Power distribution network voltage sag sag domain analysis method considering distributed power supply access

Abstract

The invention discloses a power distribution network voltage sag sag domain analysis method considering distributed power supply access, and relates to the technical field of power system electric energy quality control. According to the method, a power distribution network asymmetric short circuit three-sequence equivalent model containing a distributed power supply and sensitive equipment is constructed, a looped network is split based on a voltage lowest node when a looped network structure exists, and a voltage sag sag domain general equation and a characteristic equation under any line fault condition are established; and further through sag subsystem division and Kron order reduction processing, an order reduction node impedance matrix about fault position parameters is formed, and the fault position parameters enabling the residual voltage of the sensitive nodes to reach a preset threshold value are determined by adopting an optimization iteration mode, so that the voltage sag sag domain boundary is accurately obtained. The method can give consideration to the calculation precision and efficiency, and is suitable for the voltage sag analysis of the power distribution network containing the distributed power supply and the complex topological structure.

Description

Technical Field

[0001] This invention relates to the field of power system power quality control technology, and in particular to a method for analyzing voltage sag regions in distribution networks considering distributed generation access. Background Technology

[0002] Voltage sags, as one of the most significant power quality issues, pose a serious threat to the normal operation of sensitive equipment in modern industrial production processes. Accurate characterization of the Area of ​​Vulnerability (AOV) is crucial for voltage sag assessment and the development of mitigation strategies. AOV refers to the geographical or electrical area in a power system where a voltage sag caused by a fault prevents sensitive loads from functioning properly. With the deepening of AOV research, the concept has evolved from the initial sensitive area to the Area of ​​Severity (AOS) and concentric relaxation sag models centered on the fault point.

[0003] Existing AOV calculation methods struggle to balance efficiency and accuracy. These methods are primarily categorized into statistical and estimation methods: statistical methods require the installation of monitoring equipment at numerous nodes in the distribution network, resulting in high costs and limited accuracy; estimation methods include the fault point method and the critical distance method. The fault point method is applicable to both mesh and radial systems, but requires extensive fault simulation calculations, leading to high computational and time costs; the critical distance method cannot provide a complete global fault response view. Furthermore, with the large-scale integration of distributed generation (DG), its LVRT support time (approximately 0.625 seconds) is significantly longer than the tolerance time of most sensitive equipment, rendering traditional AOV calculation methods that ignore the dynamic characteristics of DG ineffective.

[0004] Most importantly, with the large-scale increase in the penetration rate of distributed generation (DG) in distribution networks, it has profoundly impacted the system's short-circuit current characteristics, voltage distribution, and voltage sag propagation patterns. On the one hand, the low-voltage ride-through time of DG (approximately 0.625 seconds) is significantly longer than the tolerance time of most sensitive equipment, making its dynamic response process non-negligible. On the other hand, the integration of DG alters the system's power supply structure, rendering the assumption of a single power source in traditional AOV calculation methods invalid. In particular, the control strategies of converter-type DG simultaneously affect the current injection into both positive-sequence and negative-sequence networks, while the dynamic characteristics of motor-type DG and various sensitive loads further increase the complexity of fault analysis. Furthermore, the ring network structure formed by tie lines prevalent in distribution networks allows for multiple paths of fault current flow, significantly altering the propagation range of voltage sags and posing a greater challenge to accurate AOV calculations.

[0005] In summary, traditional AOV calculation methods suffer from insufficient accuracy, low efficiency, and poor adaptability to complex networks when considering distributed generation (DG) access. Therefore, a voltage sag domain calculation method that can balance computational efficiency and accuracy and is applicable to complex distribution networks containing DG is needed. Summary of the Invention

[0006] To address the above issues, this invention proposes a voltage sag analysis method for distribution networks considering distributed power source integration. It employs a boundary solution strategy based on Kron's order reduction and a joint "optimization-iteration" approach. Through subsystem partitioning and fault location optimization inversion, it significantly improves computational efficiency while ensuring computational accuracy.

[0007] The present invention achieves the above objectives through the following technical solutions:

[0008] A method for analyzing voltage sag regions in distribution networks with distributed generation is considered. The method includes the following steps:

[0009] S1: Perform symmetric component decomposition on the distribution network containing distributed power sources and sensitive equipment, and construct equivalent models of positive sequence, negative sequence and zero sequence three-sequence networks. In the case of a distribution network with tie lines forming a ring network, split the ring network according to the node with the lowest voltage on the ring network to obtain the impedance matrix of the three-sequence nodes before and after splitting.

[0010] S2: Based on the three-sequence node impedance matrix and fault location parameters, establish a general equation for the voltage sag domain that characterizes the relationship between the three-sequence node voltage and the three-sequence short-circuit current under any line fault.

[0011] S3: Establish the corresponding voltage sag region characteristic equations according to the fault type, and solve the voltage sag region characteristic equations and the voltage sag region general equations simultaneously to obtain the three-sequence node voltages and three-sequence short-circuit currents under each fault type.

[0012] S4: Divide the path from the sensitive node to the end of the line into several recessed subsystems, and in each recessed subsystem, perform voltage discrimination on the bifurcation node or the end node of the line based on the three-order node voltage obtained in step S3 to determine the target line segment, and perform order reduction processing on the target line segment to form a reduced-order node impedance matrix with respect to the fault location parameters.

[0013] S5: Based on the reduced-order node impedance matrix and the three-sequence short-circuit current obtained in step S3, calculate the three-sequence voltage of the sensitive node, obtain the remaining voltage of the sensitive node through inverse transformation of the sequence components, and determine the fault location parameters that make the remaining voltage reach the preset voltage threshold through optimization iteration, so as to obtain the voltage sag domain boundary of the sensitive node.

[0014] As a preferred embodiment of the present invention, the equivalent model for constructing a positive-order, negative-order, and zero-order tri-order network includes:

[0015] Distributed power sources and various sensitive devices are equivalent to current sources and connected to distribution network nodes to form a general equivalent circuit for asymmetrical short circuits in the distribution network.

[0016] A virtual voltage source is introduced at the fault node, and the system voltage after the fault is decomposed into normal component and short-circuit component based on the superposition theorem. The normal component is the node voltage component under the combined action of all current sources and the virtual voltage source, and the short-circuit component is the additional voltage component when only the reverse virtual voltage source is applied.

[0017] The system is decomposed into positive-sequence, negative-sequence, and zero-sequence networks using the symmetrical component method. Three-sequence node voltage equations for normal components and short-circuit components are established respectively, forming the corresponding three-sequence node impedance matrix. The three-sequence node voltages of the system after the fault are obtained by superimposing the normal components and short-circuit components.

[0018] As a preferred embodiment of the present invention, the sensitive device includes at least a dynamic resistive load, an automatic control compensator, a speed regulating driver, and a ZIP load constructed according to a constant impedance-constant current-constant power model;

[0019] The general equivalent circuit for asymmetrical short circuits in the power distribution network consists of the following current injections:

[0020] In the orthogonal network, by A small motor and Injecting positive-sequence short-circuit current into a distributed power source of a motor type;

[0021] In positive-order and negative-order networks, by A converter-type distributed power supply and A ZIP load is injected with positive-sequence and negative-sequence short-circuit current;

[0022] In positive-order networks, negative-order networks, and zero-order networks, by An automatic control compensator injects positive-sequence, negative-sequence, and zero-sequence short-circuit currents.

[0023] As a preferred embodiment of the present invention, the step of splitting the ring network based on the node with the lowest voltage on the ring network includes:

[0024] The node with the lowest voltage on the tie line is determined by power flow calculation, and the node with the lowest voltage is selected as the split node of the ring network;

[0025] At the split node, the node number is copied and the injection current is set in the opposite direction to break the ring network and form a new set of nodes while maintaining the equivalence of the original network topology.

[0026] Based on the three-order node impedance matrix before splitting, the column vectors corresponding to the split nodes are adjusted to construct the three-order node impedance matrix of each order network after splitting. This ensures that the three-order node impedance matrices before and after splitting remain consistent at non-split nodes, and establishes a correspondence at split nodes to support the parameterized solution of fault location parameters for any line.

[0027] As a preferred embodiment of the present invention, the general equation for the voltage sag region is expressed as:

[0028] ;

[0029] In the formula, Before splitting the ring network Voltage vectors of each node in the sequence network after a short circuit. Before splitting the ring network Fault points in sequence network The voltage change vectors of each node when a short circuit occurs; Before splitting the ring network The impedance matrix of the three-order nodes of the ordered network. The three-order node impedance matrix after splitting the ring network The f-th column in; Fault point exist The fault current injected into the sequence network; After the fault The voltage components of the first n nodes in the sequence network, For the aftermath of the fault Voltage components of newly added nodes at the split branch ends in the sequence network; The radial structure obtained after splitting the ring network at branch pq. The impedance matrix of the three-order nodes of the ordered network; After splitting the ring network Equivalent node current injection vector in the sequence network; Voltage change vector The voltage drop vector of the first n components; Voltage change vector The voltage drop of the component corresponding to node p; Voltage change vector The voltage drop of the component corresponding to node n+1; The three-order node impedance matrix after splitting the ring network The p-th row of all column vectors represents the equivalent impedance vector between node p and each other node; The three-order node impedance matrix after splitting the ring network The column vectors in the q-th row represent the equivalent impedance vectors between node q and other nodes; Inject vector for equivalent node current The first in Each component, i.e., a node The equivalent injection current; Before the split Nodes in the sequence network The original equivalent injected current component; Before splitting the ring network Nodes in the sequence network The original equivalent injected current component; p is the node number of one end of the disconnected branch; q is the node number of the other end of the disconnected branch.

[0030] As a preferred embodiment of the present invention, the characteristic equation of the voltage sag region includes:

[0031] The characteristic equation for the voltage sag region of a single-phase ground fault is expressed as:

[0032] ;

[0033] Meanwhile, the characteristic equation for the voltage sag region of an interphase fault is expressed as:

[0034] ;

[0035] The characteristic equation for the voltage sag region of a two-phase ground fault is expressed as:

[0036] ;

[0037] In the formula, , , These represent the fault points. Positive-sequence fault current, negative-sequence fault current and zero-sequence fault current at the location; , , Let these represent the positive-sequence voltage, negative-sequence voltage, and zero-sequence voltage of node j, respectively. , , These are the f-th columns of the three-order node impedance matrix after splitting.

[0038] As a preferred embodiment of the present invention, the step of dividing the path from the sensitive node to the end of the line into several recessed subsystems includes: when there is no tie line in the distribution network, defining the complete path from the sensitive node to each end of the line as an independent recessed subsystem;

[0039] When a distribution network has tie lines forming a ring network, the node with the lowest voltage on each tie line is obtained based on power flow calculations. The node with the lowest voltage is taken as the end of the line, thereby forming the corresponding recessed subsystem.

[0040] In a preferred embodiment of the present invention, step S4 involves performing a reduction-order processing on the target line segment to form a reduced-order node impedance matrix with respect to the fault location parameters, including:

[0041] Sensitive nodes, fault nodes, and critical bifurcation nodes are retained in the target line segment. Other intermediate nodes are equivalently eliminated, and multiple series line impedances are merged into one equivalent impedance. This constructs a reduced-order node impedance matrix with respect to fault location parameters, ensuring that the reduced-order node impedance matrix maintains the same parameterization characteristics as the three-order node impedance matrix in step S2.

[0042] As a preferred embodiment of the present invention, the step of determining the fault location parameters that cause the remaining voltage to reach a preset voltage threshold through optimization iteration, in order to obtain the voltage sag domain boundary of the sensitive node, specifically includes:

[0043] Within the recessed subsystem and target line segment determined in step S4, initial values ​​for the fault location parameters are set. The fault location parameters are used as iterative variables, and the fault location parameters are obtained by iteratively solving the general equation for the voltage sag region. and the corresponding system node injected current vector :

[0044] According to the system node injected current vector Calculate the normal components of each sequence voltage at each node of the system without introducing fault short-circuit current. And further obtain the fault node. Normal components of voltage sequence at each point The formula is: ;

[0045] Based on the fault location parameters Constructing a reduced-order nodal impedance matrix And obtain the fault node in the reduced-order node impedance matrix. Corresponding self-impedance ;

[0046] Fault node Corresponding self-impedance and normal components of voltage sequence Substituting the corresponding characteristic equation of the voltage sag region, the parameters of the fault location are obtained by solving the equation. short circuit current ;

[0047] short-circuit current and the reduced-order nodal impedance matrix Substitute into the following formula, where For fault location parameters:

[0048] ;

[0049] The sensitive nodes are obtained by solving. Three-sequence voltage The corresponding residual voltage is obtained through inverse transformation of the sequence components; where The three-order nodal impedance matrix after splitting The k-th row in the middle; For parameters regarding fault location Three-order nodal impedance matrix The element in the k-th row and f-th column; Sensitive nodes The critical voltage of the voltage withstand curve of the connected sensitive equipment; Three-sequence voltage Obtained using the inverse Fortescue transform;

[0050] When the remaining voltage does not reach the preset voltage threshold, the fault location parameter is updated as follows: The above iterative process continues; when the remaining voltage reaches the preset voltage threshold, the corresponding fault location parameter is determined as the boundary of the voltage sag depression domain within the depression subsystem.

[0051] Compared with existing technologies, the advantages of this invention are: by employing a boundary solution strategy based on Kron's order reduction and a joint "optimization-iteration" approach, it effectively solves the problems of insufficient computational accuracy and low computational efficiency in traditional methods when considering distributed generation (DG) integration. First, the complex system is divided into multiple concave subsystems through ring network splitting. Second, the network model is simplified using Kron's order reduction method, significantly reducing computational complexity. Then, an optimization model constrained by the critical voltage of sensitive equipment is established, and the AOV boundary of each subsystem is accurately solved using an iterative algorithm. Validation results in the IEEE 33-bus system show that this method improves computational efficiency by approximately 25 times compared to the traditional fault point method, and by approximately 37 times in ring distribution networks with tie lines. Simultaneously, it accurately reflects the impact of DG integration on the AOV boundary, providing an effective technical means for voltage sag assessment and mitigation in DG-integrated distribution networks. Attached Figure Description

[0052] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is an equivalent circuit diagram of a power distribution system considering the access of various sensitive devices in this embodiment of the invention; Figure 3 This is the equivalent circuit diagram of the asymmetrical short circuit in the power distribution system in this embodiment of the invention; Figure 4 This is a schematic diagram of ring network splitting in an embodiment of the present invention; Figure 5 This is a schematic diagram showing a fault occurring at point f in line ij in an embodiment of the present invention; Figure 6 This is a schematic diagram of a 9-node system in an embodiment of the present invention; Figure 7 This is a schematic diagram of the system after the 9-node Kron reduction in an embodiment of the present invention; Figure 8 This is a schematic diagram of the IEEE 33-node topology according to an embodiment of the present invention; Figure 9 This is a schematic diagram of the voltage sag of sensitive node 3 under different DG injection powers in an embodiment of the present invention; Figure 10 A schematic diagram of the IEEE 33-node topology after split ring network provided in an embodiment of the present invention; Figure 11 This is a schematic diagram of the AOV of sensitive node 28 under different fault conditions provided in this experimental embodiment. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention are within the scope of protection of the present invention.

[0054] like Figure 1 As shown, this is an embodiment of the present invention, which provides a method for analyzing voltage sag regions in distribution networks considering distributed generation access, including the following steps:

[0055] S1: Perform symmetric component decomposition on the distribution network containing distributed power sources and sensitive equipment, and construct equivalent models of positive-sequence, negative-sequence, and zero-sequence three-sequence networks. In the case where there are tie lines forming a ring network in the distribution network, split the ring network according to the node with the lowest voltage on the ring network to obtain the impedance matrix of the three-sequence nodes before and after the split.

[0056] In this embodiment, for a distribution network with distributed power sources and multiple types of sensitive equipment, in order to accurately describe the relationship between the voltage of each node and the short-circuit current under asymmetrical short-circuit fault conditions, a general equivalent circuit for asymmetrical short circuits in the distribution network is first constructed.

[0057] Specifically, distributed generation sources and various sensitive devices connected to the distribution network are uniformly represented as current sources and connected to their respective distribution network nodes. The current source characterizes the current injected into the system by the distributed generation during a short circuit and the impact of sensitive devices on the system current under different operating conditions. In this way, the distribution network containing distributed generation sources and sensitive devices is transformed into an equivalent circuit model determined by node current injection and network impedance, such as... Figure 2 As shown. To accurately reflect the impact of different types of sensitive equipment and distributed generation (DG) on the distribution network under asymmetrical short-circuit conditions, sensitive equipment is classified into at least the following categories: small generators (G), dynamic resistance loads (DR), automatic control compensators (ACC), adjustable speed drives (ASD), and ZIP loads constructed according to the constant impedance-constant current-constant power model. Research on various sensitive equipment models such as DR, ACC, G, DG, ASD, and ZIP in the distribution network is relatively mature.

[0058] Among them, dynamic resistive loads and speed control drives mainly behave as motor-type loads during short circuits, and their short circuit characteristics can be equivalent to injecting positive-sequence current into the positive-sequence network; motor-type distributed power sources can also be equivalent to power supply units that inject current into the positive-sequence network under short circuit conditions; converter-type distributed power sources and ZIP loads will affect both the positive-sequence network and generate unbalanced current components in the negative-sequence network during short circuits, so corresponding current components are injected into the positive-sequence network and the negative-sequence network respectively; automatic control compensators may introduce zero-sequence components under asymmetrical short circuit conditions, so current components are injected into the positive-sequence network, the negative-sequence network and the zero-sequence network simultaneously.

[0059] In practical implementation, it is assumed that there exists in the distribution network. A small motor, Individual motor type distributed power supply, A converter-type distributed power supply, A ZIP payload and For each automatic control compensator, a corresponding number of current injection sources are set in the corresponding three-sequence network according to the equipment type. The amplitude and direction of each injected current can be determined according to the rated parameters, operating status, and short-circuit type of the equipment.

[0060] By using the above modeling methods, the impact of different types of distributed power sources and sensitive devices on the system current distribution under asymmetrical short-circuit conditions can be uniformly characterized at the three-order network level, thereby improving the accuracy and engineering applicability of voltage sag analysis.

[0061] When a short-circuit fault occurs in a distribution network, a virtual voltage source is introduced at the corresponding fault node. The virtual voltage source is used to characterize the impact of fault conditions on node voltages at the mathematical modeling level. Based on the superposition theorem, the post-fault system voltage is decomposed into a normal component and a short-circuit component. The normal component is the node voltage component formed under the combined action of all current sources and the virtual voltage source, used to describe the voltage state of the system before the fault and under normal operating conditions. The short-circuit component is the additional voltage component obtained when only a virtual voltage source in the opposite direction is applied, used to describe the voltage disturbance caused by the short-circuit fault.

[0062] After completing the above decomposition, the equivalent circuit of the distribution network is further decomposed into positive-sequence network, negative-sequence network, and zero-sequence network using the symmetrical component method, such as... Figure 3 As shown, the nodal voltage equations for each sequence network are established for both the normal and short-circuit components. Solving these nodal voltage equations yields the corresponding three-sequence nodal impedance matrices. Finally, by superimposing the normal and short-circuit components, the three-sequence nodal voltages of each node in the distribution network under short-circuit fault conditions are obtained, providing a foundation for subsequent voltage sag analysis.

[0063] Figure 3 middle, for The short-circuit current of the positive sequence network of a small motor injection system; Let m be the short-circuit current injected into the positive sequence network of the system. , Let m be the short-circuit currents injected into the positive-sequence and negative-sequence networks of the converter-type DG system. , , Let be the short-circuit currents of the positive-sequence, negative-sequence, and zero-sequence networks of the m ACC injection system, respectively; , These are the short-circuit currents of the positive-sequence and negative-sequence networks of the m ASD injection system, respectively. , Let be the short-circuit currents of the positive-sequence and negative-sequence networks of the system injected with m ZIP loads, respectively. , and They are short circuit points The normal components of the positive-sequence, negative-sequence, and zero-sequence voltages; , and They are short circuit points The fault components of the positive-sequence, negative-sequence, and zero-sequence voltages; assuming , and These are the positive-sequence, negative-sequence, and zero-sequence components of the short-circuit current, respectively.

[0064] When a distribution network has tie lines forming a ring network structure, it needs to be equivalently converted into a radial structure to facilitate the subsequent search and calculation of voltage sag regions. In the specific implementation process, firstly, power flow calculation is performed on the distribution network to obtain the operating voltage values ​​of the nodes on each tie line. Then, the node with the lowest voltage is determined on each tie line and selected as the ring network splitting node to ensure that the impact on the system voltage distribution is minimized after splitting.

[0065] After determining the split node, a node replication operation is performed on the split node. That is, a new node with the same electrical parameters as the original split node is generated in the mathematical model, and the corresponding connecting branch between the original node and the new node is disconnected. At the same time, injection currents in opposite directions are set at the original node and the new node to maintain the electrical equivalence of the network before and after the split.

[0066] After node replication and branch disconnection are completed, the column vectors corresponding to the split nodes are adjusted based on the pre-split three-order node impedance matrix to reconstruct the post-split positive-order, negative-order, and zero-order node impedance matrices. The post-split three-order node impedance matrix remains consistent with the pre-split matrix at non-split nodes, and a one-to-one correspondence is established only at the split nodes.

[0067] like Figure 4 As shown, in In a system with 1 node, there exists For each ring network, the network is unraveled at the point of lowest voltage on the system tie line. The set of node numbers at the points of lowest voltage in each ring network is denoted as a vector. The newly generated node number vector is The injected current phasor of the newly generated node is The injected current phasor at the original node is , Representing positive sequence, negative sequence, and zero sequence. In a fault-free state, the impedance matrix of each node in the pre-split ring network is denoted as... The impedance matrix of each sequence network node after splitting the ring network is denoted as... .

[0068] S2: Based on the three-sequence node impedance matrix and fault location parameters, a general equation for the voltage sag domain is established to characterize the relationship between the three-sequence node voltage and the three-sequence short-circuit current under any line fault.

[0069] From the node impedance matrix The physical meaning of this can be used to obtain the non-faulty nodes. voltage fault component With short-circuit nodes The relationship between them can be further derived from the superposition theorem, which allows us to determine the non-faulty nodes after a short circuit. voltage :

[0070] ;

[0071] In the formula, For normal operation, the node The voltage; Nodal impedance matrix The element in the k-th row and f-th column.

[0072] The voltage and short-circuit current of each node in the network can be obtained from the above formula. The relationship, expressed in matrix form, yields:

[0073] ;

[0074] ;

[0075] In the formula, Before splitting the ring network Voltage vectors of each node in the sequence network after a short circuit; The injected currents of ASD, ACC, DG, ZIP, G, and DR in positive-sequence, negative-sequence, and zero-sequence networks, and the current injected into the network by each device. With the voltage of the port change; for The fth column in the array.

[0076] According to the formula The nodes can be determined. After a fault occurs, the voltage at each node of the system is affected. However, the boundary of the voltage sag region may not be located exactly at a system node; it may also be located on the line. Therefore, it is necessary to construct the node impedance matrix corresponding to the fault on the line. Assuming any line , Inter-node points A short circuit fault occurred at (a new node was added). ),like Figure 5 As shown, the fault location is defined. , . Figure 5 middle, The starting point of the line To the fault point The line impedance; The starting point of the line To the finish line The line impedance.

[0077] Based on the impedance matrix of the split ring network Or the impedance matrix after splitting the ring network middle and Two columns of elements, using the following two direct pairs of impedance matrices or Modify to or :

[0078] ;

[0079] ;

[0080] During a line fault, the node impedance matrix after the ring network splits Or the node impedance matrix before ring network splitting All of these are about the location of the fault. The parametric impedance matrix is ​​shown in the following equation:

[0081] ;

[0082] Furthermore, regarding the formula Process and add information about the node. The elements are used to obtain the general equation for the voltage sag region, which is expressed as:

[0083] ;

[0084] In the formula, Before splitting the ring network Voltage vectors of each node in the sequence network after a short circuit. Before splitting the ring network Fault points in sequence network The voltage change vectors of each node when a short circuit occurs; Before splitting the ring network The impedance matrix of the three-order nodes of the ordered network. The three-order node impedance matrix after splitting the ring network The f-th column in; Fault point exist The fault current injected into the sequence network; For the aftermath of the fault The voltage components of the first n nodes in the sequence network, For the aftermath of the fault Voltage components of newly added nodes at the split branch ends in the sequence network; The radial structure obtained after splitting the ring network at branch pq. The impedance matrix of the three-order nodes of the ordered network; After splitting the ring network Equivalent node current injection vector in the sequence network; Voltage change vector The voltage drop vector of the first n components; Voltage change vector The voltage drop of the component corresponding to node p; Voltage change vector The voltage drop of the component corresponding to node n+1; The three-order node impedance matrix after splitting the ring network The p-th row of all column vectors represents the equivalent impedance vector between node p and each other node; The three-order node impedance matrix after splitting the ring network The column vectors in the q-th row represent the equivalent impedance vectors between node q and other nodes; Inject vector for equivalent node current The first in Each component, i.e., a node The equivalent injection current; Before the split Nodes in the sequence network The original equivalent injected current component; Before splitting the ring network Nodes in the sequence network The original equivalent injected current component; p is the node number of one end of the disconnected branch; q is the node number of the other end of the disconnected branch.

[0085] S3: Establish the corresponding characteristic equations of the voltage sag region according to the fault type, and solve the characteristic equations of the voltage sag region and the general equations of the voltage sag region simultaneously to obtain the three-sequence node voltage and the three-sequence short-circuit current under each fault type.

[0086] The characteristic equations for the voltage sag region include:

[0087] The characteristic equation for the voltage sag region of a single-phase ground fault is expressed as:

[0088] ;

[0089] Meanwhile, the characteristic equation for the voltage sag region of an interphase fault is expressed as:

[0090] ;

[0091] The characteristic equation for the voltage sag region of a two-phase ground fault is expressed as:

[0092] ;

[0093] In the formula, , , These represent the fault points. Positive-sequence fault current, negative-sequence fault current and zero-sequence fault current at the location; , , Let these represent the positive-sequence voltage, negative-sequence voltage, and zero-sequence voltage of node j, respectively. , , These are the f-th columns of the three-order node impedance matrix after splitting.

[0094] S4: Divide the path from the sensitive node to the end of the line into several recessed subsystems, and in each recessed subsystem, perform voltage discrimination on the bifurcation node or the end node of the line based on the three-order node voltage obtained in step S3 to determine the target line segment, and perform order reduction processing on the target line segment to form a reduced-order node impedance matrix with respect to the fault location parameters.

[0095] The entire power distribution system from the access node of sensitive equipment to the end of each line is defined as an independent recessed subsystem. If there are tie lines in the system, power flow calculations should be performed first to determine the end of the system line based on the lowest voltage point on the tie line, thus further forming a recessed subsystem. Figure 6 There is one tie line. Assuming node 5 is the point with the lowest voltage on the tie line, then node 5 is defined as the end of the line. Therefore... Figure 6 Four concave subsystems can be identified: 2→1, 2→3→4→5, 2→3→4→6→7→8→9, and 2→5.

[0096] After dividing the sag subsystems, the first step is to determine whether there are bifurcation nodes within the sag subsystems. For sag subsystem 3, a bifurcation node is present. The following formula is used to calculate whether bifurcation node 4 is located within a voltage sag region. For sag subsystem 4, the following formula is used to calculate whether line-end node 5 is located within a voltage sag region:

[0097] ;

[0098] In the sag subsystem 3, if the bifurcation node 4 is located in the voltage sag sag region, then the sag subsystem connected to it needs to be further analyzed, that is, the line from node 4 to node 9; if node 4 does not belong to the voltage sag sag region, then the boundary of the voltage sag sag region is located on the line from the sensitive node to the bifurcation node, that is, the line from node 2 to node 4.

[0099] Kronal mass reduction is applied to the selected lines to simplify the network model. Specifically, the equivalent impedance between node 4 and node 9 is... The equivalent impedance between node 2 and node 4 is Keeping the other depression subsystems unchanged, such as Figure 7 As shown.

[0100] S5: Based on the reduced-order node impedance matrix and the three-sequence short-circuit current obtained in step S3, calculate the three-sequence voltage of the sensitive node, obtain the remaining voltage of the sensitive node through inverse transformation of the sequence components, and determine the fault location parameters that make the remaining voltage reach the preset voltage threshold through optimization iteration, so as to obtain the voltage sag domain boundary of the sensitive node.

[0101] Within the recessed subsystem and target line segment determined in step S4, initial values ​​for the fault location parameters are set. The fault location parameters are used as iterative variables, and the fault location parameters are obtained by iteratively solving the general equation for the voltage sag region. and the corresponding system node injected current vector :

[0102] Based on the system node injected current vector Calculate the normal components of each sequence voltage at each node of the system without introducing fault short-circuit current. And further obtain the fault node. Normal components of voltage sequence at each point The formula is: ;

[0103] Based on fault location parameters Constructing a reduced-order nodal impedance matrix And obtain the fault node in the reduced-order node impedance matrix. Corresponding self-impedance ;

[0104] Fault node Corresponding self-impedance and normal components of voltage sequence Substituting the corresponding characteristic equation of the voltage sag region, the parameters of the fault location are obtained by solving the equation. short circuit current ;

[0105] short-circuit current and the reduced-order nodal impedance matrix Substitute into the following formula, where For fault location parameters:

[0106] ;

[0107] The sensitive nodes are obtained by solving. Three-sequence voltage The corresponding residual voltage is obtained through inverse transformation of the sequence components; where The three-order nodal impedance matrix after splitting The k-th row in the middle; For parameters regarding fault location Three-order nodal impedance matrix The element in the k-th row and f-th column; Sensitive nodes The critical voltage of the voltage withstand curve of the connected sensitive equipment; Three-sequence voltage Obtained using the inverse Fortescue transform;

[0108] When the remaining voltage does not reach the preset voltage threshold, the fault location parameter is updated as follows: The above iterative process continues; when the remaining voltage reaches the preset voltage threshold, the corresponding fault location parameter is determined as the voltage sag depression boundary within the depression subsystem.

[0109] like Figure 8 As shown, the accuracy and efficiency of the proposed method are verified using the IEEE 33-bus system as an example. The substation uses a 10MVA three-phase transformer with a resistance of 1% and a reactance of 7%. Unless otherwise specified, tie lines are not considered. The voltage sag region at node 3 under LG, LL, and LLG is characterized, as shown... Figure 9 As shown. From Figure 9 As can be seen from (b) and 9(c), different DG connection levels have a certain impact on the voltage sag region of sensitive equipment. This indicates that the existing AOV calculation method, by ignoring the influence of DG, is conservative in its calculation of the voltage sag region, thus expanding the impact range of voltage drops after faults. Furthermore, ground faults LG and LLG are more severe than phase-to-phase faults LL, therefore... Figure 9 The AOV of LG and LLG is greater than the AOV of LL fault. Figure 9 (a) It can also be observed that during an LG fault, changing the injected power of the DG does not significantly change the AOV. This is because the LG fault introduces a fault current dominated by the zero-sequence component, while the DG model established in this invention, or commonly used DGs in practice, do not provide zero-sequence current and therefore have no support capability for zero-sequence voltage. LL and LLG faults, on the other hand, mainly involve large abrupt changes in the positive and negative sequence current components. The DG design of this invention incorporates relevant negative sequence current control, thus providing support capability during LL and LLG faults and, to some extent, narrowing the range of AOV.

[0110] As can be seen from the above, different DG access levels will affect the voltage sag region to a certain extent. Ignoring the influence of DG will lead to a tightening of the AOV of sensitive nodes.

[0111] To further analyze the impact of DG access level on AOV of sensitive nodes, this section performs AOV calculation for node 13 under LLG fault, and the results are shown in Table 1.

[0112] Table 1 AOV under different DG capacities at node 13

[0113]

[0114] Through the above embodiments, this invention aims to address the shortcomings of traditional AOV calculation methods in the context of distributed generation (DG) integration by employing a Krono order reduction and "optimization-iteration" method for solving voltage sag and depression domain boundaries. The method first constructs a general equivalent circuit for asymmetric short circuits in a distribution system containing DG and various sensitive equipment, and decomposes it into positive-sequence, negative-sequence, and zero-sequence networks using the symmetric component method. Second, by splitting the ring network and depression subsystem, the complex network is decomposed into multiple independent calculation units. Third, a parameterized impedance matrix for fault location is established, and characteristic equations for different types of short circuits are combined to form a closed-loop solution system. Finally, a Krono order reduction strategy is introduced to simplify the subsystem model, and the AOV boundary is quickly located using an optimization-iteration algorithm. The proposed method has been validated in the IEEE 33-bus system for its accuracy and efficiency under different DG capacities, fault types, and network structures, significantly improving the calculation speed and characterization accuracy of AOV, and providing a reliable tool for power quality assessment and management of distribution networks containing DG.

[0115] Node 13 is far from the PCC point and located between two DGs. As shown in column 6 of Table 1, different DG access levels have a significant impact on AOV. With increasing DG access levels, AOV gradually shrinks inward, and subsystems 1 and 2 even exhibit cross-segment AOV boundaries. When the DG capacity is 0 MVA, the AOV boundaries of subsystems 1 and 2 are on lines 23-24 and 32-33, respectively; when the DG capacity is 5 MVA, the AOV boundaries of subsystems 1 and 2 shrink to lines 3-23 and 28-29, respectively.

[0116] To verify the computational accuracy and efficiency of the proposed algorithm, the AOV of sensitive node 13 was calculated under a 5MW DG access level to compare the computational accuracy and time of the proposed method with the fault point method. The computing platform hardware configuration was a personal laptop: CPU Intel Core i9-14900HX, memory 32GB. The fault point method requires traversing all possible fault points on each line in the system, with a total computation time of 5147 s. In contrast, the proposed method only calculates for bifurcation nodes, subsystem end nodes, and Kron-degraded lines, significantly reducing the computation time for voltage sag regions, with a total computation time of approximately 202 s, a speedup of 25 times, as shown in Table 2. Furthermore, compared to the calculation results of the fault point method in column 6 of the table, the proposed method also improves the accuracy of AOV boundary calculation. The accuracy of AOV boundary search is related to the iteration end threshold in the AOV calculation process mentioned above.

[0117] Table 2 Comparison of AOV calculation results for node 13 using different methods

[0118]

[0119] To improve the reliability of power distribution networks, tie lines may exist in the system. Taking the IEEE 33-bus system as an example, considering the impact of tie lines on the AOV calculation method proposed in this invention, the system tie lines are as follows: Figure 8 As shown by the dashed line. First, calculate the ring network power flow. Define the nodes with the lowest tie-line voltage (8, 12, 15, 18, 29) as the system terminals. Therefore, the system contains 7 recessed subsystems. The system after splitting the ring network is as follows: Figure 10 As shown. The AOV of node 28 under faults LG, LL, and LLG are calculated respectively, and the results are as follows. Figure 11 As shown.

[0120] Depend on Figure 11 It is evident that the impact range of LLG and LG faults on AOV is significantly greater than that of LL faults. This is consistent with the previously mentioned conclusion that "the voltage drop amplitude caused by phase-to-phase faults is lower," and also verifies that the method proposed in this invention can effectively calculate the AOV of distribution networks containing tie lines. In ring distribution systems, although the presence of tie lines improves power supply reliability, compared to radial structures, the equivalent Thevenin impedance of ring networks is smaller, resulting in a larger fault current under the same fault resistance conditions, thus causing a wider voltage drop range. Therefore, Figure 11 As can be seen, when an LLG failure occurs at any location in the entire network, sensitive node 28 is affected.

[0121] Furthermore, compared to radial networks, the spatial distribution characteristics of AOVs (Area of ​​Voltage) in ring network systems also change significantly, with multiple unconnected AOV regions appearing. This phenomenon is consistent with the earlier analysis that "multiple independent AOVs may form in a ring network." The fundamental reason is that there are multiple connection paths between fault points and sensitive nodes in ring network distribution systems. The short-circuit current distribution differs across different paths within the same ring network, resulting in different Thevenin equivalent impedances (AEs) reaching the same sensitive node from different paths within the same ring network. This leads to the splitting of the voltage sag propagation region, thereby forming multiple independent AOVs.

[0122] This shows that when the system considers DG access and forms a ring network structure, the AOV exhibits multiple unconnected regions, which is significantly different from the traditional calculation results that do not consider the dynamic characteristics of DG. This further demonstrates that the dynamic voltage support of DG causes a spatial partitioning effect in the system's voltage drop distribution characteristics; ignoring this factor in traditional algorithms leads to distorted evaluation results.

[0123] In summary, this invention aims to address the shortcomings of traditional AOV calculation methods in the context of distributed generation (DG) integration by employing a Kronenstein-based method for voltage sag domain boundary determination using an optimization-iteration approach. The method first constructs a general equivalent circuit for asymmetric short circuits in distribution systems containing DG and various sensitive equipment, and decomposes it into positive-sequence, negative-sequence, and zero-sequence networks using the symmetric component method. Second, by splitting the ring network and sag subsystem, the complex network is decomposed into multiple independent computational units. Third, a parameterized impedance matrix for fault location is established, and characteristic equations for different types of short circuits are combined to form a closed-loop solution system. Finally, a Kronenstein-based reduction strategy simplifies the subsystem model, and an optimization-iteration algorithm is used to quickly locate the AOV boundary. The proposed method has been validated in the IEEE 33-bus system for its accuracy and efficiency under different DG capacities, fault types, and network structures, significantly improving the calculation speed and characterization accuracy of AOV, and providing a reliable tool for power quality assessment and management of distribution networks containing DG.

[0124] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various variations or substitutions within the technical scope disclosed in this application, and these should all 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 method for analyzing voltage sag regions in distribution networks considering distributed generation, characterized in that, The method includes the following steps: S1: Perform symmetric component decomposition on the distribution network containing distributed power sources and sensitive equipment, and construct equivalent models of positive sequence, negative sequence and zero sequence three-sequence networks. In the case of a distribution network with tie lines forming a ring network, split the ring network according to the node with the lowest voltage on the ring network to obtain the impedance matrix of the three-sequence nodes before and after splitting. S2: Based on the three-sequence node impedance matrix and fault location parameters, establish a general equation for the voltage sag domain that characterizes the relationship between the three-sequence node voltage and the three-sequence short-circuit current under any line fault. S3: Establish the corresponding voltage sag region characteristic equations according to the fault type, and solve the voltage sag region characteristic equations and the voltage sag region general equations simultaneously to obtain the three-sequence node voltages and three-sequence short-circuit currents under each fault type. S4: Divide the path from the sensitive node to the end of the line into several recessed subsystems, and in each recessed subsystem, perform voltage discrimination on the bifurcation node or the end node of the line based on the three-order node voltage obtained in step S3 to determine the target line segment, and perform order reduction processing on the target line segment to form a reduced-order node impedance matrix with respect to the fault location parameters. S5: Based on the reduced-order node impedance matrix and the three-sequence short-circuit current obtained in step S3, calculate the three-sequence voltage of the sensitive node, obtain the remaining voltage of the sensitive node through inverse transformation of the sequence components, and determine the fault location parameters that make the remaining voltage reach the preset voltage threshold through optimization iteration, so as to obtain the voltage sag domain boundary of the sensitive node.

2. The method for analyzing voltage sag regions in distribution networks considering distributed generation access as described in claim 1, characterized in that, The equivalent model for constructing positive-order, negative-order, and zero-order tri-order networks includes: Distributed power sources and various sensitive devices are equivalent to current sources and connected to distribution network nodes to form a general equivalent circuit for asymmetrical short circuits in the distribution network. A virtual voltage source is introduced at the fault node, and the system voltage after the fault is decomposed into normal component and short-circuit component based on the superposition theorem. The normal component is the node voltage component under the combined action of all current sources and the virtual voltage source, and the short-circuit component is the additional voltage component when only the reverse virtual voltage source is applied. The system is decomposed into positive-sequence, negative-sequence, and zero-sequence networks using the symmetrical component method. Three-sequence node voltage equations for normal components and short-circuit components are established respectively, forming the corresponding three-sequence node impedance matrix. The three-sequence node voltages of the system after the fault are obtained by superimposing the normal components and short-circuit components.

3. The method for analyzing voltage sag regions in distribution networks considering distributed generation access as described in claim 1, characterized in that, The sensitive device includes at least a dynamic resistive load, an automatic control compensator, a speed control driver, and a ZIP load constructed according to a constant impedance-constant current-constant power model; The general equivalent circuit for asymmetrical short circuits in the power distribution network consists of the following current injections: In the orthogonal network, by A small motor and Injecting positive-sequence short-circuit current into a distributed power source of a motor type; In positive-order and negative-order networks, by A converter-type distributed power supply and Each ZIP load is injected with positive-sequence and negative-sequence short-circuit current; In positive-order networks, negative-order networks, and zero-order networks, by An automatic control compensator injects positive-sequence, negative-sequence, and zero-sequence short-circuit currents.

4. The method for analyzing voltage sag regions in distribution networks considering distributed generation access as described in claim 1, characterized in that, The step of splitting the ring network based on the node with the lowest voltage on the ring network includes: The node with the lowest voltage on the tie line is determined by power flow calculation, and the node with the lowest voltage is selected as the split node of the ring network; At the split node, the node number is copied and the injection current is set in the opposite direction to break the ring network and form a new set of nodes while maintaining the equivalence of the original network topology. Based on the three-order node impedance matrix before splitting, the column vectors corresponding to the split nodes are adjusted to construct the three-order node impedance matrix of each order network after splitting. This ensures that the three-order node impedance matrices before and after splitting remain consistent at non-split nodes, and establishes a correspondence at split nodes to support the parameterized solution of fault location parameters for any line.

5. The method for analyzing voltage sag regions in distribution networks considering distributed generation access as described in claim 1, characterized in that, The general equation for the voltage sag region is expressed as follows: ； In the formula, Before splitting the ring network Voltage vectors of each node in the sequence network after a short circuit. Before splitting the ring network Fault points in sequence network The voltage change vectors at each node when a short circuit occurs; Before splitting the ring network The impedance matrix of the three-order nodes of the ordered network. The three-order node impedance matrix after splitting the ring network The f-th column in; Fault point exist The fault current injected into the sequence network; After the fault The voltage components of the first n nodes in the sequence network, After the fault Voltage components of newly added nodes at the split branch ends in the sequence network; The radial structure obtained after splitting the ring network at branch pq. The impedance matrix of the three-order nodes of the ordered network; After splitting the ring network Equivalent node current injection vector in the sequence network; Voltage change vector The voltage drop vector of the first n components; Voltage change vector The voltage drop of the component corresponding to node p; Voltage change vector The voltage drop of the component corresponding to node n+1; The three-order node impedance matrix after splitting the ring network The p-th row of all column vectors represents the equivalent impedance vector between node p and each other node; The three-order node impedance matrix after splitting the ring network The column vectors in the q-th row represent the equivalent impedance vectors between node q and other nodes; Inject vector for equivalent node current The first in Each component, i.e., a node The equivalent injection current; Before the split Nodes in the sequence network The original equivalent injected current component; Before splitting the ring network Nodes in the sequence network The original equivalent injected current component; p is the node number at one end of the branch that was cut off; q is the node number at the other end of the branch that was cut off.

6. The method for analyzing voltage sag regions in distribution networks considering distributed generation access as described in claim 1, characterized in that, The characteristic equation of the voltage sag region includes: The characteristic equation for the voltage sag region of a single-phase ground fault is expressed as: ； Meanwhile, the characteristic equation for the voltage sag region of an interphase fault is expressed as: ； The characteristic equation for the voltage sag region of a two-phase ground fault is expressed as: ； In the formula, , , These represent the fault points. Positive-sequence fault current, negative-sequence fault current and zero-sequence fault current at the location; , , Let these represent the positive-sequence voltage, negative-sequence voltage, and zero-sequence voltage of node j, respectively. , , These are the f-th columns of the three-order node impedance matrix after splitting.

7. The method for analyzing voltage sag regions in distribution networks considering distributed generation access as described in claim 1, characterized in that, The method of dividing the path from the sensitive node to the end of the line into several recessed subsystems includes: when there is no tie line in the distribution network, defining the complete path from the sensitive node to each end of the line as an independent recessed subsystem; When a distribution network has tie lines forming a ring network, the node with the lowest voltage on each tie line is obtained based on power flow calculations. The node with the lowest voltage is taken as the end of the line, thereby forming the corresponding recessed subsystem.

8. The method for analyzing voltage sag regions in distribution networks considering distributed generation access as described in claim 1, characterized in that, In step S4, a reduced-order processing is performed on the target line segment to form a reduced-order nodal impedance matrix with respect to the fault location parameters, including: Sensitive nodes, fault nodes, and critical bifurcation nodes are retained in the target line segment. Other intermediate nodes are equivalently eliminated, and multiple series line impedances are merged into one equivalent impedance. This constructs a reduced-order node impedance matrix with respect to fault location parameters, ensuring that the reduced-order node impedance matrix maintains the same parameterization characteristics as the three-order node impedance matrix in step S2.

9. The method for analyzing voltage sag regions in distribution networks considering distributed generation access as described in claim 1, characterized in that, The step of determining the fault location parameters that cause the remaining voltage to reach a preset voltage threshold through an optimization iteration method, in order to obtain the voltage sag region boundary of the sensitive node, specifically includes: Within the recessed subsystem and target line segment determined in step S4, initial values ​​for the fault location parameters are set. The fault location parameters are used as iterative variables, and the fault location parameters are obtained by iteratively solving the general equation for the voltage sag region. and the corresponding system node injected current vector : According to the system node injected current vector Calculate the normal components of each sequence voltage at each node of the system without introducing fault short-circuit current. And further obtain the fault node. Normal components of voltage sequence at each point The formula is: ; Based on the fault location parameters Constructing a reduced-order nodal impedance matrix And obtain the fault node in the reduced-order node impedance matrix. Corresponding self-impedance ; Fault node Corresponding self-impedance and normal components of voltage sequence Substituting the corresponding characteristic equation of the voltage sag region, the parameters of the fault location are obtained by solving the equation. short circuit current ; short-circuit current and the reduced-order nodal impedance matrix Substitute into the following formula, where For fault location parameters: ； The sensitive nodes are obtained by solving. Three-sequence voltage The corresponding residual voltage is obtained through inverse transformation of the sequence components; where The three-order nodal impedance matrix after splitting The k-th row in the data; For parameters regarding fault location Three-order nodal impedance matrix The element in the k-th row and f-th column; Sensitive nodes The critical voltage of the voltage withstand curve of the connected sensitive equipment; Three-sequence voltage Obtained using the inverse Fortescue transform; When the remaining voltage does not reach the preset voltage threshold, the fault location parameter is updated as follows: The above iterative process continues; when the remaining voltage reaches the preset voltage threshold, the corresponding fault location parameter is determined as the boundary of the voltage sag depression domain within the depression subsystem.

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