Static voltage stability analysis method and device for hybrid DC feed-in system

Abstract

The invention relates to a static voltage stability analysis method and device for a hybrid DC feed-in system. Comprising the following steps: constructing a single-ended converter station reactive operation domain according to a boundary surface vertex formed by a converter station rated capacity constraint and an AC voltage constraint, a boundary surface vertex formed by the converter station AC voltage constraint and a sub-module capacitor voltage constraint, and a boundary surface vertex formed by the sub-module capacitor voltage constraint and the rated capacity constraint; constructing a power transfer distribution factor representing an interaction relationship between active power distribution and reactive boundary variation of the multi-terminal flexible direct current system, and decoupling to obtain a reactive feasible region boundary of the multi-terminal flexible direct current system; and performing static voltage stability analysis according to the reactive feasible region boundary. Compared with the prior art, the method improves the accuracy and reliability of static voltage stability analysis of the hybrid DC feed-in system.

Description

Technical Field

[0001] This invention relates to the field of hybrid power systems, and in particular to a method and apparatus for static voltage stability analysis of hybrid DC-DC power systems. Background Technology

[0002] my country's energy structure is rapidly transforming towards a cleaner and lower-carbon model, with a significant increase in the proportion of new energy power generation and inter-regional DC transmission in the receiving-end power grid. Currently, the East China Power Grid mainly uses converter-type high-voltage direct current (LCC-HVDC) transmission, with 14 external DC feed-in channels and a feed-in capacity of approximately 87.76 million kilowatts. Meanwhile, a series of offshore wind power projects, exemplified by the Shanghai Deep-Sea Wind Power Project, are about to commence construction, and it is expected that over 30 million kilowatts of offshore wind power will be connected to the East China Power Grid via flexible direct current transmission (VSC-HVDC). As multiple and diverse DC transmission systems converge on the same AC system, a hybrid power feed-in system is gradually taking shape.

[0003] Against this backdrop, the penetration of power electronic devices into the system has significantly increased. Multiple inverters with different control strategies operate intensively in the regional AC power grid. Their complex interactions, coupled with the volatility of renewable energy output, may lead to static voltage instability. Therefore, it is necessary to systematically evaluate the static voltage stability characteristics of a hybrid power system with a high proportion of renewable energy.

[0004] However, existing research largely focuses on dual-infeed systems and has not fully explored the active and reactive power decoupling control capabilities of flexible DC transmission, especially in terms of multi-terminal coordinated control and dynamic reactive power support characteristics. Flexible DC transmission, as an "equivalent power source" with large capacity and strong controllability, has significant advantages in control flexibility and response speed. When multiple renewable energy power plants are centrally connected to the AC grid via multi-terminal flexible DC transmission, the reactive power support capabilities of each converter station will affect each other with changes in active power distribution. Traditional analysis methods based on single-infeed models are insufficient to accurately characterize the voltage stability boundary in such scenarios.

[0005] Therefore, it is necessary to explore in depth the impact mechanism of the coordinated transmission of new energy power in multi-terminal flexible DC systems on the dynamic reactive power response of the power grid, and based on this, to construct a static voltage stability analysis scheme that can reflect the dynamic reactive power support capability of flexible DC transmission VSC-MTDC. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art by providing a static voltage stability analysis method and apparatus for hybrid DC-fed power systems. By quantifying the multi-terminal coordination and dynamic reactive power support characteristics of flexible DC, this invention solves the problem that traditional static voltage stability analysis methods based on single-infeed equivalence are difficult to accurately characterize the voltage stability boundary under multi-terminal flexible DC-fed cooperative operation scenarios. This provides a high-precision static voltage stability evaluation index for complex infeed systems and improves the accuracy and reliability of static voltage stability analysis of hybrid DC-fed systems.

[0007] The objective of this invention can be achieved through the following technical solutions: According to a first aspect of the present invention, a method for static voltage stability analysis of a hybrid DC-fed system is provided, comprising: Based on the boundary surface vertices formed by the rated capacity constraint and AC voltage constraint of the converter station, the boundary surface vertices formed by the AC voltage constraint and submodule capacitor voltage constraint of the converter station, and the boundary surface vertices formed by the submodule capacitor voltage constraint and rated capacity constraint, the reactive power operation domain of the single-ended converter station is constructed. Based on the reactive power operation domain of a single-ended converter station, a power transfer distribution factor is constructed to characterize the interaction between the active power distribution and the reactive power boundary change of a multi-ended flexible DC system, according to the node branch correlation vector, DC power flow susceptance matrix and branch equivalent reactance value. The reactive power feasible domain boundary of the multi-ended flexible DC system is obtained by decoupling based on the power transfer factor. Static voltage stability analysis is performed based on the boundary of the reactive power feasible region.

[0008] Preferably, the process of obtaining the boundary surface vertices specifically includes: Construct multi-level reactive power constraints for stable operation, including power flow constraints, AC voltage constraints, converter station rated capacity constraints, modulation ratio constraints, submodule capacitor voltage constraints, and bridge arm reactor constraints; Based on the multi-level stable operation reactive power constraint conditions, the boundary surface vertices formed by the rated capacity constraint and AC voltage constraint of the converter station, the boundary surface vertices formed by the AC voltage constraint of the converter station and the capacitor voltage constraint of the sub-module, and the boundary surface vertices formed by the capacitor voltage constraint of the sub-module and the rated capacity constraint are derived through geometric analysis.

[0009] Preferably, based on the boundary surface vertices formed by the rated capacity constraint and AC voltage constraint of the converter station, the boundary surface vertices formed by the AC voltage constraint and submodule capacitor voltage constraint of the converter station, and the boundary surface vertices formed by the capacitor voltage constraint and rated capacity constraint of the submodule, the feasible domain half-space defined by the multidimensional nonlinear inequality constraint is obtained from the vertices, thus obtaining the reactive power operation domain of the single-ended converter station.

[0010] Preferably, for the half-space of the feasible region of the lower boundary surface, the specific construction process includes: The vertices of the lower boundary surfaces formed by the converter station's rated capacity constraint and AC voltage constraint, the lower boundary surfaces formed by the converter station's AC voltage constraint and submodule capacitor voltage constraint, and the lower boundary surfaces formed by the submodule capacitor voltage constraint and rated capacity constraint are expressed as follows: , , , In the formula: ( P cv , Q cv The ) represents the vertex of the lower boundary surface formed by the rated capacity constraint and the AC voltage constraint of the converter station. P cv and Q cv These correspond to the active and reactive power at the vertices, respectively; P ov , Q ov The ) represents the vertex of the lower boundary surface formed by the AC voltage constraint of the converter station and the capacitor voltage constraint of the submodule. P ov and Q ov These correspond to the active and reactive power at the vertices, respectively; P oc , Q oc The ) represents the vertex of the lower boundary surface formed by the capacitor voltage constraint and the rated capacity constraint of the submodule. P oc and Q oc These correspond to the active and reactive power at the vertex, respectively; U s is the equivalent voltage of the AC system; Z The line impedance between the DC access point and the receiving-end AC system; This is the upper limit of the ratio of the submodule capacitor voltage fluctuation to the base value; M Modulation ratio; N This refers to the number of capacitors in the submodule. C 0 represents the capacitance value of the submodule; U 0 represents the capacitor voltage value of the submodule; Angular frequency; A The power factor angle; S n This represents the actual capacity of the converter station. Based on the vertices of the lower boundary surface, obtain the half-space of the feasible region of the lower boundary surface, specifically including: 1) If there is no vertex ( P ov ,Q ov ),but when Q OC < Q CV , , when Q OC > Q CV , , 2) If there exists a vertex ( P ov , Q ov ),but when Q OC < Q CV At that time, P CV Existing on the left P OV Therefore, , In the formula: This represents the lower boundary surface of the feasible region; This refers to the actual active power. For the vertex ( P MC , Q MC x-axis value; P VSCN The rated active power of the converter station; Q VSCN This refers to the rated reactive power of the converter station.

[0011] Preferably, the half-space of the feasible region of the upper boundary surface is obtained using the same method as that used for the half-space of the lower boundary surface, and the specific expression is as follows: , In the formula: This represents the upper boundary of the feasible region; For the vertex ( P MC , Q MC (x-axis value)

[0012] Preferably, based on the reactive power operation domain of a single-ended converter station, a power transfer distribution factor is constructed to characterize the interaction between the active power distribution and the reactive power boundary change of the multi-ended flexible DC system, according to the node branch correlation vector, the DC power flow susceptance matrix, and the branch equivalent reactance value. The reactive power feasible domain boundary of the multi-ended flexible DC system is obtained by decoupling based on the power transfer distribution factor. Specifically, this includes: Based on the branch nodal-branch correlation vector, DC power flow susceptance matrix, and equivalent reactance of the branch, the power transfer distribution factor is calculated, and its expression is: , In the formula: Converter station i In the k The power transfer distribution factor on each branch; branch road k Node branch association vector; The first element in the inverse matrix of the DC power flow susceptance matrix B0 is... i List; For the first k The equivalent reactance value of each branch; When converter station i When the active power changes, the calculation and converter station i Connecting branch roads k Equivalent power change The expression is: , , In the formula: Converter station i Changes in active power; According to the converter station i Connecting branch roads k Equivalent power change Calculate the active power of converter station j after being affected by the power fluctuation of converter station i. The expression is: , In the formula: The number of branches connected to a single-ended converter station; The number of converter stations; Converter station j The active power; Based on the reactive power operating domain of the single-ended converter station, calculate the reactive power of the receiving converter station. i Impact on converter station j reactive power The dynamic reactive power feasible domain boundary of a multi-terminal flexible DC converter station is calculated as follows: , In the formula: and These represent the upper and lower boundary surfaces of the feasible region, respectively.

[0013] Preferably, the static voltage stability analysis based on the reactive power feasible domain boundary includes: Based on the feasible domain boundary of dynamic reactive power of the multi-terminal flexible DC converter station, the reactive power partial derivative terms in the dynamic equivalent admittance and equivalent power of the flexible DC side are corrected. Based on the corrected dynamic equivalent admittance and equivalent power of the flexible DC side, the equivalent short-circuit ratio index of the hybrid DC infeed dynamic reactive power support characteristics is calculated, and the static voltage stability of the hybrid DC infeed power system is quantitatively characterized.

[0014] Preferably, the step of correcting the reactive power partial derivative terms in the dynamic equivalent admittance and equivalent power of the flexible DC side based on the feasible boundary of the dynamic reactive power region of the multi-terminal flexible DC converter station specifically includes: The DC-side Jacobian matrix is ​​transformed into a complex Jacobian matrix, expressed as: , In the formula: for Y heq,i transpose, for S heq,i Transpose of; Y heq,i , S heq,i Let the equivalent admittance and equivalent power of the hybrid feed system equipment be represented as follows: , , In the formula: and Converter station i The corresponding reactive power partial derivative term; For nodes i The voltage phase angle; For nodes i The actual active power; For nodes i The actual reactive power; U s The equivalent voltage of the AC system; Based on the dynamic reactive power operating domain of the multi-terminal flexible DC converter station, the reactive power partial derivative term is... and After correction, the corrected expression is: , , Substituting the modified reactive power partial derivative terms, we obtain the equivalent power and equivalent admittance parameters of the flexible DC side, considering the dynamic reactive power characteristics correction of the multi-terminal flexible DC converter station.

[0015] Preferably, the equivalent short-circuit ratio index for hybrid DC-fed power systems, used to calculate the dynamic reactive power support characteristics of multi-terminal flexible DC systems, quantitatively characterizes the static voltage stability of the hybrid DC-fed power system. The expression for calculating the equivalent short-circuit ratio index is as follows: , In the formula: Converter station i The corresponding hybrid feed equivalent short-circuit ratio; This assumes only the equivalent impedance of the node being analyzed. For nodes i Final equivalent power; To consider the nodes being analyzed as being affected by other nodes j The equivalent impedance affected; For nodes j Final equivalent power; U s is the equivalent voltage of the AC system; n This refers to the number of converter stations.

[0016] According to a second aspect of the present invention, a static voltage stability analysis apparatus for a hybrid DC-fed system is provided, comprising applying the above-described method, including: The first construction module is used to construct the reactive power operation domain of a single-ended converter station based on the boundary surface vertices formed by the rated capacity constraint and AC voltage constraint of the converter station, the boundary surface vertices formed by the AC voltage constraint of the converter station and the capacitor voltage constraint of the sub-module, and the boundary surface vertices formed by the capacitor voltage constraint of the sub-module and the rated capacity constraint of the sub-module. The second construction module is used to construct a power transfer distribution factor that characterizes the interaction between the active power distribution and the reactive power boundary change of the multi-terminal flexible DC system based on the node branch correlation vector, DC power flow susceptance matrix and branch equivalent reactance value, on the basis of the reactive power operation domain of the single-terminal converter station. The reactive power feasible domain boundary of the multi-terminal flexible DC system is obtained by decoupling based on the power transfer factor. The stability analysis module performs static voltage stability analysis based on the boundary of the reactive power feasible domain.

[0017] Compared with the prior art, the present invention has the following beneficial effects: (1) The present invention constructs the reactive power operation domain of a single-ended converter station based on the boundary surface vertices formed by the rated capacity constraint and AC voltage constraint of the converter station, the boundary surface vertices formed by the AC voltage constraint and sub-module capacitor voltage constraint of the converter station, and the boundary surface vertices formed by the capacitor voltage constraint and rated capacity constraint of the sub-module. Then, based on the power transfer distribution factor, the reactive power output boundary of the multi-ended converter station is decoupled, simplifying the complex nonlinear coupling system problem into a linear problem that can be processed in parallel. It can effectively reveal the interaction relationship between the active power distribution and the reactive power boundary in the multi-ended system, thereby realizing the accurate characterization of the voltage stability boundary of the hybrid DC-fed power system.

[0018] (2) By using the geometric analytical method for reactive power, due to its dimensionality reduction and simplification characteristics for complex constraints, the problem of inefficient calculation and ambiguous boundaries of traditional methods is solved, and the optimization effect of efficient analysis and accurate boundary of reactive power operating domain is achieved.

[0019] (3) Based on the feasible region of dynamic reactive power of multi-terminal flexible DC converter station, the present invention corrects the reactive power partial derivative term and calculates the dynamic equivalent admittance and equivalent power of flexible DC system. It can effectively reveal the interaction between the active power distribution and reactive power boundary change of multi-terminal flexible DC system and accurately quantify the reactive power support capability of flexible DC system. Furthermore, based on the traditional short-circuit ratio, a hybrid feed-in equivalent short-circuit ratio index considering the dynamic reactive power support capability of flexible DC system is constructed, which effectively improves the accuracy of static voltage stability assessment in the scenario of hybrid DC feed-in power system. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method of the present invention.

[0021] Figure 2 A simplified model for connecting the converter station to the AC receiving-end power grid.

[0022] Figure 3 This is a diagram showing the reactive power operation boundary coupling relationship between converter stations.

[0023] Figure 4 This is a diagram of a three-feed power system.

[0024] Figure 5 This is a mapping diagram of the flexible DC reactive power operating domain and DPHSCR.

[0025] Figure 6 The impact of different feed types at node 3 on DPHSCR.

[0026] Figure 7 The effect of VSC feed rate on DPHSCR.

[0027] Figure 8 This is a three-dimensional plot of DPHSCR under dynamic power conditions. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0029] Example 1 like Figure 1 As shown in the figure, this embodiment provides a static voltage stability analysis method for a hybrid DC-fed power system, which includes the following steps: S1. Based on the boundary surface vertices formed by the rated capacity constraint and AC voltage constraint of the converter station, the boundary surface vertices formed by the AC voltage constraint and submodule capacitor voltage constraint of the converter station, and the boundary surface vertices formed by the submodule capacitor voltage constraint and rated capacity constraint, construct the reactive power operation domain of the single-ended converter station. Specifically, this includes: S101. Based on a simplified model of a single DC converter station connected to the AC receiving-end power grid, construct multi-level reactive power constraints for stable operation at the system level, converter station level, and equipment level. Among them, the system-level reactive power constraints for stable operation include power flow constraints and AC voltage constraints; the converter station-level reactive power constraints for stable operation include converter station rated capacity constraints and modulation ratio constraints; and the equipment-level reactive power constraints for stable operation include submodule capacitor voltage constraints and bridge arm reactor constraints.

[0030] 1) A simplified model of a single DC converter station connected to the AC receiving-end power grid is as follows: Figure 2 As shown. The equivalent voltage of the AC system is Us, the AC side voltage of the converter station is Uc, and the line impedance between the DC connection point and the receiving-end AC system is Z. The relationship between the active power Pc, reactive power Qc, AC system voltage US, and AC output voltage Uc of the converter station can be expressed by equation (1): (1) In the formula: U c This refers to the AC side voltage of the converter station. U s is the equivalent voltage of the AC system; P c The active power flowing out of the converter station; Q c The reactive power flowing out of the converter station; R Line resistance; X This refers to the line reactance.

[0031] 2) System-level stability constraints 21) Current Constraints To ensure that the power flow equations of the system have solutions, equation (1) must satisfy the following constraints: (2) (3) 22) AC voltage constraint During the operation of a converter station, the stability of the AC side voltage is crucial for the safe and reliable operation of the system. To ensure the converter station operates stably within the permissible voltage range, appropriate constraints must be imposed on its AC side voltage. These constraints not only reflect the operating limits of the converter equipment itself but also embody the basic voltage level requirements of the connected AC power grid. (4) (5) In the formula: Us is the AC system voltage; B is the impedance angle; Z is the line impedance.

[0032] 3) Station-level stability operation constraints 31) Converter station rated capacity constraints During operation, the active and reactive power output of a flexible DC converter station is limited by the rated capacity of the equipment, satisfying the following: (6) In the formula: S VSCN This refers to the rated capacity of the converter station.

[0033] 2) Modulation ratio constraint The modulation ratio is one of the key parameters characterizing the output voltage capability of a converter. The magnitude of the modulation ratio directly affects the output voltage amplitude of the converter, thus influencing its active and reactive power regulation range. To ensure the normal operation of the converter, the modulation ratio must be limited within a certain safe operating range. (7) (8) In the formula: , These are the minimum modulation ratio and the maximum modulation ratio, respectively, in this embodiment. , M is the modulation ratio; U c This refers to the AC output voltage of the converter station. U dc This refers to the DC side voltage of the converter station.

[0034] This constraint ensures that the converter output voltage remains within its controllable range, preventing nonlinear operating problems such as saturation and distortion. Furthermore, the modulation ratio constraint is closely related to the AC voltage control strategy and needs to be considered in conjunction with the system's power regulation requirements, voltage control objectives, and DC-side voltage levels to improve the dynamic performance and stability of the entire converter system.

[0035] 4) Equipment-level stability constraints 41) Submodule capacitor voltage constraint In a flexible DC system composed of modular multilevel converters, the submodule capacitor voltage is a key parameter for measuring the internal energy balance and operational stability of the converter. Each submodule is equipped with a capacitor to store energy and regulate the output voltage. The voltage level of the capacitor must be maintained within a certain range to ensure that the converter outputs the target voltage waveform normally and to avoid overvoltage or undervoltage operation of the devices.

[0036] (9) In the formula: N This refers to the number of capacitors in the submodule. C 0 represents the capacitance value of the submodule; U 0 represents the capacitor voltage value of the submodule; w represents the angular frequency; A The power factor angle; This is the upper limit of the ratio of the voltage fluctuation of the submodule capacitor to the base value.

[0037] 2) Bridge arm reactor constraint To ensure that the electromagnetic transient characteristics of the converter arms meet design requirements during the operation of the DC transmission system, the parameter settings of the arm reactors must also follow specific constraints. Based on the system's electrical parameters and operating characteristics, the constraints that the arm reactors must satisfy can be derived: (10) In the formula: L This represents the reactance value of the bridge arm; U d This refers to the DC bus voltage of the converter station. This represents the maximum allowable rate of change of current. U cmax This is the maximum AC voltage; f The power grid frequency; I max This is the maximum alternating current.

[0038] S102. Based on the multi-level stable operation reactive power constraint conditions, the vertices of the multi-level stable operation reactive power constraint conditions are derived through geometric analysis. Based on the vertices, the feasible domain half-space defined by the multi-dimensional nonlinear inequality constraint is obtained, thus obtaining the reactive power operation domain of the single-end converter station.

[0039] Specifically, for the above-mentioned multi-level constraints, a geometric analysis of the reactive power feasible region of the single-ended converter station is further carried out. By mathematically deriving the vertices of the multi-level constraints, the half-space defined by the nonlinear inequality is obtained, and its feasible region structure is characterized by algebraic methods, as shown in formulas (11)-(13): (11) (12) (13) In the formula: ( P cv , Q cv The ) represents the vertex of the lower boundary surface formed by the rated capacity constraint and the AC voltage constraint of the converter station. P cv and Q cv These correspond to the active and reactive power at that vertex, respectively; P ov , Q ov The ) represents the vertex of the lower boundary surface formed by the AC voltage constraint of the converter station and the capacitor voltage constraint of the submodule. P ov and Q ov These correspond to the active and reactive power at that vertex, respectively; P oc , Q oc The ) represents the vertex of the lower boundary surface formed by the capacitor voltage constraint and the rated capacity constraint of the submodule. P oc and Q oc These correspond to the active and reactive power at that vertex, respectively. S n This represents the actual capacity of the converter station. ω is the angular frequency.

[0040] Based on the above vertices, the feasible half-space defined by multidimensional nonlinear inequality constraints can be further obtained: S1021. Obtain the half-space of the feasible region of the lower boundary surface, specifically including: 1) If there is no vertex ( P ov , Q ov ),but when Q OC < Q CV , (14) when Q OC > Q CV , , (15) 2) If there exists a vertex ( P ov , Q ov ),but when Q OC < Q CV At that time, P CV Existing on the left P OV Therefore, (16) S1022. Following the same method as S1021, obtain the half-space of the feasible region of the upper boundary surface, expressed as: (17) In the formula: and These represent the upper and lower boundary surfaces of the feasible region, respectively. This refers to the actual active power. For the vertex ( P MC , Q MC x-axis value; P VSCN The rated active power of the converter station; Q VSCN This refers to the rated reactive power of the converter station.

[0041] S1023. Based on the half-space of the feasible region of the lower boundary surface and the half-space of the feasible region of the upper boundary surface, the reactive power operation domain of the single-ended converter station is obtained.

[0042] S2. Based on the reactive power operation domain of a single-ended converter station, a power transfer distribution factor is constructed to characterize the interaction between the active power distribution and the reactive power boundary change of the multi-ended flexible DC system, according to the node branch correlation vector, DC power flow susceptance matrix, and branch equivalent reactance value. The reactive power feasible domain boundary of the multi-ended flexible DC system is obtained by decoupling based on the power transfer distribution factor. Specifically, this includes: For converter stations i In general, when its active power changes, the lines connected to it... k The equivalent power change on the surface can be expressed as: (18) (19) In the formula: Converter station i In the k The power transfer distribution factor on each branch; branch road k Node branch association vector; The first element in the inverse matrix of the DC power flow susceptance matrix B0 is... i The column, where B0 is the n*n order electric susceptance matrix of the network topology formed by the n nodes involved; For the first k The equivalent reactance value of each branch; Converter station i Changes in active power.

[0043] According to the converter station i Connecting branch roads k Equivalent power change Calculate the active power of converter station j after being affected by the power fluctuation of converter station i. The expression is: (20) In the formula: The number of branches connected to a single-ended converter station; The number of converter stations; Converter station j The active power.

[0044] Based on the reactive power operating domain of the single-ended converter station, calculate the reactive power of the receiving converter station. i Impact on converter station j reactive power The dynamic reactive power feasible domain boundary of a multi-terminal flexible DC converter station is calculated as follows: ,(twenty one) In the formula: and These represent the upper and lower boundary surfaces of the feasible region, respectively.

[0045] Figure 3 The reactive power boundary coupling relationship between two interconnected flexible DC converter stations is briefly described. i With converter station j The initial active power is respectively P i0 、P j0 At this time, the converter station i The upper and lower boundaries of reactive power operation are respectively Q i UCL ( P i0), Q i LCL ( P i0 The upper and lower boundaries of reactive power operation for converter station j are respectively... Q j UCL ( P j0 ), Q j LCL ( P j0 When the converter station i The active power appears Δ P i0 When the value changes, its own reactive power operating boundary changes accordingly. Q i UCL ( P i0 ， ), Q i LCL ( P i0 ， Converter station j The reactive power boundary was also adjusted accordingly. Q j UCL ( P j0 ， ), Q j LCL ( P j0 ， ).

[0046] S3. Perform static voltage stability analysis based on the boundary of the reactive power feasible domain.

[0047] S301. Based on the feasible domain boundary of dynamic reactive power of the multi-terminal flexible DC converter station, the dynamic equivalent admittance and equivalent power of the flexible DC side are derived.

[0048] To accurately assess the impact of the flexible support capability of flexible DC transmission on the static voltage stability of multi-infeed systems, in addition to analyzing the effects of conventional DC and flexible DC control characteristics on the equivalent parameters of DC external characteristics, it is also necessary to focus on the impact of the dynamic reactive power support characteristics of interconnected flexible DC converter stations on the equivalent parameters.

[0049] The DC-side Jacobian matrix is ​​transformed into a complex Jacobian matrix, expressed as: ,(twenty two) In the formula: forY heq,i transpose, for S heq,i Transpose of; Y heq,i , S heq,i Let the equivalent admittance and equivalent power of the hybrid feed system equipment be represented as follows: , (twenty three) ,(twenty four) In the formula: and Converter station i The corresponding reactive power partial derivative term; For nodes i The voltage phase angle; For nodes i The actual active power expression; For nodes i The actual reactive power expression; U s The equivalent voltage of the AC system; Based on the dynamic reactive power operating domain of the multi-terminal flexible DC converter station, the reactive power partial derivative term is... and After correction, the corrected expression is: , (25) (26) Substituting the modified reactive power partial derivative into equations (23) and (24), we obtain the equivalent power and equivalent admittance parameters of the flexible DC side considering the dynamic reactive power characteristics correction of the multi-terminal flexible DC converter station.

[0050] S302. Based on the dynamic equivalent admittance and equivalent power of the flexible DC side, calculate the equivalent short-circuit ratio index of the hybrid DC infeed dynamic reactive power support characteristics, and quantitatively characterize the static voltage stability of the hybrid DC infeed power system.

[0051] Substituting the corrected equivalent impedance and equivalent power of the flexible DC side back into equation (22), we can obtain the hybrid-infeed short circuit ratio (DPHSCR) that takes into account the dynamic reactive power support characteristics of the multi-terminal flexible DC. This index can reflect the static voltage stability characteristics of the multi-terminal flexible DC and conventional DC centralized feed-in power systems.

[0052] (27) In the formula: Converter station i The corresponding hybrid feed equivalent short-circuit ratio; This assumes only the equivalent impedance of the node being analyzed. For nodes i Final equivalent power; To consider the nodes being analyzed as being affected by other nodes j The equivalent impedance affected; For nodes j Final equivalent power; U s is the equivalent voltage of the AC system; n The number of converter stations; The standard for evaluating the static voltage stability of a system is as follows: a value greater than 1 indicates that the system is in a stable state, a value equal to 1 indicates that the system is in a critically stable state, and a value less than 1 indicates that the system is unstable.

[0053] Next, we will use simulations with specific application examples to verify the effectiveness of the method of the present invention.

[0054] In this embodiment, the following is constructed: Figure 4 The example shown is a simulation of a three-DC-feed power system with LCC-HVDC and VSC-HVDC connections. The main equipment parameters involved are shown in Table 1.

[0055] Table 1 Equipment Parameters The topological parameters involved are shown in Table 2.

[0056] Table 2 Network Topology (1) Analysis of the mapping relationship between the flexible DC reactive power operation domain and DPHSCR To analyze the impact of the reactive power operating domain of the flexible DC transmission line on the system's hybrid input short-circuit ratio, LCC-HVDC converters were first connected at converter stations 1 and 2, and VSC-HVDC converters were connected at converter station 3. At this point, the input power at converter stations 2 and 3 was constant, while the input power at converter station 1 changed dynamically. The mapping relationship between the reactive power operating domain of the flexible DC transmission line and the DPHSCR is as follows: Figure 5 As shown.

[0057] from Figure 5It can be seen that: 1) When the flexible DC converter station is operating in the fourth quadrant, it outputs capacitive reactive power, which can provide reactive power support to the AC grid. The lower and upper boundaries of the reactive power operating domain correspond to the upper and lower boundaries of the DPHSCR index, respectively. 2) If the multi-infeed short-circuit ratio calculation only considers the converter station capacity constraint when taking into account the reactive power support capability of the flexible DC, the evaluation index obtained is too optimistic. After further considering the multi-level operating constraints faced by the flexible DC operation on the basis of capacity constraints, the DPHSCR index range is significantly narrowed, and the judgment requirements for the static voltage stability of the system are more stringent. This is mainly because the AC system voltage constraint and modulation ratio constraint compress the reactive power output operating range of the flexible DC converter station, resulting in an increase and decrease in its corresponding equivalent power, respectively, thus making the DPHSCR range more accurate.

[0058] (2) The impact of different feed types on DPHSCR For multi-infeed systems, both the type and number of DC feeds significantly impact the system's static voltage stability. To further analyze the effectiveness of the DPHSCR index for hybrid feed systems, analyses were conducted for converter stations 1 and 2 using LCC-HVDC input, and for converter station 3 using three scenarios: no DC input, LCC-HVDC input, and VSC-HVDC input. The LCC-HVDC inputs all employed constant power-constant arc extinction angle (CP-CEA) control, while the VSC-HVDC inputs used constant power-constant power control. Figure 6 The changes in DPHSCR index with the feed power of converter station 1 are shown in three scenarios.

[0059] from Figure 6It can be seen that: 1) The DPHSCR index is represented by a single curve in both the LCC-connected and non-connected scenarios at node 3. However, after the flexible DC system is connected to node 3, there are constraints on the upper and lower limits of reactive power under the same active power output, so its DPHSCR index consists of two curves forming an index range; 2) The DPHSCR index value is the largest in the non-connected scenario at node 3, followed by the index range when connected to the flexible DC system, and the smallest in the scenario when connected to the LCC-HVDC. This is mainly because the equivalent power changes when connected to the LCC-HVDC or VSC-HVDC. Furthermore, since the equivalent power is negatively correlated with the DPHSCR index, and the equivalent power after flexible DC access is less than that of conventional DC, the DPHSCR index range of flexible DC is better than that of conventional DC access. 3) During the process of increasing active power output of conventional DC, when node 3 is connected to conventional DC, the DPHSCR of the system reaches the instability point first when P(1) is 1.38. After connecting to VSC, the system can withstand 0.73% of the feed-in power at converter station 1 compared to LCC. The main reason for this situation is that the equivalent power of LCC is the largest. During the process of its actual power increase, the index decline trend is more obvious, and it is easier to reach the instability point.

[0060] (3) The impact of VSC feed-in quantity on DPHSCR index To analyze the impact of the number of VSC-HVDC connections on the system's DPHSCR index, converter station 1 was kept connected to a conventional LCC-HVDC, and VSC-HVDCs were added sequentially to the remaining nodes. The results are as follows: Figure 7 As shown, the index range for a single node connected to a VSC-HVDC is greater than that for a dual-node connection, indicating that the more VSC-HVDCs connected, the worse the static voltage stability of the AC power grid becomes.

[0061] (4) Verification of support capability under dynamic changes in flexible DC power output Based on converter station 1 as conventional DC and converter stations 2 and 3 as flexible DC, a three-dimensional model of the DPHSCR index of the AC power grid system is established, considering multi-level, refined reactive power constraints and the dynamic output power of the flexible DC system. For example... Figure 8 As shown, Δ in the model P (2) The power change of converter station 2 is taken as 1 in this model; P (3) 0 is the initial value of the active power output of converter station 3 and takes the value of 0.2; G 2-3 The power transfer distribution factor between converter station 2 and converter station 3 is set to 0.45.

[0062] This figure shows the three-dimensional surface relationship of the static voltage stability assessment index DPGSCR of the system under different operating conditions as the active power output of converter stations 1, 2 and 3 changes. It is used to analyze the changes in the flexible DC support capability under the influence of multiple factors on the AC system voltage stability in the hybrid DC system.

[0063] It is evident that when power fluctuations occur at each flexible DC converter station, due to the power coupling relationship between the stations, the power changes caused by other stations are superimposed on the changes in the station's own power. Ultimately, this causes the system DPHSCR index, which reflects its reactive power support capability, to change in the domain of the index surface as follows: Figure 8 Changes to the gray area.

[0064] From the perspective of LCC1, the active power output of VSC3 is constant at this time. As the active power output of LCC1 increases, DPHSCR decreases, and the static voltage stability of the AC system weakens. From the perspective of VSC3, the active power output of LCC1 is constant at this time. As the active power output of VSC3 increases, the red upper surface is limited by voltage constraints, and the index value slowly decreases. When P(3) is greater than 1, the index value decreases more due to capacity constraints. The purple lower surface is limited by modulation ratio constraints, and the index value first increases and then decreases. When P(3) is greater than 1, the index value gradually increases due to capacity constraints, and the static voltage stability of the system is enhanced.

[0065] Overall, since the capacitive reactive power output from the converter station provides support for the system, the lower limit of reactive power always provides stronger support than the upper limit, which is reflected in the upper surface of the 3D graph. This example verifies the combined impact of LCC and VSC coordinated control on system voltage stability, demonstrating the effectiveness and sensitivity of this method in complex operating scenarios.

[0066] Example 2 This embodiment provides a static voltage stability analysis device for a hybrid DC-DC fed system, applying the method in Embodiment 1, including: The first construction module is used to construct the reactive power operation domain of a single-ended converter station based on the boundary surface vertices formed by the rated capacity constraint and AC voltage constraint of the converter station, the boundary surface vertices formed by the AC voltage constraint of the converter station and the capacitor voltage constraint of the sub-module, and the boundary surface vertices formed by the capacitor voltage constraint of the sub-module and the rated capacity constraint of the sub-module. The second construction module is used to construct a power transfer distribution factor that characterizes the interaction between the active power distribution and the reactive power boundary change of the multi-terminal flexible DC system based on the node branch correlation vector, DC power flow susceptance matrix and branch equivalent reactance value, on the basis of the reactive power operation domain of the single-terminal converter station. The reactive power feasible domain boundary of the multi-terminal flexible DC system is obtained by decoupling based on the power transfer factor. The stability analysis module performs static voltage stability analysis based on the boundary of the reactive power feasible domain.

[0067] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for static voltage stability analysis of a hybrid DC feed-in system, characterized in that, The method comprises the following steps: According to the boundary surface vertex formed by the converter station rated capacity constraint and the AC voltage constraint, the boundary surface vertex formed by the converter station AC voltage constraint and the sub-module capacitor voltage constraint, and the boundary surface vertex formed by the sub-module capacitor voltage constraint and the rated capacity constraint, a single-ended converter station reactive power operation domain is constructed; On the basis of the single-ended converter station reactive power operation domain, a power transfer distribution factor representing the interaction between the active power distribution and the reactive power boundary change of the multi-terminal HVDC system is constructed according to the node branch correlation vector, the DC power flow admittance matrix and the equivalent reactance value of the branch, and the reactive power feasible region boundary of the multi-terminal HVDC system is obtained by decoupling according to the power transfer distribution factor; Static voltage stability analysis is performed according to the reactive power feasible region boundary.

2. The method for static voltage stability analysis of a hybrid DC feed system according to claim 1, wherein, The boundary surface vertex, the obtaining process specifically comprises: A multi-level stable operation reactive power constraint condition is constructed, including a power flow constraint, an AC voltage constraint, a converter station rated capacity constraint, a modulation ratio constraint, a sub-module capacitor voltage constraint and a bridge arm reactor constraint; According to the multi-level stable operation reactive power constraint condition, the boundary surface vertex formed by the converter station rated capacity constraint and the AC voltage constraint, the boundary surface vertex formed by the converter station AC voltage constraint and the sub-module capacitor voltage constraint, and the boundary surface vertex formed by the sub-module capacitor voltage constraint and the rated capacity constraint are derived through geometric analysis.

3. The method for static voltage stability analysis of a hybrid DC feed system according to claim 1, wherein, According to the boundary surface vertex formed by the converter station rated capacity constraint and the AC voltage constraint, the boundary surface vertex formed by the converter station AC voltage constraint and the sub-module capacitor voltage constraint, and the boundary surface vertex formed by the sub-module capacitor voltage constraint and the rated capacity constraint, a feasible region half-space defined by a multi-dimensional nonlinear inequality constraint is obtained, and a single-ended converter station reactive power operation domain is obtained.

4. The method for static voltage stability analysis of a hybrid DC feed system according to claim 3, wherein, For the half-space of the lower boundary surface feasible region, the specific construction process comprises: The lower boundary surface vertex formed by the converter station rated capacity constraint and the AC voltage constraint, the lower boundary surface vertex formed by the converter station AC voltage constraint and the sub-module capacitor voltage constraint, and the lower boundary surface vertex formed by the sub-module capacitor voltage constraint and the rated capacity constraint, and the expression is: ， ， ， wherein: P cv , Q cv represents the vertex of the lower boundary surface formed by the converter station rated capacity constraint and the AC voltage constraint, P cv and Q cv correspond to the active power and the reactive power at the vertex, respectively; P ov , Q ov represents the vertex of the lower boundary surface formed by the converter station AC voltage constraint and the sub-module capacitor voltage constraint, P ov and Q ov correspond to the active power and the reactive power at the vertex, respectively; P oc , Q oc represents the vertex of the lower boundary surface formed by the sub-module capacitor voltage constraint and the rated capacity constraint, P oc and Q oc correspond to the active power and the reactive power at the vertex, respectively; U s is the equivalent voltage of the AC system; Z is the line impedance between the DC access point and the receiving end AC system; is the upper limit of the proportion of the sub-module capacitor voltage fluctuation relative to the base value; M is the modulation ratio; N is the number of sub-module capacitors; C 0 is the sub-module capacitor value; U 0 is the sub-module capacitor voltage value; is the angular frequency; A is the power factor angle; S n is the actual capacity of the converter station; According to the lower boundary surface vertex, the half-space of the lower boundary surface feasible region is obtained, specifically comprising: 1) if there is no vertex (V P ov , Q ov ), then When Q OC < Q CV , ， When Q OC > Q CV , ， 2) if there is a vertex (V, E) such that P ov , Q ov ), then When Q OC , Q CV there is P CV a left side P OV , so there is ， wherein: represents the lower boundary surface of the feasible region; is the actual active power; is the vertex P MC , Q MC is the abscissa value; P VSCN is the rated active power of the converter station; Q VSCN is the rated reactive power of the converter station.

5. The method for static voltage stability analysis of a hybrid DC feed system according to claim 4, wherein, The half-space of the upper boundary surface feasible region is obtained in the same way as the half-space of the lower boundary surface feasible region, and the specific expression is: ， wherein: represents the upper boundary surface of the feasible region; is the vertex ( P MC , Q MC ) x-coordinate value.

6. The method for static voltage stability analysis of a hybrid DC feed system according to claim 1, wherein, On the basis of the single-ended converter station reactive power operation domain, a power transfer distribution factor representing the interaction between the active power distribution and the reactive power boundary change of the multi-terminal HVDC system is constructed according to the node branch correlation vector, the DC power flow admittance matrix and the equivalent reactance value of the branch, and the reactive power feasible region boundary of the multi-terminal HVDC system is obtained by decoupling according to the power transfer distribution factor, specifically comprising: According to the node branch correlation vector, the DC power flow admittance matrix and the equivalent reactance value of the branch, the power transfer distribution factor is calculated, and the expression is: ， wherein: is the converter station i In the first k power transfer distribution factor on the branch is the branch k node-branch incidence vector of the branch is the column i of the inverse of the DC power flow susceptance matrix B0; is the equivalent reactance value of the branch k ​ When converter station i When the active power changes, the calculation and converter station i Connecting branch roads k Equivalent power change The expression is: ， ， In the formula: for the converter station i active power variation; According to the equivalent power variation on the branch connected with the converter station i of the converter station i k , the active power of the converter station j affected by the power fluctuation of the converter station i is calculated , and the expression is as follows: ​ ， In the formulae: is the number of branches connected to the single-end converter station; is the number of converter stations; is the active power of the converter station j ; Combining the reactive operation region of single-end converter station, the reactive power affected by the converter station i after the converter station j is calculated , the boundary of the dynamic reactive power feasible region of multi-terminal VSC-MTDC is calculated, and the calculation expression is: ， In the formulae: and respectively represent the upper and lower boundary surfaces of the feasible region.

7. The method for static voltage stability analysis of a hybrid DC feed system according to claim 1, wherein The static voltage stability analysis according to the reactive power feasible region boundary comprises: According to the dynamic reactive power feasible region boundary of the multi-terminal HVDC converter station, the reactive power partial derivative term in the dynamic equivalent admittance and the equivalent power of the HVDC side is modified; According to the modified dynamic equivalent admittance and equivalent power of the HVDC side, a hybrid feeder equivalent short-circuit ratio index of the multi-terminal HVDC dynamic reactive power support characteristic is calculated to quantitatively represent the static voltage stability of the hybrid DC feeder power system.

8. The method for static voltage stability analysis of a hybrid DC feed system according to claim 7, wherein, The reactive power partial derivative term in the dynamic equivalent admittance and equivalent power of the HVDC side is modified according to the dynamic reactive power feasible region boundary of the multi-terminal HVDC converter station, and specifically includes: The DC side Jacobian matrix is transformed into a complex Jacobian matrix and expressed as: ， where: is Y heq,i the transpose of is S heq,i the transpose of Y heq,i , S heq,i are the hybrid feed system device outer characteristic equivalent admittance and equivalent power, respectively, and are given by: ， ， wherein: and is the converter station i corresponding reactive power partial derivative; is the voltage phase angle of node i ; is the actual active power of node i ; is the actual reactive power of node i ; U s is the AC system equivalent voltage; Based on the dynamic reactive power operating domain of the multi-terminal flexible DC converter station, the reactive power partial derivative term is... and After correction, the corrected expression is: ， ， The modified equivalent power and equivalent admittance parameters of the HVDC side considering the dynamic reactive power characteristics of the multi-terminal HVDC converter station are obtained by substituting the modified reactive power partial derivative term.

9. The method for static voltage stability analysis of a hybrid DC feed system according to claim 7, wherein, The hybrid feeder equivalent short-circuit ratio index of the multi-terminal HVDC dynamic reactive power support characteristic is calculated to quantitatively represent the static voltage stability of the hybrid DC feeder power system, and the expression of the hybrid feeder equivalent short-circuit ratio index is: ， wherein: is the number of converter stations i is the corresponding hybrid feed-in equivalent short circuit ratio; is the equivalent impedance considering only the analyzed node itself; is the node i final equivalent power; is the equivalent impedance considering the analyzed node influenced by the nodes j ; is the node j final equivalent power; U s is the alternating current system equivalent voltage; n is the number of converter stations.

10. An apparatus for static voltage stability analysis of a hybrid DC feed-in system, characterized in that The method of any one of claims 1-9 is applied, comprising: The first construction module is configured to construct a single-terminal converter station reactive power operating region according to the boundary surface vertices composed of the converter station rated capacity constraint and the AC voltage constraint, the boundary surface vertices composed of the converter station AC voltage constraint and the sub-module capacitor voltage constraint, and the boundary surface vertices composed of the sub-module capacitor voltage constraint and the rated capacity constraint; The second construction module is configured to construct a power transfer distribution factor representing the interaction between the active power distribution and the reactive power boundary change of the multi-terminal HVDC system according to the node branch associated vector, the DC power flow admittance matrix and the branch equivalent reactance value on the basis of the single-terminal converter station reactive power operating region, and to decouple the power transfer distribution factor to obtain the reactive power feasible region boundary of the multi-terminal HVDC system; The stability analysis module is configured to perform static voltage stability analysis according to the reactive power feasible region boundary.

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