A low-voltage photovoltaic feasible region solving method and system considering slack node change
By considering relaxed node variations and time-by-time uncertainties in the solution of the feasible region of low-voltage photovoltaic (PV) systems, and utilizing sensitivity models and scenario analysis methods, the error problem in the solution of the feasible region of low-voltage PV systems was solved, achieving efficient and accurate PV grid connection capacity assessment.
Patent Information
- Application Number
- CN202611544086.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-10-08
- Publication Date
- 2026-11-06
AI Technical Summary
In existing methods for solving the feasible region of low-voltage photovoltaic systems, the common coupling point of medium and low voltage is treated as a voltage-constant relaxation node, which leads to large errors in the results and makes it difficult to reflect the hourly uncertainty of load and photovoltaic output.
Based on the voltage squared-active power sensitivity model of medium-voltage side nodes, a linearized power flow model of low-voltage distribution network considering the changes in relaxed nodes is established. Combining historical hourly load and solar radiation data, typical scenarios are constructed through kernel density estimation and Monte Carlo sampling to solve the photovoltaic feasible region for single time period and all time period.
It improves the accuracy and efficiency of solving the feasible region of low-voltage photovoltaic systems, can reflect the hourly uncertainty of load and photovoltaic output, reduces the amount of computation, and achieves fast and accurate solutions.
Smart Images
Figure CN123049946A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of low-voltage photovoltaic feasible region solution technology, specifically relating to a method and system for solving low-voltage photovoltaic feasible regions that considers the changes in relaxed nodes. Background Technology
[0002] The installed capacity of distributed photovoltaic (PV) power in distribution networks is growing rapidly. However, the high proportion of distributed PV access may lead to safety hazards such as node voltage exceeding limits, backflow of power, and insufficient line current carrying capacity. These physical constraints have become a rigid bottleneck restricting the further large-scale grid connection of new energy sources. Against this backdrop, scientifically assessing the distributed PV carrying capacity of distribution networks is particularly crucial. Typical methods for characterizing PV carrying capacity fall into two main categories: one starts from the overall carrying capacity of the distribution network and describes the PV carrying capacity through a statistical method of numerical accumulation, the result of which is the maximum value of the total PV access capacity at all grid-connected locations. Method one models the distributed power source acceptance capacity assessment problem as a multi-objective problem, where one objective function corresponds to maximizing the total access capacity of distributed power sources in a set of known grid-connected locations, while the other objective function minimizes total energy consumption. Method two uses the Monte Carlo random method to simulate the scenario of large-scale PV access in the distribution network, thereby fully assessing the PV absorption capacity of the distribution network. However, this method cannot provide a clear boundary for the feasible PV access capacity associated with each location. Another approach starts with the spatial coupling relationship of the maximum access capacity of distribution network nodes, using multidimensional geometric methods to construct a "photovoltaic feasible region" to characterize the carrying capacity. Compared with numerical point methods, the feasible region method can provide comprehensive information about the entire space, realizing a correlation between photovoltaic access location and access capacity. Method three represents the carrying capacity as a photovoltaic access feasible region in a high-dimensional space, uses a multi-objective optimization method to obtain the Pareto solution set, and then interpolates to obtain the safety boundary. However, this method can only obtain discrete safety boundary points and has a heavy computational burden, making it difficult to solve on a large scale. Method four uses an analytical method to solve the photovoltaic feasible region. By linearizing the power flow constraints, the distribution network safety boundary is transformed into a system of linear inequalities with photovoltaic capacity as the variable, thus enabling a fast solution to the feasible region while ensuring accuracy. However, when solving the low-voltage photovoltaic feasible region, this method usually simplifies the medium- and low-voltage common coupling points to relaxed nodes with constant voltage. This simplification leads to a large error in the solved photovoltaic feasible region results. Summary of the Invention
[0003] The purpose of this invention is to address the problems in existing low-voltage photovoltaic feasible region solution methods, which typically treat the medium- and low-voltage common junction points as voltage-constant relaxation nodes, leading to large error in the results and difficulty in reflecting the hourly uncertainty of load and photovoltaic output. This invention proposes a low-voltage photovoltaic feasible region solution method and system that considers the changes in relaxation nodes.
[0004] The technical solution of the present invention is as follows: Firstly, a method for solving the feasible region of low-voltage photovoltaic systems considering changes in relaxation nodes, comprising the following steps: Obtain the topology, line parameters, and load parameters of the low-voltage distribution network in the target area, and establish a node voltage squared-active power sensitivity model on the medium-voltage side based on the linearized DistFlow power flow equation. Sensitivity results were obtained based on the nodal voltage squared-active power sensitivity model, and a linearized DistFlow power flow model for low-voltage distribution networks considering the changes in relaxed nodes was established. Based on the linearized DistFlow power flow model of low-voltage distribution networks, safety operation constraints for low-voltage distribution networks are constructed. The state variables in the safety operation constraints of the low-voltage distribution network are analyzed to obtain a deterministic photovoltaic feasible region model containing only the photovoltaic access capacity vector; Based on historical hourly load data and solar radiation data, typical random scenarios for each time period were constructed using kernel density estimation and Monte Carlo sampling methods. Substitute typical random scenarios of each time period into the deterministic photovoltaic feasible region linear model to solve the scenario-based photovoltaic feasible region for a single time period, and obtain the comprehensive photovoltaic feasible region for a single time period through scenario intersection; The intersection of the comprehensive photovoltaic feasible regions for multiple time periods is obtained to obtain the full-time comprehensive photovoltaic feasible region that takes into account the changes in relaxed nodes and hourly operational uncertainties.
[0005] As a preferred method, the specific approach for establishing a node voltage squared-active power sensitivity model on the medium-voltage side is as follows: Construct a node-branch association matrix excluding the head node. and define the matrix The linearized DistFlow power flow equations are established as follows:
[0006] in, This represents a column vector of active power in each branch. This represents the active power of the load connected to each node. This represents a column vector representing the reactive power in each branch. This represents the reactive power of the load connected to each node. This represents the column vector of voltage magnitudes at nodes other than PPC. Indicates the voltage amplitude at point PPC. This represents the column vector of resistance for each branch. The Hadamard product symbol indicates the multiplication of corresponding elements in a matrix. This represents the column vector of reactance for each branch. Indicates transpose; When the active power of the node changes by Δ P At that time, according to the linearized DistFlow power flow equation, we get:
[0007] Therefore, the node voltage squared-active power sensitivity model is obtained as follows:
[0008] in, The change in active power at the node is represented by Δ. P The subsequent column vector of node voltage magnitudes It represents the sensitivity coefficient of the active power divided by the square of the voltage at the medium-voltage side node.
[0009] As a preferred method, the specific approach for establishing a linearized DistFlow power flow model for low-voltage distribution networks that considers changes in relaxed nodes is as follows: The squared change in voltage at relaxed node n is calculated based on the nodal voltage squared-active power sensitivity model. Substituting the squared voltage change at the relaxed nodes into the linearized DistFlow power flow equations of the low-voltage distribution network, we obtain a power flow model for the low-voltage distribution network that considers the changes at the relaxed nodes:
[0010] in, This represents the voltage at a node in a low-voltage distribution network. This represents the data in the nth row and nth column of the K matrix, which is a matrix representing the squared voltage of the medium-voltage side node versus the active power sensitivity coefficient. Represents a column vector consisting entirely of 1s. Indicates transpose. This represents the photovoltaic vector connected to a low-voltage distribution network node.
[0011] Preferably, the constraints for safe operation of low-voltage distribution networks include power flow equality constraints and distribution network safe operation inequality constraints. The power flow equality constraint is a linearized DistFlow power flow model for low-voltage distribution networks that takes into account the changes in relaxed nodes. The inequality constraints for the safe operation of the power distribution network are:
[0012] in, For node voltage constraints and Indicates the upper and lower limits of the voltage constraint; Due to line capacity constraints, Current carrying capacity expressed in the form of line power; This indicates the maximum current carrying capacity in the form of line power.
[0013] As a preferred method, the specific approach to analytically transforming the state variables in the linearized DistFlow power flow model of the low-voltage distribution network to obtain a deterministic photovoltaic feasible region model containing only the photovoltaic access capacity vector is as follows: The result is obtained by squaring the node voltage constraints: ; Substituting the low-voltage distribution network power flow model that considers relaxed node variations into the squared-processed node voltage constraints, focusing only on the upper limit constraint and simplifying, we obtain:
[0014] in, Represents the photovoltaic injected power vector. and Represents the node coupling matrix and voltage margin vector based on voltage constraints; After expanding the line capacity carrying capacity constraint, rearranging terms and performing matrix operations, we obtain the simplified line capacity carrying capacity constraint: ; By substituting variables into the adjusted line current carrying capacity constraints, we obtain:
[0015]
[0016]
[0017] in, and Represents the node coupling relationship matrix and the line current carrying capacity margin vector based on line current carrying capacity constraints; based on and A set of linear inequalities for the deterministic photovoltaic feasible region, containing only the photovoltaic access capacity vector, is established, i.e., the deterministic photovoltaic feasible region model is: .
[0018] As a preferred method, based on historical hourly load data and solar radiation data, the method of constructing typical random scenarios for each time period using kernel density estimation and Monte Carlo sampling is as follows: Historical data on photovoltaic output and user load in the target area over the past year were selected as the basic dataset, and the day was divided into multiple time periods for time-segmented analysis. The probability density functions of photovoltaic power output and load data for each time period are constructed using the kernel density estimation method. By integrating the probability density function, the cumulative distribution function of photovoltaic power output and load level for each time period is obtained; Monte Carlo sampling was performed on the cumulative distribution function of photovoltaic power output and load level for each time period to generate multiple joint scenario samples for each time period, thus completing the construction of typical random scenarios for each time period.
[0019] As a preferred approach, the method of substituting typical random scenarios of each time period into a deterministic linear model of photovoltaic feasible region to solve the scenario-based photovoltaic feasible region for a single time period, and obtaining the comprehensive photovoltaic feasible region for a single time period through the intersection of scenarios, is as follows: The node coupling matrix is independent of time and scenario; only the voltage margin vector and line current carrying capacity vector are constrained to change with the scenario. Therefore, for the s-th scenario in time period t, the photovoltaic feasible region is:
[0020] in, This represents the node coupling matrix based on voltage constraints. This represents the node coupling matrix based on line current carrying capacity constraints. Represents the photovoltaic injected power vector. This represents the equivalent voltage margin vector for the s-th scenario in time period t. This represents the equivalent line carrying capacity margin vector for the s-th scenario in time period t. This represents the photovoltaic power output coefficient in the s-th scenario during time period t. Represents the equivalent comprehensive margin vector for the s-th scenario in time period t; Solve for the photovoltaic feasible region for all scenarios in time period t, and take the intersection of the photovoltaic feasible regions for all scenarios to obtain the comprehensive photovoltaic feasible region for time period t:
[0021] in, , This represents the minimum overall margin vector for time period t. , r Represents the first in the vector r Each element.
[0022] As a preferred option, the full-time integrated photovoltaic feasible region considers relaxation node variations and hourly operational uncertainties. for:
[0023] in, , This represents the node coupling matrix based on voltage constraints. This represents the node coupling matrix based on line current carrying capacity constraints. Represents the photovoltaic injected power vector. Represents the minimum overall margin vector over the entire time period. , r Represents the first in the vector r Each element.
[0024] The beneficial effects of this invention are: 1. This invention is based on the voltage squared-active power sensitivity of medium-voltage side nodes, which can explicitly consider the relaxation node changes of the medium- and low-voltage common coupling points when solving the feasible region of low-voltage photovoltaics, thereby avoiding the error caused by the traditional method of simplifying it to constant voltage nodes and improving the accuracy of the solution results of low-voltage photovoltaics. On this basis, by using the linearized DistFlow power flow equations, the node voltage constraints and line current carrying capacity constraints are uniformly transformed into a set of linear inequalities containing only photovoltaic access capacity, which reduces the amount of computation caused by repeated power flow calculations and improves the solution efficiency.
[0025] 2. This invention combines historical hourly load and solar radiation data, constructs typical scenarios through kernel density estimation and Monte Carlo sampling, and solves the comprehensive photovoltaic feasible region using single-time-period scenario intersection and multi-time-period intersection methods. This effectively reflects the hourly uncertainty of load and photovoltaic output, and is closer to actual operating conditions. At the same time, since the node coupling relationship matrix remains consistent under different scenarios and time periods, the feasible region can be compressed by taking the minimum value of each element of the constraint right-hand side. This reduces the constraint dimension while ensuring the accuracy of the results, thereby achieving a fast and accurate solution for the low-voltage photovoltaic feasible region that considers relaxed node changes and hourly uncertainties.
[0026] Secondly, a low-voltage photovoltaic feasible region solution system considering the variation of relaxed nodes includes: The first module is used to obtain the topology, line parameters and load parameters of the low-voltage distribution network in the target area, and to establish a node voltage square-active power sensitivity model on the medium-voltage side based on the linearized DistFlow power flow equation. The second module is used to obtain sensitivity results based on the node voltage squared-active power sensitivity model and to establish a linearized DistFlow power flow model for low-voltage distribution networks that takes into account the changes in relaxed nodes. The third module is used to construct safety operation constraints for low-voltage distribution networks based on the linearized DistFlow power flow model of low-voltage distribution networks. The fourth module is used to analyze the state variables in the safety operation constraints of the low-voltage distribution network to obtain a deterministic photovoltaic feasible region model containing only the photovoltaic access capacity vector. The fifth module is used to construct typical random scenarios for each time period based on historical hourly load data and solar radiation data, using kernel density estimation and Monte Carlo sampling methods. The sixth module is used to substitute typical random scenarios of each time period into the deterministic photovoltaic feasible region linear model, solve the scenario-based photovoltaic feasible region for a single time period, and obtain the comprehensive photovoltaic feasible region for a single time period through the intersection of scenarios; The seventh module is used to find the intersection of the comprehensive photovoltaic feasible regions for multiple time periods, so as to obtain the comprehensive photovoltaic feasible region for all time periods that takes into account the changes in relaxed nodes and hourly operational uncertainties.
[0027] Thirdly, a non-transitory computer-readable storage medium is provided that stores computer instructions for causing a computer to perform the method as described in the first aspect. Attached Figure Description
[0028] Figure 1 The diagram shows a low-voltage distribution network with 53 nodes.
[0029] Figure 2 The diagram shows a flowchart for solving the feasible region of low-voltage photovoltaic systems, taking into account the changes in relaxed nodes.
[0030] Figure 3 The figure shown is a three-dimensional schematic diagram of the photovoltaic feasible region solution considering the changes in relaxed nodes, obtained by analytical method.
[0031] Figure 4 The image shown is a cross-sectional view of node 43 when a 0kW photovoltaic system is connected.
[0032] Figure 5 The image shown is a cross-sectional view of node 51 when a 0kW photovoltaic system is connected.
[0033] Figure 6 The image shown is a cross-sectional view of node 38 when a 0kW photovoltaic system is connected.
[0034] Figure 7 The diagram shows the probability distribution of photovoltaic power output.
[0035] Figure 8 The diagram shows the probability distribution of load levels.
[0036] Figure 9 The image shown is a graph of the load sampling results at time 12.
[0037] Figure 10 The image shown is a graph of the photovoltaic sampling results at time 12. Detailed Implementation
[0038] Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the drawings are merely exemplary and are intended to illustrate the principles and spirit of the invention, and are not intended to limit the scope of the invention.
[0039] Example 1: This invention proposes a method for solving the feasible region of low-voltage photovoltaic (PV) systems, considering relaxed node variations and hourly uncertainties. First, the topology and parameter information of the medium- and low-voltage distribution network are obtained. Based on the linearized DistFlow power flow equations, the node voltage squared-active power sensitivity is derived on the medium-voltage side. Then, this sensitivity is used to establish a linearized DistFlow power flow model of the low-voltage distribution network considering relaxed node variations, and node voltage constraints and line current carrying capacity constraints are further constructed. On this basis, the system state variables are analytically transformed into a system of linear inequalities containing only PV access capacity, yielding a deterministic PV feasible region. Finally, combining historical hourly load and solar radiation data, typical scenarios are constructed through kernel density estimation and Monte Carlo sampling to further solve the comprehensive PV feasible region for single-time periods and all-time periods.
[0040] by Figure 1 Taking a low-voltage distribution network with 53 nodes as an example, a method for solving the feasible region of low-voltage photovoltaic power considering the variation of relaxed nodes is proposed, such as... Figure 2 As shown, it includes the following steps: S1. Obtain the topology, line parameters, and load parameters of the low-voltage distribution network in the target area. Based on the linearized DistFlow power flow equation, establish a node voltage squared-active power sensitivity model on the medium-voltage side. S2. Obtain the sensitivity results based on the node voltage squared-active power sensitivity model, and establish a linearized DistFlow power flow model for low-voltage distribution networks that considers the changes in relaxed nodes; S3. Based on the linearized DistFlow power flow model of low-voltage distribution networks, construct safety operation constraints for low-voltage distribution networks; S4. Analyze the state variables in the safety operation constraints of the low-voltage distribution network to obtain a deterministic photovoltaic feasible region model containing only the photovoltaic access capacity vector; S5. Based on historical hourly load data and solar radiation data, typical random scenarios for each time period are constructed using kernel density estimation and Monte Carlo sampling methods; S6. Substitute typical random scenarios for each time period into the deterministic photovoltaic feasible region linear model to solve the scenario-based photovoltaic feasible region for a single time period, and obtain the comprehensive photovoltaic feasible region for a single time period through the intersection of scenarios; S7. Find the intersection of the comprehensive photovoltaic feasible regions for multiple time periods to obtain the full-time comprehensive photovoltaic feasible region that takes into account the changes in relaxed nodes and hourly operational uncertainties.
[0041] In this embodiment, step S1 specifically includes: To disregard angle information, this embodiment of the invention uses a linearized DistFlow power flow equation: in, Indicates a branchl Active power in Indicates all branches l End node j Connecting branch Active power in Indicates a branch l End node j The active power of the connected load, Indicates a branch l reactive power in Indicates all branches l End node j Connecting branch reactive power in Indicates a branch l End node j The reactive power of the connected load, Indicates a branch l The resistance in Indicates a branch l The reactance in Represents a node j voltage amplitude, Represents a node i The voltage amplitude is used to introduce a node-branch correlation matrix excluding the first node. and define the matrix ,get:
[0042] In this formula, all operations involving the squaring of a matrix represent squaring each element of the matrix.
[0043] When the active power of the node changes At that time, based on the introduction of a node-branch association matrix that does not include the head node. The DistFlow power flow equations are obtained as follows:
[0044] The node voltage squared-active power sensitivity model is obtained as follows:
[0045] in, It represents the node voltage squared - active power sensitivity coefficient.
[0046] In this embodiment, step S2 specifically includes: When in Figure 1After photovoltaic power is connected to the low-voltage distribution network, the DistFlow equation of the low-voltage distribution network needs to consider the changes of the relaxation node (i.e., node 31 in the medium-voltage distribution network). Based on the node voltage square-active power sensitivity model, the voltage square change of node 31 can be obtained as follows:
[0047] in, This indicates the voltage amplitude at node 31 on the medium-voltage side. Let the data in the 31st row and 31st column of matrix K be represented by a column vector consisting entirely of 1s. Then, after photovoltaic power is connected to the substation area below the medium-voltage node 31, the power change at the medium-voltage node 31 can be expressed as: , This represents the column vector of photovoltaic (PV) nodes connected to the low-voltage distribution network, where m represents the number of low-voltage distribution network nodes.
[0048] The linear DistFlow equation considering the changes in relaxed nodes in a low-voltage distribution network can be obtained by using the voltage square change equation of node 31:
[0049] in, This indicates the voltage of a node in a low-voltage distribution network.
[0050] In this embodiment, the safety operation constraints of the low-voltage distribution network in step S3 include power flow equality constraints and distribution network safety operation inequality constraints. Specifically, the linear DistFlow equation considering relaxed node variations in the low-voltage distribution network is used as the power flow constraint. Node voltage constraints and line current carrying capacity constraints are used as the distribution network safety operation inequality constraints.
[0051] in, and Indicates the upper and lower limits of the voltage constraint; Current carrying capacity expressed in the form of line power; This indicates the maximum current carrying capacity in the form of line power.
[0052] In this embodiment, the key to analytically solving the feasible region is to incorporate the system state variables (such as node voltages) constrained by the inequality for safe operation of the distribution network. Current carrying capacity in line power form Equivalent substitution to include only decision variables (node access photovoltaic) The expression.
[0053] For the node voltage constraint, we first square it to obtain: ; Substituting the power flow constraints (the linear DistFlow equations considering relaxed node changes in low-voltage distribution networks) into the equations, and focusing only on the upper bound constraints, we obtain: ; Simplifying the above equations yields a set of vectors related to photovoltaic injected power. Linear inequalities:
[0054] in, and This represents the node coupling matrix and voltage margin vector based on voltage constraints. .
[0055] For the line current carrying capacity constraint, expanding the line current carrying capacity constraint yields: ; By rearranging terms and performing matrix operations on the above equation, we can obtain: ; By substituting variables into the above formula, we can obtain:
[0056] in, and This represents the node coupling matrix and the line current carrying capacity margin vector based on line current carrying capacity constraints. , .
[0057] Finally, the final expression for the photovoltaic feasible region is:
[0058] Based on the final expression of the photovoltaic feasible region, the vertex search method is used to draw the graph. Figure 1 The feasible region of photovoltaic power generation at nodes 38, 43, and 51 in the low-voltage distribution network is solved, and the results are as follows: Figure 3 , Figure 4 , Figure 5 and Figure 6 As shown in the figure. Analysis shows that the calculation result has a very small error, remaining within 10%.
[0059] In this embodiment, in practical engineering applications, photovoltaic power and loads in the distribution network exhibit significant randomness and intermittency, therefore, probability density function modeling is required to describe their uncertainty. Step S5 specifically involves: First, historical photovoltaic (PV) output and user load data for the target area over the past year were selected as the basic dataset. The data sampling frequency was set to 1 hour, dividing the day into 24 time periods for time-segmented analysis. For the PV output and load data of each time period, a cumulative distribution function was constructed using kernel density estimation. Kernel density estimation achieves nonparametric fitting of the data distribution through the superposition of kernel functions, requiring no pre-defined distribution form and adaptively capturing the probabilistic characteristics of the data. Its core expression is:
[0060] In the formula, For kernel functions; for K exist x The probability density function at that location; m The total number of samples; h For sampling bandwidth, For the first i The values of each sample.
[0061] The probability distribution function of photovoltaic power output and load level is as follows: Figure 7 and Figure 8 As shown. By integrating the kernel density estimation results, the cumulative distribution function of photovoltaic power output and load level for each time period can be obtained. and , .
[0062] For 24 time periods and Monte Carlo sampling was performed separately, generating 200 samples for each time period. The sampling results at 12 noon are shown below. Figure 9 and Figure 10 As shown.
[0063] In this embodiment, step S6 specifically includes: Since sunlight is mainly concentrated between 8:00 and 17:00, this embodiment of the invention only performs hourly solutions for the photovoltaic feasible region during this period. For any given time period... In step S5, random samples of load levels and random samples of illumination radiation were constructed respectively, and 200 joint scenes were generated for each time period using Monte Carlo sampling. For the first... t Time period s The photovoltaic feasible region for each scenario can be obtained by solving step S4:
[0064] in, This represents the photovoltaic output coefficient at this point. Analysis of the above formula shows that the node coupling matrix is independent of time and scenario; therefore, the formula... It can be transformed into the following form:
[0065] For the t The 200 scenarios constructed within the time period can be solved to obtain 200 solutions as shown in the formula. The photovoltaic feasible region inequality expression shown is sufficient to find the inequality satisfying the condition by taking the intersection of the photovoltaic feasible regions of these 200 scenarios. t The photovoltaic feasible region under all safe operation constraints during the time period, namely:
[0066] in, , , , r Represents the first in the vector r Each element.
[0067] In this embodiment, step S7 specifically includes: After obtaining the comprehensive photovoltaic feasible region for each time period from 8:00 to 17:00, the intersection of the comprehensive photovoltaic feasible regions for multiple time periods is further calculated to obtain the daytime full-time photovoltaic feasible region. Since the node coupling relationship matrix on the left side of the photovoltaic feasible region remains consistent across different time periods, the same approach as finding the intersection of the single-time photovoltaic feasible regions can be used to solve the multi-time period photovoltaic feasible region. The inequality form of the full-time comprehensive photovoltaic feasible region can be expressed as:
[0068] in, Therefore, the daytime integrated photovoltaic feasible region, which ultimately considers the changes in relaxed nodes and hourly operational uncertainties, can be expressed as:
[0069] The above equation is the final expression of the feasible region for low-voltage photovoltaic systems, taking into account the changes in relaxed nodes and the uncertainty of hourly operation, as proposed in this invention.
[0070] Example 2: Based on Example 1, this embodiment of the invention provides a low-voltage photovoltaic feasible region solution system that considers the variation of relaxed nodes. This system can be used to implement the low-voltage photovoltaic feasible region solution method considering the variation of relaxed nodes as described in the foregoing embodiments. The system includes: The first module is used to obtain the topology, line parameters and load parameters of the low-voltage distribution network in the target area, and to establish a node voltage square-active power sensitivity model on the medium-voltage side based on the linearized DistFlow power flow equation. The second module is used to obtain sensitivity results based on the node voltage squared-active power sensitivity model and to establish a linearized DistFlow power flow model for low-voltage distribution networks that takes into account the changes in relaxed nodes. The third module is used to construct safety operation constraints for low-voltage distribution networks based on the linearized DistFlow power flow model of low-voltage distribution networks. The fourth module is used to analyze the state variables in the safety operation constraints of the low-voltage distribution network to obtain a deterministic photovoltaic feasible region model containing only the photovoltaic access capacity vector. The fifth module is used to construct typical random scenarios for each time period based on historical hourly load data and solar radiation data, using kernel density estimation and Monte Carlo sampling methods. The sixth module is used to substitute typical random scenarios of each time period into the deterministic photovoltaic feasible region linear model, solve the scenario-based photovoltaic feasible region for a single time period, and obtain the comprehensive photovoltaic feasible region for a single time period through the intersection of scenarios; The seventh module is used to find the intersection of the comprehensive photovoltaic feasible regions for multiple time periods, so as to obtain the comprehensive photovoltaic feasible region for all time periods that takes into account the changes in relaxed nodes and hourly operational uncertainties.
[0071] According to embodiments of the present invention, the present invention also provides an electronic device, a readable storage medium, and a computer program product.
[0072] In an exemplary embodiment, an electronic device includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method as described in Embodiment 1 above.
[0073] In an exemplary embodiment, the readable storage medium may be a non-transitory computer-readable storage medium storing computer instructions for causing the computer to perform the method described in Embodiment 1 above.
[0074] In an exemplary embodiment, the computer program product includes a computer program that, when executed by a processor, implements the method described in Embodiment 1 above.
[0075] The program code used to implement the methods of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code can be executed entirely on the machine, partially on the machine, as a standalone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.
[0076] In the context of this invention, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.
[0077] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor); and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the computer. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).
[0078] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as a data server), or computing systems that include middleware components (e.g., an application server), or computing systems that include frontend components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with embodiments of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., a communication network). Examples of communication networks include local area networks (LANs), wide area networks (WANs), and the Internet.
[0079] Computer systems can include clients and servers. Clients and servers are generally located far apart and typically interact via communication networks. Client-server relationships are created by computer programs running on the respective computers and having a client-server relationship with each other. Servers can be cloud servers, servers in distributed systems, or servers incorporating blockchain technology.
[0080] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.
Claims
1. A method for solving the feasible region of low-voltage photovoltaic systems considering the variation of relaxed nodes, characterized in that, Includes the following steps: Obtain the topology, line parameters, and load parameters of the low-voltage distribution network in the target area. Based on the linearized DistFlow power flow equation, establish a node voltage squared-active power sensitivity model on the medium-voltage side. Sensitivity results were obtained based on the nodal voltage squared-active power sensitivity model, and a linearized DistFlow power flow model for low-voltage distribution networks considering the changes in relaxed nodes was established. Based on the linearized DistFlow power flow model of low-voltage distribution networks, safety operation constraints for low-voltage distribution networks are constructed. The state variables in the safety operation constraints of the low-voltage distribution network are analyzed to obtain a deterministic photovoltaic feasible region model containing only the photovoltaic access capacity vector; Based on historical hourly load data and solar radiation data, typical random scenarios for each time period were constructed using kernel density estimation and Monte Carlo sampling methods. Substitute typical random scenarios of each time period into the deterministic photovoltaic feasible region linear model to solve the scenario-based photovoltaic feasible region for a single time period, and obtain the comprehensive photovoltaic feasible region for a single time period through scenario intersection; The intersection of the comprehensive photovoltaic feasible regions for multiple time periods is obtained to obtain the full-time comprehensive photovoltaic feasible region that takes into account the changes in relaxed nodes and hourly operational uncertainties.
2. The method for solving the feasible region of low-voltage photovoltaic systems considering the variation of relaxed nodes according to claim 1, characterized in that, The specific method for establishing a node voltage squared-active power sensitivity model on the medium-voltage side is as follows: Construct a node-branch association matrix excluding the head node. and define the matrix The linearized DistFlow power flow equations are established as follows: in, This represents a column vector of active power in each branch. This represents the active power of the load connected to each node. This represents a column vector representing the reactive power in each branch. This represents the reactive power of the load connected to each node. This represents the column vector of voltage magnitudes at nodes other than PPC. This indicates the voltage amplitude at point PPC. This represents the column vector of resistance for each branch. This is the Hadamard product symbol, indicating the multiplication of corresponding elements in a matrix. This represents the column vector of reactance for each branch. Indicates transpose; When the active power of the node changes Δ P At that time, according to the linearized DistFlow power flow equation, we get: Therefore, the node voltage squared-active power sensitivity model is obtained as follows: in, The change in active power at the node is represented by Δ. P The subsequent column vector of node voltage magnitudes It represents the sensitivity coefficient of the active power divided by the square of the voltage at the medium-voltage side node.
3. The method for solving the feasible region of low-voltage photovoltaic systems considering the variation of relaxed nodes according to claim 2, characterized in that, The specific method for establishing a linearized DistFlow power flow model for low-voltage distribution networks that considers changes in relaxed nodes is as follows: The squared change in voltage at relaxed node n is calculated based on the nodal voltage squared-active power sensitivity model. Substituting the squared voltage change at the relaxed nodes into the linearized DistFlow power flow equations of the low-voltage distribution network, we obtain a power flow model for the low-voltage distribution network that considers the changes at the relaxed nodes: in, This represents the voltage at a node in a low-voltage distribution network. This represents the data in the nth row and nth column of the K matrix, which is a matrix representing the squared voltage of the medium-voltage side node versus the active power sensitivity coefficient. Represents a column vector consisting entirely of 1s. Indicates transpose. This represents the photovoltaic vector connected to a low-voltage distribution network node.
4. The method for solving the feasible region of low-voltage photovoltaic systems considering the variation of relaxed nodes according to claim 3, characterized in that, Constraints for the safe operation of low-voltage distribution networks include power flow equality constraints and distribution network safety operation inequality constraints. The power flow equality constraint is a linearized DistFlow power flow model for low-voltage distribution networks that takes into account the changes in relaxed nodes. The inequality constraints for safe operation of the power distribution network are: in, For node voltage constraints. and Indicates the upper and lower limits of the voltage constraint; Due to line capacity constraints, Current carrying capacity expressed in the form of line power; This indicates the maximum current carrying capacity in the form of line power.
5. The method for solving the feasible region of low-voltage photovoltaic systems considering the variation of relaxed nodes according to claim 4, characterized in that, The method for analytically transforming the state variables in the linearized DistFlow power flow model of the low-voltage distribution network to obtain a deterministic photovoltaic feasible region model containing only the photovoltaic access capacity vector is as follows: The result of squaring the node voltage constraints is: ； Substituting the low-voltage distribution network power flow model that considers relaxed node variations into the squared-processed node voltage constraints, focusing only on the upper limit constraint and simplifying, we obtain: in, Represents the photovoltaic injected power vector. and Represents the node coupling matrix and voltage margin vector based on voltage constraints; After expanding the line capacity carrying capacity constraint, rearranging terms and performing matrix operations, we obtain the simplified line capacity carrying capacity constraint: ； By substituting variables into the adjusted line current carrying capacity constraints, we obtain: in, and Represents the node coupling relationship matrix and the line current carrying capacity margin vector based on line current carrying capacity constraints; based on and A set of linear inequalities for the deterministic photovoltaic feasible region, containing only the photovoltaic access capacity vector, is established, i.e., the deterministic photovoltaic feasible region model is: 。 6. The method for solving the feasible region of low-voltage photovoltaic systems considering the variation of relaxed nodes according to claim 1, characterized in that, Based on historical hourly load data and solar radiation data, the method for constructing typical random scenarios for each time period using kernel density estimation and Monte Carlo sampling is as follows: Historical data on photovoltaic output and user load in the target area over the past year were selected as the basic dataset, and the day was divided into multiple time periods for time-segmented analysis. The probability density function of photovoltaic power output data and load data for each time period is constructed using the kernel density estimation method; By integrating the probability density function, the cumulative distribution function of photovoltaic power output and load level for each time period is obtained; Monte Carlo sampling was performed on the cumulative distribution function of photovoltaic power output and load level for each time period to generate multiple joint scenario samples for each time period, thus completing the construction of typical random scenarios for each time period.
7. The method for solving the feasible region of low-voltage photovoltaic systems considering the variation of relaxed nodes according to claim 1, characterized in that, The method of substituting typical random scenarios of each time period into a deterministic linear model of photovoltaic feasible region to solve the scenario-based photovoltaic feasible region for a single time period, and obtaining the comprehensive photovoltaic feasible region for a single time period through scenario intersection is as follows: The node coupling matrix is independent of time and scenario; only the voltage margin vector and line current carrying capacity vector are constrained to change with the scenario. Therefore, for the s-th scenario in time period t, the photovoltaic feasible region is: in, This represents the node coupling matrix based on voltage constraints. This represents the node coupling matrix based on line current carrying capacity constraints. Represents the photovoltaic injected power vector. This represents the equivalent voltage margin vector for the s-th scenario in time period t. This represents the equivalent line carrying capacity margin vector for the s-th scenario in time period t. This represents the photovoltaic power output coefficient in the s-th scenario during time period t. Represents the equivalent comprehensive margin vector for the s-th scenario in time period t; Solve for the photovoltaic feasible region for all scenarios in time period t, and take the intersection of the photovoltaic feasible regions for all scenarios to obtain the comprehensive photovoltaic feasible region for time period t: in, , This represents the minimum overall margin vector for time period t. , r Represents the first in the vector r Each element.
8. The method for solving the feasible region of low-voltage photovoltaic systems considering the variation of relaxed nodes according to claim 1, characterized in that, Full-time integrated photovoltaic feasible region considering relaxation node variations and hourly operational uncertainties for: in, , This represents the node coupling matrix based on voltage constraints. This represents the node coupling matrix based on line current carrying capacity constraints. Represents the photovoltaic injected power vector. Represents the minimum overall margin vector over the entire time period. , r Represents the first in the vector r Each element.
9. A low-voltage photovoltaic feasible region solution system considering the variation of relaxed nodes, characterized in that, include: The first module is used to obtain the topology, line parameters and load parameters of the low-voltage distribution network in the target area, and to establish a node voltage square-active power sensitivity model on the medium-voltage side based on the linearized DistFlow power flow equation. The second module is used to obtain sensitivity results based on the node voltage squared-active power sensitivity model and to establish a linearized DistFlow power flow model for low-voltage distribution networks that takes into account the changes in relaxed nodes. The third module is used to construct safety operation constraints for low-voltage distribution networks based on the linearized DistFlow power flow model of low-voltage distribution networks. The fourth module is used to analyze the state variables in the safety operation constraints of the low-voltage distribution network to obtain a deterministic photovoltaic feasible region model containing only the photovoltaic access capacity vector. The fifth module is used to construct typical random scenarios for each time period based on historical hourly load data and solar radiation data, using kernel density estimation and Monte Carlo sampling methods. The sixth module is used to substitute typical random scenarios of each time period into the deterministic photovoltaic feasible region linear model, solve the scenario-based photovoltaic feasible region for a single time period, and obtain the comprehensive photovoltaic feasible region for a single time period through the intersection of scenarios; The seventh module is used to find the intersection of the comprehensive photovoltaic feasible regions for multiple time periods, so as to obtain the comprehensive photovoltaic feasible region for all time periods that takes into account the changes in relaxed nodes and hourly operational uncertainties.
10. A non-transitory computer-readable storage medium storing computer instructions, characterized in that, The computer instructions are used to cause the computer to perform the method according to any one of claims 1-8.