A distributed optimal power flow method for ac-dc hybrid power distribution network

Abstract

The application discloses a distributed optimal power flow method for AC-DC hybrid power distribution networks, and comprises the following steps: a centralized non-convex optimal power flow model of the AC-DC hybrid power distribution network is subjected to second-order cone convexity transformation to obtain a centralized second-order cone optimal power flow model; a distributed second-order cone optimal power flow model is obtained according to the centralized second-order cone optimal power flow model; all inequality constraints and variable upper and lower limit constraints in the stacked subnetwork model are used; a parallel solution is conducted on the decoupled subnetwork second-order cone optimal power flow model by using an improved augmented Lagrange relaxation method, a local solution is obtained, Jacobian matrix J l , gradient Hessian matrix and scaling matrix are calculated according to the local solution l , and a quadratic programming main problem is solved, and original residual error and dual residual error are updated; the distributed second-order cone optimal power flow model for the AC-DC hybrid power distribution network can reduce the convergence times of the traditional distributed algorithm and improve the convergence speed.

Description

Technical Field

[0001] This invention relates to the field of AC / DC hybrid power distribution system technology, and specifically to a distributed optimal power flow method for AC / DC hybrid power distribution networks. Background Technology

[0002] The development of power electronics technology has led to widespread attention on the application of hybrid AC / DC distribution systems. DC distribution networks offer higher energy conversion efficiency, better power quality, and better compatibility with distributed generation, enabling the gradual transition of distribution systems from pure AC grids to hybrid AC / DC distribution networks. A typical hybrid AC / DC distribution network consists of multiple interconnected AC and DC subnetworks, with the AC and DC components connected through converter stations.

[0003] Traditional optimal power flow problems for AC / DC hybrid distribution networks often neglect the complex AC / DC hybrid characteristics between AC and DC subnetworks and the internal operating constraints of converter stations, resulting in optimal power flow models that cannot fully reflect the complex operating characteristics of AC / DC hybrid distribution networks.

[0004] For the optimal power flow problem in AC / DC hybrid distribution networks, centralized computational methods are typically used to solve it. Although the AC and DC subnetworks are physically connected, they usually formulate their generation plans independently. Conventional centralized operation and management models cannot guarantee the privacy and operational decision-making independence of the AC and DC subnetworks. Moreover, AC / DC hybrid distribution networks typically have a multi-level architecture. In a power market environment, multiple AC and DC subnetworks are usually operated and managed by different system operators. Therefore, the resulting AC / DC optimal power flow problem is more suitable for a distributed optimization computational framework.

[0005] However, the optimal AC / DC power flow problem is nonlinear and difficult to solve. Traditional distributed solution methods mainly include the auxiliary problem principle method, the alternating direction multiplier method, the objective cascade analysis method, and the optimal condition decomposition method. However, these distributed algorithms have slow numerical convergence speed and low computational accuracy. Summary of the Invention

[0006] In view of this, the present invention provides a distributed optimal power flow method for AC / DC hybrid distribution networks, which at least solves the problem of low accuracy in the solution methods of distributed optimal power flow problems in AC / DC hybrid distribution networks in the prior art.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A distributed optimal power flow method for AC / DC hybrid distribution networks includes the following steps:

[0009] S1. Perform a second-order cone-convexity transformation on the centralized non-convex optimal power flow model of the AC / DC hybrid distribution network to obtain a centralized second-order cone-optimal power flow model.

[0010] S2. Decouple the centralized second-order cone optimal power flow model at the converter and write it in an affine coupling separable form to obtain the distributed second-order cone optimal power flow model of the AC / DC hybrid distribution network.

[0011] S3. Based on the distributed second-order cone optimal power flow model of the AC / DC hybrid distribution network, obtain the second-order cone optimal power flow models for each AC subnetwork and the DC subnetwork, and use them... All inequality constraints and variable upper and lower bound constraints in the stacked subnet model;

[0012] S4. The improved augmented Lagrangian relaxation method is used to solve the second-order cone optimal power flow model of the decoupled AC subnet and DC subnet in parallel to obtain local solutions. According to local solutions Calculate the Jacobian matrix J of the activity set at the location. l ,gradient Hessian matrix and scaling matrix

[0013] S5. Based on the Jacobi matrix J l ,gradient Hessian matrix and scaling matrix Solve the quadratic programming master problem, update the original residuals and dual residuals, and determine whether convergence has occurred.

[0014] Preferably, the specific content of S1 includes:

[0015]

[0016] Among them, C dc The objective function of a multi-terminal DC power grid is... Let l be the objective function of the AC subnet. Represents a set of communication subnets;

[0017]

[0018]

[0019] Among them, c 1g c 2g c 3g c represents the cost coefficient of the generator. loss c represents the cost factor for power loss. grid Indicates the electricity price of the upper-level power grid, This represents the active power of the root node. This represents the power loss of the k-th converter connected to the DC subgrid. This represents the active power of the generator at node g. If node g is not a generator node, then...

[0020] The constraints include:

[0021] Second-order cone constraints for branch power flow within a subnet:

[0022]

[0023]

[0024]

[0025]

[0026] The node voltage safety constraints within the AC subnet are as follows:

[0027]

[0028] The active power constraint of generators within the AC subnet is:

[0029]

[0030] The reactive power constraint of generators within the AC subnet is:

[0031]

[0032] Where, r ij and x ij This represents the resistance and reactance of branch ij. This represents the reactive power of the generator at node j. and P represents the active and reactive loads at node j. ij and Q ij Indicates the active and reactive power flowing through branch ij, l ij and u j This represents the sum of the squares of the current flowing through branch ij and the voltage magnitude at node j. This represents the lower and upper limits of the active and reactive power of the generator located at node j. u j and This represents the lower and upper limits of the squared magnitude of the voltage at node j;

[0033] Second-order cone constraint for branch power flow within a DC subgrid:

[0034]

[0035]

[0036]

[0037]

[0038] Among them, P i DC This represents the active power injected into the DC subgrid from the converter station;

[0039] The node voltage safety constraints within the DC subgrid are as follows:

[0040]

[0041] The active power constraint of generators within the DC subgrid is:

[0042]

[0043] Power balance constraints of converter nodes:

[0044]

[0045]

[0046]

[0047]

[0048] in, and This represents the power of the equivalent generator injected from the AC subnet;

[0049] Constraints on the relationship between the reactive load of the filter node and the parallel inductance of the filter node:

[0050] The reactive load at node f, i.e., on the filter, can be represented as:

[0051]

[0052] in, This represents the parallel inductance at filter node f;

[0053] Voltage relationship constraints between the AC and DC sides of the converter:

[0054]

[0055] Where, parameter M represents the modulation factor, and M∈[0,1]; U m This represents the magnitude of the node voltage at bus m, and

[0056] Active power relationship constraints between the AC and DC sides of the converter:

[0057]

[0058] Among them, the second-order cone constraint of converter power loss is:

[0059]

[0060] Reactive power limitation constraints of the converter:

[0061]

[0062] in, Q C and These represent the lower and upper limits of the converter's reactive power, respectively.

[0063] The relationship between the slope constant of the converter and the rated power and rated DC voltage of the converter:

[0064]

[0065] in, and Let represent the rated power and rated DC voltage of the k-th converter, respectively, and q represent the DC voltage change that causes a 100% change in converter power;

[0066] Converter droop control constraints:

[0067]

[0068] Among them, K k This represents the slope constant of the k-th converter; and These represent the reference values ​​for DC power and DC voltage used in droop control, respectively.

[0069] The converter slope constant is calculated as follows:

[0070]

[0071] in, and Let represent the rated power and rated DC voltage of the k-th converter, respectively, and q represent the DC voltage change that causes a 100% change in converter power;

[0072] Second-order cone constraint on converter apparent capacity:

[0073]

[0074] Preferably, the specific content of S2 includes:

[0075] Introducing consensus constraints:

[0076]

[0077]

[0078]

[0079] Based on consensus constraints, the centralized second-order cone optimal power flow model can be rewritten in an affine coupled and separable form, resulting in the distributed second-order cone optimal power flow model:

[0080]

[0081]

[0082]

[0083]

[0084] Wherein, λ,κ l ,γ l Let each represent the dual variable of the corresponding constraint. x represents the set of all AC and DC subnets. l This represents a column vector consisting of all variables in subnet l. x l , They represent x respectively l The lower and upper limits of the values; constraint (33) represents the coupling constraint between the AC subnet and the DC subnet, constraint (34) represents all inequality constraints in each subnet model, and (35) represents the upper and lower limit constraints of the variables in each subnet model.

[0085] Preferably, the specific content of S3 includes:

[0086]

[0087] in, h is used for all inequality constraints and variable upper and lower bound constraints in the stacked AC and DC subnet models. l (x l ) represents all inequality constraints in subnet l.

[0088] Preferably, the specific content in S4 includes:

[0089] S41. Initialization (z 0 ,λ 0 Choose a proportionally symmetric matrix.

[0090] S42. In In this case, the L1 loss function is defined as:

[0091]

[0092] Φ0=Φ(z 0 (38)

[0093] S43. Solve the second-order cone optimal power flow model for all decoupled AC and DC subnets in parallel:

[0094]

[0095]

[0096] S44. Based on local solutions Calculate the Jacobian matrix J of the activity set at the location. l :

[0097]

[0098] in, It is a matrix Find the i-th row and calculate the gradient.

[0099] S45. Based on local solutions calculate like:

[0100]

[0101] Then set Φ0=Φ(x) k Update the Hessian matrix. Approximate value:

[0102]

[0103] And set the scaling matrix

[0104] Otherwise set μ i =0,

[0105] Preferably, the specific content of S5 includes:

[0106]

[0107] Update the original residual and the dual residual (z,λ):

[0108] z k+1 =x k +Δx k , λk+1 =λ QP .

[0109] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a distributed optimal power flow method for AC / DC hybrid distribution networks, which has the following beneficial effects:

[0110] 1) This invention considers the AC / DC hybrid distribution system with complex AC / DC hybrid characteristics and converter station operation characteristics. For the optimal power flow problem of the AC / DC hybrid distribution network with complex operation characteristics and multiple droop control converter stations, an optimal power flow model of AC / DC hybrid distribution network based on second-order conical relaxation is proposed.

[0111] 2) For the multi-level architecture of AC / DC hybrid power distribution system, this invention proposes an affine coupling and separable form to construct a distributed optimization model for the optimal power flow problem of AC / DC hybrid power distribution network.

[0112] 3) This invention proposes a stable, efficient, and scalable improved augmented Lagrange relaxation method to solve the distributed optimal power flow problem in the resulting AC / DC hybrid distribution network. The submitted distributed second-order cone optimal power flow model for the DC hybrid distribution network can reduce the convergence times of traditional distributed algorithms and improve the convergence speed. Attached Figure Description

[0113] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0114] Figure 1 This is a schematic diagram of an AC / DC hybrid power distribution system model provided in an embodiment of the present invention;

[0115] Figure 2 This is a network topology diagram of an AC / DC hybrid power distribution system provided for experiments in this embodiment of the invention;

[0116] Figure 3 This is a schematic diagram of the results of the distributed AC / DC optimal power flow method using the alternating direction multiplier method provided in an embodiment of the present invention;

[0117] Figure 4 This is a schematic diagram showing the results of the distributed AC / DC optimal power flow method using the improved augmented Lagrange relaxation method provided in an embodiment of the present invention. Detailed Implementation

[0118] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0119] A distributed optimal power flow method for AC / DC hybrid distribution networks includes the following steps:

[0120] S1. Perform a second-order cone-convexity transformation on the centralized non-convex optimal power flow model of the AC / DC hybrid distribution network to obtain a centralized second-order cone-optimal power flow model.

[0121] S2. Decouple the centralized second-order cone optimal power flow model at the converter and write it in an affine coupling separable form to obtain the distributed second-order cone optimal power flow model of the AC / DC hybrid distribution network.

[0122] S3. Based on the distributed second-order cone optimal power flow model of the AC / DC hybrid distribution network, obtain the second-order cone optimal power flow models for each AC subnetwork and the DC subnetwork, and use them... All inequality constraints and variable upper and lower bound constraints in the stacked subnet model;

[0123] S4. The improved augmented Lagrangian relaxation method is used to solve the second-order cone optimal power flow model of the decoupled AC subnet and DC subnet in parallel, and local solutions are obtained. According to local solutions Calculate the Jacobian matrix J of the activity set at the location. l ,gradient Hessian matrix and scaling matrix

[0124] S5. Based on the Jacobi matrix J l ,gradient Hessian matrix and scaling matrix Solve the quadratic programming master problem, update the original residuals and dual residuals, and determine whether convergence has occurred.

[0125] It should be noted that:

[0126] This invention is based on a typical topology of an AC / DC hybrid distribution network, such as... Figure 1 As shown, it consists of a tuple It indicates. Among them, This represents the set of all AC and DC subnets. Represents the set of communication subnets. Denotes the set of DC subnets, and Denotes the set of converters, and Represents the set of all nodes. Represents the set of nodes in the communication subnet. This represents the set of nodes in the DC subnet. Represents the set of all converter nodes. This represents the set of nodes on the AC side of the converter. This represents the set of nodes on the DC side of the converter. This represents the set of nodes that represent the common connection point between the AC subnet and the DC subnet. This represents the filter node set. Figure 1 In the set, node k is located in the set. In the set, node f is located in the set In the set, node n is located in the set In the set, node m is located in the set middle. This represents the set of all branches.

[0127] To further implement the above technical solution, the specific content of S1 includes:

[0128]

[0129] Among them, C dc The objective function of a multi-terminal DC power grid is... Let l be the objective function of the AC subnet. Represents a set of communication subnets;

[0130]

[0131]

[0132] Among them, c 1g c 2g c 3g c represents the cost coefficient of the generator. loss c represents the cost factor for power loss. grid This indicates the electricity price of the upstream power grid, P0 G This represents the active power of the root node. This represents the power loss of the k-th converter connected to the DC subgrid. This represents the active power of the generator at node g. If node g is not a generator node, then...

[0133] The constraints include:

[0134] Second-order cone constraints for branch power flow within a subnet:

[0135]

[0136]

[0137]

[0138]

[0139] The node voltage safety constraints within the AC subnet are as follows:

[0140]

[0141] The active power constraint of generators within the AC subnet is:

[0142]

[0143] The reactive power constraint of generators within the AC subnet is:

[0144]

[0145] Where, r ij and x ij This represents the resistance and reactance of branch ij. This represents the reactive power of the generator at node j. and P represents the active and reactive loads at node j. ij and Q ij Indicates the active and reactive power flowing through branch ij, l ij and u j This represents the sum of the squares of the current flowing through branch ij and the voltage magnitude at node j. This represents the lower and upper limits of the active and reactive power of the generator located at node j. u j and This represents the lower and upper limits of the squared magnitude of the voltage at node j;

[0146] Second-order cone constraint for branch power flow within a DC subgrid:

[0147]

[0148]

[0149]

[0150]

[0151] Among them, P i DC This represents the active power injected into the DC subgrid from the converter station;

[0152] The node voltage safety constraints within the DC subgrid are as follows:

[0153]

[0154] The active power constraint of generators within the DC subgrid is:

[0155]

[0156] Power balance constraints of converter nodes:

[0157]

[0158]

[0159]

[0160]

[0161] in, and This represents the power of the equivalent generator injected from the AC subnet;

[0162] Constraints on the relationship between the reactive load of the filter node and the parallel inductance of the filter node:

[0163] The reactive load at node f, i.e., on the filter, can be represented as:

[0164]

[0165] in, This represents the parallel inductance at filter node f;

[0166] Voltage relationship constraints between the AC and DC sides of the converter:

[0167]

[0168] Where, parameter M represents the modulation factor, and M∈[0,1]; U m This represents the magnitude of the node voltage at bus m, and

[0169] Active power relationship constraints between the AC and DC sides of the converter:

[0170]

[0171] Among them, the second-order cone constraint of converter power loss is:

[0172]

[0173] Reactive power limitation constraints of the converter:

[0174]

[0175] in, Q C and These represent the lower and upper limits of the converter's reactive power, respectively.

[0176] The relationship between the slope constant of the converter and the rated power and rated DC voltage of the converter:

[0177]

[0178] in, and Let represent the rated power and rated DC voltage of the k-th converter, respectively, and q represent the DC voltage change that causes a 100% change in converter power;

[0179] Converter droop control constraints:

[0180]

[0181] Among them, K k This represents the slope constant of the k-th converter; and These represent the reference values ​​for DC power and DC voltage used in droop control, respectively.

[0182] The converter slope constant is calculated as follows:

[0183]

[0184] in, and Let represent the rated power and rated DC voltage of the k-th converter, respectively, and q represent the DC voltage change that causes a 100% change in converter power;

[0185] Second-order cone constraint on converter apparent capacity:

[0186]

[0187] The centralized second-order cone branch power flow model described in this invention is a typical second-order cone optimization problem, which can be solved using traditional centralized methods. However, AC / DC hybrid distribution networks have a typical multi-level structure, making them more suitable for distributed computing. Moreover, in the context of the electricity market, multiple AC and DC subnetworks are usually operated and managed by different system operators, making the resulting AC / DC optimal power flow problem even more suitable for a distributed computing framework. Therefore, this invention further transforms the centralized second-order cone branch power flow model into a distributed optimal power flow model.

[0188] To further implement the above technical solution, the specific content of S2 includes:

[0189] Introducing consensus constraints:

[0190]

[0191]

[0192]

[0193] Based on consensus constraints, the centralized second-order cone optimal power flow model can be rewritten in an affine coupled and separable form, resulting in the distributed second-order cone optimal power flow model:

[0194]

[0195]

[0196]

[0197]

[0198] Wherein, λ,κ l ,γ l Let each represent the dual variable of the corresponding constraint. x represents the set of all AC and DC subnets. l This represents a column vector consisting of all variables in subnet l. x l , They represent x respectively l The lower and upper limits of the values; constraint (33) represents the coupling constraint between the AC subnet and the DC subnet, constraint (34) represents all inequality constraints in each subnet model, and (35) represents the upper and lower limit constraints of the variables in each subnet model.

[0199] To further implement the above technical solution, the specific content of S3 includes:

[0200]

[0201] in, h is used for all inequality constraints and variable upper and lower bound constraints in the stacked AC and DC subnet models. l (x l ) represents all inequality constraints in subnet l.

[0202] To further implement the above technical solution, the specific contents of S4 include:

[0203] S41. Initialization (z 0 ,λ0 Choose a proportionally symmetric matrix.

[0204] S42. In In this case, the L1 loss function is defined as:

[0205]

[0206] Φ0=Φ(z 0 (38)

[0207] S43. Solve the second-order cone optimal power flow model for all decoupled AC and DC subnets in parallel:

[0208]

[0209]

[0210] S44. Based on local solutions Calculate the Jacobian matrix J of the activity set at the location. l :

[0211]

[0212] in, It is a matrix Find the i-th row and calculate the gradient.

[0213] S45. Based on local solutions calculate like:

[0214]

[0215] Then set Φ0=Φ(x) k Update the Hessian matrix. Approximate value:

[0216]

[0217] And set the scaling matrix

[0218] Otherwise set μ i =0,

[0219] To further implement the above technical solution, the specific content of S5 includes:

[0220]

[0221] Update the original residual and the dual residual (z,λ):

[0222] zk+1 =x k +Δx k , λ k+1 =λ QP .

[0223] The invention will be further illustrated below through specific experiments:

[0224] The numerical example analysis was implemented in Matlab-R2021a, using a computer with an Intel Core i5-6600K CPU 3.50GHz and 16GB RAM. The Ipopt solver was used. The network topology is as follows. Figure 2 As shown, one multi-terminal DC subnet is connected to four AC subnets. All four AC subnets are IEEE 15-node AC distribution networks, with the base power and voltage of the AC subnets set to 1 MVA and 11 kV, respectively. The base power and voltage of the DC subnets are set to 1 MW and 10 kV, respectively. The voltage amplitude limits for both the AC subnets and the multi-terminal DC subnets are set to [0.95, 1.05] pu, and the power loss cost factor c... loss Set at $100 / MWh. The branch parameters of the converter and DC subnet are shown in Tables 1 and 2, and the total active and reactive loads of the AC subnet and the node loads of the DC subnet are shown in Tables 3, 4 and 5.

[0225] Table 1

[0226]

[0227] Table 2

[0228]

[0229] Table 3

[0230]

[0231] Table 4

[0232]

[0233] Table 5

[0234]

[0235] This invention proposes a stable, efficient, and scalable improved augmented Lagrange relaxation method to efficiently solve the distributed nonlinear optimal power flow problem in AC / DC hybrid distribution networks. In this embodiment, the distributed AC / DC optimal power flow method based on the improved augmented Lagrange relaxation method is compared with the widely used Alternating Direction Multiplier Method (ADMM). During initialization, the phase angle of all node voltages in the AC subnet is set to 0, the node voltage magnitudes of both the AC subnet and the multi-terminal DC subnet are set to 1.0 pu, and the dual variable λ is set to zero. The convergence performance of the two methods is compared and evaluated using the following metrics:

[0236] 1) Variable bias, i.e., the deviation of a local variable from its optimal value: ||xx * ||2;

[0237] 2) Original residual, i.e., the degree of violation of consensus constraints: ||Ax-b||2;

[0238] 3) Dual residual, ||Σ(xz)||2;

[0239] 4) Deviation of the objective function value, Where f(x) * ) represents the objective function value calculated using the traditional centralized method.

[0240] (1) Comparison between the accurate original non-convex model and the second-order conical convex relaxation model:

[0241] First, the accuracy of the proposed second-order cone-convex relaxation model of the optimal power flow model for AC / DC hybrid distribution networks is compared with that of the accurate original non-convex model. To ensure a fair comparison, we use the default solver in Matpower to solve both the accurate original non-convex model and the convex relaxation model collectively, as shown in Table 5. It can be seen that the proposed second-order cone-convex optimal power flow model for AC / DC hybrid distribution networks has the same operating cost as the accurate original non-convex model, indicating that the proposed second-order cone-convex relaxation optimal power flow model has higher computational accuracy.

[0242] (2) Comparison of solving the distributed second-order conical convex relaxation model and the distributed primitive non-convex model using the alternating direction multiplier method:

[0243] Since the proposed second-order cone optimal power flow model has sufficiently high computational accuracy, the alternating direction multiplier method is used to solve the accurate primal non-convex model and the second-order cone convex relaxation model in a distributed manner, as shown in Table 5. We can see that for the distributed primal non-convex model, the alternating direction multiplier method requires more iterations and computation time to converge, and the solution quality (primal residuals, dual residuals, deviations in objective function values, and variable deviations) is very poor. Although the alternating direction multiplier method can achieve relatively high accuracy in solving the distributed second-order cone convex relaxation model, it requires a large number of iterations and computation time.

[0244] (3) Comparison of solving the distributed second-order cone convex relaxation model using the improved augmented Lagrange relaxation method and the alternating direction multiplier method.

[0245] Since the alternating direction multiplier method can achieve high accuracy for distributed second-order conical convex relaxation models at a higher computational cost, we compared the convergence performance of the alternating direction multiplier method and the improved augmented Lagrange relaxation method for distributed second-order conical convex relaxation models, as shown in Table 5. Figure 3-4 As shown, it is evident that the proposed improved augmented Lagrange relaxation method converges significantly faster than the alternating direction multiplier method. The alternating direction multiplier method requires 4.963 seconds and hundreds of iterations to converge, while the improved augmented Lagrange relaxation method converges in only 16 iterations and 0.804 seconds. Moreover, compared to traditional centralized computation methods, the solution error of the improved augmented Lagrange relaxation method is almost negligible, indicating that the improved augmented Lagrange relaxation method has high accuracy in solving the distributed optimal power flow problem in AC / DC hybrid distribution networks.

[0246] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A distributed optimal power flow method for AC / DC hybrid distribution networks, characterized in that, Includes the following steps: S1. Perform a second-order cone-convexity transformation on the centralized non-convex optimal power flow model of the AC / DC hybrid distribution network to obtain a centralized second-order cone-optimal power flow model. S2. Decouple the centralized second-order cone optimal power flow model at the converter and write it in an affine coupling separable form to obtain the distributed second-order cone optimal power flow model of the AC / DC hybrid distribution network. S3. Based on the distributed second-order cone optimal power flow model of the AC / DC hybrid distribution network, obtain the second-order cone optimal power flow models for each AC subnetwork and the DC subnetwork, and use them... All inequality constraints and variable upper and lower bound constraints in the stacked subnet model; S4. The improved augmented Lagrangian relaxation method is used to solve the second-order cone optimal power flow model of the decoupled AC subnet and DC subnet in parallel to obtain local solutions. According to local solutions Calculate the Jacobian matrix from the activity set at the location. ,gradient Hessian matrix and scaling matrix ; S5. Based on the Jacobi matrix ,gradient Hessian matrix and scaling matrix Solve the quadratic programming master problem, update the original residuals and dual residuals, and determine whether convergence has occurred; The specific content of S2 includes: Introducing consensus constraints: （29） （30） （31） In the formula, The set of nodes representing the common connection point between the AC subnet and the DC subnet; Based on consensus constraints, the centralized second-order cone optimal power flow model can be rewritten in an affine coupled and separable form, resulting in the distributed second-order cone optimal power flow model: （32） s.t. (33) （34） （35） in, , , Let each represent the dual variable of the corresponding constraint. This represents the set of all AC and DC subnets. Subnet A column vector consisting of all variables in , , They represent The lower and upper limits of the values; constraint (33) represents the coupling constraint between the AC subnet and the DC subnet, constraint (34) represents all inequality constraints in each subnet model, and constraint (35) represents the upper and lower limits of the variables in each subnet model; The specific content of S3 includes: （36） in, All inequality constraints and variable upper and lower bound constraints are used in the stacked AC and DC subnet models. Subnet All inequality constraints in; The specific content in S4 includes: S41. Initialize the initial values ​​of the original residual and dual residual. Choose a proportionally symmetric matrix ; S42. In In the case of defining The loss function is: （37） （38） S43. Solve the second-order cone optimal power flow model for all decoupled AC and DC subnets in parallel: （39） s.t. (40) S44. Based on local solutions Calculate the Jacobian matrix from the activity set at the location. : （41） in, It is a matrix The Line up and calculate gradient ; S45. Based on local solutions ,calculate and ,like: （42） Then set Update Hessian matrix Approximate value: （43） And set the scaling matrix ; Otherwise set , ; The specific content of S5 includes: （44） Update the original residual and dual residual : ， 。 2. The distributed optimal power flow method for AC / DC hybrid distribution networks according to claim 1, characterized in that, The specific content of S1 includes: ； in, The objective function of a multi-terminal DC power grid is... For communication subnet The objective function, Represents a set of communication subnets; (1) (2) in, , , This represents the cost coefficient of the generator. The cost factor representing power loss, Indicates the electricity price of the upper-level power grid, This represents the active power of the root node. Indicates the flow through a branch road The square of the current, Indicates a branch The resistance, This represents the set of nodes in the DC subnet. The first one connected to the DC subnet Power loss of each converter Represents a node The active power of the generator on the node, if the node If it is not a generator node, then , Represents a set of converters; The constraints include: Second-order cone constraints for branch power flow within a subnet: （3） （4） （5） （6） The node voltage safety constraints within the AC subnet are as follows: （7） The active power constraint of generators within the AC subnet is: （8） The reactive power constraint of generators within the AC subnet is: （9） in, and Indicates a branch Resistance and reactance, Represents a node The reactive power of the generator. and Represents a node Active and reactive loads at the location, and Indicates the flow through a branch road Active power and reactive power Represents a node voltage amplitude, , , , Indicates that it is located at node The lower and upper limits of the generator's active and reactive power. and Represents a node The lower and upper limits of the square of the voltage amplitude; This represents the set of nodes in the communication subnet; Second-order cone constraint for branch power flow within a DC subgrid: （10） （11） （12） （13） in, This represents the active power injected into the DC subgrid from the converter station; This represents the set of nodes on the DC side of the converter; The node voltage safety constraints within the DC subgrid are as follows: （14） The active power constraint of generators within the DC subgrid is: （15） Power balance constraints of converter nodes: （16） （17） （18） （19） in, , , , and This represents the power of the equivalent generator injected from the AC subnet; Constraints on the relationship between the reactive load of the filter node and the parallel inductance of the filter node: node That is, the reactive load on the filter can be expressed as: （20） in, Represents filter node Parallel inductors; Represents the filter node set; Voltage relationship constraints between the AC and DC sides of the converter: （21） Among them, parameters M Represents the modulation factor, and ; Indicates busbar The node voltage amplitude, and ; This represents the set of nodes on the AC side of the converter; Active power relationship constraints between the AC and DC sides of the converter: （22） Among them, the second-order cone constraint of converter power loss is: （23） Reactive power limitation constraints of converters: （24） in, and These represent the lower and upper limits of the converter's reactive power, respectively. The relationship between the slope constant of the converter and the rated power and rated DC voltage of the converter: （25） in, and These represent the rated power and rated DC voltage of the k-th converter, respectively. This represents the amount of DC voltage change that causes a 100% change in converter power. Converter droop control constraints: （26） in, This represents the slope constant of the k-th converter; and These represent the reference values ​​for DC power and DC voltage used in droop control, respectively. Second-order cone constraint on converter apparent capacity: （28）。

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