An Optimal Scheduling Method for AC / DC Hybrid Distribution Network Based on Graph Computing

Abstract

The present invention discloses an optimal scheduling method for AC / DC hybrid distribution networks based on graph computing. First, the equipment in the AC / DC hybrid distribution network is abstracted as the vertices of a graph, and an object-oriented graph model of the AC / DC hybrid distribution network is established to adapt to future power system data management based on graph databases. Secondly, based on this graph model, a collaborative optimization model for the AC / DC hybrid distribution network with a high proportion of photovoltaic energy storage is constructed, and a graph computing method for the AC / DC hybrid distribution network centered on vertices is derived. This method improves the computational efficiency and solvability of the model and protects user privacy through the decomposition of the model and parallel computing of vertices, realizing the plug-and-play of user equipment in the AC / DC hybrid distribution network.

Description

Technical Field

[0001] The invention relates to an AC / DC hybrid distribution network optimization dispatching method based on graph calculation, and belongs to the field of AC / DC hybrid distribution network operation and dispatching. Background Art

[0002] With the large-scale access of distributed resources such as photovoltaics and energy storage to the distribution network, the number of power electronic devices in the distribution network has increased, and the advantages of AC / DC hybrid distribution networks in terms of efficient operation and flexible control have become prominent, which has become a new trend in the development of distribution networks in the future. However, with the large-scale access of distributed energy storage and photovoltaics, the scale of the operation optimization model of AC / DC hybrid distribution networks has expanded dramatically, and the computational efficiency and solvability of traditional centralized algorithms have decreased, making it difficult to meet the computational requirements of large-scale distributed resources accessing AC / DC hybrid distribution networks in the future. Therefore, it is of great significance to find an efficient model calculation method for the unified model of AC / DC hybrid distribution networks.

[0003] Widely used distributed algorithms in existing research, such as ATC and ADMM, are based on distributed optimization of each sub-level or sub-region. Centralized modeling is still used in each sub-level and region. Sub-level and regional division also usually requires human participation, and the modeling versatility is poor. Graph computing methods based on graph databases have outstanding advantages in solution efficiency and scalability. They can realize fully distributed computing of vertices while protecting user privacy. However, they are currently mainly focused on power flow calculation and power supply capacity evaluation of AC systems. Graph computing has not yet been fully applied in the optimization operation of AC / DC hybrid distribution networks.

[0004] In response to the above problems, the present invention abstracts the devices in the AC / DC hybrid distribution network as vertices of a graph, and establishes an object-oriented AC / DC hybrid distribution network graph model; based on the graph model, a collaborative optimization model of an AC / DC hybrid distribution network with a high proportion of photovoltaic storage is constructed, and based on a vertex-centered AC / DC hybrid distribution network graph calculation method, an efficient solution of the AC / DC hybrid network optimization model is realized, and the scheduling strategy of the equipment is quickly obtained. At the same time, user privacy is protected, and user devices can be helped to achieve plug-and-play. Summary of the invention

[0005] Purpose of the invention: In order to meet the optimization computing needs of AC / DC hybrid distribution networks under the widespread access of photovoltaic energy storage and promote the power system data management based on graph database, the present invention provides an optimization scheduling method for AC / DC hybrid distribution networks based on graph computing.

[0006] Technical solution: In order to achieve the above-mentioned invention object, the present invention proposes an AC / DC hybrid distribution network optimization scheduling method based on graph computing, which includes the following steps:

[0007] Step 1: Introduce the concept of port and establish AC / DC hybrid distribution network diagram model;

[0008] Step 2: Associate the state variables in the AC / DC hybrid distribution network system with the ports introduced in the graphical model established in step 1, and associate the decision variables in the AC / DC hybrid distribution network system with each device to construct a coordinated optimization model of the AC / DC hybrid distribution network based on the graphical model;

[0009] Step 3: Solve the optimization model constructed in step 2 based on the vertex-centric graph computing method, obtain the optimal scheduling strategy of the equipment, and optimize the scheduling of the AC / DC hybrid distribution network according to the optimal scheduling strategy.

[0010] Furthermore, in step 1, the concept of port is introduced to establish an AC / DC hybrid distribution network diagram model. The specific method is as follows:

[0011] The concept of port is introduced, and ports are regarded as edges of the graph. Nodes and devices are regarded as vertices of the graph. A graph model of AC / DC hybrid distribution network is established. The vertices in the graph model, i.e. nodes and devices, and the edges, i.e. ports, are expressed as follows:

[0012] Equipment: It is divided into AC equipment, DC equipment and coupling equipment. The upper power grid, AC line, AC load, and photovoltaic and energy storage connected to the AC system in the AC system are abstracted as AC equipment; the DC line, DC load, and energy storage and photovoltaic connected to the DC system in the DC system are abstracted as DC equipment; the coupling equipment is the voltage source converter, which is represented by the subscript d;

[0013] Node: divided into AC node and DC node, realizing lossless energy exchange between similar associated ports, represented by subscript n;

[0014] Port: Each device contains one or more ports. The vertices consisting of devices and nodes are connected through ports. Ports are divided into AC ports and DC ports, also known as edges, represented by subscript o;

[0015] The ports in the AC / DC hybrid distribution network graph model are organized by nodes or by devices. When organized by nodes, the intersection of ports connected to different nodes is empty, and the union of ports connected to all nodes is the full set; when organized by devices, the intersection of ports connected to different devices is empty, and the union of ports connected to all devices is the full set. Assuming the full set of ports is O, the above properties are expressed as:

[0016]

[0017]

[0018] In the formula, Γ n,r and Γ n,s are the port sets connected to node r and node s respectively, N nis the total number of nodes, Γ d,e and Γ d,h is the set of ports connected to devices e and h, N d is the total number of devices, Represents the empty set.

[0019] Furthermore, in step 2, the state variables in the system are associated with the ports introduced in the graph model established in step 1, and the decision variables in the system are associated with each device, and an AC / DC hybrid distribution network optimization model based on the graph model is constructed as follows:

[0020] Objective function: Minimize the sum of the operating costs of each device in the AC / DC hybrid distribution network;

[0021]

[0022] Where: x d is the decision variable associated with device d, c d is the cost function of device d;

[0023] The cost function of each device is as follows:

[0024]

[0025] Where: t is the subscript of the dispatch period; T is the total dispatch period; c t P is the time-of-use electricity price for purchasing electricity from the upper power grid; sub,d,t The power purchased from the upper power grid; D sub It is a collection of upper-level power grid equipment; P is the energy storage operation and maintenance cost coefficient; ch,d,t and P dis,d,t are the charging and discharging power of the energy storage device during period t; ess,d is the depreciation cost coefficient of energy storage equipment; u ess,d,t D is the energy storage charging and discharging switching state variable during period t; ESS is the set of energy storage equipment; D is the set of equipment in the AC / DC hybrid distribution network; the cost of the upper grid equipment is the sum of the electricity purchase costs in each period; the energy storage operation cost includes operation and maintenance costs and depreciation costs; the cost of other equipment is 0;

[0026] Equipment operation constraints: Equipment operation constraints include power purchase constraints of the upper power grid, AC line and DC line operation constraints, voltage source converter operation constraints, energy storage operation constraints, and reactive power compensation constraints of photovoltaic inverters in the AC system;

[0027] 1) Constraints on power purchase from the upper-level power grid

[0028]

[0029]

[0030] Where P sub,d,t and Q sub,d,t are respectively the active and reactive injected power of the upper grid equipment in period t; and P sub,d They are respectively the upper and lower limits of active power injected into the upper grid; and Q sub,d They are the upper and lower limits of reactive power injected into the upper power grid respectively; P ac,o,t and Q ac,o,t are the active and reactive powers of the AC port o during period t, respectively; Γ sub,d It is a set of ports connected to the upper power grid;

[0031] 2) AC line operation constraints

[0032] When the device hour, is a set of AC line devices, assuming that its two end ports are i and j respectively, then the second-order cone form constraints of the AC line based on the graphical model are as follows:

[0033]

[0034]

[0035]

[0036]

[0037] In the formula, v ac,i,t and v ac,j,t are the squares of the voltage amplitudes at ports i and j of the AC line during period t; P ac,i,t and Q ac,i,t are the active power and reactive power of the AC line port i in period t respectively; P ac,j,t and Q ac,j,t are the active power and reactive power of the AC line port j during period t respectively; l ac,d,t is the square of the AC line current amplitude during period t; R ac,d and X ac,d are the resistance and reactance of the AC line respectively; l ac,d,max is the maximum current carrying capacity of the AC line;

[0038] 3) DC line operation constraints

[0039] When the device hour, is a set of DC line equipment, assuming that the ports at both ends are i and j respectively, and the DC line operation constraints are as follows:

[0040]

[0041]

[0042]

[0043]

[0044] In the formula, v dc,i,t and v dc,j,t are the squares of the voltage amplitudes at ports i and j of the DC line during period t; P dc,i,t and P dc,j,t are the active power of port i and port j of the DC line in period t respectively; l dc,d,t is the square of the DC line current amplitude during period t; R dc,d is the resistance of the DC line; l dc,d,max is the maximum current carrying capacity of the DC line;

[0045] 4) Voltage source converter row constraints

[0046] When device d∈D vsc When D vsc is a set of voltage source converter devices, assuming that its AC side port and DC side port are i and j respectively, then:

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] In the formula, v ac,i,t and v dc,j,t are the squares of the voltage amplitudes at the AC side port and the DC side port of the voltage source converter during period t; v vsc,d,t is the square of the voltage amplitude of the virtual port of the voltage source converter during period t; l vsc,d,t is the square of the current amplitude of the equivalent branch of the voltage source converter during period t; R vsc,d and X vsc,d are the equivalent resistance and reactance of the voltage source converter respectively; P ac,i,t and Q ac,i,tare the active and reactive power of the AC side port during period t; P vsc,d,t and Q vsc,d,t are the active and reactive powers of the virtual port of the voltage source converter during period t; P dc,j,t is the active power of the DC side port of the voltage source converter during period t; is the upper limit of reactive power compensation; μ is the voltage utilization rate of voltage source converter, which is generally 0.866; M vsc,d is the modulation ratio, with a value range of [0,1]; S vsc,N is the AC side capacity of the voltage source converter; is the upper limit of DC side power;

[0055] 5) Energy storage operation constraints

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] Where P ESS,d,max is the upper limit of energy storage charging and discharging power; β ch,d,t and β dis,d,t are the energy storage charging and discharging state variables during period t; E d,t and is the amount of energy stored at the beginning of period t; Δt is the time interval between adjacent scheduling periods; η ch,d and η dis,d are the charging and discharging efficiencies of energy storage, respectively; E N,d is the rated capacity of energy storage; Γ ESS,d is a set of ports connected to energy storage; P is the upper limit of the number of charge and discharge times of energy storage; o,t is the system active power state variable associated with port o;

[0063] 6) PV inverter operation constraints

[0064]

[0065]

[0066]

[0067] Where D PVFor photovoltaic equipment collection; is the power factor angle corresponding to the minimum power factor of the photovoltaic system; P PV,d,t is the photovoltaic active power output during period t; Q PV,d,t S is the reactive power compensation power of the photovoltaic system during period t; inv,d is the apparent capacity of the photovoltaic inverter; Γ PV,d is the port set connected to the photovoltaic system; Q o,t is the system reactive power state variable associated with port o;

[0068] Node balance constraints: Node power balance constraints include power conservation constraints and state variable consistency constraints;

[0069] 1) Power conservation constraint

[0070]

[0071]

[0072] Where: n,r is the set of ports associated with node r; N node is a collection of system nodes;

[0073] 2) State variable consistency constraints

[0074]

[0075]

[0076] Where: is the mean value of the square of the voltage amplitude of the port connected to node r; |Γ n,r | represents the number of ports connected to node r; v o,t is the state variable of the square of the system voltage amplitude associated with port o.

[0077] Furthermore, in step 3, the optimization model constructed in step 2 is solved based on the vertex-centric graph calculation method to obtain the optimal scheduling strategy of the equipment, and the AC / DC hybrid distribution network is optimized according to the optimal scheduling strategy:

[0078] Define the equipment expansion cost function (1-35) and the node indication function (1-36):

[0079]

[0080]

[0081] In the formula, Ω d is the vector x consisting of the decision variables of equipment d that satisfy the equipment operation constraints dand the vector y consisting of the port state variables connected to device d d The feasible domain of n The vector y consisting of the port state variables connected to node n that satisfy the node operation constraints n The feasible domain of

[0082] The AC / DC hybrid distribution network optimization model based on the graphical model is equivalent to:

[0083]

[0084] Where y is the vector composed of all port state variables of the system;

[0085] Based on the decomposition idea of ​​ADMM, equation (1-37) is equivalent to:

[0086]

[0087] Where z is the mirror variable of vector y; n is a vector of mirror variables of ports associated with node n;

[0088] The relaxed equality constraint (1-38) is:

[0089]

[0090] Where x is the vector of decision variables of all devices in the system; λ is the system Lagrangian multiplier vector; L(·) is the augmented Lagrangian function, and ρ is the penalty factor;

[0091] Based on ADMM, the alternating iterative solution formula for the above optimization problem (1-39) is:

[0092] {x k+1 ,y k+1}=argminL(x,y,z k ,λ k ) (1-40)

[0093] z k+1 =argminL(x k+1 ,y k+1 ,z,λ k ) (1-41)

[0094] λ k+1 =λ k +ρ(y k+1 -z k+1 ) (1-42)

[0095] Where k is the number of current iterations; x k+1The vector of all device decision variables obtained by solving the k+1th iteration; y k+1 is the vector of all port state variables updated in the k+1th iteration; z k+1 and z k are the vectors of all mirror variables updated for the k+1th and kth iterations respectively; k+1 and λ k Lagrange multiplier vector updated for the k+1th and kth iterations;

[0096] According to equations (1-1)-(1-2), equations (1-40)-(1-42) are decomposed into each device and each node:

[0097]

[0098]

[0099]

[0100] Where: The vector of decision variables of device d obtained by solving the k+1th iteration; A vector of port state variables connected to device d updated in the k+1th iteration; and are the vectors of mirror variables connected to node n updated for the k+1th and kth iterations respectively; and are the Lagrange multiplier vectors associated with node n updated for the k+1th and kth iterations respectively; The Lagrange multiplier vector associated with device d updated for the kth iteration;

[0101] Since the state variables of the associated ports of each device are independent of each other, equation (1-43) can be solved in parallel; the state variables of the ports associated with each node are independent of each other, so equation (1-44) can be solved in parallel, and equation (1-45) can be calculated in parallel;

[0102] The node update optimization problem is a quadratic convex optimization problem, and the constraints (1-31)-(1-34) are equality constraints, so the analytical solution is obtained according to the Lagrange multiplier method:

[0103]

[0104] Where: n is the set of ports associated with node n; |Γ n | represents the number of ports associated with node n; The information of the active power, reactive power and voltage amplitude square state of port o updated after the equation (1-43) is solved in parallel by each device at the k+1th iteration; It is the information of the active power, reactive power and voltage amplitude square state of the port updated after the nodes of equation (1-44) are solved in parallel at the k+1th iteration; is the Lagrange multiplier information updated by formula (1-45) at the kth iteration; α k+1 , β k+1 and γ k+1 It is the intermediate parameter when solving the k+1th iteration;

[0105] In formula (1-44), vector y k+1 、z k+1 , k+1 The relationship between the scalars in the analytical solution (1-46) is as follows:

[0106]

[0107] After obtaining the analytical solution (1-46) of equation (1-44), equation (1-46) is used to perform parallel optimization calculations on each node to speed up the iterative solution process;

[0108] Define the node raw residual after k+1 iterations and the dual residual after k+1 iterations As the criterion for iterative convergence of equations (1-43), (1-46), and (1-44):

[0109]

[0110]

[0111] In the formula, The vector of device decision variables connected to node n obtained by solving the k+1th iteration;

[0112] When the original residual and the dual residual satisfy equation (1-50), the node iteration converges. When all nodes in the system converge, the system converges, the iteration ends, and the optimal scheduling strategy for each device is output.

[0113]

[0114] Where: ε is the iterative convergence accuracy;

[0115] In summary, the graph calculation steps of the AC / DC hybrid distribution network optimization model based on graph structure are as follows:

[0116] (1) Set the number of iterations k = 0, given the initial information z k and λk ;

[0117] (2) z k and λ k Substitute into equation (1-43), solve equation (1-43) in parallel, and update the vector x composed of the device decision variables k+1 and the vector y consisting of the port state variables k+1 ;

[0118] (3) x k+1 and k+1 Substitute into formula (1-46) and calculate the vector z composed of the mirror variables after the node is updated k+1 ;

[0119] (4) Change y k+1 and z k+1 Substitute into equation (1-45) and update the Lagrange multiplier vector λ k+1 ;

[0120] (5) z k 、z k+1 and x k+1 Substitute into equations (1-48) and (1-49) to calculate the node convergence criterion and

[0121] (6) According to and Determine whether all nodes in the system have converged. If so, output the optimal scheduling strategy; otherwise, k=k+1, go to (2).

[0122] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0123] 1) The constructed AC / DC hybrid distribution network graph model can fully represent the devices and networks of the AC / DC hybrid distribution network, realize unified modeling, and facilitate plug-and-play of user devices;

[0124] 2) The line equipment model with second-order cone relaxation has good cone relaxation accuracy in graph calculation, which can improve the solution efficiency of the model to a certain extent;

[0125] 3) Vertex-centric graph computing can adapt to the optimization calculation of AC / DC hybrid distribution networks in the case of large-scale photovoltaic energy storage access, fully realize the distributed computing of each device, protect the privacy of users, and at the same time improve the solution efficiency and solvability of the model, which has high application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0126] Figure 1 Flow chart of the method of the present invention;

[0127] Figure 2 Example topology diagram of a 50-node AC / DC hybrid distribution network with a high proportion of solar energy and energy storage;

[0128] Figure 3 PV inverter reactive power variation curve;

[0129] Figure 4 (a) Energy storage capacity change curve using one charge and one discharge strategy; (b) Energy storage capacity change curve using two charges and two discharges;

[0130] Figure 5 (a) Reactive power variation curve of voltage source converter; (b) Active power variation curve of voltage source converter;

[0131] Figure 6 Figure 3. Curve diagram of iterative residual change of calculation method. DETAILED DESCRIPTION

[0132] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention by those skilled in the art all fall within the scope defined by the appended claims of the present application.

[0133] like Figure 1 As shown, the present invention proposes an AC / DC hybrid distribution network optimization scheduling method based on graph calculation, the method comprising the following steps:

[0134] Step 1: Introduce the concept of port and establish AC / DC hybrid distribution network diagram model;

[0135] Step 2: Associate the state variables in the AC / DC hybrid distribution network system with the ports introduced in the graphical model established in step 1, and associate the decision variables in the AC / DC hybrid distribution network system with each device to construct a coordinated optimization model of the AC / DC hybrid distribution network based on the graphical model;

[0136] Step 3: Solve the optimization model constructed in step 2 based on the vertex-centric graph computing method, obtain the optimal scheduling strategy of the equipment, and optimize the scheduling of the AC / DC hybrid distribution network according to the optimal scheduling strategy.

[0137] Furthermore, in step 1, the concept of port is introduced to establish an AC / DC hybrid distribution network diagram model. The specific method is as follows:

[0138] The concept of port is introduced, and ports are regarded as edges of the graph. Nodes and devices are regarded as vertices of the graph. A graph model of AC / DC hybrid distribution network is established. The vertices in the graph model, i.e. nodes and devices, and the edges, i.e. ports, are expressed as follows:

[0139] Equipment: It is divided into AC equipment, DC equipment and coupling equipment. The upper power grid, AC line, AC load, and photovoltaic and energy storage connected to the AC system in the AC system are abstracted as AC equipment; the DC line, DC load, and energy storage and photovoltaic connected to the DC system in the DC system are abstracted as DC equipment; the coupling equipment is the voltage source converter, which is represented by the subscript d;

[0140] Node: divided into AC node and DC node, realizing lossless energy exchange between similar associated ports, represented by subscript n;

[0141] Port: Each device contains one or more ports. The vertices consisting of devices and nodes are connected through ports. Ports are divided into AC ports and DC ports, also known as edges, represented by subscript o;

[0142] The ports in the AC / DC hybrid distribution network graph model are organized by nodes or by devices. When organized by nodes, the intersection of ports connected to different nodes is empty, and the union of ports connected to all nodes is the full set; when organized by devices, the intersection of ports connected to different devices is empty, and the union of ports connected to all devices is the full set. Assuming the full set of ports is O, the above properties are expressed as:

[0143]

[0144]

[0145] In the formula, Γ n,r and Γ n,s are the port sets connected to node r and node s respectively, N n is the total number of nodes, Γ d,e and Γ d,h is the set of ports connected to devices e and h, N d is the total number of devices, Represents the empty set.

[0146] Furthermore, in step 2, the state variables in the system are associated with the ports introduced in the graph model established in step 1, and the decision variables in the system are associated with each device, and an AC / DC hybrid distribution network optimization model based on the graph model is constructed as follows:

[0147] Objective function: Minimize the sum of the operating costs of each device in the AC / DC hybrid distribution network;

[0148]

[0149] Where: x d is the decision variable associated with device d, c d is the cost function of device d;

[0150] The cost function of each device is as follows:

[0151]

[0152] Where: t is the subscript of the dispatch period; T is the total dispatch period; c t P is the time-of-use electricity price for purchasing electricity from the upper power grid; sub,d,t The power purchased from the upper grid; D sub It is a collection of upper-level power grid equipment; P is the energy storage operation and maintenance cost coefficient; ch,d,t and P dis,d,t are the charging and discharging power of the energy storage device during period t; ess,d is the depreciation cost coefficient of energy storage equipment; u ess,d,t D is the energy storage charging and discharging switching state variable during period t; ESS is the set of energy storage equipment; D is the set of equipment in the AC / DC hybrid distribution network; the cost of the upper grid equipment is the sum of the electricity purchase costs in each period; the energy storage operation cost includes operation and maintenance costs and depreciation costs; the cost of other equipment is 0;

[0153] Equipment operation constraints: Equipment operation constraints include power purchase constraints of the upper power grid, AC line and DC line operation constraints, voltage source converter operation constraints, energy storage operation constraints, and reactive power compensation constraints of photovoltaic inverters in the AC system;

[0154] 1) Constraints on power purchase from the upper-level power grid

[0155]

[0156]

[0157] Where P sub,d,t and Q sub,d,t are respectively the active and reactive injected power of the upper grid equipment in period t; and P sub,d They are respectively the upper and lower limits of active power injected into the upper grid; and Q sub,d They are the upper and lower limits of reactive power injected into the upper power grid respectively; P ac,o,t and Q ac,o,t are the active and reactive powers of the AC port o during period t, respectively; Γ sub,d A set of ports connected to the upper power grid;

[0158] 2) AC line operation constraints

[0159] When the device hour, is a set of AC line devices, assuming that its two end ports are i and j respectively, then the second-order cone form constraints of the AC line based on the graphical model are as follows:

[0160]

[0161]

[0162]

[0163]

[0164] In the formula, v ac,i,t and v ac,j,t are the squares of the voltage amplitudes at ports i and j of the AC line during period t; P ac,i,t and Q ac,i,t are the active power and reactive power of the AC line port i in period t respectively; P ac,j,t and Q ac,j,t are the active power and reactive power of the AC line port j during period t respectively; l ac,d,t is the square of the AC line current amplitude during period t; R ac,d and X ac,d are the resistance and reactance of the AC line respectively; l ac,d,max is the maximum current carrying capacity of the AC line;

[0165] 3) DC line operation constraints

[0166] When the device hour, is a set of DC line equipment, assuming that the ports at both ends are i and j respectively, and the DC line operation constraints are as follows:

[0167]

[0168]

[0169]

[0170]

[0171] In the formula, v dc,i,t and v dc,j,t are the squares of the voltage amplitudes at ports i and j of the DC line during period t; P dc,i,t and P dc,j,t are the active power of port i and port j of the DC line in period t respectively; l dc,d,t is the square of the DC line current amplitude during period t; R dc,d is the resistance of the DC line; l dc,d,max is the maximum current carrying capacity of the DC line;

[0172] 4) Voltage source converter row constraints

[0173] When device d∈D vsc When D vsc is a set of voltage source converter devices, assuming that its AC side port and DC side port are i and j respectively, then:

[0174]

[0175]

[0176]

[0177]

[0178]

[0179]

[0180]

[0181] In the formula, v ac,i,t and v dc,j,t are the squares of the voltage amplitudes at the AC side port and the DC side port of the voltage source converter during period t; v vsc,d,t is the square of the voltage amplitude of the virtual port of the voltage source converter during period t; l vsc,d,t is the square of the current amplitude of the equivalent branch of the voltage source converter during period t; R vsc,d and X vsc,d are the equivalent resistance and reactance of the voltage source converter respectively; P ac,i,t and Q ac,i,t are the active and reactive power of the AC side port during period t; P vsc,d,t and Q vsc,d,t are the active and reactive powers of the virtual port of the voltage source converter during period t; P dc,j,t is the active power of the DC side port of the voltage source converter during period t; is the upper limit of reactive power compensation; μ is the voltage utilization rate of voltage source converter, which is generally 0.866; M vsc,d is the modulation ratio, with a value range of [0,1]; S vsc,N is the AC side capacity of the voltage source converter; is the upper limit of DC side power;

[0182] 5) Energy storage operation constraints

[0183]

[0184]

[0185]

[0186]

[0187]

[0188]

[0189] Where P ESS,d,max is the upper limit of energy storage charging and discharging power; β ch,d,t and β dis,d,t are the energy storage charging and discharging state variables during period t; E d,t and is the amount of energy stored at the beginning of period t; Δt is the time interval between adjacent scheduling periods; η ch,d and η dis,d are the charging and discharging efficiencies of energy storage, respectively; E N,d is the rated capacity of energy storage; Γ ESS,d is a set of ports connected to energy storage; P is the upper limit of the number of charge and discharge times of energy storage; o,t is the system active power state variable associated with port o;

[0190] 6) PV inverter operation constraints

[0191]

[0192]

[0193]

[0194] Where D PV For photovoltaic equipment collection; is the power factor angle corresponding to the minimum power factor of the photovoltaic system; P PV,d,t is the photovoltaic active power output during period t; Q PV,d,t S is the reactive power compensation power of the photovoltaic system during period t; inv,d is the apparent capacity of the photovoltaic inverter; Γ PV,d is the port set connected to the photovoltaic system; Q o,t is the system reactive power state variable associated with port o;

[0195] Node balance constraints: Node power balance constraints include power conservation constraints and state variable consistency constraints;

[0196] 1) Power conservation constraint

[0197]

[0198]

[0199] Where: n,ris the set of ports associated with node r; N node is the system node set;

[0200] 2) State variable consistency constraints

[0201]

[0202]

[0203] Where: is the mean value of the square of the voltage amplitude of the port connected to node r; |Γ n,r | represents the number of ports connected to node r; v o,t is the state variable of the square of the system voltage amplitude associated with port o.

[0204] Furthermore, in step 3, the optimization model constructed in step 2 is solved based on the vertex-centric graph calculation method to obtain the optimal scheduling strategy of the equipment, and the AC / DC hybrid distribution network is optimized according to the optimal scheduling strategy:

[0205] Define the equipment expansion cost function (1-35) and the node indication function (1-36):

[0206]

[0207]

[0208] In the formula, Ω d is the vector x consisting of the decision variables of equipment d that satisfy the equipment operation constraints d and the vector y consisting of the port state variables connected to device d d The feasible domain of n A vector y consisting of the port state variables connected to node n that satisfy the node operation constraints n The feasible domain of

[0209] The AC / DC hybrid distribution network optimization model based on the graphical model is equivalent to:

[0210]

[0211] Where y is the vector composed of all port state variables of the system;

[0212] Based on the decomposition idea of ​​ADMM, equation (1-37) is equivalent to:

[0213]

[0214] Where z is the mirror variable of vector y; n is a vector of mirror variables of ports associated with node n;

[0215] The relaxed equality constraint (1-38) is:

[0216]

[0217] Where x is the vector of decision variables of all devices in the system; λ is the system Lagrangian multiplier vector; L(·) is the augmented Lagrangian function, and ρ is the penalty factor;

[0218] Based on ADMM, the alternating iterative solution formula for the above optimization problem (1-39) is:

[0219] {x k+1 ,y k+1}=argminL(x,y,z k ,λ k ) (1-40)

[0220] z k+1 =argminL(x k+1 ,y k+1 ,z,λ k ) (1-41)

[0221] λ k+1 =λ k +ρ(y k+1 -z k+1 ) (1-42)

[0222] Where k is the number of current iterations; x k+1 The vector of all device decision variables obtained by solving the k+1th iteration; y k+1 is the vector of all port state variables updated in the k+1th iteration; z k+1 and z k are the vectors of all mirror variables updated for the k+1th and kth iterations respectively; k+1 and λ k Lagrange multiplier vector updated for the k+1th and kth iterations;

[0223] According to equations (1-1)-(1-2), equations (1-40)-(1-42) are decomposed into each device and each node:

[0224]

[0225]

[0226]

[0227] Where: The vector of decision variables of device d obtained by solving the k+1th iteration; A vector of port state variables connected to device d updated in the k+1th iteration; and are the vectors of mirror variables connected to node n updated for the k+1th and kth iterations respectively; and are the Lagrange multiplier vectors associated with node n updated for the k+1th and kth iterations respectively; The Lagrange multiplier vector associated with device d updated for the kth iteration;

[0228] Since the state variables of the associated ports of each device are independent of each other, equation (1-43) can be solved in parallel; the state variables of the ports associated with each node are independent of each other, so equation (1-44) can be solved in parallel, and equation (1-45) can be calculated in parallel;

[0229] The node update optimization problem is a quadratic convex optimization problem, and the constraints (1-31)-(1-34) are equality constraints, so the analytical solution is obtained according to the Lagrange multiplier method:

[0230]

[0231] Where: n is the set of ports associated with node n; |Γ n | represents the number of ports associated with node n; The information of the active power, reactive power and voltage amplitude square state of port o updated after the equation (1-43) is solved in parallel by each device at the k+1th iteration; It is the information of the active power, reactive power and voltage amplitude square state of the port updated after the nodes of equation (1-44) are solved in parallel at the k+1th iteration; is the Lagrange multiplier information updated by formula (1-45) at the kth iteration; α k+1 , β k+1 and γ k+1 It is the intermediate parameter when solving the k+1th iteration;

[0232] In formula (1-44), vector y k+1 、z k+1 , k+1 The relationship between the scalars in the analytical solution (1-46) is as follows:

[0233]

[0234] After obtaining the analytical solution (1-46) of equation (1-44), equation (1-46) is used to perform parallel optimization calculations on each node to speed up the iterative solution process;

[0235] Define the node raw residual after k+1 iterations and the dual residual after k+1 iterations As the criterion for iterative convergence of equations (1-43), (1-46), and (1-44):

[0236]

[0237]

[0238] In the formula, The vector of device decision variables connected to node n obtained by solving the k+1th iteration;

[0239] When the original residual and the dual residual satisfy equation (1-50), the node iteration converges. When all nodes in the system converge, the system converges, the iteration ends, and the optimal scheduling strategy for each device is output.

[0240]

[0241] Where: ε is the iterative convergence accuracy;

[0242] In summary, the graph calculation steps of the AC / DC hybrid distribution network optimization model based on graph structure are as follows:

[0243] (1) Set the number of iterations k = 0, given the initial information z k and λ k ;

[0244] (2) z k and λ k Substitute into equation (1-43), solve equation (1-43) in parallel, and update the vector x composed of the device decision variables k+1 and the vector y consisting of the port state variables k+1 ;

[0245] (3) x k+1 and k+1 Substitute into formula (1-46) and calculate the vector z composed of the mirror variables after the node is updated k+1 ;

[0246] (4) y k+1 and z k+1 Substitute into equation (1-45) and update the Lagrange multiplier vector λ k+1 ;

[0247] (5) z k 、z k+1 and x k+1 Substitute into equations (1-48) and (1-49) to calculate the node convergence criterion and

[0248] (6) According to and Determine whether all nodes in the system have converged. If so, output the optimal scheduling strategy; otherwise, k=k+1, go to (2).

[0249] Case Analysis

[0250] This article adopts Figure 2 The 50-node AC / DC hybrid distribution network with a high proportion of photovoltaic storage is shown as an example. The system active load and reactive load peaks are 4945kW and 2300kVar, respectively, and the root node voltage is 1.0pu; the upper limit of the reactive compensation of the voltage source converter is 300kVar, and the equivalent resistance and reactance are 0.5Ω and 1.5Ω, respectively; to simulate the large-scale access scenario of distributed photovoltaic and energy storage, a total of 20 distributed photovoltaic units are connected, with a total installed capacity of 2400kW; 24 distributed energy storage units are connected, with a total installed capacity of 1330kWh. The abstract graph model of the system contains a total of 50 nodes, 144 devices, 193 ports, and a total scheduling period of T = 24.

[0251] The present invention first analyzes the device scheduling strategy: the absolute convergence accuracy of the iteration process is set to ε = 0.001, and after 295 iterations, the controllable resource scheduling strategy is as follows: Figure 3-5 shown.

[0252] Depend on Figure 3 It can be seen that due to the limitation of the minimum power factor of the photovoltaic inverter, the reactive power of the photovoltaic inverter increases with the increase of photovoltaic output. Most of the photovoltaic inverters send reactive power to the AC system to achieve local balance of reactive power in the AC system; while a few photovoltaic inverters absorb part of the reactive power from the AC system to ensure the transmission of photovoltaic active power, thereby avoiding voltage exceeding the limit at the photovoltaic grid-connected node.

[0253] Depend on Figure 4 It can be seen that since the depreciation cost of energy storage in the model is positively correlated with the energy storage capacity, most energy storage adopts a one-charge-one-discharge mechanism, and only a small number of energy storage with a smaller depreciation cost coefficient operates with a two-charge-two-discharge mechanism. For energy storage that adopts a one-charge-one-discharge mechanism, the main charging time is concentrated between 2:00 and 4:00 in the morning when the electricity purchase price is low, and the discharge time is mainly concentrated between 18:00 and 20:00 when the load demand is large and the electricity price is high; the energy storage that adopts a two-charge-two-discharge mechanism adds one discharge during the peak of noon electricity consumption at 9:00-12:00 and one charge during the peak of photovoltaic output at 14:00-16:00, further improving the economy of system operation.

[0254] Depend on Figure 5(a) It can be seen that since the voltage source converters in the calculation example are relatively close to the end of the feeder, the voltage source converters basically provide reactive power compensation to the AC system, thereby reducing the power transmission from the head end to the end, reducing network losses, and improving the economy of system operation; Figure 5 (b) It can be seen that during the period of high PV output (10:00-15:00), the DC system transmits excess active power to the AC system through the voltage source converter; while during the period of low PV output, the AC system transmits active power to the DC system, thereby supporting the DC load.

[0255] Secondly, when the absolute convergence accuracy ε = 0.001, the dual residual of the original residual of the convergence process of the graph calculation method is as follows Figure 6 As shown, the operating cost comparison with the centralized computing method is shown in Table 1.

[0256] Table 1 Comparison of operating costs of different calculation methods

[0257]

[0258] Depend on Figure 6 It can be seen that the graph calculation converges after 295 iterations, and has good convergence overall; but as the number of iterations increases, its convergence speed gradually decreases, especially after 150 times, the convergence speed becomes extremely slow. If you need to speed up its convergence speed, you can use the improved method of adaptive step size ADMM. As shown in Table 1, the total system operating cost calculated by graph calculation is very close to that of centralized calculation, with an error of only 0.069%. Due to the parallel computing capability of graph calculation, its computing efficiency is significantly higher than that of centralized calculation, and because the large model is decomposed in graph calculation, its solvability is also significantly improved relative to centralized calculation.

[0259] Then, the graph calculation optimization cost and solution efficiency under different absolute convergence accuracy are shown in Table 2.

[0260] Table 2 Graph calculation optimization cost under different convergence accuracy

[0261]

[0262] As can be seen from Table 2, as the absolute convergence accuracy decreases, the model optimization cost gradually decreases, that is, the optimality increases; at the same time, as the absolute convergence accuracy decreases, the number of iterations increases, and the solution efficiency decreases relatively, but overall the solution efficiency of graph computing is significantly lower than that of centralized computing. Therefore, graph computing has a broad application prospect in the future when distributed resources are accessed on a large scale.

[0263] So far, the intelligent cross-span design method for beam bridges based on generative adversarial neural networks proposed by the present invention has been completed, and the intelligent cross-span design of overpass bridges and navigable bridges has been completed. However, the above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. Any modification made on the basis of the technical solution according to the technical idea proposed by the present invention falls within the protection scope of the present invention.

Claims

1. An optimal scheduling method for AC-DC hybrid distribution network based on graph computing, characterized in that, it includes the following steps: Step 1: Introduce the concept of ports and establish a graph model of the AC-DC hybrid distribution network; Step 2: Correlate the state variables in the AC-DC hybrid distribution network system to each port introduced in the graph model established in Step 1, and correlate the decision variables in the AC-DC hybrid distribution network system to each device, and construct a coordinated optimization model of the AC-DC hybrid distribution network based on the graph model; Step 3: Solve the optimization model constructed in Step 2 based on the graph computing method centered on vertices, obtain the optimal scheduling strategy of the devices, and perform optimal scheduling of the AC-DC hybrid distribution network according to the optimal scheduling strategy; In the said Step 1, the method of introducing the concept of ports and establishing a graph model of the AC-DC hybrid distribution network is as follows: Introduce the concept of ports, regard the ports as the edges of the graph, and regard both the nodes and the devices as the vertices of the graph, and establish a graph model of the AC-DC hybrid distribution network. The vertices in the graph model, that is, the nodes and devices, and the edges, that is, the ports, are described as follows: Devices: Divided into AC devices, DC devices and coupling devices. The superior grid, AC lines, AC loads in the AC system, and the photovoltaic and energy storage connected to the AC system are all abstracted as AC devices; the DC lines, DC loads in the DC system, and the energy storage and photovoltaic connected to the DC system are all abstracted as DC devices; the coupling device is the voltage source converter, denoted by the subscript d; Nodes: Divided into AC nodes and DC nodes, which realize lossless energy exchange between ports of the same type, denoted by the subscript n; Ports: Each device contains one or more ports. The vertices composed of devices and nodes are connected through ports. The ports are divided into AC ports and DC ports, also called edges, denoted by the subscript o; The ports in the graph model of the AC-DC hybrid distribution network are organized by nodes or by devices. When organized by nodes, the intersection of the ports connected by different nodes is empty, and the union of the ports connected by all nodes is the complete set; when organized by devices, the intersection of the ports connected by different devices is empty, and the union of the ports connected by all devices is the complete set. Let the complete set of ports be O, then it is expressed as: where Γ n,r and Γ n,s are the sets of ports connected to nodes r and s respectively, N n is the total number of nodes, Γ d,e and Γ d,h are the sets of ports connected to devices e and h respectively, N d is the total number of devices, represents the empty set.

2. The optimal scheduling method for the AC-DC hybrid distribution network based on graph computing according to claim 1, characterized in that, in the said Step 2, the state variables in the system are all correlated to each port introduced in the graph model established in Step 1, and the decision variables in the system are correlated to each device, and the following optimization model of the AC-DC hybrid distribution network based on the graph model is constructed: Objective function: Minimize the sum of the operating costs of each device in the AC-DC hybrid distribution network as the goal; where x d is the decision variable associated with device d, and c d is the cost function of device d; The cost functions of each device are as follows: In the formula, t is the subscript of the scheduling period; T is the total scheduling period; c t is the time-of-use electricity price for purchasing electricity from the superior power grid; P sub,d,t is the power of purchasing electricity from the superior power grid; D sub is the set of equipment of the superior power grid; is the operation and maintenance cost coefficient of energy storage; P ch,d,t and P dis,d,t are the charging and discharging powers of the energy storage equipment at time t respectively; λ ess,d is the depreciation cost coefficient of the energy storage equipment; u ess,d,t is the state variable for energy storage charge-discharge switching during period t; D ESS is the set of energy storage devices; D is the set of devices in the AC / DC hybrid distribution network; among them, the cost of the superior grid equipment is the sum of the power purchase costs for each period; the energy storage operation cost includes the operation and maintenance cost and the depreciation cost; the costs of the remaining equipment are 0; Device operation constraints, the device operation constraints include the power purchase constraint of the superior grid, the operation constraints of AC lines and DC lines, the operation constraints of the voltage source converter, the operation constraints of energy storage, and the reactive power compensation constraint of the photovoltaic inverter in the AC system; 1) Power purchase constraint of the superior grid Wherein, P sub,d,t and Q sub,d,t are respectively the active and reactive injection powers of the superior power grid equipment in the t period; and P sub,d are respectively the upper and lower limits of the active power injected by the superior power grid; and Q sub,d are respectively the upper and lower limits of the reactive power injected by the superior power grid; P ac,o,t and Q ac,o,t are respectively the active and reactive powers of the AC port o in the t period; Γ sub,d is the set of ports connected to the superior power grid; 2) Operation constraints of AC lines When the device is a set of AC line devices, and the two end ports are set as i and j respectively, then the second-order cone form constraints of the AC line based on the graph model are as follows: Where, v ac,i,t and v ac,j,t are respectively the squares of the voltage amplitudes at ports i and j of the AC line during period t; P ac,i,t and Q ac,i,t are respectively the active power and reactive power at port i of the AC line during period t; P ac,j,t and Q ac,j,t are respectively the active power and reactive power at port j of the AC line during period t; l ac,d,t is the square of the amplitude of the AC line current during period t; R ac,d and X ac,d are respectively the resistance and reactance of the AC line; l ac,d,max is the maximum current-carrying capacity of the AC line; 3) Operation constraints of DC lines When the device is a set of DC line devices, and let the ports at both ends be port i and port j respectively. The DC line operation constraints are as follows: where, v dc,i,t and v dc,j,t are the squares of the voltage amplitudes at ports i and j of the DC line during period t, respectively; P dc,i,t and P dc,j,t are the active powers at ports i and j of the DC line during period t, respectively; l dc,d,t is the square of the DC line current amplitude during period t; R dc,d is the resistance of the DC line; l dc,d,max is the maximum current-carrying capacity of the DC line. 4) Operation constraints of the voltage source converter When the device d ∈ D vsc where D vsc is a set of voltage source converter devices. Let its AC side port and DC side port be i and j respectively, then we have: where \(v\) ac,i,t and \(v\) dc,j,t are respectively the squares of the voltage amplitudes at the AC - side port and the DC - side port of the voltage - source converter during the time period \(t\); \(v\) vsc,d,t is the square of the voltage amplitude of the virtual port of the voltage - source converter during the time period \(t\); \(l\) vsc,d,t is the square of the amplitude of the equivalent - branch current of the voltage - source converter during the time period \(t\); \(R\) vsc,d and \(X\) vsc,d are respectively the equivalent resistance and reactance of the voltage - source converter; \(P\) ac,i,t and \(Q\) ac,i,t are respectively the active and reactive powers at the AC - side port during the time period \(t\); \(P\) vsc,d,t and \(Q\) vsc,d,t are respectively the active and reactive powers of the virtual port of the voltage - source converter during the time period \(t\); \(P\) dc,j,t is the active power at the DC - side port of the voltage - source converter during the time period \(t\); is the upper limit of the reactive - power compensation power; \(\mu\) is the voltage utilization rate of the voltage - source converter, usually taken as \(0.866\); \(M\) vsc,d is the modulation ratio, with a value range of \([0,1]\); \(S\) vsc,N is the AC - side capacity of the voltage - source converter; is the upper limit value of the DC - side power; 5) Operation constraints of energy storage Where, P ESS,d,max is the upper limit of the energy storage charge-discharge power; β ch,d,t and β dis,d,t are the energy storage charge and discharge state variables at time t respectively; E d,t and are the electricity quantities at the start of the energy storage time period t; Δt is the time interval between adjacent scheduling time periods; η ch,d and η dis,d are the charge and discharge efficiencies of the energy storage respectively; E N,d is the rated capacity of the energy storage; Γ ESS,d is the set of ports connected to the energy storage; is the upper limit of the charge-discharge times of the energy storage; P o,t is the system active power state variable associated with port o; 6) Operation constraints of the photovoltaic inverter Where D PV is the set of photovoltaic devices; is the power factor angle corresponding to the minimum power factor of the photovoltaic system; P PV,d,t is the active power output of the photovoltaic system during period t; Q PV,d,t is the reactive power compensation power of the photovoltaic system during period t; S inv,d is the apparent capacity of the photovoltaic inverter; Γ PV,d is the set of ports connected to the photovoltaic system; Q o,t is the system reactive power state variable associated with port o; Node balance constraint: The node power balance constraint includes power conservation constraint and state variable consistency constraint; 1) Power conservation constraint where: Γ n,r is the set of ports associated with node r; N node is the set of system nodes; 2) State variable consistency constraint Where: is the mean value of the square of the port voltage amplitude connected to node r; |Γ n,r | represents the number of ports connected to node r; v o,t is the state variable of the square of the system voltage amplitude associated with port o.

3. A hybrid AC-DC distribution network optimal scheduling method based on graph calculation according to claim 2, characterized in that, in the step 3, based on the graph calculation method centered on vertices, the optimization model constructed in step 2 is solved to obtain the optimal scheduling strategy of the equipment, and the hybrid AC-DC distribution network is optimized and scheduled according to the optimal scheduling strategy: Define the equipment expansion cost function formula (1-35) and the node indicator function formula (1-36): where, Ω d is the feasible region of the vector x d composed of decision variables of device d that satisfy the device operation constraints d and the vector y n composed of port status variables connected to device d; Ψ n is the feasible region of the vector y composed of port status variables connected to node n that satisfy the node operation constraints; The hybrid AC-DC distribution network optimization model based on the graph model is equivalent to: In the formula, y is a vector composed of all port state variables of the system; Based on the decomposition idea of ADMM, formula (1-37) is equivalent to: where z is the mirror variable of vector y; z n is the vector composed of the mirror variables of the ports associated with node n; The equality constraint of formula (1-38) is relaxed as: In the formula, x is a vector composed of all equipment decision variables of the system; λ is the system Lagrange multiplier vector; L(·) is the augmented Lagrangian function, and ρ is the penalty factor; Based on ADMM, the alternating iteration solution formula of the above formula (1-39) is: {x k+1 ,y k+1} = argmin L(x, y, z k , λ k ) (1 - 40) z k+1 = argminL(x k+1 , y k+1 , z, λ k ) (1-41) λ k+1 = λ k + ρ(y k+1 - z k+1 ) (1 - 42) where k is the current iteration solution number; x k+1 is a vector composed of all device decision variables obtained by the (k + 1)-th iteration solution; y k+1 is a vector composed of all port status variables updated by the (k + 1)-th iteration; z k+1 and z k are vectors composed of all mirror variables updated by the (k + 1)-th and k-th iterations respectively; λ k+1 and λ k are Lagrange multiplier vectors updated by the (k + 1)-th and k-th iterations; According to formulas (1-1)-(1-2), formulas (1-40)-(1-42) are decomposed to each equipment and each node: Wherein: is a vector composed of decision variables of device d obtained by the (k + 1)-th iterative solution; is a vector composed of port status variables connected to device d updated in the (k + 1)-th iteration; and are vectors composed of mirror variables connected to node n updated in the (k + 1)-th and k-th iterations respectively; and are Lagrange multiplier vectors related to node n updated in the (k + 1)-th and k-th iterations respectively; is a Lagrange multiplier vector related to device d updated in the k-th iteration; Since the associated port state variables of each equipment are independent of each other, formula (1-43) can be solved in parallel; the state variables of the ports associated with each node are independent of each other, so formula (1-44) can be solved in parallel, and formula (1-45) can be calculated in parallel; The node update optimization problem is a quadratic convex optimization problem, and the constraints (1-31)-(1-34) are equality constraints. Therefore, the analytical solution is obtained according to the Lagrange multiplier method: where: Γ n is the set of ports associated with node n; |Γ n | represents the number of ports associated with node n; is the information of the active power, reactive power, and squared voltage magnitude state of port o updated after parallel solution of each device by Equation (1-43) at the (k + 1)-th iteration; is the information of the active power, reactive power, and squared voltage magnitude state of the port updated after parallel solution of each node by Equation (1-44) at the (k + 1)-th iteration; is the Lagrange multiplier information updated by Equation (1-45) at the k-th iteration; α k+1 , β k+1 and γ k+1 are intermediate parameters during the solution at the (k + 1)-th iteration; The vector y in Equation (1-44) k+1 , z k+1 , λ k+1 and the scalar relationships in its analytical solution Equation (1-46) are as follows: After obtaining the analytical solution formula (1-46) of formula (1-44), each node is optimized and calculated in parallel by formula (1-46) to accelerate the iterative solution process; Define the original residual of the node after the (k + 1)-th iteration and the dual residual after the (k + 1)-th iteration as the convergence criteria for the iterations in equations (1-43), (1-46), and (1-44): wherein, is a vector composed of device decision variables connected to node n obtained by the (k + 1)-th iterative solution; When the original residual and the dual residual satisfy formula (1-50), the node iteration converges. When all nodes of the system converge, the system converges, the iteration ends, and the optimal scheduling strategy of each equipment is output; In the formula: ε is the iteration convergence accuracy; In summary, the graph calculation steps of the hybrid AC-DC distribution network optimization model based on the graph structure are as follows: (1) Set the number of iterations \(k = 0\), and given the initial information \(z\) k and \(\lambda\) k ; (2) Substitute z k and λ k into Equation (1-43), solve Equation (1-43) in parallel, and update the vector x k+1 composed of device decision variables and the vector y k+1 ; (3) Substitute x k+1 and y k+1 into Equation (1-46) to calculate the vector z k+1 formed by the updated mirror variables of the node; (4) Substitute y k+1 and z k+1 into equation (1-45) to update the Lagrange multiplier vector λ k+1 ; (5) Substitute z k , z k+1 and x k+1 into equations (1-48) and (1-49) to calculate the node convergence criteria and (6) According to and determine whether all nodes of the system converge. If they converge, output the optimal scheduling strategy; otherwise, k = k + 1, and go to (2).

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