Method and system for power flow calculation and static voltage stability analysis of active power distribution network considering reactive power control of inverters

Abstract

This invention discloses a method and system for power flow calculation and static voltage stability analysis of active distribution networks considering inverter reactive power control. The method first analyzes the static characteristics of the inverter under different control modes, constructs a reactive power-voltage relationship model, and classifies distributed generation into PQ, PV, and PQ(V) types. During the forward-backward iteration process, a reactive power correction equation is introduced to achieve accurate power flow solutions for distributed generation (DG) with diverse control strategies. Based on the reactive power-voltage response characteristics of the DG, the system Jacobian matrix is ​​corrected, and a stability index is constructed by calculating the dominant eigenvalues ​​of the contracted Jacobian matrix. Based on the dominant mode participation factor and V-Q sensitivity, voltage-weak nodes and optimal compensation locations are identified. This invention considers both inverter reactive power control strategies and accurately evaluates the static voltage stability margin of active distribution network systems with a high proportion of DG, improving the accuracy of identifying voltage-weak nodes and selecting reactive power compensation locations in active distribution networks.

Description

Technical Field

[0001] This invention pertains to static voltage stability analysis of power systems, and relates to a method and system for active distribution network power flow calculation and static voltage stability analysis that takes into account inverter reactive power control. Background Technology

[0002] With the construction of new power systems, the penetration rate of distributed generation (DG), including photovoltaic (PV), wind power, and energy storage, in distribution networks is continuously increasing. According to relevant data, by the end of 2024, the cumulative installed capacity of distributed PV reached 370 million kilowatts, accounting for 42% of the total installed PV capacity in China. It has become an important form of new energy consumption. The large-scale integration of DG has transformed the operating characteristics of the distribution network from a single load to an active distribution network where loads and power sources coexist, exhibiting bidirectional power flow with the transmission network, fundamentally changing the distribution network's form. However, due to the volatility of new energy sources, when supply exceeds demand, backflow can occur, leading to line congestion and voltage exceeding limits, resulting in large power flow fluctuations and potential power output problems.

[0003] New-type distributed generation (DG) is mostly connected to the grid through inverters, and its static characteristics are more complex. The control modes are divided into grid-connected and grid-following types, and include various strategies such as constant power, constant voltage and droop control. Due to capacity limitations, its external characteristics are flexible and diverse, which increases the difficulty of distribution network analysis.

[0004] To accurately assess the operating status of distribution networks with a high proportion of distributed generation (DG), power flow calculations and static voltage stability assessments are required. Due to the numerous nodes and radial distribution network structure, current technologies employ the forward-backward substitution method for evaluation and analysis. However, this traditional method assumes constant load power and cannot handle DGs whose characteristics change with control strategies. Furthermore, the Newton-Raphson method is computationally too intensive for large-scale distribution networks.

[0005] In terms of static voltage stability assessment, existing L-index, VI-based indexes, and modal analysis methods have two main shortcomings: First, existing indexes are mostly based on the assumption of constant power load, ignoring the power regulation characteristics of distributed generation (DG), which leads to the analysis no longer meeting the assumptions. Second, the model accuracy is insufficient, as the impact of DG static characteristics and reactive power exceeding limits is not taken into account when calculating the Jacobian matrix, making it difficult to accurately identify weak links and instability risks in the system, and difficult to accurately reflect the impact of DG reactive power control strategies and static characteristics on the voltage stability of the distribution network. Summary of the Invention

[0006] In view of the defects and shortcomings of the existing technology, the present invention aims to overcome the shortcomings of the existing static voltage stability analysis of distribution networks, which does not fully consider the reactive power regulation characteristics and capacity limiting of distributed generation inverters, resulting in insufficient evaluation accuracy. The present invention proposes an active distribution network static voltage stability analysis method that takes into account the reactive power control of inverters. Under the premise of accurately reflecting the static characteristics of inverters under different control strategies, the method uses a stability index based on the dominant characteristic value to achieve quantitative evaluation of the distribution system, providing an effective means for identifying voltage weak nodes and optimizing reactive power compensation in distribution networks with a high proportion of distributed generation.

[0007] According to a first aspect of the present invention, a method for calculating the power flow and analyzing the static voltage stability of an active distribution network considering inverter reactive power control is proposed, comprising the following steps:

[0008] (1) Read active distribution network data containing inverters: obtain the network topology, line parameters and inverter data of active distribution network, analyze the static characteristics of inverter under different control modes, construct reactive power-voltage relationship model, and classify DG into three types: PQ type, PV type and PQ(V) type.

[0009] (2) Calculate the power flow of the active distribution network based on the reactive power correction equation: In the iterative process of the forward-backward substitution method, a reactive power correction equation is introduced to correct the reactive power for different types of DG, and the steady-state power flow and voltage of each node of the distribution network are calculated.

[0010] (3) Calculate the static voltage stability index of the active distribution network based on the dominant eigenvalue: Correct the system Jacobian matrix according to the reactive power-voltage response characteristics of the inverter, calculate the dominant eigenvalue of the contracted Jacobian matrix, and construct the static voltage stability index of the active distribution network.

[0011] (4) Determine the weak voltage nodes and optimal compensation locations in the active distribution network: Calculate the participation factors of each node based on the eigenvectors corresponding to the dominant eigenvalues ​​to identify the weak voltage nodes in the system, and combine the VQ sensitivity to determine the most effective reactive power compensation nodes for improving the system voltage stability.

[0012] As an optional implementation, in step (1), the reactive power-voltage relationship model includes:

[0013] For a PQ type DG, Q = Q ref ;

[0014] For a PV-type DG, U = U ref ;

[0015] For a PQ(V) type DG, Q = Q ref +k u / k q (U ref-U);

[0016] Among them, Q and Q ref These represent the actual reactive power output of the DG inverter and the setpoint of the DG inverter's reactive power output, respectively; U represents the actual voltage amplitude at the grid connection point of the DG inverter; U ref This indicates the voltage reference value at the grid connection point of the DG inverter; k q k represents the reactive power-voltage droop factor. u This represents the voltage feedback gain coefficient in reactive power-voltage integrated control; where k u / k q = k uq , which represents the equivalent voltage regulation gain.

[0017] Furthermore, the reactive power-voltage relationship model also includes power limiting constraints:

[0018] -Q max ≤ Q ≤ Q max ;

[0019] In the formula, Q max This represents the maximum reactive power output of the DG inverter.

[0020] Furthermore, when the calculated Q exceeds the power limiting constraint, the PV-type or PQ(V)-type node degenerates into a PQ-type node, and its output reactive power is Q. max or -Q max .

[0021] As an optional implementation, in step (2), the reactive power correction process for the PV-type DG includes:

[0022] Establish the node impedance matrix Z N = TZ b T T N represents the total number of unbalanced nodes in the distribution network; b represents the total number of branches in the distribution network; Z b Z represents the branch impedance matrix; N T represents the node impedance matrix; T represents the N×b path-branch incidence matrix; T T This represents the transpose of matrix T;

[0023] As an optional implementation, the method for modifying the system Jacobian matrix J includes:

[0024] 1) PQ type DG, no correction is made to J;

[0025] 2) When the reactive power of the PV-type DG is within the adjustment range, delete the corresponding row and column in J;

[0026] 3) PQ(V) type DG, J QVThe i-th diagonal element is corrected to J QV,ii -k uq The remaining elements remain unchanged.

[0027] As an optional implementation, in step (3), the static voltage stability index α m The calculation process is as follows:

[0028] Calculate the contracted Jacobian matrix J R ;

[0029] For J R Eigenvalue decomposition is performed, and the eigenvalue with the smallest magnitude is selected as the dominant eigenvalue. The magnitude of this dominant eigenvalue is defined as the static voltage stability index: α. m =min(λ1, λ2, λ3,…,λ h );

[0030] Where h is J R Order.

[0031] As an optional implementation, in step (4), the method for identifying voltage-weak nodes includes:

[0032] Calculate the dominant eigenvalue λ w The corresponding participation factors p of each node kw :p kw = u kw v kw ; where u kw and u kw These are the k-th elements of the left and right eigenvectors corresponding to the dominant eigenvalues, respectively, where k = 1, 2, ..., N;

[0033] For p kw Sorting from largest to smallest, the node with the largest participation factor is the weakest node in the system voltage.

[0034] As an optional implementation, in step (4), the method for determining the reactive power compensation node includes:

[0035] according to Obtain the VQ sensitivity information of each node;

[0036] Nodes with high VQ sensitivity to voltage-weak nodes are selected as reactive power compensation connection points. For example, for voltage-weak nodes, the node with the highest sensitivity value is selected as the optimal reactive power compensation connection point. In another embodiment, nodes can be sorted in descending order of their values, and the top 10% (configurable and modifiable) of nodes are selected as reactive power compensation connection points.

[0037] Furthermore, simulation verification is conducted through the design of numerical examples, specifically including:

[0038] The verification was carried out based on a distribution network system with DG, to check the numerical accuracy of the proposed power flow algorithm, compare and analyze the superiority of the dominant characteristic value index, and verify the effectiveness of the voltage weak node identification and reactive power compensation strategy.

[0039] According to a second aspect of the present invention, a computer system is provided, comprising:

[0040] One or more processors;

[0041] The memory stores operable instructions that, when executed by the one or more processors, cause the one or more processors to perform operations, including the aforementioned flow of the active distribution network power flow calculation and static voltage stability analysis method taking into account inverter reactive power control.

[0042] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0043] 1. The power flow algorithm for distribution networks that takes into account the reactive power control of inverters proposed in this invention classifies DG into three types: PQ type, PV type and PQ(V) type according to the reactive power control strategy of inverters. The reactive power correction equations of the nodes in PV type and PQ(V) type DG are derived respectively, which improves the calculation accuracy and speed of power flow in distribution networks containing DG.

[0044] 2. A static voltage stability index for active distribution networks based on dominant eigenvalues ​​was constructed. Compared with the traditional L index (which is based on the continuity assumption), it has significant advantages in active distribution networks with a high proportion of distributed generation (DG). By taking into account the reactive power control of the inverter, this index can more accurately assess the static voltage stability margin of the system. This invention captures discontinuous stability mutations caused by DG inverter limiting by modifying the Jacobian matrix. For the special operating condition of DG reactive power output exceeding the limit, the mutation of this index can provide timely warning of the decrease in static voltage stability caused by DG reactive power exceeding the limit.

[0045] 3. The node participation factor analysis based on dominant mode proposed in this invention can accurately identify voltage-weak nodes in the system, providing clear targets for power grid operation and maintenance. Combined with the VQ sensitivity matrix, it can not only discover weak points, but also pinpoint the reactive power compensation location with the best support effect for weak nodes, realizing global optimization of compensation location and providing reliable technical support for improving the voltage stability of distribution networks. Attached Figure Description

[0046] Figure 1 This is a flowchart of an active distribution network power flow calculation and static voltage stability analysis method considering inverter reactive power control, according to an embodiment of the present invention.

[0047] Figure 2 This is a schematic diagram of a DG reactive power control strategy according to an embodiment of the present invention.

[0048] Figure 3 This is a topology diagram of an IEEE 33-node distribution network with DG according to an embodiment of the present invention.

[0049] Figure 4 This is a typical day's wind power, photovoltaic, and load power curve of an embodiment of the present invention.

[0050] Figure 5 This is a comparison of the node voltage magnitude power flow results obtained by the improved forward-backward substitution method and the OpenDSS simulation results in one embodiment of the present invention. The blue line represents the OpenDSS simulation results, and the red line represents the calculation results of the improved forward-backward substitution method.

[0051] Figure 6 This is an embodiment of the present invention, where each node in the distribution network participates in the dominant mode.

[0052] Figure 7 This is the VQ sensitivity of nodes 7 and 9 in one embodiment of the present invention, where the blue line represents the VQ sensitivity of node 9 and the red line represents the VQ sensitivity of node 7.

[0053] Figure 8 This is an indicator α of one embodiment of the present invention. m and α L A schematic diagram showing the change curve as the load increases. Detailed Implementation

[0054] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0055] like Figure 1 The process shown, according to an embodiment of the present invention, for active distribution network power flow calculation and static voltage stability analysis considering inverter reactive power control, includes the following steps:

[0056] (1) Read active distribution network data containing inverters: obtain the network topology, line parameters and inverter data of active distribution network, analyze the static characteristics of inverter under different control modes, construct reactive power-voltage relationship model, and classify DG into three types: PQ type, PV type and PQ(V) type.

[0057] (2) Calculate the power flow of the active distribution network based on the reactive power correction equation: In the iterative process of the forward-backward substitution method, a reactive power correction equation is introduced to correct the reactive power for different types of DG, and the steady-state power flow and voltage of each node of the distribution network are calculated.

[0058] (3) Calculate the static voltage stability index of the active distribution network based on the dominant eigenvalue: Correct the system Jacobian matrix according to the reactive power-voltage response characteristics of the inverter, calculate the dominant eigenvalue of the contracted Jacobian matrix, and construct the static voltage stability index of the active distribution network.

[0059] (4) Determine the weak voltage nodes and optimal compensation locations in the active distribution network: Calculate the participation factors of each node based on the eigenvectors corresponding to the dominant eigenvalues ​​to identify the weak voltage nodes in the system, and combine the VQ sensitivity to determine the most effective reactive power compensation nodes for improving the system voltage stability.

[0060] Combining the above-mentioned active distribution network power flow calculation and static voltage stability analysis method considering inverter reactive power control proposed in this invention, it breaks through the limitation of simply treating the load as a constant power in traditional distribution network analysis. By analyzing the inverter control strategy, distributed generation (DG) is subdivided into three types: PQ type, PV type, and PQ(V) type. In the forward-backward iteration process, a reactive power correction equation is introduced to achieve accurate solution of power flow for DG with diverse control strategies. It can more accurately simulate the steady-state power flow of distribution networks with a high proportion of DG under complex control modes. Combined with the calculation results, the maximum voltage deviation of this method is only 0.0005 pu, which fully verifies its high accuracy characteristics.

[0061] In the method of this invention, the system Jacobian matrix is ​​corrected based on the reactive power-voltage response characteristics of the distributed generation (DG). A stability index is constructed by calculating the dominant eigenvalues ​​of the contracted Jacobian matrix, and voltage-weak nodes and optimal compensation locations are identified based on the dominant mode participation factor and VQ sensitivity. Compared with the traditional L index, the index constructed by this invention, based on the dominant eigenvalues, takes into account the active reactive power support capability of the inverter. The evaluation results are more consistent with the actual operating conditions of the active distribution network. It can sensitively detect node model degradation (such as degradation from PV type to PQ type) caused by the reactive power output of DG reaching the physical capacity limit, thereby providing timely early warning of the decrease in the static voltage stability of the system. When the system approaches the voltage collapse edge, the index of this invention can accurately approach zero, effectively overcoming the problem that traditional indexes may fail in high-proportion DG scenarios.

[0062] As an optional implementation, in step (1), based on the characteristic that the output power of DG under static conditions is strongly correlated with the active and reactive power control strategies adopted, the active power control of DG adopts maximum power point tracking control and frequency droop control strategies; the reactive power control adopts constant reactive power control, constant voltage control, V / Q droop control and reactive power-voltage integrated control methods. For simplicity, in the embodiment of the present invention, the influence of frequency fluctuation is ignored in the static analysis scenario, and it is assumed that DG is working at a constant active power (such as in the maximum power point tracking state) for analysis.

[0063] Under static conditions, the input of the proportional-integral (PI) controller in the inverter's reactive power control strategy should be zero. Therefore, the reactive power and voltage of DG under different control strategies satisfy the following:

[0064] Q = Q ref

[0065] U = U ref

[0066] Q = Q ref +k u (U ref -U)

[0067] Q = Q ref +k u / k q (U ref -U)

[0068] Among them, Q and Q ref These represent the actual reactive power output of the DG inverter and the setpoint of the DG inverter's reactive power output, respectively; U represents the actual voltage amplitude at the grid connection point of the DG inverter; U ref This indicates the voltage reference value at the grid connection point of the DG inverter; k q This represents the reactive power-voltage droop factor (corresponding to V / Q droop control); k u This represents the voltage feedback gain coefficient in reactive power-voltage integrated control; where k u / k q = k uq , which represents the equivalent voltage regulation gain.

[0069] According to the reactive voltage characteristics of DG described in the formula, they can be divided into three categories:

[0070] 1) PQ type DG, i.e., Q = Q ref With active and reactive power set to constant values, when constant power factor control is used, we have:

[0071] Q = P × tanΦ;

[0072] In the formula, Φ represents the power factor angle, which is used for constant power factor control;

[0073] 2) PV type DG, that is, U = U ref Its active power and voltage are set values, while reactive power is to be determined.

[0074] 3) PQ(V) type DG, i.e., Q = Q ref +k u (U ref -U) and Q = Q ref +k u / k q (U ref -U); at this point, Q is interpreted as an analytic function of U.

[0075] It should be noted that V / Q droop control is a combined reactive power-voltage control at k q The special case when =1 is used. In this example, the reactive power of PQ(V) type DG is uniformly represented in the following way:

[0076] Q = Q ref +k u / k q (U ref -U).

[0077] Meanwhile, considering the limitation of the inverter's physical capacity, the above analysis did not take into account the impact of the power limiting stage. In reality, due to the inverter's capacity constraints, its reactive power output is also limited to a certain extent. Therefore, in this example, a power limiting constraint is further added to the above model, and its actual reactive power output satisfies the inequality:

[0078] -Q max ≤ Q ≤ Q max ;

[0079] In the formula: Q max Q represents the maximum reactive power output of the DQ inverter. When the calculated Q exceeds this range, the PV or PQ(V) type node will degenerate into a PQ type node, with its output reactive power being Q. max or -Q max .

[0080] For PQ-type DG, it is treated as a negative PQ load in power flow calculation and static voltage stability analysis; while for the other two types of DG, they need to be treated separately according to their static characteristics.

[0081] As an optional implementation, in step (2), during the iterative process of the forward-backward substitution method, a reactive power correction equation is introduced to correct the reactive power for different types of DG, and the steady-state power flow and voltage of each node of the distribution network are calculated. For different types of DG, the implementation process includes:

[0082] (1) For a PV-type DG, suppose the distribution network has N+1 nodes and b branches, and the branch impedance matrix is ​​Z b If the path-branch correlation matrix is ​​an N×b matrix T, then the nodal impedance matrix is ​​expressed as:

[0083] Z N = TZ b T T ;

[0084] Where N represents the total number of unbalanced nodes in the distribution network; b represents the total number of branches in the distribution network; Z b Z represents the branch impedance matrix; N T represents the node impedance matrix; T This represents the transpose of matrix T;

[0085] For the node where the PV-type DG is located, let Z is a diagonal matrix formed by the conjugate voltages of the PV nodes. pv For matrix Z N The matrix formed by the rows and columns corresponding to the PV nodes; in the process of using the forward-backward substitution method, the reactive power correction of the DG in the (k+1)th iteration is:

[0086] ;

[0087] In the formula, H x and H y They are The real and imaginary parts of the matrix, Set the voltage amplitude value for the PV node. and Let be the real and imaginary parts of the PV node voltage in the k-th iteration, respectively. Let be the amplitude of the PV node voltage in the k-th iteration;

[0088] Then, according to Continue the forward and backward substitution calculations until convergence. and Let represent the reactive power of the PV node at the (k+1)th and kth iterations, respectively. This represents the reactive power correction amount of the PV node in the k-th iteration.

[0089] It should be noted that during the iteration process, when Q exceeds the reactive power output allowable range of DG, the node will degenerate into a PQ node and continue to perform power flow calculations as a PQ node;

[0090] (2) For PQ(V) type DG, during the forward and backward iteration process, the reactive power at the k-th iteration is:

[0091] Q (k) = Q ref +k uq (U ref -U (k) );

[0092] In the formula, k uq = k u / k q At that time, k uq =0, DG is transformed into PQ type DG.

[0093] As an optional implementation, in step (3), the system Jacobian matrix is ​​corrected according to the reactive power-voltage response characteristics of the inverter, the dominant eigenvalues ​​of the contracted Jacobian matrix are calculated, and the static voltage stability index of the active distribution network is constructed. The implementation process includes:

[0094] For a distribution network containing distributed generation (DG), let the node where the DG is located be numbered i. Then the reactive power equation for that node is:

[0095] ;

[0096] To reflect the impact of DG reactive power control on static voltage stability, matrix J is modified as follows:

[0097] 1) The PQ type DG does not have reactive power regulation capability, so there is no need to correct J;

[0098] 2) When the reactive power of the PV type DG is within the adjustment range, node i is a PV node and its voltage is not considered a variable. Therefore, the corresponding row and column in matrix J should be deleted.

[0099] 3) The reactive power increment of PQ(V) type DG satisfies the following relationship with the voltage microvariable at the node:

[0100] ΔQ dg,i = -k uq ΔU i ;

[0101] Therefore, it is necessary to put J QV The i-th diagonal element is corrected to J QV,ii -k uq The remaining elements remain unchanged;

[0102] For a given steady-state operating point, the power correction equation for the distribution network is:

[0103] ;

[0104] in:

[0105] ΔQ = ΔQ DG – ΔQ L ;

[0106] ΔP = ΔP DG - ΔP L ;

[0107] In the formula, P DG Q DG For the increase in active and reactive power of DG; ΔP L ΔQ LΔU and Δθ represent the active and reactive load increments of the node load, respectively; ΔU and Δθ represent the node voltage magnitude and phase angle microvariables, respectively; J Pθ J PV J Qθ J QV These are the corresponding submatrices of the Jacobian matrix J; assuming the distribution network DG and the active power of the load are constant, i.e., ΔP = 0, then: ΔQ = J R ΔU;

[0108] , denotes the contracted Jacobian matrix, J R The eigenvalue matrix is ​​λ, λ=diag(λ1,λ2,λ3,…,λ h ), h is J R Order, where λ i The corresponding left and right feature vectors are respectively , ;

[0109] Shrinking Jacobian matrix J R The left and right eigenvector matrices are as follows:

[0110] ;X R =[v1v 1 … v h ];

[0111] ;X L =[u1u 1 … u h ];

[0112] Define the modal voltage vector U m = X L ΔU, modal reactive power vector Q m = X L ΔQ, then U m =λ -1 Q m .

[0113] λ i To represent system voltage stability, the eigenvalue with the smallest magnitude is selected as the dominant eigenvalue, and the magnitude of this dominant eigenvalue is defined as the static voltage stability index.

[0114] α m =min(λ1, λ2, λ3,…,λ h );

[0115] Quantitative analysis of the voltage stability of the entire distribution network, where α m When the voltage is 0, the power distribution network will experience voltage collapse.

[0116] As an optional implementation, in step (4), the participation factor of each node is calculated based on the eigenvector corresponding to the dominant eigenvalue to identify voltage-weak nodes in the system, and then combined with VQ sensitivity to determine the most effective reactive power compensation node for improving system voltage stability. The implementation process includes:

[0117] Configuration Node The VQ sensitivity is:

[0118] ;

[0119] In the formula: p ki =u ki v ki p ki For node participation factors, u ki v ki They are respectively , The k-th element, p ki Reflects λ i right The contribution, let λ w For matrix J R The dominant characteristic value, and its corresponding dominant mode, plays a dominant role in the static voltage stability of the distribution network.

[0120] For p kw Sort the nodes from largest to smallest and identify the nodes with the largest participating factors. These nodes are the weak nodes in the system voltage, and their static voltage stability is relatively weak.

[0121] According to an embodiment of the present invention, the power correction equation shows that:

[0122] ;

[0123] in, This reflects the VQ sensitivity information of each node. Therefore, selecting nodes with greater VQ sensitivity for weak voltage nodes for reactive power compensation can improve control performance.

[0124] Furthermore, in embodiments of the present invention, verification is conducted based on a distribution network system containing DG to check the numerical accuracy of the proposed power flow algorithm, compare and analyze the superiority of the dominant eigenvalue indices, and verify the effectiveness of the voltage weak node identification and reactive power compensation strategies; the steps include:

[0125] like Figure 3As shown, the IEEE 33-node system was modified by connecting distributed photovoltaic (DG1-DG4) systems at nodes 6, 12, 22, and 32, and distributed wind power (DG5 and DG6) systems at nodes 17 and 25, respectively. The iterative power flow algorithm based on the reactive power correction equation from the aforementioned embodiment of the present invention was used to solve the steady-state power flow distribution under a certain operating scenario. The solution results were compared with the simulation results from OpenDSS software to verify the accuracy of the power flow calculation method of the present invention.

[0126] By gradually increasing the system load growth factor until the distribution network approaches the critical state of voltage collapse, the superiority of the dominant characteristic value index over the L index is analyzed by comparing the change curves of the dominant characteristic value index and the L index with load growth, and the accuracy of voltage weak node identification and the effectiveness of reactive power compensation in this paper are verified.

[0127] As a specific example, combined with Figure 3 As shown, the above-mentioned active distribution network power flow calculation and static voltage stability analysis method considering inverter reactive power control was applied to a case study system with distributed generation (DG) and the implementation steps for power flow calculation and static voltage stability assessment are as follows:

[0128] Step 1: Read the active distribution network data containing the inverter.

[0129] The structure of the DG-containing distribution network in this embodiment is as follows: Figure 3 As shown in Table 1, distributed photovoltaic (DG1-DG4) generators are connected at nodes 6, 12, 22, and 32, respectively, and distributed wind power (DG5 and DG6) generators are connected at nodes 17 and 25, respectively. The DG parameters are shown in Table 1. The wind power, photovoltaic, and load power curves for a typical day are shown in Table 2. Figure 4 As shown.

[0130] The static voltage stability of the simulation system under different scenarios is analyzed. It is assumed that DG1-DG4 are PQ(V) type DGs, and k is taken as... u =0.7, k q =0.3; DG5-DG6 are PV type DGs with reference voltages of 1.02pu and 1.00pu respectively. Power flow calculation is performed using the DG and load power scenario at 12:00 as an example.

[0131] Table 1. Distributed Generation Parameters

[0132] DG1 6 Photovoltaics 2.00 1.5 0 -0.45 0.45 1.00 0.3 0.7 DG2 12 Photovoltaics 2.00 1.5 0 -0.45 0.45 1.00 0.3 0.7 DG3 22 Photovoltaics 1.50 1.0 0 -0.30 0.30 1.00 0.3 0.7 DG4 32 Photovoltaics 1.50 1.2 0 -0.36 0.36 1.00 0.3 0.7 DG5 17 wind power 1.50 1.0 0 -0.30 0.30 1.00 0.3 0.7 DG6 25 wind power 1.50 1.0 0 -0.30 0.30 1.00 0.3 0.7

[0133] Constructing a reactive power-voltage relationship model: Under static conditions, the output power of the distributed generator (DG) is closely related to the active and reactive power control strategies employed; for a PQ-type DG, Q = Q refThe active and reactive power are set to constant values. When constant power factor control is used, Q = P × tanΦ; for PV-type DG, such as U = U ref As shown, its active power and voltage are set values, while reactive power is to be determined; for PQ(V) type DG, such as Q = Q ref +k u / k q (U ref As shown in -U), Q can be represented as an analytic function of U.

[0134] Step 2: Calculate the power flow of the active distribution network based on the reactive power correction equation.

[0135] Set the initial voltage of each node in the distribution network as follows: Set the convergence precision to 10. -4 .

[0136] For PQ(V) type DGs connected to nodes 6, 12, 22, and 32: In each iteration, based on the current node voltage amplitude... Using the formula Q = Q ref +k u / k q (U ref -U) Update the reactive power output of DG. If the calculated Q exceeds the limiting range of [-0.45, 0.45]MVar (for DG1, DG2) or [-0.30, 0.30]MVar (for DG3, DG4), it is fixed as a boundary value, and the node is treated as a PQ node. For PV-type nodes connected to nodes 17 and 25: during the iteration process, the reactive power increment required to maintain the target voltage (1.02pu and 1.00pu, respectively) is calculated using the iterative formula, and the injected current is corrected. Similarly, it checks whether the limit is exceeded; if the limit is exceeded, it degenerates into a PQ node.

[0137] Taking a typical scenario at 12:00 noon as an example, after 6 iterations, the power flow converges, and the voltage and phase angle of each node are as follows: Figure 4 As shown in the figure. The calculation results show that the voltage at node 12 is the highest, at 1.027 pu. At this time, due to the large photovoltaic output and relatively small load, a power backflow of 2.105 MW occurs on line 1-2.

[0138] Step 3: Calculate the static voltage stability index of the active distribution network based on the dominant characteristic value.

[0139] Taking a typical scenario at 16:00 on a given day as an example, for the PQ(V) type DG connected to nodes 6, 12, 22, and 32, based on its reactive power-voltage droop characteristics, the corresponding diagonal elements in the system Jacobian matrix are corrected to J. QV,ii-0.7 / 0.3; For the PV-type DG connected to nodes 17 and 25, its voltage is constant under non-over-limit conditions, so the row and column corresponding to this node are removed from the Jacobian matrix. Then, eigenvalue decomposition is performed on the corrected contracted Jacobian matrix to calculate the dominant eigenvalue index α of the system. m The value is 0.0307, ​​which quantifies the stability margin of the distribution network before voltage collapse under the current operating conditions.

[0140] Step 4: Identify weak voltage nodes and determine the optimal compensation location.

[0141] Taking a typical scenario at 8:00 AM as an example, and assuming that all distributed generation (DG) uses reactive power-voltage integrated control, the system is in a critical state when the load factor increases to 6.96. The participation factors of each node are calculated as follows: Figure 6 As shown, the results indicate that nodes 7 and 9 have the largest participation factors, thus identifying them as voltage-weak nodes; based on matrix J... R -1 The VQ sensitivities of nodes 7 and 9 are shown in the attached figure. Figure 7 As shown, node 33 has the highest sensitivity values ​​to both nodes 7 and 9, thus determining node 33 as the optimal reactive power compensation access point.

[0142] Step 5: Simulation verification using numerical examples.

[0143] Compare the power flow calculation results obtained in step 3 with the simulation results calculated by OpenDSS software, such as... Figure 5 As shown, the maximum voltage deviation is only 0.0005 pu and the maximum phase angle deviation is 0.047°, which verifies the accuracy of the active distribution network power flow algorithm based on the reactive power correction equation in handling various inverter reactive power control strategies.

[0144] Taking a typical scenario at 16:00 on a given day as an example, DG1-DG4 employ reactive power-voltage integrated control, while DG5-DG6 employ constant voltage control, causing the load growth coefficient β to gradually increase from 1.0, and α... m Indicators and Indicator α L The change curve is as follows Figure 8 As shown. For ease of analysis, α is defined. L The static voltage stability is reflected by α = 1 - L. L ∈[0,1], and α L The smaller the value, the weaker the system voltage stability.

[0145] As shown in the figure, the indicator curve of this invention exhibits significant piecewise jump characteristics, enabling sensitive detection of DG operating state transitions. Specifically, when the load increases to specific nodes (such as 1.25 times and 1.87 times), the indicator shows a numerical jump, accurately corresponding to the physical process of the inverter transitioning from PV / PQ(V) type to PQ type. In contrast, the traditional L indicator only shows a smooth downward curve, failing to reveal such abrupt changes caused by control constraints. When the system load increases to 6.05 times, approaching the critical point, the indicator value of this invention approaches zero, accurately warning of the critical instability state; while α... L The index value is 0.5379, which is still far from its instability threshold. The L index is based on a constant power load model and does not consider the active voltage support capability of the DG inverter, leading to its failure in high-proportion DG scenarios. This confirms that the index of this invention can more accurately determine the static voltage stability limit of the distribution network.

[0146] Under the critical state of the system, the compensation strategy determined in step 4 is verified by injecting 0.2MVar reactive power at node 33, α m The value increased significantly from 0.0033 to 0.0108; if the same amount of reactive power is injected at node 25, α... m The value was only increased to 0.0043. This result verifies the correctness of the weak node identification and reactive power compensation location method of the present invention.

[0147] In conjunction with the implementation of the active distribution network power flow calculation and static voltage stability analysis method considering inverter reactive power control in the above embodiments, this invention also proposes a computer system, including: one or more processors and a memory. The memory is used to store operable instructions.

[0148] When the aforementioned instructions are executed by the one or more processors, the one or more processors perform operations, including the flow of the active distribution network power flow calculation and static voltage stability analysis method considering inverter reactive power control in the aforementioned embodiments.

[0149] In summary, the proposed method for active distribution network power flow calculation and static voltage stability analysis, which considers inverter reactive power control, overcomes the shortcomings of existing assessment techniques that fail to fully account for the active reactive power support capability and physical capacity constraints of distributed generation (DG). This method first establishes three types of node models—PQ, PV, and PQ(V)—by analyzing the inverter control strategy. A reactive power correction equation is introduced into the iterative algorithm to correct DG reactive power, achieving rapid and high-precision solutions for distribution network power flow under complex control modes. Furthermore, a dominant eigenvalue index is constructed by modifying the Jacobian matrix. This index not only quantifies the stability margin of the system but also sensitively captures node model degradation and stability mutations caused by DG reactive power output reaching its limit. Based on this, combined with critical mode participation factor and VQ sensitivity analysis, accurate location of voltage-weak nodes and global optimization of reactive power compensation location are achieved. Compared with existing technologies, this method effectively overcomes the limitations of the traditional L index in distribution networks with a high proportion of DG, providing a scientific and accurate theoretical basis and technical support for the static voltage stability assessment, voltage-weak node identification, and reactive power compensation location selection of active distribution networks.

[0150] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Those skilled in the art can make various modifications and refinements without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention shall be determined by the claims.

Claims

1. A method for calculating power flow and analyzing static voltage stability in an active distribution network considering inverter reactive power control, characterized in that, Includes the following steps: (1) Obtain the network topology, line parameters and inverter data of the active distribution network, analyze the static characteristics of the inverter under different control modes, construct the reactive power-voltage relationship model, and classify distributed generation (DG) into three types: PQ type, PV type and PQ(V) type. (2) In the iterative process of the forward-backward substitution method, reactive power correction equations are introduced to correct reactive power for different types of DG, and the steady-state power flow and voltage of each node of the distribution network are calculated. (3) Based on the reactive-voltage response characteristics of the inverter, the system Jacobian matrix is ​​corrected, the dominant eigenvalues ​​of the contracted Jacobian matrix are calculated, and the static voltage stability index of the active distribution network is constructed. (4) Calculate the participation factor of each node based on the eigenvector corresponding to the dominant eigenvalue, identify the voltage weak nodes in the system, and determine the reactive power compensation nodes in combination with VQ sensitivity.

2. The method for active distribution network power flow calculation and static voltage stability analysis considering inverter reactive power control as described in claim 1, characterized in that, In step (1), the reactive power-voltage relationship model includes: For a PQ type DG, Q = Q ref ; For a PV-type DG, U = U ref ; For a PQ(V) type DG, Q = Q ref +k u / k q (U ref -U); Among them, Q and Q ref These represent the actual reactive power output of the DG inverter and the setpoint of the DG inverter's reactive power output, respectively; U represents the actual voltage amplitude at the grid connection point of the DG inverter; U ref This indicates the voltage reference value at the grid connection point of the DG inverter; k q k represents the reactive power-voltage droop factor. u This represents the voltage feedback gain coefficient in reactive power-voltage integrated control; where k u / k q =k uq , which represents the equivalent voltage regulation gain.

3. The method for active distribution network power flow calculation and static voltage stability analysis considering inverter reactive power control as described in claim 2, characterized in that, The reactive power-voltage relationship model also includes power limiting constraints: -Q max ≤ Q ≤ Q max ; In the formula, Q max This represents the maximum reactive power output of the DG inverter. Furthermore, when the calculated Q exceeds the power limiting constraint, the PV-type or PQ(V)-type node degenerates into a PQ-type node, and its output reactive power is Q. max or -Q max .

4. The method for active distribution network power flow calculation and static voltage stability analysis considering inverter reactive power control as described in claim 2, characterized in that, In step (2), the reactive power correction process for PV-type DG includes: Establish the node impedance matrix Z N = TZ b T T N represents the total number of unbalanced nodes in the distribution network; b represents the total number of branches in the distribution network; Z b Z represents the branch impedance matrix; N T represents the node impedance matrix; T represents the N×b path-branch incidence matrix; T T This represents the transpose of matrix T; For a node containing a PV-type DG, defined as a PV node, the reactive power correction amount for the DG in the (k+1)th iteration using the forward-backward substitution method is: ； H x and H y They are The real and imaginary parts of the matrix, Set the voltage amplitude value for the PV node. and Let be the real and imaginary parts of the PV node voltage in the k-th iteration, respectively. Let be the amplitude of the PV node voltage in the k-th iteration; according to Continue the forward and backward subtraction calculations until convergence; in, and Let represent the reactive power of the PV node at the (k+1)th and kth iterations, respectively. This represents the reactive power correction amount of the PV node in the k-th iteration.

5. The method for active distribution network power flow calculation and static voltage stability analysis considering inverter reactive power control according to claim 4, characterized in that, In step (2), the node where the PQ(V) type DG is located is defined as the PQ(V) node. During the forward and backward iteration process, the reactive power at the k-th iteration is: Q (k) = Q ref +k uq (U ref -U (k) ); In the formula, k uq = k u / k q At that time, k uq =0, DG is transformed into PQ type DG.

6. The method for active distribution network power flow calculation and static voltage stability analysis considering inverter reactive power control as described in claim 1, characterized in that, In step (3), the method for correcting the system Jacobian matrix J includes: 1) PQ type DG, no correction is made to J; 2) When the reactive power of the PV-type DG is within the adjustment range, delete the corresponding row and column in J; 3) PQ(V) type DG, J QV The i-th diagonal element is corrected to J QV,ii -k uq The remaining elements remain unchanged.

7. The method for active distribution network power flow calculation and static voltage stability analysis considering inverter reactive power control according to claim 1, characterized in that, In step (3), the static voltage stability index α m The calculation process is as follows: Calculate the contracted Jacobian matrix J R ; For J R Eigenvalue decomposition is performed, and the eigenvalue with the smallest magnitude is selected as the dominant eigenvalue. The magnitude of this dominant eigenvalue is defined as the static voltage stability index: α. m =min(λ1, λ2, λ3,…,λ h ); Where h is J R Order.

8. The method for active distribution network power flow calculation and static voltage stability analysis considering inverter reactive power control according to claim 1, characterized in that, In step (4), the method for identifying voltage weak points includes: Calculate the dominant eigenvalue λ w The corresponding participation factors p of each node kw :p kw = u kw v kw ; where u kw and u kw These are the k-th elements of the left and right eigenvectors corresponding to the dominant eigenvalues, respectively, where k = 1, 2, ..., N; For p kw Sorting from largest to smallest, the node with the largest participation factor is the weakest node in the system voltage.

9. The method for active distribution network power flow calculation and static voltage stability analysis considering inverter reactive power control according to claim 1, characterized in that, In step (4), the method for determining the reactive power compensation node includes: according to Obtain the VQ sensitivity information of each node; Select nodes with high VQ sensitivity for voltage-weak nodes as reactive power compensation access points.

10. A computer system comprising one or more processors and a memory, characterized in that, The memory stores operable instructions that, when executed by the one or more processors, cause the one or more processors to perform the steps of the method as described in any one of claims 1 to 9.

Images