Active and reactive power collaborative optimization method for microgrid based on equivalent projection theory

Abstract

The application discloses a micro-grid active-reactive power collaborative optimization method based on equivalent projection theory and relates to the technical field of power system operation optimization. The method comprises the following steps: constructing a two-layer optimization framework of the micro-grid, wherein the upper layer is a distribution network and the lower layer is a micro-grid comprising distributed photovoltaic, fan, micro gas turbine and energy storage system; under the premise of ensuring voltage safety, taking the sum of the distribution network network loss, distribution network operation cost and micro-grid operation cost as the minimum target; by aggregating the feasible region of the micro-grid, forming a micro-grid equivalent model to participate in the optimal operation of the distribution network, and using the equivalent projection theory to decompose the overall model into the optimization sub-models of the distribution network and the micro-grid, the coupling solution is realized through the interaction variable. The method can effectively protect the privacy information of the micro-grid, reduce the calculation complexity, realize the efficient collaborative operation of the distribution network and the micro-grid, thereby improving the voltage quality, reducing the network loss and reducing the system operation cost.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system operation optimization, and in particular to an active-reactive power collaborative optimization method for distribution-microgrid based on equivalent projection theory. BACKGROUND

[0002] With high penetration of distributed energy in distribution networks, source-load uncertainty and volatility are significantly enhanced, which easily induces problems such as node voltage upper / lower limit, network loss rise and operation cost increase. At the operation level, it is difficult to balance voltage quality and economy in high penetration scenarios only by relying on traditional reactive power compensation or tap voltage regulation, so the industry gradually focuses on the role and necessity of active-reactive power collaboration in voltage regulation and loss suppression.

[0003] The engineering landing of cross-layer (distribution network-microgrid) collaborative optimization is still restricted by communication / computation overhead and data boundary constraints: centralized methods have strong dependence on full network data, large computation and communication burden, and privacy out-of-domain risk; distributed methods can be calculated in a decentralized manner, but often rely on multiple iterations, have high communication burden and are susceptible to model convexity and parameter configuration, making it difficult to stably support high-frequency / real-time applications.

[0004] The invention patent with application number CN 202410508558.4 discloses a multi-microgrid distribution system collaborative optimization operation method based on equivalent projection theory, which projects the microgrid operation feasible region and uploads it to the distribution network layer, and carries out collaborative optimization combined with distribution network reconfiguration (DNR) and intelligent soft switch (SOP). The research focuses on reducing the system operation cost while ensuring privacy. The SOP is explicitly used as a network-side flexibility device, which has continuous reactive power compensation and accurate active power control capability, but the overall optimization target and solution process of the framework mainly focuses on cost minimization and network-side flexibility utilization.

[0005] However, the reactive power collaborative interaction between distribution and microgrid is not systematically modeled and optimized as the core decision object. Although the SOP has local reactive power capability, the cross-layer coordination of existing solutions focuses more on uploading the projected feasible region of the microgrid and carrying out unified optimization based on cost guidance, without considering the "reactive power interaction between distribution and microgrid" as an independent cross-layer mechanism, and without considering the voltage quality index as a clear target. In the high penetration scenario of distributed energy, this gap easily leads to insufficient voltage regulation capability and difficulty in suppressing node voltage limit. In addition, the target side lacks direct attention to voltage quality. The existing solution mainly focuses on system cost minimization, without considering voltage deviation / limit risk as the main optimization target or key constraint for reactive power interaction, making it difficult to meet the rigid demand for voltage stability in the high penetration scenario of distributed energy.

[0006] Therefore, for the high penetration rate distributed energy scene, the prior art still has obvious deficiencies in the systematic modeling and optimization of the reactive power coordination between the distribution and micro layers and the voltage quality orientation, which leads to difficulty in effectively inhibiting voltage out-of-limit and synchronously controlling network loss and cost under the premise of guaranteeing privacy and communication affordability. SUMMARY

[0007] In view of the above problems, the application provides a distribution-micro grid active-reactive power coordinated optimization method based on equivalent projection theory, aiming to reduce the voltage deviation and network loss of the distribution grid, so as to realize efficient coordinated operation of the distribution grid and the micro grid, reduce the network loss of the system while ensuring the safe operation range of the system voltage, and take into account the economy of system operation.

[0008] The application achieves the above-mentioned purposes through the following technical solutions:

[0009] The distribution-micro grid active-reactive power coordinated optimization method based on equivalent projection theory comprises the following steps:

[0010] A distribution-micro grid coordinated optimization operation framework is established, the upper layer is a distribution grid, including distributed photovoltaic and loads directly connected to the distribution grid; the lower layer is at least one micro grid, including distributed energy and loads inside the micro grid; the distributed energy at least includes distributed photovoltaic, wind turbines, micro gas turbines and energy storage systems;

[0011] Based on the distribution-micro grid coordinated optimization operation framework, a distribution-micro grid coordinated active-reactive power optimization operation model is constructed, taking the sum of the distribution grid network loss, the distribution grid operation cost and the micro grid operation cost as the optimization objective;

[0012] The active power feasible region and the reactive power feasible region of the distributed energy inside the micro grid are aggregated to construct a micro grid equivalent model to participate in the optimization operation of the distribution grid;

[0013] Based on the equivalent projection theory, the distribution-micro grid coordinated active-reactive power optimization operation model is equivalently decomposed into a distribution grid optimization sub-model and a micro grid optimization sub-model, the coupling solution of the distribution grid optimization sub-model and the micro grid optimization sub-model is realized through interaction variables, the distribution grid optimization sub-model calculates the optimal value of the interaction variables under the constraint of the micro grid equivalent model, and the micro grid optimization sub-model generates the active power and reactive power output strategy of each distributed energy inside the micro grid under the constraint of the optimal value of the interaction variables, so as to be executed by the micro grid.

[0014] As a preferred scheme of the application, in the distribution-micro grid coordinated optimization operation framework, an information interaction channel and an energy interaction channel are arranged between the distribution grid and the micro grid;

[0015] The information exchange channel is used to transmit distributed photovoltaic power output forecasts, distribution network load demand, and microgrid equivalent models between the distribution network and each microgrid.

[0016] The energy exchange channel is used for bidirectional transmission of active and reactive power between the distribution network and each microgrid.

[0017] The distribution network optimizes voltage quality, reduces network losses, and improves operational economy by adjusting the active and reactive power outputs of distributed photovoltaic power.

[0018] The microgrid provides power support to the distribution network and smooths out system power fluctuations by adjusting the active and reactive power outputs of its internal distributed energy sources.

[0019] As a preferred embodiment of the present invention, the objective function of the distribution-microgrid coordinated active-reactive power optimization operation model is... Represented as: ;

[0020] Among them, distribution network losses Represented as: ;

[0021] Distribution network operating costs Represented as: ;

[0022] Microgrid operating costs Represented as: ;

[0023] In the formula, A correction factor greater than 0 is used to ensure that the values ​​of distribution network losses, distribution network operating costs, and microgrid operating costs are on the same order of magnitude. For nodes The set of all end nodes of the initial node; for Flowing through the side road at all times The square of the current amplitude; branch road The resistance value; For the set of distribution network nodes; This represents the number of time periods in the scheduling cycle. For the upper-level power grid Time-of-use electricity pricing at any given moment; For distribution network nodes In The amount of electricity purchased from the upstream power grid at all times; For the number of microgrids, Indicates the first Microgrids; For the distribution network in time-of-use electricity price; the access node of the microgrid purchases electricity from the power grid at time; the generation cost of the micro-turbine; the active power injected by the micro-turbine into the node at time; the charge-discharge operation cost of the energy storage system; the active power injected by the energy storage system into the node at time.

[0024] As a preferred scheme of the present application, in the coordinated active-reactive power optimization operation model of the microgrid, the power grid constraint conditions include: power grid flow constraint, node power balance constraint, safe operation constraint and distributed photovoltaic inverter control constraint.

[0025] The node power balance constraint is expressed as:

[0026] ;

[0027] The distributed photovoltaic inverter control constraint is expressed as:

[0028] ;

[0029] In the formula, is the set of all initial nodes with the node as the terminal node; , are respectively the active power and the reactive power flowing through the branch at time; , are respectively the active power and the reactive power injected by the photovoltaic inverter into the node at time; , are respectively the net active load and the reactive load injected into the node at time; is the reactive power injected by the power grid into the access node of the microgrid at time; is the active power flowing through the branch at time; is the reactance value of the branch ; is the reactance value of the branch At any time, the upstream transmission network connects to the distribution network access node. Injected reactive power; for Time Branch The reactive power flowing through; For nodes The set of all initial nodes of the first node;

[0030] for Photovoltaic injection node The upper limit of active power at that location; For nodes The rated capacity of the photovoltaic inverter; This is the minimum power factor of the photovoltaic inverter; This is the minimum power factor angle of the photovoltaic inverter.

[0031] As a preferred embodiment of the present invention, the microgrid constraints in the distribution-microgrid coordinated active-reactive power optimization operation model include:

[0032] The active and reactive power output constraints of distributed photovoltaic systems are consistent with the control constraints of the distributed photovoltaic inverters.

[0033] The active and reactive power output constraints of the wind turbine are represented as follows:

[0034] ;

[0035] The active and reactive power output constraints of a micro gas turbine are expressed as follows:

[0036] ;

[0037] The output constraint of the energy storage system is expressed as:

[0038] ;

[0039] The power balance constraint of a microgrid is expressed as:

[0040] ;

[0041] In the formula, , They are respectively Microgrids at nodes The active power and reactive power of the wind turbine: To connect to the distribution network node microgrids in The upper limit of active power output of the wind turbine at any given time; , These are the nodes connected to the distribution network. microgrids in The upper and lower limits of the reactive power output of the wind turbine at all times;

[0042] , They are respectively Timing of micro gas turbine injection node The upper and lower limits of active power; for Timing of micro gas turbine injection node reactive power; For nodes Rated capacity of the inverter for the micro gas turbine;

[0043] , They are respectively Real-time energy storage system at nodes The upper limit of active power for charging and discharging; for Real-time energy storage system to nodes Injected reactive power; for Always access node The maximum apparent power of the microgrid energy storage system; for; , They are respectively time, Time Node The energy stored in the energy storage system; for Time Node The upper limit of the energy storage capacity of the energy storage system; , They are nodes The initial and final values ​​of the stored energy in the energy storage system during the scheduling cycle;

[0044] , They are respectively Always access node The net active and reactive loads in the microgrid.

[0045] As a preferred embodiment of the present invention, the construction of the microgrid equivalent model specifically includes:

[0046] Based on the maximum and minimum power output of individual devices and energy migration requirements, the distributed energy sources within the microgrid are modeled to form the individual feasible regions of the distributed energy sources.

[0047] The energy migration requirement is expressed as follows: ;

[0048] wherein, , are the upper and lower bounds of the energy transfer demand, respectively; are the upper and lower limits of the distributed energy unit output; is the unit time of the optimal scheduling period;

[0049] Aggregating all the unit feasible regions, the Minkowski sum operation is used to form the accurate operation feasible region of the microgrid as a whole, denoted as: ;

[0050] wherein, is the upper or lower limit of the accurate operation feasible region of the microgrid as a whole; is the upper or lower bound of the energy transfer demand, i.e. or ; is the index of the distributed energy within the microgrid; is the total number of distributed energies; denotes the calculation of the Minkowski sum;

[0051] The trajectory screening is performed on the accurate operation feasible region using a binary structure, which is converted into a matrix inequality form, denoted as:

[0052] ;

[0053] wherein, denotes the feasible region vector arranged in descending order of time; is the dimensional complete binary structure of all trajectory sets; denotes the dimensional column vector composed of all node data of the trajectory without the root node; , denote the upper and lower limits of the operation feasible region corresponding to the trajectory , respectively; is the matrix transpose operation;

[0054] Define , and establish the corresponding relationship between the trajectory and the feasible region vector to obtain the equivalent form , so the matrix inequality is equivalent to: , i.e. as the accurate operation feasible region model of the microgrid;

[0055] wherein, is the value of the trajectory at the time ; is the 1- Time trajectory Summation of values To accumulate to time Take 1- Time Feasible region power vector arranged in descending order of time

[0056] The accurate operation feasible region model is approximately solved by using a k-order approximation method to obtain a micro-grid equivalent model, which is expressed as:

[0057] In the formula, The number of trajectories conforming to the k-order approximation method The trajectory The value at time The value at time The approximation order taken by the k-order approximation method

[0058] As a preferred scheme of the present application, the micro-grid collaborative active-reactive optimization operation model based on the equivalent projection theory is equivalently decomposed into a distribution network optimization sub-model and a micro-grid optimization sub-model, which specifically includes:

[0059] The decision variables in the distribution network and the micro-grid are divided into interactive variables between the distribution network and the micro-grid And the local variables of the distribution network The local variables of the micro-grid ;

[0060] Based on the equivalent projection theory, the local variables are eliminated without changing the optimality of the system, and only a set of inequality constraints about the interactive variables Characterize the operation characteristics of the micro-grid; at the same time, the micro-grid operation cost Is converted into an inequality form by using To represent the micro-grid operation cost, and the variable Is introduced to limit The value, wherein Take any value greater than the upper bound of the operation cost Of the micro-grid , then the micro-grid collaborative active-reactive optimization operation model is expressed as:

[0061] ;

[0062] In the formula, Indicates the distribution network constraint condition; Indicates the micro-grid constraint condition; Is the coordination variable of the micro-grid And the distribution network; Is the distribution network and​​ a set of microgrid coordination variables;

[0063] will be augmented with interaction variables, the distribution network and the microgrid are only coupled through local variables only appear in the microgrid constraints, but no longer appear in the microgrid objective function;

[0064] define the operation feasible region of each microgrid, denoted as: ;

[0065] wherein, denotes a polyhedron in space; and denote the dimension of the interaction variable and the local variable ;

[0066] the operation feasible region of the microgrid on the equivalent projection model on the subspace is denoted as:

[0067] ;

[0068] wherein, is the equivalent projection of the operation feasible region of the microgrid on the subspace; denotes the dimension of the polyhedron;

[0069] each microgrid submits the corresponding equivalent projection model instead of the original model to participate in the optimal operation of the distribution network, and the distribution-microgrid collaborative active-reactive power optimization operation model is equivalent to the decomposition of the distribution network optimization sub-model and the microgrid optimization sub-model, wherein the distribution network optimization sub-model is denoted as:

[0070] ;

[0071] the microgrid optimization sub-model is denoted as:

[0072] ;

[0073] wherein, , is the optimal value of the interaction variable solved by the distribution network optimization sub-model.

[0074] as a preferred scheme of the present application, the microgrid optimization sub-model generates the active power and reactive power output strategies of the internal distributed energy of the microgrid under the constraint of the optimal value of the interaction variable, including:

[0075] The micro-grid optimization sub-model is decomposed into each distributed energy according to the optimal solution of the local variable and is the boundary condition, the optimal solution of the local variable is calculated , and the total output of the micro-grid is decomposed into each distributed energy, and the decomposition model is represented as:

[0076] ;

[0077] In the formula, is the decomposition error, represents the specific output of the i-th distributed energy in the micro-grid .

[0078] The beneficial effects of the present application are: the micro-grid organically aggregates the operation feasible region of the distributed energy, constructs a micro-grid accurate operation feasible region model, can effectively protect the privacy information of the internal parameters of the micro-grid, and at the same time, the k-order approximate model is used to approximate the accurate operation feasible region model, the approximate model can significantly reduce the model calculation burden under the condition of meeting the calculation accuracy; the active-reactive power optimization operation method of the distribution-micro-grid cooperation is proposed, compared with the independent optimization operation of each power grid, the voltage deviation and network loss of the distribution network can be significantly reduced, and the total operation cost of the system is reduced, and the safety and economy of the system operation are significantly improved; the operation feasible region of the micro-grid layer is projected to the distribution network system based on the equivalent projection theory, and the micro-grid is in the form of dimensionality reduction equivalent model Participate in the optimization operation of the distribution network layer, and the consistency of the decision results of the distribution network layer and the optimality of the micro-grid layer can be realized through single information interaction, and the efficient solution of the collaborative optimization of the distribution network and the micro-grid is realized. BRIEF DESCRIPTION OF DRAWINGS

[0079] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor. Among them:

[0080] Figure 1 is the flow chart of the method of the present application;

[0081] Figure 2 is the schematic diagram of the distribution-micro-grid collaborative optimization operation framework in the embodiment of the present application;

[0082] Figure 3 is the development trend diagram of the binary structure in the embodiment of the present application;

[0083] Figure 4 ​​A system topology diagram in an embodiment of the present application;

[0084] Figure 5 A typical daily load curve and a PV output prediction curve diagram of a distribution network in an embodiment of the present application;

[0085] Figure 6 A daily load curve diagram of four microgrids in an embodiment of the present application;

[0086] Figure 7 A voltage amplitude diagram of each node at each time in Case 1 in an embodiment of the present application;

[0087] Figure 8 A voltage amplitude diagram of each node at each time in Case 2 in an embodiment of the present application;

[0088] Figure 9 A voltage amplitude diagram of each node at each time in Case 3 in an embodiment of the present application. DETAILED DESCRIPTION

[0089] To make the objectives, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions of the embodiments of the present application will be described below in detail with reference to the accompanying drawings of the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the described embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art belong to the scope of protection of the present application.

[0090] Embodiment 1

[0091] As shown in the figure, one embodiment of the present application provides a distribution-microgrid active-reactive power collaborative optimization method based on equivalent projection theory, comprising the following steps: Figure 1

[0092] S101: Establish a distribution-microgrid collaborative optimization operation framework, the upper layer is a distribution network layer, and the lower layer is a microgrid layer, including at least one microgrid;

[0093] S102: Based on the distribution-microgrid collaborative optimization operation framework, a distribution-microgrid collaborative active-reactive power optimization operation model is constructed, taking the sum of the distribution network network loss, the distribution network operation cost and the microgrid operation cost as the optimization objective, aiming to reduce the distribution network voltage deviation and network loss, and improve the economy of system operation;

[0094] S103: Aggregate the active power feasible region and the reactive power feasible region of the distributed energy in the microgrid, and construct a microgrid equivalent model with privacy protection without losing accuracy to participate in the optimization operation of the distribution network;

[0095] ​S104: Based on the equivalent projection theory, the active-reactive power collaborative optimization operation model of the distribution-microgrid is equivalently decomposed into a distribution network optimization sub-model and a microgrid optimization sub-model, the coupling solution of the distribution network optimization sub-model and the microgrid optimization sub-model is realized through an interactive variable, the distribution network optimization sub-model calculates the optimal value of the interactive variable under the constraint of the microgrid equivalent model, and the microgrid optimization sub-model generates the active power and reactive power output strategy of each distributed energy in the microgrid under the constraint of the optimal value of the interactive variable, so as to realize the goal of improving the voltage quality of the distribution network and optimizing the system operation.

[0096] Embodiment 2

[0097] This embodiment further introduces the method in embodiment 1 in combination with specific calculation formula and examples.

[0098] S201: The distribution-microgrid collaborative optimization operation framework of this embodiment is shown in Figure 2 The upper layer distribution network (Distribution Network, DN) includes distributed photovoltaic (Photovoltaic, PV) and load (Load), and the lower layer microgrid (Microgrid, MG) includes distributed energy resources (Distributed Energy Resources, DER) and load (Load) in each microgrid. The distributed energy resources include distributed photovoltaic (PV), wind turbine (Wind Turbine, WT), microturbine (Microturbine, MT), energy storage system (Energy Storage System, ESS), etc.

[0099] Figure 2 The main grid in the figure usually refers to a large-scale public power system, which is uniformly operated and controlled by a power transmission network and a superior dispatching center. It is connected with the distribution network (Distribution Network, DN), and provides power support to the lower-level distribution network and microgrid, and can also absorb the reverse power of the distributed energy and the microgrid. Among them, the information flow (dotted arrow) represents the information flow, which refers to the transmission process of control information, dispatching instructions, operation state data and other signals exchanged between the distribution network, the microgrid and the main grid in the power system. The energy flow (solid arrow) represents the energy flow / power flow, which refers to the actual transmission and exchange of electric energy (active power, reactive power) between the main grid, the distribution network and the microgrid in the power system.

[0100] In the S201 power grid-microgrid collaborative optimization operation framework, an independent information interaction channel and an energy interaction channel are arranged between the power grid and the microgrid. The information interaction channel is used to transmit the power grid distributed photovoltaic output prediction, the power grid load demand, and the operation feasible region (aggregated overall feasible region or microgrid equivalent model) of the microgrid between the power grid and each microgrid. The power grid formulates a system dispatching strategy according to the above information, and issues the microgrid output information to each microgrid, so as to realize the collaborative optimization between the systems.

[0101] The energy interaction channel is used for bidirectional transmission of active power and reactive power between the power grid and each microgrid. The power grid adjusts the active power and reactive power output of the distributed photovoltaic to realize voltage quality optimization, network loss reduction, and operation economic improvement. The microgrid adjusts the active power and reactive power output of the internal distributed energy to provide power support to the power grid and suppress system power fluctuation.

[0102] Specifically, the objective function of the power grid-microgrid collaborative active-reactive power optimization operation model is represented as:

[0103] Wherein, the power grid network loss is represented as:

[0104] The power grid operation cost is represented as:

[0105] The microgrid operation cost is represented as:

[0106] In the formula, is a correction coefficient greater than 0, used to ensure that the numerical values of the power grid network loss, the power grid operation cost, and the microgrid operation cost are of the same order of magnitude; is the node set of all end nodes with the node as the initial node; is the square of the current amplitude flowing through branch at time ; is the resistance value of branch ; is the power grid node set;

[0107] is the time-of-use electricity price of the upper-level power grid at time ; is the power grid node at time ;​​​​The amount of electricity purchased from the upstream power grid at all times; For the number of microgrids, Indicates the first Microgrids; For the distribution network in Time-of-use electricity pricing at any given moment; For access nodes microgrids in The amount of electricity purchased from the distribution network at all times; The cost of generating electricity from a micro gas turbine; for Timing of micro gas turbine injection node Active power at the location; The charging and discharging operating costs of the energy storage system; for Real-time energy storage system to nodes Injected active power.

[0108] The distribution network constraints include distribution network power flow constraints, node power balance constraints, safe operation constraints, and distributed photovoltaic inverter control constraints. Among these, the distribution network power flow constraints employ a widely used distribution network branch power flow model. The current constraints and voltage drop constraints related to this branch model are shown below:

[0109] ;

[0110] ;

[0111] The node power balance constraint is expressed as:

[0112] ;

[0113] Safe operation constraints are expressed as follows:

[0114] ;

[0115] ;

[0116] The control constraints for distributed photovoltaic inverters are expressed as follows:

[0117] ;

[0118] In the formula, , They represent Time Node The square of the voltage amplitude, Time Node The square of the voltage amplitude; For nodes The set of all initial nodes of the terminal node; , are respectively active power and reactive power flowing through branch at time , are respectively active power and reactive power injected by PV inverter into node at time , are respectively net active load and reactive load injected into node at time is reactive power injected by distribution network into microgrid access node at time is the reactance value of branch ; is reactive power injected by upper transmission network into distribution network access node at time is active power flowing through branch at time is reactive power flowing through branch at time is the square of the maximum value of the current amplitude allowed to flow through branch ;

[0119] , are respectively the square sum and the square minimum of the voltage amplitude maximum value of node ; is the square of the maximum value of the current amplitude allowed to flow through branch ;

[0120] is active power upper limit value at PV injection node at time is the rated capacity of the PV inverter at node ; is the minimum power factor of the PV inverter, usually a given constant; is the minimum power factor angle of the PV inverter.

[0121] The microgrid constraint conditions include:

[0122] Distributed PV active and reactive power output constraints, consistent with distributed PV inverter control constraints;

[0123] Fan active and reactive power output constraints, expressed as:

[0124] ;

[0125] The active and reactive power output constraints of the micro gas turbine are expressed as:

[0126] ;

[0127] The output constraints of the energy storage system are expressed as:

[0128] ;

[0129] The power balance constraints of the microgrid are expressed as:

[0130] ;

[0131] wherein , are the active and reactive power of the wind turbine of the microgrid at the time instant at the node ; is the upper limit of the active power output of the wind turbine of the microgrid at the time instant at the node ; , are the upper and lower limits of the reactive power output of the wind turbine of the microgrid at the time instant at the node ;

[0132] , are the upper and lower limits of the active power injected by the micro gas turbine at the time instant at the node ; is the reactive power injected by the micro gas turbine at the time instant at the node ; is the inverter rated capacity of the micro gas turbine at the node ;

[0133] , are the upper limits of the active power charged and discharged by the energy storage system at the time instant at the node ; is the reactive power injected by the energy storage system at the time instant at the node ; is the maximum apparent power of the energy storage system of the microgrid at the time instant at the node ; is the apparent power of the microgrid at the time instant , respectively are the storage power of the energy storage system at the time node the time node the storage power of the energy storage system at the time node the time node the upper limit value of the storage power of the energy storage system at the time node between 10~90% of the upper limit value, so as to protect the battery; , , respectively are the initial value and the final value of the storage power of the energy storage system at the time node in the dispatching cycle, and the two are equal, which is determined by the state of charge of the energy storage system;

[0134] , respectively are the net active load and the reactive load in the microgrid connected to the node at the time node .

[0135] S202: Due to the requirements of independent operation of each level of power grid, private user data, etc., it is difficult for the distribution network to collect global information for optimal scheduling, so it is necessary to aggregate the active and reactive power operation feasible region of the distributed energy within the microgrid, and construct a microgrid equivalent model that protects privacy without losing accuracy to participate in the optimal operation of the distribution network.

[0136] (1) Single feasible region model of distributed energy

[0137] The maximum and minimum power output of the single device and the energy transfer demand are taken as the basic constraints to model each distributed energy within the microgrid to form a single feasible region of distributed energy;

[0138] wherein the energy transfer demand is expressed as: ;

[0139] In the formula, , respectively are the upper and lower boundaries of the energy transfer demand; is the upper and lower limit of the output of the distributed energy single; is the unit time of the optimal scheduling cycle, i.e. 1 hour.

[0140] (2) Accurate operation feasible region model of microgrid

[0141] The calculation of the active and reactive power operation feasible region of the microgrid is actually the calculation of the Minkowski sum of the active and reactive power output feasible regions of the G distributed energy contained therein.

[0142] ​​The Minkowski sum operation is used to aggregate all the individual feasible regions to form the overall microgrid precise operation feasible region, denoted as: ;

[0143] wherein, is the upper or lower bound of the energy boundary of the overall microgrid precise operation feasible region; is the upper or lower bound of the energy migration demand, i.e. or ; is the index of the distributed energy within the microgrid; is the total number of distributed energies; denotes the calculation of the Minkowski sum;

[0144] The trajectory screening is performed on the precise operation feasible region using a binary structure, which is converted into a matrix inequality form, denoted as:

[0145] ;

[0146] wherein, denotes the feasible region vector arranged in descending order of time; is the dimensional complete binary structure of all trajectories; , denote the upper and lower bounds of the operation feasible region corresponding to the trajectory ; is the matrix transpose operation; denotes the dimensional column vector composed of all node data of the trajectory without the root node, The development trend of the microgrid is shown in FIG. 1. Figure 3

[0147] The data in the binary structure is specified as follows: the value of the root node is 0; the value of the left child node of each node is 0, and the value of the right child node is -1 or 1; if a node is the right child node of its parent node, and the value of all ancestor nodes of the node is 0, then the value of the node is 1, if the value of a certain ancestor node of the node is not 0, then the value of the node will be opposite to the sign of the value of its closest non-zero ancestor node.

[0148] The binary structure traverses all nodes in the above manner.

[0149] Define , and establish the correspondence between the trajectory and the feasible region vector to obtain the equivalent form , then the matrix inequality is equivalent to: , which is the precise operation feasible region model of the microgrid.​

[0150] wherein, is the trajectory is the value of the trajectory at time t; is the value of the trajectory at time t; is the summation of the values of the trajectory at time t; is the summation of the values of the trajectory at time t; is the feasible region power vector arranged in descending order of time.

[0151] According to the parity of the number of non-zero nodes in the binary structure trajectory, the upper and lower limits of the accurate operation feasible region model of the microgrid can be calculated accordingly;

[0152] When the number of non-zero nodes in the binary structure trajectory is odd, the upper and lower limit parameter calculation formulas are respectively:

[0153] ;

[0154] ;

[0155] When the number of non-zero nodes in the binary structure trajectory is even, the upper and lower limit parameter calculation formulas are respectively:

[0156] ;

[0157] ;

[0158] , respectively, the binary structure trajectory is the first and last non-zero element index, defined as: ; ;

[0159] In the formula, , respectively, the distributed energy in the microgrid is the upper and lower energy boundaries of the distributed energy in the microgrid at time t, , respectively, the upper and lower power boundaries of the distributed energy in the microgrid at time t, is the T-dimensional vector composed of ; is the T-dimensional vector composed of

[0160] It is worth noting that , and The elements in the matrix are arranged in descending order of time. This exact operational feasible region model indicates that the total energy consumed by the flexible resource cluster in each time period is always constrained by upper and lower limits. Furthermore, it is easy to see from the expression that the number of constraints in this model is not related to the number of aggregated distributed energy resources, but is exponentially related to the number of layers in the complete binary structure, i.e., the number of time periods. Excluding the invalid trajectory with all zeros on the leftmost side of the complete binary structure, the exact operational feasible region model contains 2T-1 valid trajectories that are not all zeros. Each trajectory corresponds to two parameters: upper and lower limits. Considering both active and reactive power, the total number of parameters is... Under intraday optimization conditions The number of parameters is usually set to 24, resulting in a total of 67,108,860 parameters, which is computationally unacceptable.

[0161] (3) k-order approximate model of the feasible region of microgrid operation

[0162] The k-th order approximation method is used to approximate the solution of the exact operational feasible region model, resulting in the microgrid equivalent model, which is expressed as: ;

[0163] In the formula, To determine the number of trajectories that conform to the k-th order approximation method; For trajectory exist The value at time; This is the approximation order chosen by the k-th order approximation method.

[0164] This method selects the appropriate trajectory based on the number of non-zero nodes in each trajectory. The k-order approximation selects trajectories with no more than [number missing] non-zero nodes. The trajectory is used to construct constraints. As the approximation order increases, the computational accuracy improves, but the computational complexity also increases. Therefore, the computational order must be determined based on the specific circumstances. Since the microgrid aggregates the active and reactive power operating feasible regions of distributed energy sources, calculates the upper and lower limits of microgrid output and uploads them to the distribution network for coordinated optimization, the distribution network no longer collects the specific parameters of the distributed energy sources within the microgrid.

[0165] S203: Non-iterative solution of active and reactive power optimization operation model of distribution-microgrid based on equivalent projection theory

[0166] Based on the different properties of variables in the system, the decision variables in the distribution network and the interaction variables between the distribution network and the microgrid are classified. (such as the interaction power between the two) and local variables of the distribution network microgrids local variables The active-reactive power optimization operation model of a distribution-microgrid can be expressed in the following form:

[0167] ;

[0168] For the above model, due to the existence of interaction variables , the distribution network layer and the microgrid layer cannot be independently optimized. If the value of can be fixed, the joint optimization operation model can be solved by layering. Therefore, the application adopts an equivalent projection-based method to eliminate local variables without changing the system optimality, and only represents the operation characteristics of the microgrid through a set of inequality constraints about the interaction variables ; at the same time, the microgrid operation cost is converted into an inequality form by the upper bound graph, and is used to represent the microgrid operation cost, and the variable is introduced to limit the value of , wherein takes any value greater than the upper bound of the operation cost of the microgrid , and the coordinated active-reactive power optimization operation model of the distribution-microgrid is represented as:

[0169] ;

[0170] In the formula, represents the distribution network constraint condition; represents the microgrid constraint condition; is the coordination variable of the microgrid and the distribution network; is the set of coordination variables of the distribution network and microgrids;

[0171] Taking as the augmented interaction variable of the microgrid , the distribution network and the microgrid are only coupled through , and the local variable only appears in the microgrid constraint condition, but no longer appears in the microgrid objective function, effectively protecting the privacy information such as the cost of the microgrid layer.

[0172] The operation feasible region of each microgrid is defined and represented as: ;

[0173] In the formula, represents a polyhedron in space; and represent the dimensions of variables and ;

[0174] The operation feasible region of the microgrid is in The equivalent projection model on the subspace is represented as:

[0175]

[0176] In the formula, The operation feasible region of the micro-grid on the equivalent projection on the subspace; The dimension of the polyhedron is represented as:

[0177] Each micro-grid submits a corresponding equivalent projection model instead of the original model to participate in the optimal operation of the distribution network, and the distribution-micro-grid collaborative active-reactive optimal operation model is equivalent to decomposition of a distribution network optimization sub-model and a micro-grid optimization sub-model, wherein the distribution network optimization sub-model is represented as:

[0178]

[0179] The micro-grid optimization sub-model is represented as:

[0180]

[0181] In the formula, , The optimal value of the interaction variable solved by the distribution network optimization sub-model is represented as:

[0182] The micro-grid optimization sub-model takes the optimal value of the interaction variable and as a boundary condition, calculates the optimal solution of the local variable , that is, the optimal operation point of the micro-grid, and decomposes the total output of the micro-grid to each distributed energy source, and the decomposition model is represented as:

[0183]

[0184] In the formula, The decomposition error is represented as: The specific output of the i-th distributed energy source in the micro-grid is represented as: The model aims to realize accurate decomposition of the total output power of the micro-grid to each distributed energy source inside.

[0185] Embodiment 2 of the present application realizes efficient non-iterative solution of the distribution-micro-grid collaborative active-reactive optimal operation model through S201-S203. On the one hand, the privacy information inside the micro-grid is protected, and on the other hand, the voltage quality of the distribution network is significantly improved, the network loss of the distribution network and the cost of system operation are reduced, and the present application has wide engineering application value.

[0186] Embodiment 3

[0187] ​​​​​This embodiment takes the improved IEEE-33 node system as an example to simulate, analyze and verify the active-reactive power collaborative optimization method of the micro-grid based on the equivalent projection theory of the application, and the system topology is shown in Figure 4 .

[0188] The distributed photovoltaic is connected to the distribution network nodes 7, 11, 18, 19, 27 and 33 respectively, and the installation capacity is 1.0, 1.0, 2.5, 1.0, 1.25 and 1.25 MVA respectively; four micro-grids are connected to the nodes 15, 22, 24 and 31 of the distribution network respectively. The voltage level of the distribution network is 12.66 kV, the total active load is 3715 kW, and the total reactive load is 2300 kvar. The voltage amplitude of node 1 is set to 1.00 p.u., and the voltage safety range of the remaining nodes is 0.95-1.05 p.u. The micro-grid accurate operation feasible region model is calculated by selecting the second order approximation, the typical daily load curve of the distribution network and the PV output prediction curve are shown in Figure 5 , and the daily load curve of the four micro-grids is shown in Figure 6 .

[0189] In order to verify the effectiveness of the method proposed in the application, the following three scenarios are set respectively:

[0190] Case 1: The distribution network and the micro-grid are independently optimized and operated;

[0191] Case 2: The equivalent projection method is used for collaborative optimization of the distribution network and the micro-grid, and the reactive power support of the micro-grid to the distribution network is not considered;

[0192] Case 3: The reactive power support of the micro-grid to the distribution network is considered on the basis of Case 2.

[0193] (1) Analysis of the voltage optimization results of the distribution network

[0194] The voltage amplitude of each node of the distribution network at each time under different scenarios is shown in Figure 7-9 .

[0195] As can be seen from the figure, in Case 1, during the period of 10:00-14:00, the high output level of PV in the distribution network causes the voltage to rise, thereby causing the voltage of some weak nodes to exceed the upper limit. Especially at 12:00, the voltage amplitude of node 18 of the distribution network is as high as 1.0732 p.u. During the period of 18:00-24:00, the high load level in the distribution network and the low output level of PV cause the voltage to drop, thereby causing the voltage of some nodes to be below the lower limit. Especially at 20:00, the voltage amplitude of node 18 is as low as 0.9339 p.u. The total voltage deviation of the distribution network in 24 hours is 0.6710 p.u.

[0196] In Case 2, since the reactive power support from microgrid to distribution grid is not considered, the reactive power supply-demand balance of distribution grid and microgrid is maintained respectively. The voltage of each node meets the safe operation range, but the voltage fluctuation of distribution grid is still large, and the total voltage deviation is 0.4306 p.u.

[0197] In Case 3, since the reactive power support from microgrid to distribution grid is considered, the reactive power generated by distributed energy in microgrid first meets the reactive power demand of microgrid, and the remaining part is injected into distribution grid. The total voltage deviation of distribution grid is reduced to 0.2428 p.u., which is reduced by 43.62% compared with Case 2 and 63.82% compared with Case 1. The above results show that the proposed active-reactive power collaborative optimization method of distribution-microgrid can effectively alleviate the problem of voltage fluctuation of distribution grid and improve the voltage quality of the grid.

[0198] (2) System operation cost analysis

[0199] Table 1 Cost comparison under different scenarios

[0200]

[0201] Table 1 shows the cost comparison under different scenarios. Compared with Case 1, Case 2 and Case 3 have significant reduction in the cost of purchasing electricity from distribution grid. The reason is that microgrid can effectively cooperate with distribution grid. When the PV output of distribution grid is excessive, microgrid can absorb the excess electricity; when the PV output of distribution grid is insufficient and the load demand of microgrid itself is small, microgrid can send power back to distribution grid, reducing the cost of purchasing electricity from the main grid. In addition, in Case 3, microgrid also provides additional reactive power support for distribution grid, further reducing the network loss of distribution grid and thus reducing the operation cost of distribution grid. In terms of the operation cost of microgrid, Case 2 and Case 3 are basically the same, and the active power output strategy of microgrid 1-4 is also roughly the same. However, the operation cost of microgrid 4 in Case 2 and Case 3 increases compared with Case 1. The main reason is that microgrid 4 is adjacent to node 33 with weak voltage, and when the PV output of this node is small and insufficient to meet the load demand, the node voltage will appear below the lower limit. To avoid the voltage drop of distribution grid, the MT in microgrid 4 increases the power to raise the voltage, thereby increasing the operation cost of microgrid 4.

[0202] Although the system operation cost of Case 3 is only reduced by $55.58 compared to Case 2, Case 3 performs better in reducing voltage fluctuation and network loss of the distribution network. Specifically, the total cost is reduced by 12.30% for Case 2 compared to Case 1, while the total cost is reduced by 12.87% for Case 3 compared to Case 1. These results show that achieving coordinated active and reactive power optimization of the distribution-microgrid can effectively reduce the total operation cost of the system.

[0203] The above results show that constructing a coordinated active and reactive power optimization model of the distribution-microgrid, coordinating the interactive active and reactive power of the microgrid and the distribution network, can improve the voltage quality of the distribution network, reduce the network loss of the system, and balance the economy of the system operation.

[0204] The above describes only a specific implementation of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of various changes or replacements within the technical scope disclosed by the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for active-reactive power collaborative optimization of microgrid based on equivalent projection theory, characterized in that, The method comprises: An optimal operation framework of the distribution-microgrid coordination is established, wherein an upper layer is a distribution grid including distributed photovoltaic and load directly connected to the distribution grid, and a lower layer is at least one microgrid including distributed energy and load within the microgrid, and the distributed energy includes at least distributed photovoltaic, fan, micro gas turbine and energy storage system; Based on the optimal operation framework of the distribution-microgrid coordination, a distribution-microgrid coordinated active-reactive power optimal operation model is constructed, and a sum of distribution grid network loss, distribution grid operation cost and microgrid operation cost is taken as an optimization objective; The objective function of the coordinated active-reactive optimal operation model of the microgrid is represented as: ; Wherein, the power distribution network network loss is represented as: ; Power distribution network operating costs is represented as: ; Microgrid operating cost is represented as: ; In the formula, is a correction coefficient greater than 0, used to ensure that the numerical values of the power distribution network network loss, the power distribution network operation cost and the microgrid operation cost are of the same order of magnitude; is a node set of all end nodes of the initial node; is the square of the current amplitude flowing through branch at time ; is the resistance value of branch ; is a power distribution network node set; is the number of dispatching cycle periods; is the time-of-use electricity price of the upper-level power grid at time ; is the electricity purchased by the power distribution network node from the upper-level power transmission grid at time ; is the number of microgrids, denotes the th microgrid; is the time-of-use electricity price of the power distribution network at time ; is the electricity purchased by the microgrid connected to node from the power distribution network at time ; is the power generation cost of the micro gas turbine; is the active power injected by the micro gas turbine into node at time ; is the charge and discharge operation cost of the energy storage system; is the active power injected by the energy storage system into node at time Active power feasible region and reactive power feasible region of the distributed energy within the microgrid are aggregated to construct an equivalent model of the microgrid for participating in the optimal operation of the distribution grid; Based on equivalent projection theory, the distribution-microgrid coordinated active-reactive power optimal operation model is equivalently decomposed into a distribution grid optimization submodel and a microgrid optimization submodel, and the distribution grid optimization submodel and the microgrid optimization submodel are coupled and solved through an interaction variable, the distribution grid optimization submodel calculates an optimal value of the interaction variable under the constraint of the equivalent model of the microgrid, and the microgrid optimization submodel generates an active power and reactive power output strategy of each distributed energy within the microgrid under the constraint of the optimal value of the interaction variable, so as to be executed by the microgrid; The distribution-microgrid coordinated active-reactive power optimal operation model is equivalently decomposed into the distribution grid optimization submodel and the microgrid optimization submodel based on the equivalent projection theory, and specifically includes: classifying decision variables in the distribution grid and in the microgrid into interaction variables between the distribution-microgrid and local variables of the distribution grid , local variables of the microgrid , local variables of the microgrid ; Based on the equivalent projection theory, local variables are eliminated without changing the optimality of the system, and only a set of interaction variables is used. The inequality constraints characterize the operating characteristics of the microgrid; simultaneously, the operating cost of the microgrid is represented by the superordinate diagram. Transform it into an inequality form using Representing the operating cost of a microgrid, and introducing variables. limit The possible values ​​of , where Take a value greater than microgrid Operating costs For any value of the supremum, the distribution-microgrid coordinated active-reactive power optimization operation model is expressed as: ； wherein denotes the distribution grid constraints; denotes the microgrid constraints; is the microgrid coordinated variables with the distribution grid; is the set of distribution grid and microgrid coordinated variables; Will As a microgrid The augmented interaction variables, the distribution network and the microgrid are only through Coupling, local variables It only appears in the microgrid constraints, and no longer in the microgrid objective function; The feasible operation region of each microgrid is defined and denoted as: ; wherein represents a polyhedron in space; with represents the dimension of the interaction variable and the local variable ; Microgrid The feasible region of operation of the microgrid in The equivalent projection model of the feasible region of operation of the microgrid in the subspace is represented as: ； In the formula, For microgrids The feasible operating domain is Equivalent projection on the subspace; Describe the dimension of a polyhedron; Each microgrid submits a corresponding equivalent projection model to replace the original model to participate in the optimal operation of the distribution grid, and the distribution-microgrid coordinated active-reactive power optimal operation model is equivalently decomposed into the distribution grid optimization submodel and the microgrid optimization submodel, wherein the distribution grid optimization submodel is represented as: ； The microgrid optimization submodel is represented as: ； In the formula, , is the optimal value of the interaction variable solved by the power distribution network optimization sub-model.

2. The method of claim 1, wherein, In the optimal operation framework of the distribution-microgrid coordination, an information interaction channel and an energy interaction channel are arranged between the distribution grid and the microgrid; The information interaction channel is used for transmitting distribution grid distributed photovoltaic output prediction, distribution grid load demand and microgrid equivalent model between the distribution grid and each microgrid; The energy interaction channel is used for transmitting bidirectional active power and reactive power between the distribution grid and each microgrid; The distribution grid adjusts active power and reactive power output of the distributed photovoltaic to realize voltage quality optimization, network loss reduction and operation economy improvement; The microgrid adjusts active power and reactive power output of the distributed energy within the microgrid to provide power support to the distribution grid and suppress system power fluctuation.

3. The method of claim 2, wherein, In the distribution-microgrid coordinated active-reactive power optimal operation model, the constraint conditions of the distribution grid include distribution grid power flow constraint, node power balance constraint, safe operation constraint and distributed photovoltaic inverter control constraint; The node power balance constraint is represented as: ； The distributed photovoltaic inverter control constraint is represented as: ； In the formula, For nodes The set of all initial nodes of the terminal node; , They are respectively Time Branch Active power and reactive power flowing through; , They are respectively Photovoltaic inverters to nodes Injected active power and reactive power; , They are respectively Injecting nodes at all times Net active load and reactive load; for Distribution network access nodes to microgrids Injected reactive power; for Time Branch The active power flowing through; branch road The reactance value; for At any time, the upstream transmission network connects to the distribution network access node. Injected reactive power; for Time Branch The reactive power flowing through; For nodes The set of all initial nodes of the first node; is instantaneous photovoltaic injection node active power upper limit value at the node; is rated capacity of the photovoltaic inverter at the node; is is 4. The method of claim 3, wherein, In the distribution-microgrid coordinated active-reactive power optimal operation model, the constraint conditions of the microgrid include: Distributed photovoltaic active and reactive power output constraint is consistent with the distributed photovoltaic inverter control constraint; Fan active and reactive power output constraint is represented as: ； The active and reactive power output constraints of the micro gas turbine are represented as: ； The energy storage system output constraints are represented as: ； The micro grid power balance constraints are represented as: ； In the formula, , They are respectively Microgrids at nodes The active power and reactive power of the wind turbine: To connect to the distribution network node microgrids in The upper limit of active power output of the wind turbine at any given time; , These are the nodes connected to the distribution network. microgrids in The upper and lower limits of the reactive power output of the wind turbine at all times; , are respectively upper and lower limit values of the active power injected by the micro gas turbine at the instant t; are respectively reactive power injected by the micro gas turbine at the instant t; are respectively reactive power injected by the micro gas turbine at the instant t; are respectively inverter rated capacity of the micro gas turbine at the node , are respectively the upper limit value of the active power of the energy storage system at the node charging and discharging at the moment; is the reactive power injected by the energy storage system to the node at the moment; is the maximum apparent power of the micro-grid energy storage system connected to the node at the moment; is; , are respectively the storage capacity of the energy storage system at the node at the moment, at the moment the storage capacity of the energy storage system at the node ; is the upper limit value of the storage capacity of the energy storage system at the node at the moment; , are respectively the initial value and the final value of the storage capacity of the energy storage system at the node in the dispatching period;​​​​ , They are respectively Always access node The net active and reactive loads in the microgrid.

5. The method of claim 4, wherein, The micro grid equivalent model is built, and specifically includes: The maximum and minimum power outputs of the single device and the energy migration demand are taken as basic constraints to model each distributed energy in the micro grid, thereby forming a single feasible region of the distributed energy; wherein the energy migration demand is expressed as: ; In the formula, , are the upper and lower boundaries of the energy migration demand, respectively; are the upper and lower limits of the distributed energy unit output, respectively; is the unit time of the optimization scheduling period. The Minkowski sum operation is used to aggregate all the individual feasible regions to form the overall feasible region of the microgrid, which is denoted as: ; In the formula, The upper limit or lower limit of the feasible energy boundary of the accurate operation of the micro-grid as a whole; The upper limit or lower limit of the energy migration demand, that is, Or ; The index of the distributed energy in the micro-grid; The total number of distributed energy; Indicates the calculation of the Minkowski sum; The accurate operation feasible region is subjected to trajectory screening by using a binary structure, and is converted into a matrix inequality form and represented as: ； wherein, represents the feasible region vectors arranged in descending order of time; is all the trajectory sets of the complete binary structure of dimension represents the trajectory the set of all node data excluding the root node of the upper dimension column vector; , respectively represent the upper and lower limits of the operating feasible region corresponding to the trajectory respectively represent the upper and lower limits of the operating feasible region corresponding to the trajectory is the matrix transpose operation; Definition and establish the correspondence between the trajectory and the feasible region vector The equivalent form is obtained The matrix inequality is equivalent to , that is, as the accurate operation feasible region model of microgrid; wherein, is the trajectory at the value of the time instant; is 1- the trajectory of the sum of the values; is the cumulative to the time instant; takes the value 1- the time instant; is the feasible region power vector ordered in decreasing order of time; The k-order approximation method is used to solve the accurate operation feasible region model, and a microgrid equivalent model is obtained, which is expressed as: ; wherein is the number of trajectories that fit the kth order approximation method; is the trajectory at time is the value of the trajectory at time is the order of approximation taken by the kth order approximation method.

6. The method of claim 5, wherein, The micro grid optimization sub-model generates the active and reactive power output strategies of each distributed energy in the micro grid under the constraint of the optimal value of the interaction variable, including: The microgrid optimization sub-model uses the optimal values ​​of interaction variables. and Calculate local variables as boundary conditions. The optimal solution decomposes the total output of the microgrid into distributed energy sources, and the decomposition model is expressed as: ； In the formula, is the decomposition error, represents the specific output of the microgrid th distributed energy.

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