributed transactions are balanced by the upper-level power grid using retail or grid connection prices, the corresponding balancing costs are defined as the balancing costs shared by distributed users. The rules for allocating distributed transaction balancing costs among users follow the principle of proportional allocation based on transaction volume, specifically expressed as follows:

[0099]

[0100] In the formula, This represents a group of electricity buyers. Represents the set of electricity retailers; the allocation ratio coefficient η c，τ Represents users participating in distributed transactions The allocation ratio of the total energy trading volume; the overall energy balance cost can be expressed as:

[0101]

[0102] In the formula, and These represent the retail electricity price at which a user purchases electricity from the upstream power grid and the on-grid electricity price at which a user sells the electricity they generate to the upstream power grid, respectively. P represents the total inelastic load that directly trades with the upstream power grid during the time period τ under node i; 0，τ This represents the net power injected from the root node into the upper-level power grid;

[0103] apportionment ratio coefficient η c，τ Specifically, the proportion of trading volume is expressed as follows:

[0104]

[0105] In the formula, This represents the energy injected by user C into the distribution network; This represents the total balancing energy required by the distributed market; This represents the total energy transaction volume in the distributed market.

[0106] Therefore, the utility of users participating in distributed transactions comprises two parts: the discomfort costs caused by load adjustment and the energy cost savings from participating in distributed transactions, which can be specifically expressed as:

[0107]

[0108] In the formula, This represents a distributed transaction payment from user c to user m during time period τ. This represents a distributed transaction payment from user m to user c during time period τ. Clearly, distributed payments for users within a single transaction period must satisfy complementary constraints.

[0109] The problem with the integrated distributed transaction and operation model is to maximize the overall utility while meeting the operational safety constraints of the distribution network. The value of user c's participation in distributed transactions is defined as a negative energy cost. The utility of a user participating in a distributed transaction is their value minus the total payment of the distributed transaction. This represents the theoretical total payoff of a user to all other users in the market, according to the VCG mechanism. Incorporating complementary constraints... We can deduce that total utility equals the user's total value function. Therefore, the objective function of the integrated distributed transaction and operation model includes discomfort costs and distributed transaction balancing costs, specifically:

[0110]

[0111] Its constraints include power distribution network security constraints, namely active power balance constraints, reactive power balance constraints, voltage boundary constraints, current boundary constraints, voltage drop constraints, and user electricity demand constraints.

[0112] (5) Zero-sum symmetric distributed settlement method

[0113] The value of user c participating in distributed transactions is defined as a negative energy cost, specifically expressed as:

[0114]

[0115] The user's distributed transaction volume and total transaction payment can be obtained through the following rules:

[0116] f) The distributed transaction volume of users is the optimal solution that maximizes the total value of all users, specifically:

[0117]

[0118] g) The total payment for a user's distributed transaction is the increase in the total value of other users when the user exits the distributed transaction, specifically:

[0119]

[0120]

[0121]

[0122] In the formula, This represents the total value when user c leaves the distributed trading market and other users choose the optimal electricity consumption. This represents the optimal electricity consumption for user m when user c exits the distributed trading market. The value of what is below.

[0123] h) Define the utility of a user participating in a distributed transaction as their value minus the total payment of the distributed transaction, specifically:

[0124]

[0125] In the formula, This represents the theoretical total payout from a user to all other users in the market, according to the VCG mechanism.

[0126] i) Due to the near-zero-sum condition for payment and settlement problems in distributed transactions when there are no distribution network constraints. Both are true; the actual payment from user c to user m can be specifically represented as:

[0127]

[0128] In the formula Furthermore, distributed payment satisfies the symmetric complementarity constraint.

[0129] j) When the distribution network constraints are valid, for the payment and settlement problem of distributed transactions, for any user c, the constraints are... If this holds true, then the user's utility under actual payment is greater than the utility under theoretical payment. This satisfies the interests of rational individual users participating in the market; therefore, when the distribution network constraints are effective, the actual payment from user c to user m can also be specifically expressed as:

[0130]

[0131] (6) A distributed solution algorithm based on the shared form of the alternating multiplier method

[0132] Solving the distributed transaction and operation integrated model under the constraints of the aforementioned power distribution network typically requires a central system operator with access to all user and node information. The collection of large amounts of user and node data poses challenges to communication and data security. Therefore, this paper designs a distributed solution algorithm based on the shared alternating multiplier method. Distributed computation is completed through limited information exchange between adjacent nodes and users to ensure user privacy and data security.

[0133] d) Use Representing user variables The objective function, The function representing the node variables represents the overall balancing cost, thus the distributed transaction problem under the security constraints of a single-time distribution network can be specifically represented as:

[0134]

[0135]

[0136]

[0137]

[0138]

[0139]

[0140] In the formula, Represents user variable x c The copy variable z at the node c The constant difference; This represents the flexible load upper and lower bound constraints for producer and consumer users; z i The variables representing distribution network nodes include node active power injection, reactive power injection, node voltage, line current from the node to the mother node, line active power, and line reactive power. Indicates the constraints of the distribution network; y (j)i The variable z representing node i i The variable is copied at the adjacent node j; This represents the branch power flow equality constraint; x c -z c +c c =0 and z i -y (i)j =0 represents the consistency constraints for node variables and user variables, respectively.

[0141] e) The extended augmented Lagrangian function of the above-mentioned distributed transaction problem under the security constraints of a single-time distribution network can be specifically expressed as:

[0142]

[0143] In the formula, π c and μ (i)j They represent the equality constraints x respectively c -z c +c c =0 and z i -y (i)j =0 extended augmented Lagrange multipliers; ζ1>0 and ζ2>0 denote penalty factors.

[0144] The steps of the alternating multiplier method iterative algorithm in each iteration can be represented as:

[0145]

[0146]

[0147]

[0148]

[0149]

[0150] In the formula, It represents the active power balance, reactive power balance, and voltage drop equation constraints of the distribution network.

[0151] For z i The variable update problem can be represented as:

[0152]

[0153]

[0154] Use v i The above z represents i The augmented Lagrange multipliers for the variable update problem are then expressed as:

[0155]

[0156] In order to x c Using node z during variable update i Use variables to replace the user-side z i Variable, node z i Treating the variable as a fixed quantity, for the above z i Solving the variable optimization problem yields the following:

[0157]

[0158] In the formula, This represents the total number of users connected to node i; z i x i c i , π i These represent user variable z. c x c c c , π c The sum at node i.

[0159] Substituting the above equation into the Lagrange multiplier π c The update steps can be obtained That is, all users under the same node i All variables are the same.

[0160] f) Thus, the specific steps of the shared-form alternating multiplier iterative algorithm are as follows:

[0161]

[0162]

[0163]

[0164]

[0165]

[0166] In the formula, This represents the total number of users connected to node i; z i x i c i , π i These represent user variable z. c x c c c , π c The sum at node i.

[0167] See appendix Figure 2 This is a flowchart of the distributed solution algorithm for the integrated distributed transaction and operation model. The specific information exchange and distributed execution methods are described below.

[0168] Before the x variable is updated, the user receives the node active power variable z from the distribution network node to which it is connected. i and extended Lagrange multipliers π i Then, all users update the variable x in parallel based on their local variables and the variable information obtained from the connected nodes, and pass the updated x variable to the connected nodes. After receiving the updated x variable from all connected users, the nodes then... Calculate the x variable at each node. Simultaneously, each node updates its local replicated variable y using the z variable passed from its neighboring nodes and passes the updated y to its neighboring nodes. Afterward, each node, based on its local and received variable information, calculates the new z variable in parallel according to the z update steps.

[0169] The user variable x, node variables z, y, π, and μ are then updated and iterated according to the calculation method shown in the following formula:

[0170]

[0171]

[0172]

[0173]

[0174]

[0175] In the formula, This represents the total number of users connected to node i; z i x i c i , π i These represent user variable z. c x c c c , π c The sum at node i.

[0176] The specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, which are not intended to limit the scope of protection of the present invention. All equivalent models or equivalent algorithm flows made using the content of the present invention specification and drawings, and which are directly or indirectly applied to other related technical fields, are within the scope of patent protection of the present invention.

Claims

1. A method for integrating distributed energy trading and operation under the constraints of a power distribution network, characterized in that, The method involves: establishing an integrated distributed trading and operation model based on the Vickrey-Clarke-Groves (VCG) mechanism under distribution network constraints; addressing the asymmetry of distributed payments in the VCG model by proposing a zero-sum symmetric distributed settlement method that can effectively quantify distributed energy trading and operation and maintenance service costs; and using a distributed solution algorithm based on the alternating multiplier method to solve the convex optimization problem of distributed energy trading construction under distribution network constraints, thereby obtaining the distribution network operation optimization results. Establish a zero-sum symmetric distributed settlement method, specifically as follows: a) Define the utility of a user participating in a distributed transaction as their value minus the total payment of the distributed transaction, specifically: In the formula, Represents the total payment cost of a user's distributed transactions; ρ c The calculation method is as follows: The value of user c participating in distributed transactions is defined as a negative energy cost, specifically expressed as: The distributed transaction volume of a user is obtained through the following method: The user's distributed transaction volume is the optimal solution to the problem of maximizing the total value of distributed transactions, specifically: Total payment fee ρ for distributed transactions by users c The increase in the total value of other users when a user exits the distributed transaction is specifically: In the formula, This represents the total value when user c leaves the distributed trading market and other users choose the optimal electricity consumption. This represents the optimal electricity consumption for user m when user c exits the distributed trading market. The value of the following; b) In the absence of distribution network constraints, the payment and settlement problem for distributed transactions is approximately zero-sum. Both are true; the actual payment from user c to user m Specifically, it is expressed as follows: In the formula Furthermore, distributed payment satisfies the symmetric complementarity constraint; When the distribution network constraints are valid, for the payment and settlement problem of distributed transactions, the constraints for any user c are as follows: If this holds true, then the user's utility under actual payment is greater than the utility under theoretical payment, that is...

2. The method for integrated distributed energy trading and operation under the constraints of a power distribution network as described in claim 1, characterized in that, The objective function of the integrated distributed transaction and operation model includes discomfort cost and distributed transaction balancing cost, specifically: In the formula, This represents the discomfort cost for user c. This represents the overall cost allocation for distributed transactions. User discomfort costs This indicates that the user has changed their original habit of using electricity. The resulting costs take the form of a quadratic deviation penalty: In the formula, α c This indicates user C's willingness to adjust their electricity consumption requirements. This indicates the user's actual electricity consumption after the adjustment; User's distributed transaction balancing cost allocation The allocation rule is based on the proportion of transaction volume, specifically expressed as follows: In the formula, This represents a group of electricity buyers. Represents the set of electricity retailers; the allocation ratio coefficient η c,τ Represents users participating in distributed transactions The proportion of the total energy trading volume allocated; the overall energy balance cost. Represented as: In the formula, and These represent the retail electricity price at which a user purchases electricity from the upstream power grid and the on-grid electricity price at which a user sells the electricity they generate to the upstream power grid, respectively. P represents the total inelastic load that directly trades with the upstream power grid during the time period τ under node i; 0，τ This represents the net power injected from the root node into the upper-level power grid; apportionment ratio coefficient η c，τ Specifically, the proportion of trading volume is expressed as follows: In the formula, This represents the energy injected by user C into the distribution network; This represents the total balancing energy required by the distributed market; This represents the total energy transaction volume in the distributed market.

3. The method for integrated distributed energy trading and operation under the constraints of a power distribution network as described in claim 1, characterized in that, The distributed transaction and operation integrated model, which includes network node variables and user variables, is solved using the alternating multiplier method based on a shared form. The specific steps are as follows: a) Use User variables The objective function, The function representing the node variables represents the overall balancing cost, thus the distributed transaction problem under the security constraints of a single-time distribution network can be specifically represented as: In the formula, User variable x c The copy variable z at the node c The constant difference; This represents the user's flexible load upper and lower bound constraints; z i It represents the node variables of the distribution network, including node active power injection, reactive power injection, node voltage, line current from the node to the mother node, line active power and line reactive power; Indicates the constraints of the distribution network; y (j)i The variable z representing node i i The variable is copied at the adjacent node j; Indicates branch flow power equality constraints; x c -z c +c c =0 and z i -y (i)j =0 represents the consistency constraint for node variables and user variables, respectively; b) The extended augmented Lagrangian function of the distributed transaction problem under single-time distribution network security constraints is specifically expressed as: In the formula, π c and μ (i)j They represent the equality constraints x, respectively. c -z c +c c =0 and z i -y (i)j =0 extended augmented Lagrange multipliers; ζ1>0 and ζ2>0 denote penalty factors; The steps of the alternating multiplier method iterative algorithm in each iteration are represented as follows: In the formula, It represents the equation constraints for active power balance, reactive power balance, and voltage drop in the distribution network; For z i The variable update problem is represented as: Use v i Indicate z i The augmented Lagrange multipliers for the variable update problem are represented by the augmented Lagrange function as follows: In order to x c Using node z during variable update i Use variables to replace the user-side z i Variable, node z i Treating the variable as a fixed quantity for z i Solving the variable optimization problem yields the following: In the formula, z represents the total number of users connected to node i; i x i c i , π i These represent user variable z. c x c c c , π c The sum at node i; Substituting the above equation into the Lagrange multiplier π c Update steps, get That is, all users under the same node i All variables are the same; c) The specific steps of the shared-form alternating multiplier iterative algorithm are as follows: In the formula, This represents the total number of users connected to node i; z i x i c i , π i These represent user variable z. c x c c c , π c The sum at node i.

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