A power distribution network voltage reactive power regulator sparse robust planning method

Abstract

This invention discloses a sparse robust planning method for voltage reactive power regulators in distribution networks, belonging to the field of power system and automation technology. The method includes: constructing a steady-state decision consistency model based on the electromagnetic coupling topology of the voltage reactive power regulator; establishing a linearized error discretization masking criterion based on the steady-state decision consistency model to map the nonlinear physical characteristics of the voltage reactive power regulator to a linear voltage support mode; constructing a sparse discrete robust planning model based on the economically effective coverage index and the linear voltage support mode, with the minimum generalized investment cost over the entire life cycle as the objective function and the voltage security of all nodes in the network under arbitrary source-load fluctuation uncertainty scenarios as the constraint; and solving the sparse discrete robust planning model to obtain the location and capacity determination scheme for the voltage reactive power regulator. This invention achieves an organic unity of physical fidelity, computational efficiency, economy, and robustness in the planning scheme for voltage reactive power regulators.

Description

Technical Field

[0001] This invention belongs to the field of power system and its automation technology, and particularly relates to a sparse robust planning method for voltage reactive power regulators in distribution networks. Background Technology

[0002] With the advancement of "dual-carbon" goals and the construction of new power systems, the distribution network is undergoing profound structural changes. The high proportion of distributed photovoltaic and wind power integration, along with the growth of new loads such as electrified transportation, is transforming the distribution network from a traditional unidirectional radial network into an active distribution network with deep integration of power sources, grids, loads, and energy storage. However, constrained by the high impedance of distribution network lines, especially in rural areas or over long distances, the high R / X ratio, and the randomness and volatility of renewable energy output, the distribution network faces unprecedented bidirectional voltage limit challenges, seriously threatening the safe and stable operation of the power grid.

[0003] Currently, the main technical means for voltage regulation in distribution networks include utilizing the remaining capacity of photovoltaic inverters, energy storage systems, intelligent soft switches, and traditional mechanical automatic voltage regulators. However, these existing technologies all have significant drawbacks in practical applications. While using photovoltaic inverters for voltage regulation is low-cost, it is limited by the coupling characteristics of active and reactive power capacity. During periods of abundant sunlight, the reactive power regulation margin is extremely low. Furthermore, at the end of low-voltage distribution networks where resistance is dominant, reactive power regulation alone is insufficient, and forced voltage regulation often requires reducing active power output, sacrificing economic efficiency. Although energy storage systems possess four-quadrant regulation capabilities, their high investment costs and limited cycle life make them extremely inefficient for simply solving voltage exceedance problems. Intelligent soft switches or unified power quality controllers, with power electronics at their core, offer precise control and rapid response, but require huge initial investments and are poorly suited to rural distribution networks with weak infrastructure and high cost sensitivity. Traditional automatic voltage regulators are inexpensive, but their tap adjustment is slow, they have dead zones, and they can only adjust the voltage amplitude, lacking reactive power coordination capabilities, making it difficult to cope with high-frequency voltage fluctuations.

[0004] In recent years, a novel voltage and reactive power regulator combining the advantages of electromagnetic coupling and power electronic control has been proposed. This device employs a three-winding isolated electromagnetic coupling structure, capable of directly injecting voltage vectors through series windings and providing reactive power support through parallel windings. However, existing planning methods for such devices have serious shortcomings: Firstly, its unique "series voltage regulation - parallel energy extraction" working mechanism leads to a "voltage backlash effect," meaning that to increase downstream voltage, active power must be extracted from upstream, resulting in additional voltage drops on high-impedance lines and further voltage drops upstream. This nonlinear physical characteristic is often ignored in existing planning models based on linearized power flow, leading to physically infeasible planning results. Secondly, directly using a mixed-integer nonlinear programming model with nonlinear constraints results in extremely high computational complexity, making it difficult to solve in large-scale distribution networks and scenarios with massive uncertainties.

[0005] In summary, existing technologies lack a site selection and capacity planning method that can accurately quantify the nonlinear physical boundaries of voltage and reactive power regulators, maintain computational efficiency, and effectively address the dual uncertainties of source and load. How to achieve sparse, economical, and robust configuration of such equipment in large-scale distribution networks while ensuring the physical fidelity of the model is a pressing technical challenge. Summary of the Invention

[0006] To address the aforementioned technical issues, this invention provides a sparse robust planning method for voltage and reactive power regulators (VVRs) in distribution networks. This method aims to accurately define the physical operating boundaries of equipment by constructing a VVR steady-state decision consistency model that considers voltage backlash effects. By utilizing the linearized error discretization masking criterion, complex nonlinear physical constraints are mapped into high-fidelity linear voltage support modes, thereby decoupling physical nonlinearity from computational linearity at the mathematical programming level. Finally, through the sparse discrete robust planning model, a precise layout of a very small number of devices is achieved while ensuring voltage safety in all weather conditions and scenarios, significantly reducing the investment cost of power grid transformation.

[0007] This invention provides a sparse robust planning method for voltage reactive power regulators in power distribution networks, including: Based on the electromagnetic coupling topology of the voltage reactive power regulator, a steady-state decision consistency model considering the voltage backlash effect is constructed. Based on the steady-state decision consistency model, a linearized error discretization masking criterion is established to map the nonlinear physical characteristics of the voltage reactive power regulator into a linear voltage support mode. Based on the impedance distribution of distribution network lines, the voltage regulation conduction characteristics of voltage and reactive power regulators, the risk weight of node voltage over-limit, and the generalized installation cost, an economically effective coverage index is constructed. Based on the economically effective coverage index and the linear voltage support mode, a sparse discrete robust programming model is constructed with the minimum generalized investment cost over the entire life cycle as the objective function and the voltage safety of all nodes in the network under any source load fluctuation uncertainty scenario as the constraint. Solving the sparse discrete robust programming model yields the location and capacity scheme for the voltage reactive power regulator.

[0008] Optionally, based on the electromagnetic coupling topology of the voltage reactive power regulator, a steady-state decision consistency model considering the voltage backlash effect is constructed, including: Based on the three-winding isolated electromagnetic coupling topology of the voltage reactive power regulator, a source-containing two-port network model is constructed using the equivalent theorem, which serves as the basic architecture of the steady-state decision consistency model. Based on the fixed-point principle, a nonlinear implicit function equation describing the coupling relationship between series voltage injection and parallel power extraction of the voltage reactive power regulator is established as the core expression of the steady-state decision consistency model. Solving the nonlinear implicit function equation yields the steady-state voltage feasible region and equivalent voltage support mode of the voltage reactive power regulator under specific operating conditions.

[0009] Optionally, based on the steady-state decision consistency model, a linearized error discretization masking criterion is established to map the nonlinear physical characteristics of the voltage reactive power regulator into a linear voltage support mode, including: The order of magnitude relationship between the truncation error of the linearized power flow model of the distribution network and the voltage response generated by the minimum discrete adjustment step size of the voltage reactive power regulator is analyzed. Based on the aforementioned order of magnitude relationship, a masking coefficient is defined; When the masking coefficient is greater than the preset threshold, it is determined that the voltage gain generated by the physical adjustment step of the voltage reactive power regulator is greater than the linearization cutoff error. Based on the judgment results, the nonlinear physical characteristics of the voltage reactive power regulator are mapped to a linear voltage support mode by replacing the nonlinear power flow constraint with a static sensitivity kernel.

[0010] Optionally, the economically effective coverage index is used to quantify the cost-effectiveness of installing voltage and reactive power regulators at each candidate node and to identify key locations for voltage management in the distribution network.

[0011] Optionally, a sparse discrete robust programming model is constructed, with the objective function being the minimum generalized investment cost over the entire life cycle, and the constraint being the voltage safety of all nodes in the network under arbitrary source load fluctuation uncertainty scenarios. This model includes: The objective function is to minimize the generalized investment cost over the entire life cycle of the voltage reactive power regulator. The voltage safety of all nodes in the entire network under uncertain source-load fluctuation scenarios is taken as a constraint. The voltage support mode is used to describe the regulation effect of the voltage reactive power regulator on the grid voltage, transforming the nonlinear programming problem into a mixed integer linear programming problem, and thus completing the construction of a sparse discrete robust programming model.

[0012] Optionally, the sparse discrete robust programming model is solved to obtain the location and capacity setting scheme of the voltage reactive power regulator, including: The sparse discrete robust programming model is decomposed into a main problem and sub-problems using a column and constraint generation algorithm for iterative solution. The main problem is to find the optimal voltage and reactive power regulator location and capacity setting scheme under the current set of key scenarios. The sub-problem is to find the worst voltage over-limit scenario and the maximum default amount in the entire network under a fixed location scheme; By iterating alternately between the main problem and sub-problems, key scenarios are dynamically selected and cutting plane constraints are generated until the maximum default amount converges to zero, and the final planning scheme is output.

[0013] Optionally, the voltage regulation conduction characteristics are represented by a voltage regulation transmission matrix, whose matrix elements characterize the voltage control efficiency of a specific node when a voltage regulator is installed in a specific branch.

[0014] Optionally, the generalized installation cost includes fixed construction costs and variable costs related to line capacity, wherein the variable costs are determined based on the line's rated apparent power, the voltage reactive power regulator's capacity ratio coefficient, and the unit capacity cost.

[0015] On the other hand, the present invention also provides an electronic device including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0016] On the other hand, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0017] Compared with the prior art, the present invention has the following advantages and technical effects: This invention first constructs a steady-state decision consistency model considering the voltage backlash effect based on the electromagnetic coupling topology of the voltage reactive power regulator. This model can accurately quantify the voltage backlash effect unique to voltage reactive power regulators in weak grid environments. Specifically, when the device draws active power from upstream to boost downstream voltage, it generates an additional voltage drop on high-impedance lines, causing a further drop in upstream voltage—a nonlinear physical characteristic. This model avoids the physical infeasibility of planning schemes caused by neglecting the impact of parallel energy extraction on upstream voltage, ensuring the effectiveness and feasibility of the planning results in practical engineering.

[0018] This invention, based on a steady-state decision consistency model, establishes a linearized error discretization masking criterion, mapping the nonlinear physical characteristics of the voltage reactive power regulator to a linear voltage support mode. This criterion cleverly utilizes the characteristic that the voltage gain generated by the minimum discrete adjustment step size of the voltage reactive power regulator is much larger than the truncation error of the linearized power flow model, enabling complex nonlinear physical constraints to be linearized using a static sensitivity kernel. Furthermore, a column and constraint generation algorithm is employed to solve the sparse discrete robust programming model. Through iterative interaction between the main problem and subproblems, the planning problem for large-scale distribution networks under massive uncertainty scenarios can converge within seconds, significantly improving computational efficiency.

[0019] This invention further constructs an economically effective coverage index based on the impedance distribution of distribution network lines, the voltage regulation conduction characteristics of voltage regulators, the risk weight of voltage exceedance at nodes, and generalized installation costs. This index can quantify the cost-effectiveness of installing voltage regulators at each candidate node and accurately identify the key hub locations for distribution network voltage management. Based on this, and combined with linear voltage support modes, a sparse discrete robust programming model is constructed with the objective of minimizing the generalized investment cost over the entire life cycle and the constraint of voltage safety at all nodes in the network under arbitrary source-load fluctuation uncertainty scenarios. Through this model, only a very small number of key nodes need to be equipped to cover the entire network's voltage exceedance risk, while effectively resisting extreme and severe scenarios caused by dual source-load uncertainties, ensuring the voltage safety of the distribution network under all-weather conditions, and significantly reducing the investment cost of power grid upgrades and transformations. Attached Figure Description

[0020] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a topology diagram of the voltage reactive power regulator in an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the principle of voltage backlash effect in an embodiment of the present invention, wherein... Figure 2 (a) is the phasor diagram of the voltage regulation mechanism. Figure 2 (b) is a voltage regulation characteristic curve; Figure 3 This is a schematic diagram illustrating the iterative convergence of the model in an embodiment of the present invention; Figure 4 This is a flowchart illustrating the solution process for the column and constraint generation algorithm in an embodiment of the present invention. Detailed Implementation

[0021] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0022] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0023] Example 1 This embodiment provides a sparse robust planning method for voltage and reactive power regulators in distribution networks, including: Based on the electromagnetic coupling topology of the voltage reactive power regulator, a steady-state decision consistency model considering the voltage backlash effect is constructed. Based on the steady-state decision consistency model, a linearized error discretization masking criterion is established to map the nonlinear physical characteristics of the voltage reactive power regulator into a linear voltage support mode. Based on the impedance distribution of distribution network lines, the voltage regulation conduction characteristics of voltage and reactive power regulators, the risk weight of node voltage over-limit, and the generalized installation cost, an economically effective coverage index is constructed. Based on the economically effective coverage index and the linear voltage support mode, a sparse discrete robust programming model is constructed with the minimum generalized investment cost over the entire life cycle as the objective function and the voltage safety of all nodes in the network under any source load fluctuation uncertainty scenario as the constraint. Solving the sparse discrete robust programming model yields the location and capacity scheme for the voltage reactive power regulator.

[0024] As a specific implementation method, the simulated distribution network system is the IEEE 33-node distribution system, and the actual distribution systems TEST-34 and TEST-57, specifically including the following steps: Step 1: Definition and initialization of basic parameters for distribution network and new voltage-var regulator (VVR): Figure 1This is a topology diagram of the voltage reactive power regulator in this embodiment. As shown in the figure, the voltage reactive power regulator adopts a three-winding isolated electromagnetic coupling structure, including a primary-side parallel excitation winding, a secondary-side series voltage regulating winding, and a secondary-side parallel compensation winding. Through this topology, the voltage reactive power regulator can directly inject voltage vector into the line through the series winding, and can also draw power from the grid and provide reactive power support through the parallel winding, thereby achieving coordinated regulation of voltage amplitude and reactive power.

[0025] Step 11: Define the distribution network topology: Assume the distribution network is a radial network, represented as shown in the figure. ,in For a set of nodes, This is a set of branches. The total number of nodes. Define the system reference voltage. .

[0026] For any node Obtain its injected active power and reactive power Historical data or prediction range. For any branch. Obtain its resistance and reactance .

[0027] Step 12: Define the VVR topology parameters: The VVR adopts a three-winding isolated electromagnetic coupling structure, including a primary-side parallel excitation winding, a secondary-side series voltage regulating winding, and a secondary-side parallel compensation winding.

[0028] Define the set of candidate installation locations for the VVR. This refers to all branches except the source node. For nodes installed on branches... VVR is defined as the discrete turns ratio coefficient of its series transformer. The set of values Step length .

[0029] Define the generalized installation cost of VVR Its fixed construction cost And the variable costs associated with line capacity: (1) In the formula: For generalized installation costs, Fixed construction costs, including civil engineering, controller and communication module costs; For the line Rated apparent power; This is the ratio of the rated capacity of the VVR equipment to the line transmission capacity, and its value is the maximum transformation ratio coefficient. Cost per unit of rated capacity of equipment, and The product represents the cost per unit of line transmission capacity.

[0030] Step 2: Construct a VVR steady-state decision consistency model that considers voltage backlash effect: Based on the three-winding isolated electromagnetic coupling topology of VVR, a source-containing two-port network model is constructed using Thevenin's equivalent theorem. Based on the fixed-point principle, a nonlinear implicit function equation describing the coupling relationship between series voltage injection and parallel power extraction of VVR is established, and the steady-state voltage feasible region and equivalent voltage support mode of VVR under specific operating conditions are obtained by solving the equation, thus quantifying the physical limitation of the voltage backlash effect on the voltage regulation capability.

[0031] To quantify the nonlinear impact of VVR access on grid voltage, a two-port equivalent model incorporating source-grid-load-storage characteristics needs to be established.

[0032] Step 21: Construct the equivalent circuit of the source two-port network: Based on Thevenin's theorem, the upstream network of the VVR installation point is equivalent to the Thevenin potential. and equivalent impedance The downstream network is equivalent to a constant power load. .

[0033] According to Kirchhoff's laws, the input voltage of VVR and output voltage The following nonlinear coupling relationship is satisfied: (2) (3) In the formula, For load current, The internal impedance of the device. The susceptance value applied on the parallel side, λ This represents the discrete turns ratio coefficient of a series transformer.

[0034] Step 22: Derive the implicit function equation for the voltage backlash effect: By combining the equations from step 21 and eliminating intermediate variables, we obtain the implicit function equations in the complex domain that describe the steady-state characteristics of VVR: (4) The equation reveals the voltage backlash effect: the second term on the right-hand side of the equation represents the nonlinear coupling voltage drop. (Coefficient) This indicates that when VVR increases the voltage ( When the voltage regulation ratio is increased, the upstream impedance of the system will be converted to the load side by the square of the transformation ratio, which will increase the upstream voltage drop and offset part of the voltage regulation effect, i.e., "voltage backlash".

[0035] Step 23: Solve for the feasible region of steady-state voltage based on the fixed-point principle: Define the equation in step 22 as standard fixed-point form. A fixed-point iterative operator is constructed to calculate the steady-state voltage solution of VVR under specific operating conditions. : (5) In the formula: The initial voltage value is the fixed-point iteration voltage.

[0036] This yields the steady-state voltage feasible region of VVR. and specific locations Equivalent voltage support mode in the worst-case scenario : (6) In the formula, For the worst-case scenario parameter set, Configured for maximum VVR output. This represents the node voltage amplitude without VVR. The maximum effective voltage boost that VVR can provide, after considering the backlash effect, has been quantified. To determine the steady-state voltage solution operator for VVR after considering voltage backlash.

[0037] Figure 2 This is a schematic diagram illustrating the principle of the voltage backlash effect in this embodiment, wherein... Figure 2 (a) in the diagram is the phasor diagram of the voltage regulation mechanism. Figure 2 (b) in the diagram shows the voltage regulation characteristic curve. As can be seen from the phasor diagram, when the voltage regulator injects voltage through the series winding to boost the downstream voltage, it needs to draw active power from the upstream, leading to an increase in upstream current. This, in turn, generates an additional voltage drop across the upstream line impedance, causing the upstream node voltage to drop further, forming a "voltage backlash effect." The characteristic curve illustrates the nonlinear relationship between the voltage regulator's output voltage boost and the upstream voltage drop under different line impedance conditions, verifying the physical limitation of this effect on voltage regulation capability.

[0038] Figure 3 This diagram illustrates the model iteration convergence in this embodiment. It shows the convergence process when using the fixed-point iteration method to solve the steady-state decision consistency model considering voltage backlash. As the number of iterations increases, the calculated voltage value gradually approaches the steady-state solution, reflecting the numerical stability of the nonlinear implicit function equation solution and providing a theoretical basis for establishing the subsequent linearization error discretization masking criterion.

[0039] Step 3: Establish the linearization error discretization masking criterion: The order of magnitude relationship between the truncation error of the linearized power flow model of the distribution network and the voltage response generated by the minimum discrete adjustment step size of the VVR is analyzed. A masking coefficient is defined, and when the masking coefficient is greater than a preset threshold, it is determined that the voltage gain generated by the physical adjustment step size is significantly greater than the linearization truncation error. Based on this criterion, a static sensitivity kernel is used to replace the nonlinear power flow constraint, and the nonlinear physical characteristics of the VVR are mapped to a linear voltage support mode, thereby realizing the linearization and order reduction of the model.

[0040] To address the difficulty of embedding nonlinear models into planning models, this step demonstrates the feasibility of using linear models.

[0041] Step 31: Calculate the linearization truncation error: Let the voltage amplitude of the distribution network node be... It is the injected power vector function At the reference operating point Performing a first-order Taylor expansion, its linearization truncation error Lagrange remainder term The physical order of magnitude is: (7) In the formula, For short-circuit impedance, Operating voltage, This is a power disturbance. In actual distribution networks, Usually in On the order of PU.

[0042] Step 32: Calculate the voltage response with the minimum discrete adjustment step size: The VVR uses on-load tap adjustment, with the minimum adjustment step size... Its first-order direct support effect on node voltage. for: (8) In the formula, It is the differential voltage distribution rate of the tap. V nom is the rated voltage of the distribution network.

[0043] For 10kV distribution networks Approximately pu.

[0044] Step 33: Define the masking coefficient And establish guidelines: Define the masking coefficient The ratio of the physical adjustment step size response to the model-calculated background noise: (9) In the formula, The maximum value of the Lagrange remainder term for the linearized truncation error. like If the condition is met, then the discrete masking criterion is satisfied. This means that the error introduced by the linearization model is confined to the dead zone of the discrete decision variables and is insufficient to cross the boundary of the integer constraint.

[0045] Based on this principle, this embodiment uses a static sensitivity matrix in the subsequent planning model. Alternative nonlinear power flow equations: (10) In the formula: Sij The elements of the node voltage sensitivity matrix represent branches. j Voltage injection amplitude at the location For nodes i voltage amplitude The partial derivatives, It is the baseline operating point.

[0046] Step 3: Construct the Economic Effective Coverage Index (EECI): Taking into account the impedance distribution of distribution network lines, the conduction characteristics of VVR voltage regulation, the risk weight of node voltage exceeding limits, and the generalized installation cost, an economically effective coverage index is constructed. This index is used to quantify the cost-effectiveness of installing VVRs at each candidate node, identify the key hub locations for distribution network voltage management, and provide a site selection basis for sparse planning.

[0047] To guide sparse site selection, the overall value of each candidate location needs to be quantified.

[0048] Step 41: Construct the voltage-regulated transmission matrix : Matrix elements Characterization in branch Install VVR on nodes Voltage control efficiency.

[0049] For downstream nodes: .

[0050] For upstream or bypass nodes, the sensitivity of reactive power injection on the parallel side is utilized: ,in For nodes i For branch roads k Voltage sensitivity coefficient of reactive power injection, is the series-parallel coupling coefficient.

[0051] Step 42: Calculate the EECI index: Taking into account the effectiveness of regulation, node risk weights, and installation costs, candidate locations are defined. EECI: (11) In the formula, This is the set of nodes at risk of exceeding voltage limits. For nodes Importance weight, The equivalent voltage support mode calculated in step 23, This is a normalization coefficient. A higher EECI value indicates a higher cost-effectiveness ratio at that location, making it more suitable for VVR installation.

[0052] Step 5: Construct a sparse discrete robust programming model: With the objective function of minimizing the generalized investment cost over the entire life cycle of the VVR, and with the voltage safety of all nodes in the network under uncertain source-load fluctuation scenarios as the constraint, a sparse discrete robust programming model is constructed. The linearized voltage support mode obtained in step two is used to describe the regulation effect of the VVR on the grid voltage, thus transforming the nonlinear programming problem into a mixed-integer linear programming problem.

[0053] Step 51: Define decision variables and objective function: Define a binary decision variable vector ,in Indicates the location Install VVR. This indicates that you do not wish to install it.

[0054] The objective function is to minimize the generalized investment cost. : (12) In the formula: This is the set of all candidate installation locations. Candidate position k The cost is a binary decision variable that takes into account both equipment purchase costs and line capacity constraints.

[0055] Step 52: Construct a semi-infinite programming constraint system: Requirements in any uncertain scenario ( Under the polyhedral uncertainty set of source load fluctuations, the voltages of all nodes in the system All maintained at the safety threshold Inside.

[0056] Based on the linear masking criterion, the voltage constraint is described using the principle of linear superposition: (13) In the formula, For the scene The reference voltage when VVR is not installed. The lower voltage limit allowed for safe system operation. The upper limit of voltage allowed for safe system operation. The set of all nodes in the system. For the set of uncertainties in load fluctuations, For position Voltage injection to nodes The impact.

[0057] Step 6: Solve the planning model based on the Constraint-and-Column Generation Algorithm (C&CG): The sparse discrete robust programming model is decomposed into a main problem and sub-problems using a column and constraint generation algorithm for iterative solution. The main problem seeks the optimal VVR location and capacity setting scheme under the current set of key scenarios. The sub-problems seek the worst voltage overrun scenario and the maximum default amount in the entire network under a fixed location scheme. Through the alternating iteration of the main and sub-problems, key scenarios are dynamically selected and cutting plane constraints are generated until the maximum default amount converges to zero, and the final planning scheme is output.

[0058] Since the model in step 5 contains infinitely many scenario constraints, the C&CG algorithm is used to decompose it into a main problem and sub-problems for iterative solution.

[0059] Step 61: Initialization: Set the number of iterations Initialize the key scene set Set convergence threshold .

[0060] Step 62: Solve the Master Problem: In the currently known set of key scenarios Next, find the optimal location solution. This is a mixed-integer linear programming (MILP) problem: (14) In the formula: For the first The optimal addressing scheme obtained in the next iteration. This is a collection of key scenarios.

[0061] Solve using a commercial solver.

[0062] Step 63: Solve the subproblem: In fixed site selection scheme Next, we will search for the most severe risk scenarios across the entire network. and the corresponding most severe default node That is, to solve for the maximum voltage violation. : (15) In the formula, This indicates the maximum voltage violation.

[0063] This subproblem can be transformed into a two-level linear programming problem, which can then be converted into a single-level MILP solution using KKT conditions or dual transformations.

[0064] Step 64: Convergence assessment and cutting plane generation: like The current solution It has covered all risks, the algorithm has converged, and the optimal addressing scheme is output.

[0065] like This indicates the existence of uncovered blind spots. In this scenario Add to key scenario set Generate new cutting plane constraints and return to step 62, let Continue iterating.

[0066] Step 65: Output the result: Output the final set of VVR installation locations, quantity, and corresponding investment costs.

[0067] Figure 4 This is a flowchart illustrating the solution process of the column and constraint generation algorithm in this embodiment. As shown in the figure, the algorithm decomposes the sparse discrete robust programming model into a main problem and sub-problems for iterative solution: the main problem finds the optimal voltage and reactive power regulator location and capacity setting scheme under the current set of key scenarios; the sub-problems find the worst voltage over-limit scenario and the maximum default amount in the entire network under a fixed location scheme; through the alternating iteration of the main and sub-problems, key scenarios are dynamically selected and cutting plane constraints are generated until the maximum default amount converges to zero, and the final planning scheme is output.

[0068] This embodiment provides a sparse robust planning method for voltage reactive power regulators in a distribution network, which has the following beneficial effects: 1. High physical fidelity: The VVR steady-state decision consistency model constructed in this embodiment accurately quantifies the "voltage backlash effect" unique to VVR in weak power grid environments, avoiding the physical infeasibility of the planning scheme caused by ignoring the impact of parallel side energy extraction on upstream voltage, and ensuring the effectiveness of the planning results in actual engineering.

[0069] 2. High computational efficiency: The linearization error discretization masking criterion proposed in this embodiment cleverly utilizes the characteristic that the VVR discrete adjustment step size is much larger than the linearization truncation error, transforming the complex nonlinear physical model into a high-fidelity linear model, enabling the planning problem in large-scale distribution networks and massive scenarios to converge in seconds using the C&CG algorithm.

[0070] 3. Balancing economy and robustness: This embodiment, by constructing EECI and sparse robust programming models, can accurately identify key nodes in grid voltage management. Only a very small number of key nodes need to be equipped to cover the risk of voltage exceeding the limit across the entire grid. At the same time, this method can effectively resist extreme and severe scenarios caused by the dual uncertainty of source and load, ensuring the voltage safety of the distribution network under all-weather conditions and significantly reducing the investment cost of grid upgrading and transformation.

[0071] To demonstrate its feasibility, this embodiment compares the voltage quality indicators of three nodes—IEEE-33, TEST-34, and TEST-57—before and after applying the method of this embodiment, as shown in Table 1. The data in the table shows that before the treatment, the average voltage deviations for the three nodes were 3.05%, 6.44%, and 4.83%, respectively, with maximum deviations reaching 8.10%, 9.01%, and 9.68%, respectively. After treatment using the method of this invention, the average deviations decreased to 1.08%, 1.09%, and 1.41%, respectively, and the maximum deviations decreased to 4.59%, 4.32%, and 4.86%, respectively. The results indicate that the method proposed in this embodiment can effectively suppress voltage exceedances and significantly improve the voltage quality of the distribution network.

[0072] Table 1 On the other hand, this embodiment also provides an electronic device, including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0073] On the other hand, this embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0074] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A sparse robust planning method for voltage reactive power regulators in power distribution networks, characterized in that, include: Based on the electromagnetic coupling topology of the voltage reactive power regulator, a steady-state decision consistency model considering the voltage backlash effect is constructed. Based on the steady-state decision consistency model, a linearized error discretization masking criterion is established to map the nonlinear physical characteristics of the voltage reactive power regulator into a linear voltage support mode. Based on the impedance distribution of distribution network lines, the voltage regulation conduction characteristics of voltage and reactive power regulators, the risk weight of node voltage over-limit, and the generalized installation cost, an economically effective coverage index is constructed. Based on the economically effective coverage index and the linear voltage support mode, a sparse discrete robust programming model is constructed with the minimum generalized investment cost over the entire life cycle as the objective function and the voltage safety of all nodes in the network under any source load fluctuation uncertainty scenario as the constraint. Solving the sparse discrete robust programming model yields the location and capacity scheme for the voltage reactive power regulator.

2. The method according to claim 1, characterized in that, Based on the electromagnetic coupling topology of the voltage reactive power regulator, a steady-state decision consistency model considering the voltage backlash effect is constructed, including: Based on the three-winding isolated electromagnetic coupling topology of the voltage reactive power regulator, a source-containing two-port network model is constructed using the equivalent theorem, which serves as the basic architecture of the steady-state decision consistency model. Based on the fixed-point principle, a nonlinear implicit function equation describing the coupling relationship between series voltage injection and parallel power extraction of the voltage reactive power regulator is established as the core expression of the steady-state decision consistency model. Solving the nonlinear implicit function equation yields the steady-state voltage feasible region and equivalent voltage support mode of the voltage reactive power regulator under specific operating conditions.

3. The method according to claim 1, characterized in that, Based on the steady-state decision consistency model, a linearized error discretization masking criterion is established to map the nonlinear physical characteristics of the voltage reactive power regulator into a linear voltage support mode, including: The order of magnitude relationship between the truncation error of the linearized power flow model of the distribution network and the voltage response generated by the minimum discrete adjustment step size of the voltage and reactive power regulator is analyzed. Based on the aforementioned order of magnitude relationship, a masking coefficient is defined; When the masking coefficient is greater than the preset threshold, it is determined that the voltage gain generated by the physical adjustment step of the voltage reactive power regulator is greater than the linearization cutoff error. Based on the judgment results, the nonlinear power flow constraint is replaced by a static sensitivity kernel, and the nonlinear physical characteristics of the voltage reactive power regulator are mapped into a linear voltage support mode.

4. The method according to claim 1, characterized in that, The economically effective coverage index is used to quantify the cost-effectiveness of installing voltage and reactive power regulators at each candidate node and to identify key locations for voltage management in the distribution network.

5. The method according to claim 1, characterized in that, A sparse discrete robust programming model is constructed with the objective function of minimizing the generalized investment cost over the entire life cycle and the constraint of voltage safety for all nodes in the network under arbitrary source-load fluctuation uncertainty. This model includes: The objective function is to minimize the generalized investment cost over the entire life cycle of the voltage reactive power regulator. The voltage safety of all nodes in the entire network under uncertain source-load fluctuation scenarios is taken as a constraint. The voltage support mode is used to describe the regulation effect of the voltage reactive power regulator on the grid voltage, transforming the nonlinear programming problem into a mixed integer linear programming problem, and thus completing the construction of a sparse discrete robust programming model.

6. The method according to claim 1, characterized in that, Solving the sparse discrete robust programming model yields the location and capacity selection scheme for the voltage reactive power regulator, including: The sparse discrete robust programming model is decomposed into a main problem and sub-problems using a column and constraint generation algorithm for iterative solution. The main problem is to find the optimal voltage and reactive power regulator location and capacity setting scheme under the current set of key scenarios. The sub-problem is to find the worst voltage over-limit scenario and the maximum default amount in the entire network under a fixed location scheme; By iterating alternately between the main problem and sub-problems, key scenarios are dynamically selected and cutting plane constraints are generated until the maximum default amount converges to zero, and the final planning scheme is output.

7. The method according to claim 1, characterized in that, The voltage regulation conduction characteristics are represented by a voltage regulation transmission matrix, whose matrix elements characterize the voltage control efficiency of a specific node when a voltage regulator is installed in a specific branch.

8. The method according to claim 1, characterized in that, The generalized installation cost includes fixed construction costs and variable costs related to line capacity. The variable costs are determined based on the line's rated apparent power, the voltage and reactive power regulator's capacity ratio coefficient, and the unit capacity cost.

9. An electronic device comprising a memory, a processor, and a computing program stored in the memory and executable on the processor, characterized in that, When the processor executes the computing program, it implements the method of any one of claims 1-8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1-8.

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