A sensitivity propagation-based unbalanced distribution network voltage support early warning method and system

Abstract

The application discloses a kind of unbalanced distribution network voltage support early warning method and system based on sensitivity propagation, belong to power system technical field.The method includes: based on the network topology structure and element characteristics of unbalanced distribution network, composite bus model is constructed;Based on composite bus model, enhanced Jacobian matrix is constructed, and voltage response relationship is obtained based on enhanced Jacobian matrix;Based on voltage response relationship and branch phase separation reactive power change relationship, branch phase separation reactive-voltage support coefficient matrix is constructed;Based on branch phase separation reactive-voltage support coefficient matrix, multi-phase voltage support directed graph is obtained;Based on multi-phase voltage support directed graph, support gap type voltage out-of-limit early warning quantity is obtained, and out-of-limit risk early warning is carried out based on support gap type voltage out-of-limit early warning quantity.The application can identify the influence of insufficient branch phase separation support capability on downstream node voltage risk, improve the accuracy of complex distribution network voltage out-of-limit early warning and support path identification ability.

Description

Technical Field

[0001] This invention belongs to the field of power system technology, specifically relating to a method and system for early warning of voltage support in unbalanced distribution networks based on sensitivity propagation. Background Technology

[0002] With the high proportion of distributed energy sources connected to the grid and the mixed connection of single-phase, two-phase, and three-phase loads, the distribution network operation exhibits significant imbalance characteristics. At the same time, the output of distributed power sources such as photovoltaics is volatile and uncertain, causing the power flow of the distribution network to gradually change from the traditional unidirectional radial type to a multi-source active type. Problems such as node voltage exceeding limits, insufficient local reactive power support, and frequent operation of voltage regulating equipment have become more prominent.

[0003] Existing methods for assessing and providing early warning of voltage support in distribution networks have the following shortcomings. Firstly, the analytical efficiency and adaptability of the underlying voltage response relationships are insufficient. When the system contains multiphase Delta / Wye mixed loads, step voltage regulators, and smart inverters with Volt-VAR droop control characteristics, traditional single-phase balance models struggle to accurately describe the voltage response relationships in unbalanced networks. While numerical perturbation power flow methods can obtain approximate results, they require repeated calls to the power flow program, resulting in significant computational overhead and failing to meet the needs of online assessment and real-time early warning.

[0004] On the other hand, existing voltage support capability assessments mostly focus on the node level, such as identifying weak nodes and voltage-related regions based on node reactive power-voltage sensitivity, short-circuit ratio, or electrical distance between nodes. While these methods can reflect the local response of node voltage to power disturbances, they struggle to further characterize the transmission direction of reactive power support capability between different phases of the branch, cross-phase coupling relationships, and the impact of changes in upstream support links on downstream node voltage risks. Therefore, when the reactive power support capability of critical branches deteriorates, existing methods struggle to identify weak support paths and their impact on downstream node voltage exceedance risks from the perspective of branch phase-by-phase support propagation.

[0005] In summary, existing technologies still have shortcomings in analyzing voltage response relationships in unbalanced distribution networks, characterizing the reactive power-voltage support capacity of branch phases, and providing early warning of voltage overruns along support paths. As a result, the accuracy and foresight in predicting voltage overrun risks in complex distribution networks need to be improved. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for early warning of voltage support in unbalanced distribution networks based on sensitivity propagation. This method, taking into account the effects of multiphase loads, distributed energy smart inverters, and step voltage regulators, analyzes and obtains the voltage response relationship between power injection, voltage regulation equipment operation, and node voltage changes in unbalanced distribution networks. Furthermore, it converts this voltage response relationship into a branch-phase reactive power-voltage support relationship. By constructing a branch-phase reactive power-voltage support coefficient set, a multiphase voltage support directed graph, and a support gap-type voltage exceedance early warning quantity, this invention can identify the impact of insufficient branch-phase support capacity on downstream node voltage risks, improving the accuracy of voltage exceedance early warning and the support path identification capability in complex distribution networks.

[0007] To achieve the above objectives, the present invention provides the following solution: a method for early warning of voltage support in unbalanced distribution networks based on sensitivity propagation, comprising the following steps: S1: Construct a composite bus model based on the network topology and component characteristics of the unbalanced distribution network; S2: Construct an enhanced Jacobian matrix based on the composite bus model, and obtain the voltage response relationship based on the enhanced Jacobian matrix; S3: Based on the voltage response relationship and the branch phase reactive power change relationship, construct the branch phase reactive power-voltage support coefficient group; the branch phase reactive power-voltage support coefficient group includes the corresponding RPVS index of each branch. S4: Based on the branch phase reactive power-voltage support coefficient group, a multiphase voltage support directed graph is obtained; S5: Based on the multiphase voltage support directed graph, obtain the support gap type voltage over-limit warning quantity, and perform over-limit risk warning based on the support gap type voltage over-limit warning quantity.

[0008] More preferably, S1 includes the following steps: S11: Model the nodes in the unbalanced distribution network as a composite bus that includes Wye-type connected loads, Delta-type connected loads, and distributed energy sources with Volt-VAR intelligent inverter control characteristics; through matrix transformation, convert Delta-type connected loads into equivalent Wye-type connected loads, and take into account the droop control characteristics of distributed energy sources that dynamically adjust reactive power according to terminal voltage deviation, and establish a multiphase current injection balance equation; S12: Analyze the power coupling relationship of heterogeneous loads and convert the multiphase current injection balance equation into a three-phase injection current equivalent equation; S13: Based on the three-phase injection current equivalent equation, and combined with the distributed energy intelligent inverter control standard, the photovoltaic output is converted into the Volt-VAR dynamic segmented response form and active power output constraints. After modeling all active nodes of the unbalanced distribution network, the composite bus model is obtained.

[0009] More preferably, S2 includes the following steps: S21: Construct the complex admittance matrix of the unbalanced network with step voltage regulator taps, and convert the network complex current and voltage equations into real augmented forms; S22: Perform a first-order Taylor expansion of the real augmented form at the current running point, and construct the enhanced Jacobian matrix equation by combining the partial derivative matrix derived from the composite bus model. S23: The voltage response relationship is obtained by analytically inverting the chain rule and the total differential matrix of the enhanced Jacobian matrix equation after polar coordinate transformation.

[0010] More preferably, S3 includes the following steps: S31: Construct the branch phase RPVS index based on the voltage response relationship and the branch local response relationship; S32: Construct the series support attenuation relationship and parallel support superposition relationship of the branch phase RPVS index.

[0011] More preferably, S4 includes the following steps: S41: Define the phase vertices of each node and the effective supporting edges of RPVS; S42: Generate the multiphase voltage support directed graph based on the effective support edge of RPVS, and trace the upstream support path of the target phase of the target node.

[0012] More preferably, S5 includes the following steps: S51: Calculate the voltage limit margin of the target phase at the target node and the reactive power support required to maintain the voltage within the limit. S52: Calculate the equivalent phase-by-phase voltage support capability of the target phase at the target node based on the multiphase voltage support directed graph; S53: Based on the difference between the required reactive power support and the equivalent phase voltage support capability, construct a support gap type voltage over-limit early warning quantity and trigger a graded early warning.

[0013] The present invention also provides an unbalanced distribution network voltage support early warning system based on sensitivity propagation, comprising: Model building module: used to build composite bus models based on the network topology and component characteristics of unbalanced distribution networks; Response analysis module: used to construct an enhanced Jacobian matrix based on the composite bus model, and to obtain the voltage response relationship based on the enhanced Jacobian matrix; Support coefficient group construction module: used to construct the branch phase reactive power-voltage support coefficient group based on the voltage response relationship and the branch phase reactive power change relationship; Support Directed Graph Generation Module: Used to obtain a multiphase voltage support directed graph based on the branch phase reactive power-voltage support coefficient group; Support gap early warning module: used to obtain the support gap type voltage over-limit early warning quantity based on the multiphase voltage support directed graph, and to perform over-limit risk early warning based on the support gap type voltage over-limit early warning quantity.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention provides a method and system for early warning of voltage support in unbalanced distribution networks based on sensitivity propagation. By establishing a composite bus model including 1-3 phase mixed loads, the Volt-VAR droop characteristics of intelligent inverters, and the action of step voltage regulators, and embedding its power injection and control relationships into a real-valued enhanced Jacobian matrix, the response relationship of node voltage to power injection and voltage regulation equipment action under the current operating section can be analytically obtained. Based on this, the present invention further combines the reactive power variation relationship of each phase of the branch to construct a branch-specific reactive power-voltage support coefficient set, which is used to characterize the phase-specific support and cross-phase coupling effects of reactive power variations in different branches and different operating phases on downstream node voltage. Furthermore, a multiphase voltage support directed graph is generated based on the branch phase reactive power-voltage support coefficient group. Combined with the voltage limit margin of the target phase of the target node, the reactive power support required to maintain the voltage from exceeding the limit, and the equivalent phase voltage support capability of the upstream path, a support gap type voltage limit exceeding early warning quantity is constructed. This allows for early identification of the downstream node voltage limit exceeding risk when the branch phase support capability is insufficient, thereby improving the accuracy of voltage support early warning and the support path identification capability of complex distribution networks. Attached Figure Description

[0015] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are 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.

[0016] Figure 1 This is a flowchart illustrating the steps of an unbalanced distribution network voltage support early warning method based on sensitivity propagation, as provided in an embodiment of the present invention. Figure 2 This is a schematic diagram illustrating the analytical process of the relationship between the real-valued enhanced Jacobian matrix and voltage response provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the branch phase reactive power-voltage support coefficient group and RPVS propagation equivalent provided in the embodiment of the present invention; Figure 4 This is a schematic diagram of the multiphase voltage support directed graph generation process based on the RPVS index provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of upstream support path tracing for a target node provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of the support gap type voltage over-limit early warning mechanism provided in an embodiment of the present invention; Figure 7 This is a structural block diagram of an unbalanced distribution network voltage support early warning device based on sensitivity propagation, provided in an embodiment of the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] Example 1: This embodiment provides a voltage support early warning method for unbalanced distribution networks based on sensitivity propagation. Addressing the voltage support assessment problem in distribution networks under the combined effects of multi-phase load imbalance, reactive power regulation by distributed energy inverters, and step voltage regulator operation, the method first constructs a composite bus model and a real-valued augmented Jacobian matrix to analytically obtain the response relationship between node voltage and power injection and voltage regulation equipment operation. Second, combining the reactive power variation relationship of each phase in the branch, the node voltage response relationship is converted into a branch-phase reactive power-voltage support coefficient set, which includes the corresponding RPVS index for each branch. Finally, a multi-phase voltage support directed graph is constructed based on the RPVS index, and the risk of exceeding the limit for the target phase of downstream nodes is identified through a support gap-type voltage exceedance early warning quantity. Therefore, this embodiment does not directly use the node voltage response relationship as the basis for exceeding the limit judgment, but further characterizes the process of reactive power support capability propagating along the branch-phase units to downstream nodes. Starting from the relationship between the branch-phase RPVS index, the upstream support path, and the reactive power support required by the target node, it achieves early warning of voltage exceedance risks in unbalanced distribution networks.

[0020] In this embodiment, the voltage response relationship is obtained through a composite bus model and a real-valued augmented Jacobian matrix. Furthermore, a branch-specific reactive power-voltage support coefficient set is constructed by combining the reactive power variation relationship of each phase. Based on the RPVS index in this coefficient set, a multi-phase voltage support directed graph can be formed, with each phase of the node as the vertices, the effective reactive power support relationship as the directed edges, and the RPVS index as the edge weights. By tracing the upstream support path of the target phase of the target node, and combining the voltage limit margin and required reactive power support of the target phase, a support gap-type voltage exceedance early warning quantity can be constructed, thereby achieving early warning of voltage exceedance risks in unbalanced distribution networks.

[0021] Specifically, such as Figure 1 As shown, this embodiment provides an early warning method for unbalanced distribution network voltage support based on sensitivity propagation, including the following steps: S1: Based on the network topology and component characteristics of unbalanced distribution networks, the power coupling relationship of heterogeneous components in unbalanced distribution networks is analyzed, and a composite bus model including multiphase loads, distributed energy intelligent inverters and step voltage regulators is constructed.

[0022] In this embodiment, S1 includes the following steps: S11: Model the nodes in the unbalanced distribution network as a composite bus that includes Wye-type connected loads, Delta-type connected loads, and distributed energy sources with Volt-VAR intelligent inverter control characteristics; through matrix transformation, convert Delta-type connected loads into equivalent Wye-type connected loads, and take into account the droop control characteristics of distributed energy sources that dynamically adjust reactive power according to terminal voltage deviation, and establish multiphase current injection balance equations.

[0023] Specifically, the system parameters are first input and the model is initialized. The input system parameters include, but are not limited to: the network topology of the unbalanced distribution network, the multiphase impedance parameters of the lines, the transformer ratio, the Delta / Wye load distribution characteristics, the DER location and control dead zone parameters, and the initialized model is the constructed multiphase composite bus model.

[0024] This embodiment takes the input system parameters of multiphase loads and distributed energy connection methods and rated power as an example. For a distribution network with severe imbalance characteristics, because traditional single-type nodes cannot truly reflect the physical characteristics of heterogeneous loads, the nodes in the network are... The model is constructed as a composite entity encompassing multiple operating states, and its multiphase current injection balance equation is shown below: (1) In the formula, Represents a node exist The total injected current vector of the phase; Represents a node Phase injection current generated by a Wye-type (star-connected) load; Represents a node Phase injection current after equivalent transformation of Delta-type (triangle) connected load; Represents a node The phase current injected by the distributed energy source; a , b , c These represent phases A, B, and C of the power distribution network, respectively.

[0025] S12: Analyze the power coupling relationship of heterogeneous loads and convert the multiphase current injection balance equation into the three-phase injection current equivalent equation.

[0026] This embodiment takes a Wye-type connected load as an example. Since it is directly grounded or connected to the neutral point, its current injection can be directly obtained through the node phase voltage. The relationship between its phase voltage and power is expressed as follows: (2) In the formula, and These represent the Wye load at... The given active and reactive power of the phase; Represents a node The actual phase voltage; Represents the operation of conjugate complex numbers; j Represents the imaginary unit, satisfying .

[0027] For Delta-type connected loads, the actual power consumed is not based on single-phase voltage, but on inter-line voltage. To standardize calculations, the inter-line current injection must be mapped to the phase nodes via the inter-phase coupling transformation matrix. The equivalent equation for the three-phase current injection is: (3) In the formula, and These represent Delta loads between lines. (For example The active and reactive power between phases; This represents the line voltage difference between two phases; This represents the standard Delta-Wye current phase-to-phase coupling transformation matrix.

[0028] in, (4) S13: Based on the three-phase injection current equivalent equation, combined with the distributed energy intelligent inverter control standard, the photovoltaic output is converted into the Volt-VAR dynamic segmented response form and active power output constraints. After modeling all active nodes of the unbalanced distribution network, a composite bus model is obtained.

[0029] Under modern power grid standards, inverters are no longer purely PQ (constant power) nodes. Transforming the reactive power output characteristics of photovoltaic inverters in the distribution network to a dynamic droop control domain can be achieved by using a nonlinear piecewise control function to convert the inverter's reactive power output into dynamic parameters strongly coupled to the terminal voltage. The resulting Volt-VAR dynamic response is expressed as follows: (5) In the formula, Indicating distributed energy in The actual reactive power output; This represents the slope coefficient of the droop feedback control in the intelligent inverter. This indicates the center reference voltage of the control dead zone; and These represent the lower and upper limits of the voltage control dead zone, respectively. This indicates the maximum allowable reactive power capacity of the inverter.

[0030] Furthermore, the active power output characteristics of distributed energy sources are dynamically constrained by reactive power output as follows: (6) In the formula, Indicates that the smart inverter is in The rated maximum apparent power of the phase; This represents the dynamic active power output that satisfies the apparent power physical boundary conditions.

[0031] In summary, nodes The composite busbar model is represented as: (7) In the formula, Represents a node The composite bus current injection vector; Represents a node The phase voltage vector; Represents a node The line voltage vector; and These represent the three-phase active power and reactive power vectors of the Wye-type load, respectively. and These represent the line-to-line active power and reactive power vectors of Delta-type loads, respectively. and These represent the active power vector and the reactive power vector determined by the terminal voltage of the distributed energy source, respectively.

[0032] This embodiment utilizes the droop mechanism of a smart inverter to transform a constant power source into a sensitivity adaptive adjustment domain dominated by terminal voltage deviation through dynamic response dead zone and its upper and lower limit boundary constraints. After modeling all active nodes of the distribution network, a composite bus model covering multiphase asymmetry factors and active control characteristics can be obtained.

[0033] S2: Construct the admittance matrix based on the composite bus model and convert the admittance matrix into a real augmented form; construct the enhanced Jacobian matrix by combining the nonlinear power injection equation and control equation of the composite bus, and analyze the voltage response relationship between the node voltage magnitude and phase angle and the changes in active power injection, reactive power injection and regulator tap position.

[0034] First, a complex admittance matrix for the unbalanced network considering the tap positions of the step voltage regulator (SVR) is established and transformed to the real component domain. Specifically, by combining the principle of separating the real and imaginary parts, the complex admittance matrix and the complex voltage-current equations are converted into a real-valued augmented form, resulting in a real-valued decoupled architecture. Simultaneously, the nonlinear power injection partial derivative matrix of the composite bus is directly constructed. Finally, based on the first-order Taylor expansion of the composite bus equations, the network admittance parameters are integrated with the partial derivatives of the composite load and inverter using the total differential analytical inversion method to form an enhanced Jacobian matrix, completing the analysis of the voltage response relationship. The calculated voltage response relationship is used to characterize the response characteristics of the node voltage amplitude and phase angle under the current operating section as a function of power injection and voltage regulation equipment. Figure 2 The diagram shows the analytical process for enhancing the relationship between the Jacobian matrix and the voltage response.

[0035] Specifically, S2 includes the following steps: S21: Construct the complex admittance matrix of the unbalanced network with step voltage regulator (SVR) taps, and convert the network complex current-voltage equations into real augmented forms.

[0036] For distribution networks, when the SVR tap is activated, its complex admittance matrix is ​​typically dynamically changing. In this case, a corrected network admittance matrix including tap variables can be directly constructed. The baseline admittance matrix is ​​formed by the rated parameters of the lines and transformers; the incremental admittance matrix is ​​usually related to the correction amount caused by the tap change. In this embodiment, the unbalanced network complex admittance matrix considering the SVR is expressed in the following linear combination form: (8) In the formula, This represents the base rated admittance matrix; Indicates the first The regulator changes the gear. The increment of the admittance matrix caused by time; This represents the collection of voltage regulators across the entire network.

[0037] The relationship between the specific tap ratio coefficient of the SVR and its mechanical gear step size is expressed as follows: (9) In the formula, This indicates the current discrete physics level value; This indicates the per-unit change in voltage during single-step adjustment. This indicates the reference value for the rated voltage.

[0038] Since the voltage amplitude does not satisfy the Cauchy-Riemann differentiability condition in the complex domain, in order to directly solve the voltage and power using partial derivatives analytically, the complex equations are decomposed into two independent systems of real equations. The complex equations are then transformed into an augmented real form consisting of real and imaginary parts, as follows: (10) In the formula, and These represent the real and imaginary parts of the current vector injected into all nodes in the network, respectively. and These represent the real and imaginary parts of the voltage vector at all nodes in the network, respectively. and The conductivity matrix block and the susceptance matrix block represent the power grid admittance matrix, respectively.

[0039] S22: Perform a first-order Taylor expansion of the real augmented form at the current running point, and construct the enhanced Jacobian matrix equation by combining the partial derivative matrix derived from the multiphase composite bus model.

[0040] In this embodiment, for a local sub-block of the Jacobian matrix, the exact partial derivative matrix of the real part of the current with respect to the real part of the voltage is... And the exact partial derivative matrix of the imaginary part of the current with respect to the imaginary part of the voltage. The internal elements are as follows: (11) In the formula, and Representing nodes respectively Real part of injected current For nodes Real part of voltage partial derivatives and nodes Imaginary part of injected current For nodes Imaginary part of voltage The partial derivative coefficients; and Representing nodes respectively The real and imaginary parts of the injected current; and Representing nodes respectively The real and imaginary parts of voltage.

[0041] Because the system takes into account the Volt-VAR droop characteristics of the smart inverter, with nodes Taking controlled distributed energy (DER) as an example, each partial derivative element in equation (11) is obtained by analytically differentiating the current injection equation and Volt-VAR control equation of the aforementioned composite bus model, i.e., equations (1) to (7), at the current operating point. Specifically, when the node voltage is outside the control dead zone (i.e. When ), according to the chain rule, and It will include by The introduced additional micro-business items, with For example, its analytical expression is as follows: (12) In the formula, Represents a node The real part of the voltage; Represents a node The imaginary part of the load injection current.

[0042] Among them, due to This item is for The partial derivatives are non-zero, thus accurately mapping the reactive voltage response characteristics of the inverter to... In the diagonal elements of the matrix.

[0043] Then, calculate the total network injection current for each tap. The biased directional quantity. Finally, the above... and The derivative terms are filled into the corresponding positions in the augmented real matrix to form the complete augmented Jacobian matrix equation: (13) In the formula, and Let represent the real part increment vector and the imaginary part increment vector of the injected current at all nodes in the network, respectively. and Let represent the real part increment vector and the imaginary part increment vector of the voltage at all nodes in the network, respectively. This represents the vector of changes in the tap position of the step voltage regulator across the entire network.

[0044] S23: Obtain the voltage response relationship by taking the chain rule and analytical inversion of the total differential matrix of the enhanced Jacobian matrix equation after polar coordinate transformation.

[0045] The enhanced Jacobian matrix is ​​used to define total differential relationships in Cartesian coordinates. However, engineering scheduling focuses more on voltage magnitudes in polar coordinates. and phase angle By introducing a polar coordinate chain transformation matrix This maps the Cartesian coordinate relationship to the polar coordinate domain. In this embodiment, the transformation matrix equation is expressed as: (14) In the formula, and These represent the voltage amplitude increment vector and voltage phase angle increment vector of all network nodes, respectively.

[0046] After completing the coordinate system transformation, the matrix equations obtained through the above total differential reconstruction can be analytically inverted to obtain the voltage response relationship, which includes the voltage magnitude and phase angle with respect to active power injection, reactive power injection, and changes in regulator tap position. Its specific expression is shown in the following equation: (15) In the formula, , , These represent the sub-matrices representing the system voltage magnitude in response to active power, reactive power, and transformer taps, respectively. Used to characterize the response of changes in reactive power injection in each phase of a node to changes in the node voltage amplitude; , , These represent the sub-matrices representing the voltage response of the system voltage phase angle to active power, reactive power, and transformer taps, respectively. and These represent the incremental vectors of active power injection and reactive power injection for each phase of the entire network nodes, respectively.

[0047] S3: Based on the voltage response relationship and the reactive power change relationship of each branch phase, a branch phase reactive power-voltage support coefficient group is constructed. In this embodiment, the branch phase reactive power-voltage support coefficient group includes the corresponding RPVS index for each branch. The RPVS index is used to represent the support effect of the reactive power change of a specified phase in a specified branch on the voltage change of the target phase at the receiving end node. The support effect includes the support effect of the phase itself and the cross-phase coupling support effect.

[0048] like Figure 3 As shown, the branch phase RPVS index is used to describe the supporting effect of the reactive power change of a specified phase of the branch on the target phase voltage of the receiving node.

[0049] Figure 3 The upper part is an equivalent model of series branch support. Figure 3 In the upper part, Node 1 represents the upstream reactive power support source; Node 2 and Node 3 represent the bus nodes on the support path; L1 and L2 represent the branches connecting Node 1 and Node 2, and Node 2 and Node 3, respectively. , and These represent the target phase voltage magnitude increments at nodes 1, 2, and 3, respectively. This represents the incremental reactive power regulation power transmitted to node 3 along the series support path; and These represent the response coefficients of reactive power transmission in branches L1 and L2 to changes in the amplitude of their sending-end voltage, respectively. and These represent the reactive power-voltage support coefficients of branch L1 and branch L2, respectively. The reactive power support capacity in the series path is transmitted sequentially through branch L1 and branch L2. Therefore, the equivalent support capacity of the path is affected by the support capacity of both branches and the propagation attenuation characteristics.

[0050] Figure 3 The lower part is the equivalent model of parallel branch support. Figure 3 In the second half, and Node 1 and Node 2 represent the sending nodes of two parallel support paths, respectively; Node 3 represents the target node for the aggregation of support capabilities; L1 and L2 represent two parallel branches. , and These represent the target phase voltage magnitude increments at the corresponding nodes; and These represent the response coefficients of the reactive power transmission of the two branches to changes in the amplitude of the sending-end voltage, respectively. and These represent the reactive power-voltage support coefficients of the two parallel branches, respectively. This represents the reactive power adjustment increment formed by the convergence of the two upstream support paths at target node 3. For parallel support relationships, the effective support capabilities and weights of each path should be superimposed to obtain the equivalent phase voltage support capability that the target node can obtain.

[0051] For series branches, the equivalent relationship of support attenuation can be calculated based on the RPVS index along the path; for parallel branches, the equivalent relationship of support superposition can be calculated based on the RPVS index of different branches at the converging node. Through the above processing, the equivalent phase voltage support capability that the target phase of the target node can obtain from the upstream support path can be obtained.

[0052] S3 includes the following steps: S31: Construct the branch phase RPVS index based on voltage response relationship and branch local response relationship.

[0053] Voltage response relationships can characterize the impact of changes in reactive power injection in each phase of a node on the voltage amplitude of the target phase at the target node. For connected nodes... With nodes For multi-phase branches, a local response relationship can be established between the reactive power increment of each phase of the branch and the voltage amplitude and phase angle increments of each phase at both ends of the branch. Furthermore, by chaining the local response relationship with the reactive power-voltage response relationship according to the node phase indices, the branch-specific RPVS index can be obtained. (16) In the formula, Indicates a branch The phase RPVS index is used to characterize the branch. of When the reactive power of a phase changes, for the receiving end node of The supporting effect generated by the phase voltage amplitude; Indicates the receiving node of Phase voltage amplitude; Indicates a branch of Phase reactive power; and These represent the operating phases of the distribution network, and , A, B, and C can be chosen to represent phase A, phase B, and phase C of the distribution network, respectively. When When, it indicates the supporting role of the original phase; when When, it indicates the cross-phase coupling support effect.

[0054] S32: Construct the series support attenuation relationship and parallel support superposition relationship of the branch phase RPVS index.

[0055] A power distribution network is a complex network composed of multiple cascaded branches. For series branches, the reactive power-voltage support capability is affected by factors such as line impedance, reactive power loss, and downstream load during transmission, exhibiting a gradual attenuation characteristic. In this embodiment, the series support attenuation relationship is expressed as: (17) In the formula, This represents the equivalent phase RPVS index on the target support path; This represents the set of branches along the direction of reactive power propagation. Indicates a branch The propagation attenuation coefficient of the reactive power-voltage support capability transmission process; This represents the set of branches that constitute the upstream support path of the target; This indicates that the support path is located on a branch. Upstream, and prior to the branch road A set of branches that transmit reactive power support capabilities.

[0056] In this embodiment, the propagation attenuation coefficient is expressed as: (18) In the formula, Indicates a branch reactive power loss; Indicates a branch The reactive power flowing into this branch from the transmitting end.

[0057] Equation (18) reveals the reactive power loss of the line. An increase in reactive power will cause the reactive power-voltage support capability to decrease gradually along the path.

[0058] On the other hand, during the support superposition process of parallel branches at the convergence node, multiple upstream support paths can work together on the target node. In this embodiment, the parallel support superposition relationship is as follows: (19) In the formula, Represents the target node The obtained equivalent phase RPVS index; Indicates the target node to be injected. The set of all incoming branch lines; Indicates a branch The supporting superimposed weight coefficient.

[0059] By understanding the attenuation relationship of series supports and the superposition relationship of parallel supports, the propagation, attenuation, and convergence process of reactive power-voltage support capacity in the physical grid can be reconstructed.

[0060] S4: Based on the branch-phase reactive power-voltage support coefficient set, a multiphase voltage support directed graph is obtained, and the upstream support path of the target phase of the target node is traced. For example... Figure 4 , Figure 5 The diagram shows the process of generating a multiphase voltage support directed graph based on the RPVS index and the upstream support path tracing diagram of the target node and target phase.

[0061] Figure 5 This illustrates the path tracing relationship when multiple upstream reactive power support sources exist for the target node. Figure 5 middle, and These represent upstream support sources capable of providing reactive power regulation to the target node; Nodes 1 to 5 represent bus nodes in the distribution network. , , and These represent the voltage amplitude of the target phase at the corresponding node; and These represent the equivalent impedances of the branches between node 1 and node 2, and between node 2 and node 3, respectively. The shaded areas in the figure represent upstream support path 1 and upstream support path 2, formed by different support sources, respectively.

[0062] In a multiphase voltage support directed graph, starting from the target phase at the target node, the path is backtracked upstream along the directed edge that satisfies the effective support edge criterion of RPVS until the target is reached. or The source nodes are represented, thus obtaining the set of upstream support paths corresponding to the target node. Different support paths can contain independent branches, or they can have common branches or shared propagation segments; for common branches, they are only included once when calculating the equivalent phase voltage support capacity of the target node to avoid double-counting the support contribution.

[0063] S4 includes the following steps: S41: Define the phase vertices of the node and the effective support edges of RPVS.

[0064] Each operating phase of each bus node is treated as a vertex in a multiphase voltage support directed graph. For connection nodes... With nodes branch road Based on the amplitude and sign of the branch phase RPVS index, determine the branch Can a change in the reactive power of a certain phase affect the receiving-end node? The target phase voltage is effectively supported. When the RPVS index amplitude is greater than the preset effective support threshold, and the corresponding reactive power support direction can restore the target phase voltage of the target node to the allowable range, the branch phase unit is determined as an effective reactive power support edge; otherwise, the corresponding effective reactive power support edge is not established. The determination relationship is expressed as follows: (20) In the formula, Indicates a branch of relative receiving node of Effective supporting edge rights formed by phases; This indicates the preset effective support threshold; Indicates a branch of Phase reactive power change for receiving node of Whether the phase voltage meets the voltage recovery direction criterion is set to 1 if it does not meet the criterion.

[0065] S42: Generate a multiphase voltage support directed graph based on the effective support edge of RPVS, and trace the upstream support path of the target phase of the target node.

[0066] Based on the effective RPVS support edges determined in S41, a multiphase voltage support directed graph is generated with each phase of the node as a vertex, the effective reactive power support relationship as a directed edge, and the RPVS index as the edge weight. For the target phase of the target node, a path search is performed upstream along the effective reactive power support edges in the multiphase voltage support directed graph, starting from the target phase of the target node, to obtain the set of upstream support paths corresponding to the target node.

[0067] In this embodiment, a depth-first search algorithm is used to search for the upstream support path of the target phase of the target node in the multiphase voltage support directed graph. The depth-first search algorithm is only used as a path search tool and is not used as a direct basis for determining the risk of voltage exceedance. By tracing the set of upstream support paths, the main sources of reactive power support for the target phase of the target node can be determined, and a foundation can be provided for subsequent calculation of equivalent phase voltage support capacity and construction of support gap-type voltage exceedance early warning quantity.

[0068] S5: Obtain the over-limit warning quantity of the support gap type voltage based on the multiphase voltage support directed graph, and perform over-limit risk warning based on the support gap type voltage over-limit warning quantity.

[0069] like Figure 6 The diagram shown illustrates a support mechanism for a gap-type voltage over-limit early warning system. S5 includes the following steps: S51: Calculate the voltage limit margin of the target phase at the target node and the reactive power support required to maintain the voltage within the limit.

[0070] The voltage limit margin of the target phase at the target node can be determined based on the distance between the current voltage and the upper or lower voltage limit, and its expression can be expressed as: ;(twenty one) In the formula, Represents the target node of Phase voltage limit margin; Represents the target node of Equivalent to the amplitude of the preceding voltage; and These represent the lower limit and upper limit of the allowable voltage, respectively.

[0071] When the target phase of the target node is close to the lower voltage limit, the required reactive power support amount is used to represent the reactive power support capability required to maintain the voltage of the target phase at or above the lower limit; when the target phase of the target node is close to the upper voltage limit, the required reactive power support amount is used to represent the reactive power regulation capability required to suppress the voltage of the target phase from continuing to rise.

[0072] Furthermore, based on the voltage limit margin of the target phase at the target node and the reactive power-voltage response relationship, the reactive power support required to maintain the voltage of the target phase at the target node within the limit can be calculated, and its expression is as follows: ;(twenty two) In the formula, Indicates maintaining the target node of The amount of reactive power required to keep the phase voltage within limits; This indicates the preset voltage safety margin threshold. Represents the target node of Phase reactive power-voltage response coefficient. When Less than If this occurs, it indicates that the target phase voltage safety margin at the target node is insufficient, and reactive power support needs to be supplemented.

[0073] S52: Calculate the equivalent phase voltage support capability of the target phase at the target node based on the directed graph of multiphase voltage support.

[0074] In a multiphase voltage support directed graph, the upstream support path set of the target phase at the target node is traced, and the support capacity is equivalently calculated based on the phase RPVS index of each branch along the path, yielding the equivalent phase voltage support capacity that the target phase at the target node can obtain. The equivalent phase voltage support capacity that the target phase at the target node can obtain is expressed as: ;(twenty three) In the formula, Represents the target node of The equivalent phase voltage support capability that can be obtained from the upstream support path; Represents the target node of The corresponding set of upstream support paths; Indicates the first The equivalent phase RPVS index of the upstream support path; Indicates the first In the path The reactive power support margin that can be provided.

[0075] For series support paths, the support attenuation can be equivalently calculated based on the RPVS index of the path; for parallel support paths, the support superposition can be equivalently calculated based on the RPVS index of different paths.

[0076] S53: Based on the difference between the required reactive power support and the equivalent phase voltage support capability, construct a support gap type voltage over-limit early warning quantity and trigger a graded early warning.

[0077] The difference between the reactive power support required to maintain the voltage of the target phase at the target node within the limit and the equivalent phase voltage support capability that can be obtained is used as the support gap-type voltage over-limit warning quantity, and its expression is as follows: ;(twenty four) In the formula, Represents the target node of Phase support gap type voltage over-limit warning quantity; This represents the amount of reactive power required to maintain the target phase voltage at the target node within its limit. This indicates the equivalent phase voltage support capability that the target phase at the target node can obtain.

[0078] When the voltage over-limit warning amount of the support gap type exceeds the preset threshold, it is determined that there is a risk of voltage over-limit in the target phase of the target node, and the key branch phase unit is located according to the upstream support path that caused the support gap, thereby triggering a graded warning.

[0079] Based on the relationship between the support gap type voltage over-limit warning quantity and the preset threshold, the graded warning results of the target phase of the target node can be determined, and the judgment relationship is expressed as follows: (25) In the formula, Represents the target node of Phase voltage over-limit warning level; and These represent the Level 1 and Level 2 warning thresholds, respectively. When... When the value is 0, it indicates no warning; when... When it equals 1, it indicates a general warning; when A value of 2 indicates a severe warning.

[0080] Example 2: like Figure 7As shown, this embodiment provides a voltage support early warning system for unbalanced distribution networks based on sensitivity propagation, including: a model construction module for constructing a composite bus model based on the network topology and component characteristics of the unbalanced distribution network; a response analysis module for constructing an enhanced Jacobian matrix based on the composite bus model and obtaining the voltage response relationship based on the enhanced Jacobian matrix; a support coefficient group construction module for constructing a branch phase reactive power-voltage support coefficient group based on the voltage response relationship and the branch phase reactive power change relationship; a support directed graph generation module for obtaining a multi-phase voltage support directed graph based on the branch phase reactive power-voltage support coefficient group; and a support gap early warning module for obtaining a support gap type voltage over-limit early warning quantity based on the multi-phase voltage support directed graph and performing over-limit risk early warning based on the support gap type voltage over-limit early warning quantity.

[0081] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for early warning of unbalanced distribution network voltage support based on sensitivity propagation, characterized in that, Includes the following steps: S1: Construct a composite bus model based on the network topology and component characteristics of the unbalanced distribution network; S2: Construct an enhanced Jacobian matrix based on the composite bus model, and obtain the voltage response relationship based on the enhanced Jacobian matrix; S3: Based on the voltage response relationship and the branch phase reactive power change relationship, construct the branch phase reactive power-voltage support coefficient group; The branch phase reactive power-voltage support coefficient group includes the corresponding RPVS index for each branch. S4: Based on the branch phase reactive power-voltage support coefficient group, a multiphase voltage support directed graph is obtained; S5: Based on the multiphase voltage support directed graph, obtain the support gap type voltage over-limit warning quantity, and perform over-limit risk warning based on the support gap type voltage over-limit warning quantity.

2. The method for early warning of unbalanced distribution network voltage support based on sensitivity propagation according to claim 1, characterized in that, S1 includes the following steps: S11: Model the nodes in the unbalanced distribution network as a composite bus that includes Wye-type connected loads, Delta-type connected loads, and distributed energy sources with Volt-VAR intelligent inverter control characteristics; through matrix transformation, convert Delta-type connected loads into equivalent Wye-type connected loads, and take into account the droop control characteristics of distributed energy sources that dynamically adjust reactive power according to terminal voltage deviation, and establish a multiphase current injection balance equation; S12: Analyze the power coupling relationship of heterogeneous loads and convert the multiphase current injection balance equation into a three-phase injection current equivalent equation; S13: Based on the three-phase injection current equivalent equation, and combined with the distributed energy intelligent inverter control standard, the photovoltaic output is converted into the Volt-VAR dynamic segmented response form and active power output constraints. After modeling all active nodes of the unbalanced distribution network, the composite bus model is obtained.

3. The method for early warning of unbalanced distribution network voltage support based on sensitivity propagation according to claim 1, characterized in that, S2 includes the following steps: S21: Construct the complex admittance matrix of the unbalanced network with step voltage regulator taps, and convert the network complex current and voltage equations into real augmented forms; S22: Perform a first-order Taylor expansion of the real augmented form at the current running point, and construct the enhanced Jacobian matrix equation by combining the partial derivative matrix derived from the composite bus model. S23: The voltage response relationship is obtained by analytically inverting the chain rule and the total differential matrix of the enhanced Jacobian matrix equation after polar coordinate transformation.

4. The method for early warning of unbalanced distribution network voltage support based on sensitivity propagation according to claim 1, characterized in that, S3 includes the following steps: S31: Construct the branch phase RPVS index based on the voltage response relationship and the branch local response relationship; S32: Construct the series support attenuation relationship and parallel support superposition relationship of the branch phase RPVS index.

5. The method for early warning of unbalanced distribution network voltage support based on sensitivity propagation according to claim 1, characterized in that, S4 includes the following steps: S41: Define the phase vertices of each node and the effective supporting edges of RPVS; S42: Generate the multiphase voltage support directed graph based on the effective support edge of RPVS, and trace the upstream support path of the target phase of the target node.

6. The method for early warning of unbalanced distribution network voltage support based on sensitivity propagation according to claim 1, characterized in that, S5 includes the following steps: S51: Calculate the voltage limit margin of the target phase at the target node and the reactive power support required to maintain the voltage within the limit. S52: Calculate the equivalent phase-by-phase voltage support capability of the target phase at the target node based on the multiphase voltage support directed graph; S53: Based on the difference between the required reactive power support and the equivalent phase voltage support capability, construct a support gap type voltage over-limit early warning quantity and trigger a graded early warning.

7. A voltage support early warning system for unbalanced distribution networks based on sensitivity propagation, the system being used to implement the method as described in any one of claims 1-6, characterized in that, include: Model building module: used to build composite bus models based on the network topology and component characteristics of unbalanced distribution networks; Response analysis module: used to construct an enhanced Jacobian matrix based on the composite bus model, and to obtain the voltage response relationship based on the enhanced Jacobian matrix; Support coefficient group construction module: used to construct the branch phase reactive power-voltage support coefficient group based on the voltage response relationship and the branch phase reactive power change relationship; Support Directed Graph Generation Module: Used to obtain a multiphase voltage support directed graph based on the branch phase reactive power-voltage support coefficient group; Support gap early warning module: used to obtain the support gap type voltage over-limit early warning quantity based on the multiphase voltage support directed graph, and to perform over-limit risk early warning based on the support gap type voltage over-limit early warning quantity.

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