A power grid flow optimization method considering distribution robust joint opportunity constraints

Abstract

The application discloses a power grid power flow optimization method considering distribution robust joint opportunity constraints, and the method comprises the following steps: acquiring an uncertain distribution considering wind power output uncertainty; establishing a voltage upper limit / lower limit joint opportunity constraint of a power grid node; constructing a conic constraint group considering the voltage upper limit / lower limit joint opportunity constraint according to the voltage joint opportunity constraint of the power grid node; constructing a target function with the optimization target of minimizing power grid network active power loss by considering the uncertain distribution; constructing a power grid power flow quadratic programming model according to the target function and the conic constraint group; obtaining optimal decision variables by solving the power grid power flow quadratic programming model through an optimization solver, and applying the optimal decision variables to a radial topological structure power grid to realize the power grid power flow optimization process considering the distribution robust joint opportunity constraints. The application solves the technical problem that it is difficult to accurately process the multi-node voltage joint over-limit risk in the existing distribution robust dispatching method.

Description

Technical Field

[0001] This invention relates to the field of collaborative optimization technology for grid voltage over-limit risk and operating loss, and in particular to a grid power flow optimization method that considers the joint opportunity constraint of the split-blown rod. Background Technology

[0002] With the deepening of the "dual-carbon" strategy, the installed capacity of new energy sources such as distributed wind power in distribution networks continues to climb, accelerating the transformation of traditional power grids into a new type of power system dominated by new energy sources. However, the strong randomness and volatility of wind power generation make it highly susceptible to reverse power flow after a high proportion of wind power is integrated into the grid, significantly exacerbating the uncertainty of system operation and the risk of extreme overvoltage. How to achieve a Pareto optimal trade-off between distribution network operation losses and voltage security while taking into account the uncertainty of wind power output has become a key problem that urgently needs to be solved in the field of power dispatching.

[0003] Existing research methods for handling the uncertainty of new energy output mainly fall into two categories: stochastic optimization and robust optimization. Stochastic optimization relies heavily on the precise probability distribution of uncertain variables and typically constructs scheduling models based on scenario analysis or chance constraints. However, in actual engineering projects, the true distribution of wind power output is often difficult to obtain accurately. When historical samples are limited, this method easily overlooks the "long-tail risk" of frequent extreme values, leading to a false sense of security in the scheduling scheme. Robust optimization, on the other hand, constructs an uncertainty set to characterize the absolute worst-case scenario. While it has strong risk resistance, its defense strategies are often too extreme and conservative, frequently requiring the use of a large amount of reactive power resources for voltage suppression. This results in a surge in the actual physical network losses of the system, leading to excessively high economic costs and making it difficult to meet the high-efficiency operation requirements under high-proportion wind power integration.

[0004] Partial Browsing optimization combines the advantages of robust optimization and stochastic optimization, producing scheduling results that balance economy and robustness, and has been widely adopted as an uncertainty-based approach. Partial Browsing optimization does not require knowledge of the precise probability distribution of random variables; it only needs to construct an uncertain set containing the true probability distribution and make decisions under the worst-case probability distribution, thus solving the problem of obtaining the probability distribution parameters of some random variables in stochastic optimization. However, existing partial Browsing optimization methods for distribution networks still have shortcomings in handling voltage safety constraints. Although some methods consider voltage safety through chance constraints, they mostly use semi-invariant methods to process each node independently, making it difficult to accurately account for the joint risk of simultaneous voltage exceedances at multiple nodes. Furthermore, approximation errors often lead to overly conservative scheduling schemes and higher network losses. Summary of the Invention

[0005] This invention provides a power flow optimization method that considers the joint chance constraints of the split-blown rods to overcome the above-mentioned technical problems.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: A power flow optimization method considering the joint chance constraints of distributed bar rods, specifically including the following steps: S1: For radial topology power grids, based on Fuzzy sets are used to obtain the uncertain distribution considering the uncertainty of wind power output; joint opportunity constraints of voltage upper / lower limits for grid nodes are established based on static security domains; S2: Based on Inequalities and conditional risk value are used to construct a conical constraint group that considers the upper / lower voltage joint opportunity constraint based on the voltage joint opportunity constraint of the grid node. S3: By considering the uncertain distribution, an objective function is constructed with minimizing the active power loss of the power grid as the optimization objective; and based on the objective function and the conical constraint group, a power flow quadratic programming model is constructed with the active power regulation, reactive power regulation and auxiliary variables of each power grid node as decision variables. S4: Solve the power flow quadratic programming model by optimizing the solver to obtain the optimal decision variables. Apply the optimal decision variables to the radial topology power grid to realize the power flow optimization process considering the joint chance constraints of the distributed bar.

[0007] Furthermore, S1 specifically includes the following steps: S11: Obtain the active power injection of each node in a radial topology power grid. Reactive power injection at nodes for: (1) In the formula: , Let these represent the active power regulation vector and reactive power regulation vector of the power grid nodes, respectively. ; , Represents the active power load vector and reactive power load vector of a power grid node; Represents the set of system nodes and ; This represents the total number of nodes in a radially topological power grid. This represents the vector of uncertainties injected into the active power of a node, and is based on... Fuzzy set theory and historical sample data sets will The uncertain distribution is expressed as: (2) (3) In the formula: mThis represents the number of historical data vectors in the historical sample dataset; Represents the set of historical sample data and ; Represents the vector of uncertainties Composition Dimensional support set; express The radius of the sphere and ||·|| represents the norm; express The Group of historical data vectors and ; express The empirical probability distribution; express The empirical probability distribution; S12: Any grid node in a radial topology power grid The corresponding upper voltage limit opportunity constraints and lower voltage limit opportunity constraints are expressed as follows: (4) In the formula: , Representing power grid nodes The base reactive power load and the base active power load; Representing power grid nodes Active and reactive power regulation of distributed power sources; Representing grid nodes k The coefficients of the hyperplane boundary of the safety region corresponding to the upper limit of voltage active power and reactive power. ; Indicates intermediate parameters and ; (5) In the formula: Represents a power grid node j With grid nodes k The set of downstream power grid nodes; This indicates the path from the root node of the power grid to the next node. j The total equivalent resistance and total equivalent reactance along the path; Indicates from the power grid node k The total equivalent resistance and total equivalent reactance along the path from the starting point to the root node of the power grid; Indicates from the power grid node sThe total equivalent resistance and total equivalent reactance along the path from the starting point to the root node of the power grid; s Represents a power grid node j With grid nodes k The first intersection upstream; S13: Based on S11 to S12, the joint opportunity constraint of the upper and lower voltage limits is defined and obtained as follows: (6) In the formula: P r The functional form representing probability; Risk parameters representing joint opportunity constraints; Indicates used for description Probability distribution of uncertainty The corresponding fuzzy set; A,B Represents the matrix coefficients of the joint opportunity constraint of the upper and lower voltage limits, and when When, the matrix coefficients corresponding to the voltage upper limit joint opportunity constraint; when At that time, the matrix coefficients corresponding to the lower voltage limit joint opportunity constraint; (7) After rearranging the terms in line (6), the formula can be rewritten as follows: (8) In the formula: , , express The j A vector consisting of row elements; express The j The vector composed of row elements; then the joint chance constraint of the upper / lower voltage limit is equivalent to: (9) Furthermore, S2 specifically includes the following steps: S21: Based on The inequality decouples equation (9) into a chance constraint for a single grid node: (10) In the formula: This represents the average value of the risk parameter under a one-sided opportunity constraint, and ; S22: Define the measurable loss function according to formula (10) for:

[0008] And based on the measurable loss function By introducing conditional value of risk, the opportunity constraints of individual grid nodes in formula (10) are adjusted. The convex approximation operation is expressed as follows: (11) In the formula: This represents the continuous auxiliary decision-making variable introduced when dealing with the opportunity constraints of the j-th power grid node; , The representation indicates that the probability distribution is... The expected value operator obtained below; Represents the loss function At confidence level Conditional Value at Risk (VaR); S23: By considering For fuzzy sets, formula (11) can be rewritten as: (12) Based on the minimax theorem, according to formula (11), we obtain: (13) S24: According to formula (11), we can obtain: (14) Will Substituting into formula (14) yields: (15) In the formula: express affine function and for n 3D column vector; And when considering the expected solution of formula (15), formula (15) can be equivalent to: (16) (17) S25: Based on the Lagrangian function and strong duality theory, combined with formula (17), formula (16) can be expressed as: (18) In the formula: The Lagrange factor corresponding to the constraint condition expressed by equation (17) and ; According to the minimax theorem, formula (18) can be equivalent to: (19) S26: By introducing auxiliary variables Formula (19) can be expressed as: (20) For formula (20), when When, the inequality regarding the auxiliary variable becomes: (twenty one) Then, according to formula (21), we can obtain: (twenty two) And by introducing perturbation variables Formula (22) can be rewritten as: (twenty three) S27: Regarding the disturbance variable in formula (23) The maximization subproblem is given by the following constraints: (twenty four) And under the premise of satisfying constraint (24), formula (23) can be rewritten as: (25) S28: Based on S21 to S27, a conical constraint group considering the joint opportunity constraint of the upper and lower voltage limits can be obtained; and the conical constraint group considering the joint opportunity constraint of the upper voltage limits is: (26) The conical constraint group considering the lower voltage limit combined with the opportunity constraint is as follows: (27).

[0009] Furthermore, S3 specifically includes the following steps: S31: By considering the aforementioned uncertain distribution, the objective function with the optimization objective of minimizing the active power loss of the power grid network is constructed as follows: (28) In the formula: Describes the node equivalent resistance matrix of the distribution network and ; In representing the flow from the root node of the distribution network to the power grid nodes With grid nodes During power supply, the total equivalent resistance of the overlapping paths on the power supply path; This represents the set of all line branches in a power distribution network system. Represents a power grid node The set of all downstream power grid nodes; This represents the reference voltage at the root node of the power grid; This indicates the active power loss in the power grid network; S32: Based on the minimax decision criterion, formula (28) can be expressed as: (29) make (30) Define the auxiliary function according to formula (29) for: (31) Based on formula (31) and formula (17), we can obtain: (32) (33) S33: Based on formulas (32) and (33), the Lagrange function can be obtained. for: (34) In the formula: Represents the Lagrange factor and ; S34: Based on the strong duality condition and the saddle point theorem, formula (34) is transformed into: (35) By introducing auxiliary variables The dual problem of formula (35) can be expressed as: (36) S35: Introduce intermediate variables based on the definition of dual norm. This makes the constraints of formula (35) equivalent: (37) In the formula: Indicate intermediate variables of Norm and ; According to duality theory, when At that time, according to formula (29), the power flow objective function of the power grid can be constructed with the active power regulation, reactive power regulation and auxiliary variables of each power grid node as decision variables; The power flow objective function is then combined with a conical constraint group that considers the joint chance constraints of the upper and lower voltage limits to form a power flow quadratic programming model.

[0010] Furthermore, the power flow quadratic programming model described in S35 is as follows: (38).

[0011] Furthermore, the optimization solver for the power grid power flow quadratic programming model in S4 adopts a commercial optimization solver. .

[0012] Beneficial effects: This invention provides a power flow optimization method considering the joint chance constraints of the distributed blue bar. First, based on... Fuzzy set theory is used to obtain the uncertain distribution considering the uncertainty of wind power output; a joint opportunity constraint of voltage upper / lower limits is established for grid nodes based on the static security domain; this invention lays the foundation for the linearization of the joint opportunity constraint of voltage upper / lower limits by transforming the nonlinear constraint of voltage into a linear constraint of power injection at grid nodes. Compared with independent opportunity constraints, the joint opportunity constraint effectively considers the coupling effect of multiple interrelated uncertainties and is more suitable for distribution network stability studies under the background of multiple disturbance coupling; secondly, based on The method of deterministic transformation of joint opportunity constraints based on inequalities and conditional risk value is proposed, namely, constructing a conical constraint group that considers the joint opportunity constraints of voltage upper / lower limits. Finally, a power flow quadratic programming model is established based on duality theory and solved using an optimization solver. This solves the problem of difficulty in accurately handling the joint voltage limit risk of multiple nodes in the existing sub-Blu-rod scheduling method, and thus realizes power flow optimization considering the joint opportunity constraints of sub-Blu-rods. Attached Figure Description

[0013] 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 some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 This is a flowchart of a power flow optimization method considering the joint chance constraint of the split-Bluer bar according to the present invention; Figure 2 This is a schematic diagram of the system architecture of the IEEE 33 power grid node used in the example of this embodiment; Figure 3 For this embodiment The effect of radius on optimization results is shown in the figure. Figure 4 This is a graph showing the impact of sample size on the optimization results in this embodiment. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0016] This embodiment provides a power flow optimization method considering the joint chance constraints of the split-blob rods, such as... Figure 1 As shown, the specific steps include: S1: For radial topology power grids, based on Fuzzy set theory is used to obtain the uncertain distribution considering the uncertainty of wind power output; based on the static security domain, joint opportunity constraints on the upper and lower voltage limits of grid nodes are established, specifically including the following steps: S11: Obtain the active power injection of each node in a radial topology power grid. Reactive power injection at nodes for: (1) In the formula: , Let these represent the active power regulation vector and reactive power regulation vector of the power grid nodes, respectively. ; , Represents the active power load vector and reactive power load vector of a power grid node; Represents the set of system nodes and ; This represents the total number of nodes in a radially topological power grid. This represents the vector of uncertainties injected into the active power of a node, and in this embodiment, the vector is taken into account. True probability distribution If it is unknown, then based on Fuzzy set theory and historical sample data sets will The uncertain distribution is expressed as: (2) (3) In the formula: m This represents the number of historical data vectors in the historical sample dataset; Represents the set of historical sample data and ; Represents the vector of uncertainties Composition Dimensional support set; express The radius of the sphere and ||·|| represents the norm; express The Group of historical data vectors and ; express The empirical probability distribution; express The empirical probability distribution; S12: Any grid node in a radial topology power grid Its voltage amplitude must be kept within a safe range. Internally, power grid nodes are set up. j The active power regulation is The reactive power regulation is This embodiment considers static security domains and power grid nodes. j The corresponding upper voltage limit opportunity constraints and lower voltage limit opportunity constraints are expressed as follows: (4) In the formula: , Representing power grid nodes The base reactive power load and the base active power load; Representing power grid nodes Active and reactive power regulation of distributed power sources; Representing grid nodes k The coefficients of the hyperplane boundary of the safety domain corresponding to the upper limit of active power and reactive power of the voltage; ; Indicates intermediate parameters and In this embodiment , It can be generated through the distribution network topology and line impedance, specifically: (5) In the formula: Represents a power grid node j With grid nodes k The set of downstream power grid nodes; This indicates the path from the root node of the power grid to the next node. j The total equivalent resistance and total equivalent reactance along the path; Indicates from the power grid node k The total equivalent resistance and total equivalent reactance along the path from the starting point to the root node of the power grid; Indicates from the power grid node s The total equivalent resistance and total equivalent reactance along the path from the starting point to the root node of the power grid; s Represents a power grid node j With grid nodes k The first intersection upstream; Indicates from the power grid node jThe total impedance from the starting point to the root node of the power grid. Indicates from the power grid node k The total impedance from the starting point to the root node of the power grid; similarly, Represents a power grid node s The total impedance from the starting point to the root node of the power grid; This indicates that the first and last two points are respectively power grid nodes. g and power grid nodes h The route, Indicates the line The impedance value; Indicates that by power grid node j The set of routes that form the path to power grid node 0; S13: In this embodiment, in order to effectively consider the spatial coupling characteristics of voltage fluctuations at multiple nodes in the distribution network and strictly ensure that all nodes in the entire network simultaneously meet the operating standards, a joint opportunity constraint is adopted to comprehensively control the global voltage over-limit risk. The voltage joint opportunity constraint is divided into upper voltage limit constraint and lower voltage limit constraint, that is, the upper voltage limit / lower voltage limit joint opportunity constraint is defined and obtained based on S11 to S12 as follows: (6) In the formula: P r The functional form representing probability; Risk parameters representing joint opportunity constraints; Indicates used for description Probability distribution of uncertainty The corresponding fuzzy set; A,B Represents the matrix coefficients of the joint opportunity constraint of the upper and lower voltage limits, and when When, the matrix coefficients corresponding to the voltage upper limit joint opportunity constraint; when At that time, the matrix coefficients corresponding to the lower voltage limit joint opportunity constraint; (7) After rearranging the terms in line (6), the formula can be rewritten as follows: (8) In the formula: , , express The j A vector consisting of row elements; express The j The vector composed of row elements; then the joint chance constraint of the upper / lower voltage limit is equivalent to: (9) S2: Based on Inequalities and conditional risk value, constructing a conical constraint group considering upper and lower voltage joint opportunity constraints based on the voltage joint opportunity constraints of the grid nodes, specifically includes the following steps: S21: Since formula (9) is difficult to solve directly, this embodiment adopts... The inequality decomposes it into n Individual grid node opportunity constraints, while strictly guaranteeing the upper bound of the system's global over-limit risk, significantly reduce the solution dimensionality and computational complexity of the optimization model. To simplify calculations, this embodiment... Adopting an equal distribution strategy, based on The inequality decouples formula (9) into a chance constraint for a single grid node, i.e., the approximate feasible solution set is: (10) In the formula: This represents the average value of the risk parameter under a one-sided opportunity constraint, and In this embodiment, the upper and lower voltage limits need to be considered simultaneously, so the risk parameters of the single-sided opportunity constraint are equally divided. S22: To effectively overcome the dimensionality curse of traditional opportunity constraints—which are non-convex and difficult to solve—and to achieve precise quantitative control of tail-end over-limit depth under extreme power grid conditions, while strictly suppressing the average over-limit depth under extreme tail scenarios, this embodiment introduces conditional value of risk (VoV). A convex approximation is performed on each opportunity constraint. In this embodiment, the measurable loss function is defined according to formula (10). for:

[0017] And based on the measurable loss function By introducing conditional value of risk, according to The standard mathematical definition applies to the chance constraints of a single grid node in formula (10). The convex approximation operation transforms the joint chance constraint into the following: One opportunity constraint is a blue rod The format is: (11) In the formula: A measure of the specific probability distribution to which an uncertain variable (wind power output) belongs; This represents a continuous auxiliary decision-making variable introduced when dealing with the opportunity constraint of the j-th power grid node, and its mathematical meaning represents the risk value corresponding to the constraint. The critical threshold of ); , The representation indicates that the probability distribution is... The expected value operator obtained below; Represents the loss function At confidence level The conditional risk value; in this embodiment, the probability of encountering such a situation in the distribution network is quantified in a physical sense as: The severity of system voltage exceeding limits under extreme wind power disturbance scenarios.

[0018] S23: In this embodiment, the non-convex opportunity constraint that originally contained a complex function is replaced by the probability distribution integral function implicit in formulas (9) and (10), which is equivalent to the integral function of the auxiliary variable. The convex optimization form quantifies the expected out-of-bounds amount under extreme tail scenarios, thus ensuring the strict solvability of the reactive power and voltage safety dispatch model for the distribution network. Therefore, by considering... For fuzzy sets, formula (11) can be rewritten as: (12) Due to the division of blu sticks The model satisfies convex-concave properties and has a compact feasible region. Based on the minimax theorem, the order of finding extrema in the above nested operations can be interchanged, i.e., according to formula (11): (13) S24: Since the outer layer of the inequality in formula (11) is for finding the infimum and the overall requirement is less than or equal to 0, this is mathematically equivalent to making Release the continuous decision variables in the optimization model and make their internal expectation expression less than or equal to 0. Thus, this embodiment can remove the outer lower bound operator inf. According to formula (11), we can obtain: (14) Will Substituting into formula (14) yields: (15) In the formula: express affine function and for n 3D column vector; And when considering the expected solution of formula (15), that is, the worst-case expected solution of the subproblem in the inner layer of formula (15), formula (15) can be equivalent to: (16) (17) S25: Based on the Lagrangian function and strong duality theory, combined with formula (17), formula (16) can be expressed as: (18) In the formula: The Lagrange factor corresponding to the constraint condition expressed by equation (17) and ; According to the minimax theorem, formula (18) can be equivalent to: (19) S26: By introducing auxiliary variables Formula (19) can be expressed as: (20) For formula (20) Some parts will be discussed separately: when When, the inequality regarding the auxiliary variable becomes: (twenty one) when When, the inequality regarding the auxiliary variable becomes: (twenty two) Then, according to formula (22), we can obtain: (twenty three) And by introducing perturbation variables Formula (23) can be rewritten as: (twenty four) S27: Regarding the extremely severe disturbances within formula (24), i.e. The maximization subproblem of the perturbation variable, according to the conjugate property of norms, is solved if and only if the coefficient vector... The dual norm is less than or equal to When the maximum value of the subproblem converges to 0, its maximum value will diverge to positive infinity. To ensure that the model has a solution, constraints must be imposed, expressed as follows: (25) Through the above strong dual reconstruction, the maxima subproblem involving the optimization of the infinite-dimensional worst-case scenario is completely eliminated. Under the premise of satisfying formula (25), the original Brønsted bar chance constraint satisfies the following linear constraint: (26) S28: In summary, considering the joint chance constraint of the voltage upper limit, the subbulb bar The constraints are ultimately equivalently transformed into the following explicit conical form, i.e., based on S21 to S27, a conical constraint group considering the joint opportunity constraints of the upper and lower voltage limits can be obtained; and the conical constraint group considering the joint opportunity constraints of the upper voltage limits is: (27) The conical constraint group considering the lower voltage limit combined with the opportunity constraint is as follows: (28).

[0019] S3: By considering the aforementioned uncertain distribution, an objective function is constructed with the goal of minimizing the active power loss of the power grid network; and based on the objective function and the conical constraint group, a power flow quadratic programming model is constructed with the active power regulation, reactive power regulation, and auxiliary variables of each power grid node as decision variables, specifically including the following steps: S31: By considering the aforementioned uncertain distribution, the objective function with the optimization objective of minimizing the active power loss of the power grid network is constructed as follows: (29) In the formula: Describes the node equivalent resistance matrix of the distribution network and ; In representing the flow from the root node of the distribution network to the power grid nodes With grid nodes During power supply, the total equivalent resistance of the overlapping paths on the power supply path; express A fuzzy set, which contains the true probability distribution of all possible uncertainties; This represents the set of all line branches in a power distribution network system. Represents a power grid node The set of all downstream power grid nodes (including power grid nodes) itself); This represents the reference voltage of the grid root node (typically 1.0 pu); This indicates the active power loss in the power grid network; S32: Based on the minimax decision criterion, formula (29) can be expressed as: (30) make (31) For a given historical dataset c It is certain, and it is consistent with... and Irrelevant; Define the auxiliary function according to formula (30). for: (32) Considering the law of total probability, we can obtain the following from formula (32) combined with formula (17): (33) (34) S33: Based on formulas (33) and (34), the Lagrange function can be obtained. for: (35) In the formula: Represents the Lagrange factor and ; S34: Based on the strong duality condition and the saddle point theorem, formula (35) is transformed into: (36) By introducing auxiliary variables The dual problem of formula (36) can be expressed as: (37) S35: Introduce intermediate variables based on the definition of dual norm. The constraints of formula (36) are equivalent: (38) In the formula: Indicate intermediate variables of Norm and ; According to duality theory, when When the time is right, equation (38) must hold. Therefore, according to equation (30), a power flow objective function can be constructed with the active power regulation, reactive power regulation, and auxiliary variables of each power grid node as decision variables. At this time, the objective function is transformed into a quadratic function form, which can be solved quickly using the quadratic programming method. The power flow objective function and the conical constraint group considering the joint chance constraints of the upper and lower voltage limits together constitute the power flow quadratic programming model, and the power flow quadratic programming model is: (39).

[0020] S4: Solver optimized by commercial optimization Solving the aforementioned power flow quadratic programming model yields optimal decision variables. These optimal decision variables are then applied to a radial topology power grid to achieve power flow optimization considering the joint opportunity constraints of distributed Brussels branches. This embodiment uses the established distributed Brussels branch joint opportunity constraint scheduling model for the distribution network, with the active power adjustment of each node as the basis. Reactive power regulation The paper presents a power flow quadratic optimization model with auxiliary multipliers generated by dual transformation as decision variables. The objective function is a strictly convex quadratic function, and the constraints are all linear functions of the aforementioned decision variables. Therefore, this model is a typical convex quadratic programming (Convex QP) problem, which can be solved efficiently using the quadratic programming method.

[0021] Compared with existing technologies, the beneficial effects of the method described in this embodiment are as follows: To address the significant challenges brought by the integration of high-proportion wind power generation to the optimization of distribution network operation, and considering the shortcomings of commonly used deterministic methods, robust optimization, and stochastic optimization in handling uncertainties, as well as the difficulty in accurately handling the risk of joint voltage exceedance of multiple nodes in existing sub-Browsing scheduling methods, the method described in this embodiment is proposed based on sub-Browsing optimization and static voltage safety domain theory: First, based on... Fuzzy set theory is used to obtain the uncertain distribution considering the uncertainty of wind power output; a joint opportunity constraint of voltage upper / lower limits is established for grid nodes based on the static security domain; this invention lays the foundation for the linearization of the joint opportunity constraint of voltage upper / lower limits by transforming the nonlinear constraint of voltage into a linear constraint of power injection at grid nodes. Compared with independent opportunity constraints, the joint opportunity constraint effectively considers the coupling effect of multiple interrelated uncertainties and is more suitable for distribution network stability studies under the background of multiple disturbance coupling; secondly, based on The method of deterministic transformation of joint opportunity constraints based on inequalities and conditional risk value is proposed, namely, constructing a conical constraint group that considers the joint opportunity constraints of voltage upper / lower limits. Finally, a power flow quadratic programming model is established based on duality theory and solved using an optimization solver. This solves the problem of difficulty in accurately handling the joint voltage limit risk of multiple nodes in the existing sub-Blu-rod scheduling method, and thus realizes power flow optimization considering the joint opportunity constraints of sub-Blu-rods.

[0022] To verify the effectiveness of the method described in this embodiment, tests were conducted as shown in the attached figure. Figure 2 The proposed optimization method is tested using an IEEE 33-node distribution network. The system comprises 33 nodes with a base voltage of 12.66 kV. To simulate the operation of the power system under stringent safety requirements, the voltage fluctuation range of the nodes is limited to [0.95, 1.03] pu in this embodiment. In this embodiment, a distributed wind turbine with an installed capacity of 1.2 MW is connected to nodes 4, 9, 13, 20, and 30 respectively. Simultaneously, distributed power sources with reactive power regulation capabilities are configured at nodes 6, 15, 18, 23, and 28, with their regulation range set within ±0.5 MVar. The original data used in the simulation is derived from fuzzy sets constructed from renewable energy generation output data from southeastern Australia from 2012 to 2013. In the algorithm test, the sample size of the method described in this embodiment is set to 200, and the risk level parameter of the joint chance constraint is uniformly set to 0.1. The default values ​​for the examples are... Radius is 10 -4 .

[0023] Table 1 below illustrates the differences in network loss and computation speed among different methods. Traditional Robust Optimization (RO), to ensure absolute safety under any extreme boundary conditions, directly makes decisions based on the worst-case physical scenario of simultaneous full-scale wind power generation (1.2 MW), resulting in extremely high defensive costs for the system. It aims for a network loss of 0.0735 MW, but it does not involve complex probability calculations and takes only 0.34 seconds. The Monte Carlo Scenario Approach (MC-SAA) precisely discretizes the probability distribution through 3500 specific scenarios. After reasonably discarding 10% of high-risk scenarios, it calculates a low network loss of 0.0367 MW. However, because this process requires solving a mixed integer programming problem containing thousands of discrete binary variables, the computation time is as long as 89.496 seconds. In contrast, the method described in this embodiment achieves a balance between economy and solution speed. The method described in this embodiment yields an expected network loss of 0.0393 MW in 8.2367 seconds. This indicates that the method of the present invention avoids the time-consuming problem of integer planning in MC-SAA, while its network loss result is significantly lower than the absolute defense cost in RO.

[0024] Table 1. Comparison of network loss and computation speed for different methods

[0025] To clarify the method described in this embodiment The influence of radius on network loss was investigated through sensitivity testing of this radius. The radius determines the deviation between the allowable worst-case probability distribution and the empirical distribution within the fuzzy set. (See attached diagram) Figure 3 As shown: when the radius is extremely small, the fuzzy set is extremely compressed, and the model makes decisions almost entirely based on the empirical distribution of 200 initial historical data points. Its network loss result (0.0374 MW) is close to that of MC-SAA. As the radius gradually increases, the model allows the worst-case probability distribution to shift towards the high-risk range, increasing the system's reactive power output and consequently raising the network loss. When the radius increases to 10... -2 At the order of magnitude, the sub-robust model pushes all probability measures to the physical boundary of the support set (i.e., 1.2 MW). At this point, the worst probability distribution found by the method described in this embodiment is mathematically equivalent to the extreme deterministic boundary considered by traditional robust optimization. Therefore, its network loss converges to 0.0735 MW for the RO method. This phenomenon indicates that by adjusting... The radius effectively facilitates the transition of the model from empirical data-driven to absolute physical boundary defense. Finally, experiments evaluated the impact of historical observation sample size on the optimization results. Based on Theoretically, this experiment employs an adaptive radius strategy where the radius is inversely proportional to the square root of the sample size. As attached Figure 4As shown, when the historical sample size increased from 50 to 500, the expected network loss of the system steadily decreased from 0.0411 MW to 0.0390 MW. In the small sample phase, because the data did not fully reflect the actual power output fluctuations, the model maintained system safety through a large defense radius, resulting in a high initial network loss. As the number of samples increased, the empirical distribution gradually approached the true distribution, and the model was able to gradually reduce the overly conservative margin used to avoid unknown risks based on more reliable statistical information, thereby reducing the overall network loss. Regarding the algorithm's computation time, as the sample size increased to 500, the size of the auxiliary matrix also increased, increasing the computation time. However, thanks to the solution mechanism of the convex optimization method, the overall process time remained around 20 seconds. This experiment verified that the method described in this embodiment can stably maintain good solution efficiency and continuously optimize operating costs as historical data accumulates.

[0026] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention 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 or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A power flow optimization method considering the joint chance constraints of distributed bar structures, characterized in that, Specifically, the following steps are included: S1: For radial topology power grids, based on Fuzzy sets are used to obtain the uncertain distribution considering the uncertainty of wind power output; joint opportunity constraints of voltage upper / lower limits for grid nodes are established based on static security domains; S2: Based on Inequalities and conditional risk value are used to construct a conical constraint group that considers the upper / lower voltage joint opportunity constraint based on the voltage joint opportunity constraint of the grid node. S3: By considering the uncertain distribution, an objective function is constructed with minimizing the active power loss of the power grid as the optimization objective; and based on the objective function and the conical constraint group, a power flow quadratic programming model is constructed with the active power regulation, reactive power regulation and auxiliary variables of each power grid node as decision variables. S4: Solve the power flow quadratic programming model by optimizing the solver to obtain the optimal decision variables. Apply the optimal decision variables to the radial topology power grid to realize the power flow optimization process considering the joint chance constraints of the distributed bar.

2. The power flow optimization method considering the joint chance constraints of the distributed bar as described in claim 1, characterized in that, S1 specifically includes the following steps: S11: Obtain the active power injection of each node in a radial topology power grid. Reactive power injection at nodes for: （1） In the formula: , Let these represent the active power regulation vector and reactive power regulation vector of the power grid nodes, respectively. ; , Represents the active power load vector and reactive power load vector of a power grid node; Represents the set of system nodes and ; This represents the total number of nodes in a radially topological power grid. This represents the vector of uncertainties injected into the active power of a node, and is based on... Fuzzy set theory and historical sample data sets will The uncertain distribution is expressed as: （2） （3） In the formula: m This represents the number of historical data vectors in the historical sample dataset; Represents the set of historical sample data and ; Represents the vector of uncertainties Composition Dimensional support set; express The radius of the sphere and ||·|| represents the norm; express The Group of historical data vectors and ; express The empirical probability distribution; express The empirical probability distribution; S12: Any grid node in a radial topology power grid The corresponding upper voltage limit opportunity constraints and lower voltage limit opportunity constraints are expressed as follows: （4） In the formula: , Representing power grid nodes The base reactive power load and the base active power load; Representing power grid nodes Active and reactive power regulation of distributed power sources; Representing grid nodes k The coefficients of the hyperplane boundary of the safety region corresponding to the upper limit of voltage active power and reactive power. ; Indicates intermediate parameters and ; （5） In the formula: Represents a power grid node j With grid nodes k The set of downstream power grid nodes; This indicates the path from the root node of the power grid to the next node. j The total equivalent resistance and total equivalent reactance along the path; Indicates from the power grid node k The total equivalent resistance and total equivalent reactance along the path from the starting point to the root node of the power grid; Indicates from the power grid node s The total equivalent resistance and total equivalent reactance along the path from the starting point to the root node of the power grid; s Represents a power grid node j With grid nodes k The first intersection upstream; S13: Based on S11 to S12, the joint opportunity constraint of the upper and lower voltage limits is defined and obtained as follows: （6） In the formula: P r The functional form representing probability; Risk parameters representing joint opportunity constraints; Indicates used for description probability distribution of uncertainty The corresponding fuzzy set; A,B Represents the matrix coefficients of the joint opportunity constraint of the upper and lower voltage limits, and when When, the matrix coefficients corresponding to the voltage upper limit joint opportunity constraint; when At that time, the matrix coefficients corresponding to the lower voltage limit joint opportunity constraint; （7） After rearranging the terms in line (6), the formula can be rewritten as follows: （8） In the formula: , , express The j A vector consisting of row elements; express The j The vector composed of row elements; then the joint chance constraint of the upper / lower voltage limit is equivalent to: （9）。 3. The power flow optimization method considering the joint chance constraints of the distributed bar as described in claim 2, characterized in that, S2 specifically includes the following steps: S21: Based on The inequality decouples equation (9) into a chance constraint for a single grid node: （10） In the formula: This represents the average value of the risk parameter under a one-sided opportunity constraint, and ; S22: Define the measurable loss function according to formula (10) for: And based on the measurable loss function By introducing conditional value of risk, the opportunity constraints of individual grid nodes in formula (10) are adjusted. The convex approximation operation is expressed as follows: （11） In the formula: This represents the continuous auxiliary decision-making variable introduced when dealing with the opportunity constraints of the j-th power grid node; , The representation indicates that in the probability distribution The expected value operator obtained below; Represents the loss function At confidence level Conditional Value at Risk (VaR); S23: By considering For fuzzy sets, formula (11) can be rewritten as: （12） Based on the minimax theorem, according to formula (11), we obtain: （13） S24: According to formula (11), we can obtain: （14） Will Substituting into formula (14), we can obtain: （15） In the formula: express affine function and for n 3D column vector; And when considering the expected solution of formula (15), formula (15) can be equivalent to: （16） （17） S25: Based on the Lagrangian function and strong duality theory, combined with formula (17), formula (16) can be expressed as: （18） In the formula: The Lagrange factor corresponding to the constraint condition expressed by equation (17) and ; According to the minimax theorem, formula (18) can be equivalent to: （19） S26: By introducing auxiliary variables Formula (19) can be expressed as: （20） For formula (20), when When, the inequality regarding the auxiliary variable becomes: （21） Then, according to formula (21), we can obtain: （22） And by introducing perturbation variables Formula (22) can be rewritten as: （23） S27: Regarding the disturbance variable in formula (23) The maximization subproblem is given by the following constraints: (twenty four) And under the premise of satisfying constraint (24), formula (23) can be rewritten as: （25） S28: Based on S21 to S27, a conical constraint group considering the joint opportunity constraint of the upper and lower voltage limits can be obtained; and the conical constraint group considering the joint opportunity constraint of the upper voltage limits is: （26） The conical constraint group considering the lower voltage limit combined with the opportunity constraint is as follows: （27）。 4. The power flow optimization method considering the joint chance constraints of the split-blob rods according to claim 3, characterized in that, S3 specifically includes the following steps: S31: By considering the aforementioned uncertain distribution, the objective function with the optimization objective of minimizing the active power loss of the power grid network is constructed as follows: （28） In the formula: Describes the node equivalent resistance matrix of the distribution network and ; In representing the flow from the root node of the distribution network to the power grid nodes With grid nodes During power supply, the total equivalent resistance of the overlapping paths on the power supply path; This represents the set of all line branches in a power distribution network system. Represents a power grid node The set of all downstream power grid nodes; This represents the reference voltage at the root node of the power grid; This indicates the active power loss in the power grid network; S32: Based on the minimax decision criterion, formula (28) can be expressed as: （29） make (30) Define the auxiliary function according to formula (29) for: （31） Based on formula (31) and formula (17), we can obtain: （32） （33） S33: Based on formulas (32) and (33), the Lagrange function can be obtained. for: （34） In the formula: Represents the Lagrange factor and ; S34: Based on the strong duality condition and the saddle point theorem, formula (34) is transformed into: （35） By introducing auxiliary variables The dual problem of formula (35) can be expressed as: （36） S35: Introduce intermediate variables based on the definition of dual norm. This makes the constraints of formula (35) equivalent: （37） In the formula: Indicate intermediate variables of norm and ; According to duality theory, when At that time, according to formula (29), the power flow objective function of the power grid can be constructed with the active power regulation, reactive power regulation and auxiliary variables of each power grid node as decision variables; The power flow objective function is then combined with a conical constraint group that considers the joint chance constraints of the upper and lower voltage limits to form a power flow quadratic programming model.

5. A power flow optimization method considering joint chance constraints of distributed bar as described in claim 4, characterized in that, The power flow quadratic programming model described in S35 is: （38）。 6. A power flow optimization method considering joint chance constraints of distributed bar as described in claim 5, characterized in that, The optimization solver used in S4 to solve the power flow quadratic programming model employs a commercial optimization solver. .

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