Symmetrical current three-wire common inductance direct current power flow control transient analysis method and system

Abstract

The invention provides a symmetrical current three-wire common inductance direct current power flow control transient analysis method and system. The method comprises the following steps: S1, establishing a modal space model of a symmetrical current control three-wire common inductance type direct current power flow controller; s2, a dynamic segmentation method is adopted for the modal space model, and a transfer function matrix of the autonomous system is obtained; and S3, performing transient oscillation characteristic analysis on the autonomous system by using a singular value analysis method, and outputting an analysis result. And S4, analyzing the influence of different types of parameters on the transient oscillation contribution degree. According to the direct current power flow controller transient state analysis method based on singular value decomposition, transient state oscillation characteristics closer to multi-end direct current transmission are obtained in the three-wire direct current power flow controller topology, and reference is provided for more comprehensive and more-dimensional direct current power flow transient state oscillation suppression.

Description

Technical Field

[0001] The present invention relates to the field of electrical engineering, and in particular to a transient analysis method and system for symmetrical current three-wire shared inductor DC power flow control, and in particular to a transient oscillation characteristic analysis method for a three-wire shared inductor DC power flow controller based on symmetrical current control. Background Art

[0002] In order to respond to climate change and accelerate the clean and low-carbon transformation of energy, the gradual reduction and replacement of fossil energy has become a new force in promoting the transformation of energy to clean and low-carbon. At the same time, DC loads mainly composed of electric transportation vehicles and photovoltaic storage and direct flexible are also developing rapidly. The new DC transmission system is widely used due to its flexible controllability and high efficiency. However, with the access of a large number of distributed power sources, diversified loads and a high proportion of power electronic equipment, the new DC transmission system faces major challenges of randomness and volatility. Flexible DC transmission technology has the advantages of large transmission capacity and low harmonic content, which can improve the reliability and flexibility of the new DC transmission system.

[0003] As a typical application of flexible DC transmission technology, multi-terminal flexible DC transmission technology has outstanding advantages in multi-grid interconnection and multi-power supply, and can give full play to the economy and flexibility of DC transmission. However, due to the mesh structure of the multi-terminal DC transmission system and the lack of power flow control means, the DC transmission network will have problems such as uneven power flow distribution and limited section transmission capacity. The DC power flow controller can actively control the power flow distribution to solve problems such as limited section transmission capacity, and at the same time can improve the flexibility of the DC transmission network and promote the overall consumption of new energy. By adopting the transient oscillation analysis method of the three-line shared inductor DC power flow controller based on symmetrical current control, the non-fault transient oscillation of the DC transmission network containing the three-line DC power flow controller can be suppressed in a targeted manner.

[0004] The transient characteristics analysis method of three-line shared inductor DC power flow controller based on symmetrical current control mainly includes modal space modeling of three-line DC power flow controller, dynamic segmentation of three-line DC power flow controller, singular value decomposition of autonomous DC power flow controller and contribution of different parameter types to DC power flow controller oscillation. In terms of small signal model and transfer function matrix construction of three-line DC power flow controller, most of the existing studies are aimed at analysis and modeling of coupled inductor, coupled capacitor or shared capacitor three-line DC power flow controller, and there is no small signal modeling and transfer function construction work based on shared inductor three-line DC power flow controller. In terms of transient characteristics analysis of three-line shared inductor, there is no literature that studies the contribution of different types of system parameters to transient oscillation of DC power flow controller based on modal space segmentation method and singular value analysis method.

[0005] Liu Siqi, Zhu Miao, Zhong Xu, et al. Three-line DC power flow controller with dual-degree-of-freedom control capability [J]. Automation of Electric Power Systems, 2019, 43(18): 75-81. A new three-line DC power flow controller topology is proposed, and the working principle and dual-objective control strategy are designed to achieve dual-degree-of-freedom power flow control, but it does not involve the modal space modeling and dynamic segmentation method of the three-line DC power flow controller; while this application is based on a three-line shared inductor DC power flow controller with symmetrical current control, and carries out modal space modeling based on small signal modeling and dynamic segmentation considering state variable division, and obtains the mathematical model of the three-line DC power flow controller in detail and comprehensively. In addition, this document does not involve the study of the transient process of the power flow controller.

[0006] Wang Weiyu, Zhang Yiping, Li Shuaihu, et al. Design of damping controller for grid-connected flexible DC system based on disturbance observation [J]. Power System Technology, 2024, 48(06): 2262-2271. A method for analyzing the oscillation characteristics of AC and DC systems based on singular value decomposition technology is proposed, and the damping suppression of key oscillation modes is realized by using quadratic optimal feedback control, but it does not involve the analysis of transient oscillation characteristics of non-fault switching of DC power flow controllers; while the present application is based on a three-line shared inductor DC power flow controller with symmetrical current control, and adopts modal space modeling and dynamic segmentation methods to quantify the non-fault transient modes of the three-line power flow controller. In addition, the literature does not classify and study the parameters that potentially affect transient oscillations.

[0007] The present invention aims to provide a better reference for non-fault transient oscillation suppression of a DC power transmission system including a three-line DC power flow controller by identifying the contribution of parameters of different damping types and different injection power types to transient oscillation. Summary of the invention

[0008] In view of the defects in the prior art, an object of the present invention is to provide a transient analysis method and system for symmetrical current three-wire shared inductor DC power flow control.

[0009] A transient analysis method for symmetrical current three-wire shared inductor DC power flow control provided by the present invention includes:

[0010] Step S1: establishing a modal space model of a symmetrical current controlled three-line shared inductor DC power flow controller;

[0011] Step S2: Using a dynamic segmentation method on the modal space model to obtain the transfer function matrix of the autonomous system;

[0012] Step S3: Use singular value analysis to analyze transient oscillation characteristics of the autonomous system and output the analysis results.

[0013] Preferably, it also includes:

[0014] Step S4: Analyze the influence of different types of parameters on the contribution of transient oscillation.

[0015] Preferably, the step S1 comprises:

[0016] Perform transient analysis on the shared inductor L and obtain the current differential equation in its switching sub-mode;

[0017] Perform transient analysis on the line inductance and capacitance respectively, and obtain the current differential equation of the line inductance and the voltage differential equation across the capacitor;

[0018] The transient analysis of the capacitor in the VSC is performed to obtain the differential equation of the voltage across the capacitor, and the modal space model is constructed using the differential equation.

[0019] Preferably, step S2 comprises:

[0020] The small signal model of the three-line DC power flow controller is dynamically divided according to whether it is completely controlled by the PI double-loop control, and the controllable system and the autonomous system are obtained.

[0021] Construct the state space equations of the controllable system and the autonomous system, and obtain the small signal model of the autonomous system;

[0022] Convert the small signal model of the autonomous system into a transfer function matrix.

[0023] Preferably, step S3 comprises:

[0024] Decompose the transfer function matrix of the autonomous system into a series of feature spaces based on singular value decomposition;

[0025] According to the different frequency characteristics presented in different feature spaces, the maximum singular value of the oscillation amplitude of the reaction state variable under different transient oscillation frequencies is extracted.

[0026] Preferably, step S4 comprises:

[0027] Change the resistance of the autonomous line and the controlled line respectively, keep the resistance of other lines unchanged, and observe the change of the maximum singular value of the system;

[0028] The autonomous injection power and the controlled injection power are changed respectively, and the changes of the maximum singular value of the system are observed.

[0029] A symmetrical current three-wire shared inductor DC power flow control transient analysis system provided by the present invention comprises:

[0030] Module M1: Establish the modal space model of the symmetrical current controlled three-line shared inductor DC power flow controller;

[0031] Module M2: Dynamic segmentation method is used for the modal space model to obtain the transfer function matrix of the autonomous system;

[0032] Module M3: Use singular value analysis to analyze the transient oscillation characteristics of the autonomous system and output the analysis results.

[0033] Preferably, it also includes:

[0034] Module M4: Analyze the impact of different types of parameters on the contribution of transient oscillations.

[0035] Preferably, the module M1 comprises:

[0036] Perform transient analysis on the shared inductor L and obtain the current differential equation in its switching sub-mode;

[0037] Perform transient analysis on the line inductance and capacitance respectively, and obtain the current differential equation of the line inductance and the voltage differential equation across the capacitor;

[0038] The transient analysis of the capacitor in the VSC is performed to obtain the differential equation of the voltage across the capacitor, and the modal space model is constructed using the differential equation.

[0039] Preferably, the module M2 comprises:

[0040] The small signal model of the three-line DC power flow controller is dynamically divided according to whether it is completely controlled by the PI double-loop control, and the controllable system and the autonomous system are obtained.

[0041] Construct the state space equations of the controllable system and the autonomous system, and obtain the small signal model of the autonomous system;

[0042] Convert the small signal model of the autonomous system into a transfer function matrix.

[0043] Preferably, the module M3 includes:

[0044] Decompose the transfer function matrix of the autonomous system into a series of feature spaces based on singular value decomposition;

[0045] According to the different frequency characteristics presented in different feature spaces, the maximum singular value of the oscillation amplitude of the reaction state variable under different transient oscillation frequencies is extracted.

[0046] Preferably, the module M4 includes:

[0047] Change the resistance of the autonomous line and the controlled line respectively, keep the resistance of other lines unchanged, and observe the change of the maximum singular value of the system;

[0048] The autonomous injection power and the controlled injection power are changed respectively, and the changes of the maximum singular value of the system are observed.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] 1. The present invention makes full use of the transient analysis method of DC power flow controller based on singular value decomposition, and obtains transient oscillation characteristics that are closer to multi-terminal DC transmission in the topology of three-line DC power flow controller, providing a reference for more comprehensive and multi-dimensional DC power flow transient oscillation suppression.

[0051] 2. The present invention innovatively applies modal space modeling and dynamic segmentation methods to the topology of a three-line DC power flow controller. By dividing the system into a controllable part that is completely controlled by PI and an autonomous part that is not completely controlled by PI, a mathematical model of the autonomous part corresponding to the transient oscillation of the three-line power flow controller is given specifically.

[0052] 3. The present invention uses the singular value decomposition method, which is more adaptable than the traditional modal analysis method, for transient oscillation analysis of the autonomous three-line DC power flow controller, and analyzes the transient oscillation characteristics of the three-line power flow controller more comprehensively and rigorously based on numerical analysis.

[0053] 4. The present invention conducts targeted research on different damping type parameters and different injection power type parameters, thereby obtaining the contribution of different types of parameters to the transient oscillation of the three-line DC power flow controller, providing a multi-dimensional reference for the transient oscillation suppression of the multi-terminal DC power flow controller.

[0054] Other beneficial effects of the present invention will be explained in the specific implementation manner through the introduction of specific technical features and technical solutions. Through the introduction of these technical features and technical solutions, those skilled in the art should be able to understand the beneficial technical effects brought about by the technical features and technical solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0056] Figure 1 This is a topology diagram of a symmetrical current controlled three-wire shared inductance DC power flow controller in the present invention.

[0057] Figure 2 It is a schematic diagram of the working sub-mode of the No. 1 symmetrical current controlled three-line shared inductance type DC power flow controller in the present invention.

[0058] Figure 3 It is a schematic diagram of the working sub-mode of the No. 2 symmetrical current controlled three-line shared inductance type DC power flow controller in the present invention.

[0059] Figure 4 It is a schematic diagram of the working sub-mode of the three-line shared inductance DC power flow controller with three symmetrical current control in the present invention.

[0060] Figure 5 The control i of the present invention 14 Double-loop PI block diagram.

[0061] Figure 6 The control i of the present invention 14 Internal block diagram of the dual-loop PI.

[0062] Figure 7 The control i of the present invention 34 Double-loop PI block diagram.

[0063] Figure 8 The control i of the present invention 34 Internal block diagram of the dual-loop PI.

[0064] Fig. 9 It is the Bode diagram corresponding to the maximum singular value of the transfer function matrix at different frequencies in the present invention.

[0065] Fig.10 In the present invention, R is changed a , R c , keeping other line resistances unchanged, schematic diagram of the change of the system's maximum singular value.

[0066] Fig.11 In the present invention, P is changed 1 , P 2 , schematic diagram of the change of the system's maximum singular value.

[0067] Fig.12 It is a schematic diagram of a four-terminal ring network DC transmission system in the present invention.

[0068] Fig.13 This is a common inductor current waveform diagram in the experiment of contribution of different damping types to oscillation in the present invention.

[0069] Fig.14 The capacitance C in the experiment of the contribution of different damping types to oscillation in the present invention 2 Voltage waveform diagram.

[0070] Fig.15 This is a common inductor current waveform diagram in the experiment of different injection power types' contribution to oscillation in the present invention.

[0071] Fig.16 The capacitance C in the experiment of the contribution of different injection power types to oscillation in the present invention is 2 Voltage waveform diagram.

[0072] Fig.17 The present invention is a flow chart of the method. DETAILED DESCRIPTION

[0073] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0074] The technical solution of the present application is a method for analyzing the transient oscillation characteristics of a three-line shared inductor DC power flow controller with symmetrical current control based on four-terminal DC transmission. The method for analyzing the transient oscillation characteristics of a three-line power flow controller mainly includes modal space modeling of the three-line power flow controller, dynamic segmentation of the three-line power flow controller, singular value analysis of the three-line autonomous power flow controller, and analysis of the contribution of different types of parameters to transient oscillations. Modal space modeling is carried out for the three-line shared inductor DC power flow controller with symmetrical current control, and then a dynamic segmentation method is adopted based on a complete three-line small signal model to obtain the transfer function matrix of the autonomous three-line DC power flow controller. The transient oscillation characteristics of the autonomous system are analyzed using a singular value analysis method with better adaptability than the traditional modal analysis method, and the maximum singular value changes of parameters of different damping types and different injection power types are comprehensively considered to obtain the transient oscillation characteristics of the three-line shared inductor DC power flow controller. Fig.17 As shown, the specific implementation means are as follows:

[0075] 1. Modal space modeling of symmetrical current control three-line shared inductor DC power flow controller

[0076] Refer to Figure 1 The three-line symmetrical current control shared inductor DC power flow controller shown in the figure is studied. The connecting hub units Part 1, Part 2, and Part 3 can be regarded as three equivalent voltage sources connected in series to the line line 14 、line 24 and line 34 The connection hub unit exchanges energy with the energy hub unit in turn under specific switching states. Through the energy hub unit, part of the energy can be transferred between the three DC lines to achieve DC power flow control. Symmetrical current control refers to the control of the transmission lines at both ends of the three-line topology. 14 、line 34 The current is controlled without affecting the intermediate transmission line 24 The current is controlled by a current control method.

[0077] Under steady-state operation, the entire switching cycle can be divided into three switching sub-modes, such as Figure 2 — Figure 4 As shown, its operating mechanism is briefly described as follows:

[0078] (1) Switching sub-mode 1: QA1A On / Q A2A Shutdown / Q A3A Shutdown, C 1 -D As1A -Q A1 -LD Bs1B -Q B1B Forming loop 1, such as Figure 2 As shown. During the duration of this switching sub-mode stage, the line current I 14 Energy is transferred to the shared inductor L, and the current change of the shared inductor L increases linearly.

[0079] (2) Switching submode 2: Q A1A Shutdown / Q A2A Shutdown / Q A3A When C 3 -D As3A -Q A3 -LD Bs3B -Q B3B Forming loop 2, such as Figure 3 As shown. During the duration of this switching sub-mode stage, the line current I 34 Energy is transferred to the shared inductor L, and the current change of the shared inductor L increases linearly.

[0080] (3) Switching sub-mode 3: Q A1A Shutdown / Q A2A On / Q A3A Turn off, then C 2 -D As2A -Q A2 -LD Bs2B -Q B2B Forming loop 3, such as Figure 4 As shown. Energy flows from the shared inductor L to the line current I 24 The current change of the shared inductor L decreases linearly.

[0081] Setting switch Q A1A , Q A2A and Q A3A The duty cycle is D 1 , D 2 and (1-D 1 -D 2 ).

[0082] (1) Transient analysis of shared inductor L: When the switching sub-mode is 1, that is, in [0,D 1 T S ] time, the capacitor voltage uC 1 Added across the shared inductor L; when the switch is in sub-mode 2, that is, [D 1 T S ,(D1 +D 2 )T S ] time, the capacitor voltage uC 2 Added across the common inductor L; When the switch is in sub-mode 3, that is, [(D 1 +D 2 )T S ,(1-D 1 -D 2 )T S ] time, the capacitor voltage uC 3 Added across the shared inductor L. The current i of the shared inductor L L The differential equation is shown in formula (1):

[0083]

[0084] (2) Line inductance L 12 Transient analysis: line 12 The voltages at both ends are respectively VSC1 (voltage source converter) port voltage u 1 and VSC2 port voltage u 2 , line 12 The voltage on the resistor is i 12 R 12 , line inductance L 12 The current i 12 The differential equation is shown in formula (2):

[0085]

[0086] (3) Line inductance L 14 Transient analysis: line 14 The voltages at both ends are respectively VSC1 port voltage u 1 and VSC4 port voltage and capacitor C 1 The voltage and (u 4 +u C1 ), line 14 The voltage on the resistor is i 14 R 14 , line inductance L 14 The current i 14 The differential equation is shown in formula (3):

[0087]

[0088] (4) Line inductance L 23 Transient analysis: line 23 The voltages at both ends are respectively VSC2 port voltage u 2 and VSC3 port voltage u 3 , line23 The voltage on the resistor is i 23 R 23 , line inductance L 23 The current i 23 The differential equation is shown in formula (4):

[0089]

[0090] (5) Line inductance L 24 Transient analysis: line 24 The voltages at both ends are respectively VSC2 port voltage u 2 and VSC4 port voltage and capacitor C 2 The voltage and (u 4 +u C2 ), line 24 The voltage on the resistor is i 24 R 24 , line inductance L 24 The current i 24 The differential equation is shown in (5):

[0091]

[0092] (6) Line inductance L 34 Transient analysis: line 34 The voltages at both ends are respectively VSC3 port voltage u 3 and VSC4 port voltage and capacitor C 3 The voltage and (u 4 +u C3 ), line 34 The voltage on the resistor is i 34 R 34 , line inductance L 34 The current i 34 The differential equation is shown in (6):

[0093]

[0094] (7) Capacitor C 1 Transient analysis: When the switch is in sub-mode 1, that is, in [0,D 1 T S ] time, the current flowing through the capacitor C 1 The current of line 14 Current i 14 The current i of the shared inductor L L The difference (i 14 -i L ); in switch sub-modes 2 and 3, that is, in [D 1 T S ,TS ] time, the current flowing through the capacitor C 1 The current of line 14 Current i 14 Capacitor C 1 Voltage across the two ends u C1 The differential equation is shown in (7):

[0095]

[0096] (8) Capacitor C 2 Transient analysis: When the switch is in sub-mode 1, that is, in [0,D 1 T S ] time, the current flowing through the capacitor C 2 The current of line 24 Current i 24 ; When the switch submode 2, that is, in [D 1 T S ,(D 1 +D 2 )T S ] time, the current flowing through the capacitor C 2 The current of line 24 Current i 24 The current i of the shared inductor L L The difference (i 24 -i L ); When the switch submode is in 3, that is, in [(D 1 +D 2 )T S ,(1-D 1 -D 2 )T S ] time, the current flowing through the capacitor C 2 The current of line 24 Current i 24 ; Capacitor C 2 Voltage across the two ends u C2 The differential equation is shown in (8):

[0097]

[0098] (9) Capacitor C 3 Transient analysis: In switching submodes 1 and 2, that is, in [0, (D 1 +D 2 )T S ] time, the current flowing through the capacitor C 3 The current of line 34 Current i 34 ; When the switch submode is in 3, that is, in [(D 1 +D 2 )T S,(1-D 1 -D 2 )T S ] time, the current flowing through the capacitor C 3 The current of line 34 Current i 34 The current i of the shared inductor L L The difference (i 34 -i L );Capacitor C 3 Voltage across the two ends u C3 The differential equation is shown in (9):

[0099]

[0100] (10) Capacitor C in VSC1 s1 Transient analysis: Flow through capacitor C s1 The current is the VSC1 theoretical current (P 1 / u 1 ) minus line line 12 and line 14 The sum of the current (i 12 +i 14 ). Among them, P 1 is the output power of VSC1. Capacitor C s1 Voltage across the two ends u 1 The differential equation is shown in (10):

[0101]

[0102] (11) Capacitor C in VSC2 s2 Transient analysis: Flow through capacitor C s2 The current is the VSC2 theoretical current (P 2 / u 2 ) minus line line 23 and line 24 The sum of the current (i 23 +i 24 ), plus line line 12 Current i 12 Among them, P 2 is the output power of VSC2. Capacitor C s2 Voltage across the two ends u 2 The differential equation is shown in formula (11):

[0103]

[0104] (12) Capacitor C in VSC3 s3 Transient analysis: Flow through capacitor C s3 The current is the VSC3 theoretical current (P3 / u 3 ) minus line line 34 Current i 34 , plus line line 23 Current i 23 Among them, P 3 is the output power of VSC3. Capacitor C s3 Voltage across the two ends u 3 The differential equation is shown in (12):

[0105]

[0106] (13)Control i 14 Dynamic analysis of PI current loop: The control block diagram of PI double loop is as follows: Figure 5 As shown by Figure 6 It can be seen that the differential term of the current loop is ( Represents ξ 1 The differential of equivalent) is line line 14 Current reference value i 14ref and line 14 Current i 14 The difference (i 14ref -i 14 ). PI current loop differential term The differential equation is shown in (13):

[0107]

[0108] (14)Control i 14 Dynamic analysis of PI voltage loop: voltage loop differential term is the capacitance C 1 Voltage reference value u C1ref With capacitor C 1 Voltage across the two ends u C1 The difference (u C1ref -u C1 ). Among them, k pC1 PI Control 14 PI current loop proportionality coefficient, k iC1 PI Control 14 PI current loop integral coefficient. PI voltage loop differential term The differential equation is shown in (14):

[0109]

[0110] (15)Control i 34 Dynamic analysis of PI current loop: The control block diagram of PI double loop is as follows: Figure 7 As shown by Figure 8 It can be seen that the differential term of the current loop is ( Represents ξ 3 The differential of equivalent) is line line 34 Current reference value i 34ref and line 34 Current i 34 The difference (i 34ref -i 34 ). PI current loop differential term The differential equation is shown in (15):

[0111]

[0112] (16)Control i 34 Dynamic analysis of PI voltage loop: voltage loop differential term is the capacitance C 3 Voltage reference value u C3ref With capacitor C 3 Voltage across the two ends u C3 The difference (u C3ref -u C3 ). Among them, k pC2 PI Control 34 The PI current loop proportional coefficient,

[0113] k iC2 PI Control 14 PI current loop integral coefficient. PI voltage loop differential term The differential equation of is shown in (16):

[0114]

[0115] 2. Dynamic division of symmetrical current control three-line shared inductor DC power flow controller

[0116] The small signal model of the three-line DC power flow controller is dynamically divided into two parts: a controllable system and an autonomous system, depending on whether it is completely controlled by the PI double-loop control. 14 、i 34 、u C1 、u C3 、x 1 、x 2 、x 3 and x 4 If the system is completely controlled by the PI double loop, these eight state variables can be classified as controllable systems, and the other state variables can be classified as autonomous systems.

[0117] ΔX 1 =[Δi 14 ΔuC1 Δi 34 Δu C3 Δξ 1 Δξ 2 Δξ 3 Δξ 4 ] T (17)

[0118] ΔX 2 =[Δi L Δi 12 Δi 23 Δi 24 Δu C2 Δu 1 Δu 2 Δu 3 ] T (18)

[0119] Among them, DX 1 Represents the state variable vector of the controllable system, DX 2 Represents the state variable vector of the autonomous system. The state space equations of the controllable system and the autonomous system can be expressed as shown in equations (19) and (20), respectively:

[0120]

[0121] Among them, A 1 represents the system matrix of the controllable system, B 1 represents the input matrix of the controllable system, u 1 A represents the input variable vector of the controllable system. 2 represents the system matrix of the autonomous system, B 2 represents the input matrix of the autonomous system, u 2 Represents the input variable vector of the autonomous system.

[0122] Since the state variable Di 14 、Di 34 、Du C1 、Du C3 With input variable Dd 1 and Dd 2 All of them cannot be obtained from the autonomous system, so these five variables are classified as input variables of the autonomous system. That is, the input variable vector of the autonomous system can be expressed as shown in formula (21):

[0123] Δu 2 =[Δd 1 Δd 2 Δi 14 Δu C1 Δi 34 Δu C3 ]T (twenty one)

[0124] Then, the small signal model of the autonomous system can be expressed as shown in formula (22):

[0125]

[0126] In order to study the influence of the input variable disturbance of each autonomous system on the oscillation of the state variable of each autonomous system, it is first necessary to transform the state space model of equation (22) into a transfer function matrix:

[0127]

[0128] In the formula, G iLd1 (s) represents the duty cycle 1 variable disturbance Dd in the input variable of the autonomous system 1 The shared inductor current small signal Di is used as the state variable of the autonomous system L The transfer function of G iLd2 (s) represents the duty cycle 2 disturbance Dd in the input variable disturbance of the autonomous system 2 The shared inductor current small signal Di is used as the state variable of the autonomous system L The transfer function of G iLi14 (s) represents the line in the autonomous system input variable disturbance 14 Current disturbance Di 14 The shared inductor current small signal Di is used as the state variable of the autonomous system L The transfer function of G iLuC1 (s) represents the capacitance C in the input variable disturbance of the autonomous system 1 Voltage disturbance Du C1 The shared inductor current small signal Di is used as the state variable of the autonomous system L The transfer function of G iLi34 (s) represents the line in the autonomous system input variable disturbance 34 Current Di 34 The shared inductor current small signal Di is used as the state variable of the autonomous system L The transfer function of G iLuC3 (s) represents the capacitance C in the input variable disturbance of the autonomous system 3 Voltage disturbance Du C3 The shared inductor current small signal Di is used as the state variable of the autonomous system L The transfer function of G i12d1 (s) represents the duty cycle 1 variable disturbance Dd in the input variable of the autonomous system 1 To the autonomous system state variable line 12 Current small signal Di 12 The transfer function of G i23d1(s) represents the duty cycle 1 variable disturbance Dd in the input variable of the autonomous system 1 To the autonomous system state variable line 23 Current small signal Di 23 The transfer function of G i24d1 (s) represents the duty cycle 1 variable disturbance Dd in the input variable of the autonomous system 1 To the autonomous system state variable line 24 Current small signal Di 24 The transfer function of G uC2d1 (s) represents the duty cycle 1 variable disturbance Dd in the input variable of the autonomous system 1 To the autonomous system state variable capacitor C 2 Voltage small signal Du C2 The transfer function of G u1d1 (s) represents the duty cycle 1 variable disturbance Dd in the input variable of the autonomous system 1 The voltage source converter VSC1 input voltage small signal Du in the autonomous system state variable 1 The transfer function of G u2d1 (s) represents the duty cycle 1 variable disturbance Dd in the input variable of the autonomous system 1 The voltage source converter VSC2 input voltage small signal Du in the autonomous system state variable 2 The transfer function of G u3d1 (s) represents the duty cycle 1 variable disturbance Dd in the input variable of the autonomous system 1 The voltage source converter VSC3 input voltage small signal Du in the autonomous system state variable 3 The transfer function of .

[0129] Transfer function matrix G iLd1 (s), G iLd2 (s), G iLi14 (s), G iLuC1 (s), G iLi34 (s), G iLuC3 (s), G i12d1 (s), G i23d1 (s), G i24d1 (s), G uC2d1 (s), G u1d1 (s), G u2d1 (s) and G u3d1 (s) can be calculated by formula (24):

[0130]

[0131] Among them, C 2 represents the output matrix of the autonomous system, C 2(i,:), (i=1,2,3…,8) represents the i-th row vector of the autonomous system output matrix. s represents the Laplace operator, and I represents the unit vector of 8 rows and 8 columns. d1 , B d2 , B i14 , B uC1 , B i34 and B uC3 are the 1st, 2nd, 3rd, 4th, 5th and 6th column vectors of the autonomous system input matrix respectively.

[0132] The transfer function matrix G of the three-line shared inductor DC power flow controller is established, as shown in formula (25):

[0133]

[0134] Among them, DY 2 Represents the output variable of the autonomous system.

[0135] 3. Singular Value Analysis of the Autonomous System of Symmetrical Current Control Three-Line DC Power Flow Controller

[0136] Singular value decomposition can decompose the transfer function matrix of the autonomous system of the symmetrical current controlled three-line DC power flow controller into a series of feature spaces. According to the different frequency characteristics presented in different feature spaces, the maximum singular value of the oscillation amplitude of the reaction state variable under different transient oscillation frequencies can be extracted.

[0137] G=USV T (26)

[0138] Among them, U and V are the left eigenvector matrix and the right eigenvector matrix respectively, S is the diagonal matrix of singular values, and its main diagonal elements are the singular values ​​s of the transfer function matrix G in descending order. 1 ,...,s n The sum of the squares of s is equal to the eigenvalue l of the transfer function matrix. The outer product of the matrix U and the matrix V can form a series of subspaces, all of which constitute a completely orthogonal basis of the matrix G, so the matrix G can be expressed as:

[0139]

[0140] Among them, s k is the kth singular value of the transfer function matrix, u k v k T It is the kth eigenspace of the transfer function matrix.

[0141] For an input vector v k , the system output response at frequency w can be calculated as shown in formula (28):

[0142] G(jω)vk =σ k u k (28)

[0143] Among them, the row vector u k With column vector v k are the output and input vectors of the system, s k is the system singular value, which is also the amplitude gain between the input and output vectors. Therefore, the singular value can characterize the transient oscillation amplitude caused by the state variables of the autonomous three-line DC power flow controller under the disturbance of the input variables. Among all input vectors at all frequencies, the maximum transient oscillation value can be characterized by the maximum singular value. The Bode plot corresponding to the maximum singular value of the transfer function matrix can be obtained through frequency sweep analysis as shown in Fig. 9 As shown in the figure, the contribution of different types of parameters to transient oscillation is analyzed.

[0144] 4. Analysis of the contribution of different types of parameters to transient oscillation of three-line DC power flow controller

[0145] Considering the line 23 、line 24 Current i 23 、i 24 Not directly controlled by dual-loop PI, line 14 、line 34 Current i 14 、i 34 Directly controlled by dual-loop PI. Define line resistance R 23 , R 24 is the autonomous line resistance R a , line resistance R 14 , R 34 is the controlled line resistance R c , let R 14 =R 34 =R c ,R 23 =R 24 =R a ; Change R a , R c , keeping other line resistances unchanged and equal to 1.2W, the maximum singular value of the system changes as follows Fig.10 As shown. Fig.10 It can be seen that under the condition of the same resistance change, the change of the autonomous line resistance Ra has a greater impact on the transient oscillation.

[0146] Define the output power P of voltage source converter VSC2 2 is the autonomous injection power, VSC1 and VSC3 output power P 1 , P 3 For the controlled injection power, change P1 , P 2 , change P 1 Keep P 2 =P 3 =1500W, change P 2 Keep P 1 =P 3 =1500W, the maximum singular value of the system changes as follows Fig.11 As shown. Fig.11 It can be seen that under the same injection power change, the autonomous injection power P 2 The change of has a greater impact on transient oscillation.

[0147] The above is a basic embodiment of the present invention. The technical solution of the present invention is further described below through a preferred embodiment.

[0148] Example 1

[0149] In such Fig.12 The transient oscillation characteristics of the three-line shared inductor DC power flow controller based on symmetrical current control are verified in the four-terminal ring network DC transmission system shown in FIG. Fig.12 As shown, it is placed on the VSC4 side, active control line 14 、line 34 Current. Respectively change the autonomous line resistance R a , controlled line resistance R c , autonomous injection power P 2 With the controlled injection power P 1 , verifying the effectiveness of this method in revealing the transient oscillation analysis of the three-line DC power flow controller topology. The initial parameters of the system are shown in Table 1.

[0150] Table 1: Parameters of a four-terminal DC transmission system with a symmetrical current controlled three-line DC power flow controller

[0151]

[0152]

[0153] Table 2: Experimental parameters of different damping types' contribution to oscillation

[0154]

[0155] Table 3: Experimental parameters of different injection power types for oscillation contribution

[0156]

[0157] Set line line 14 The reference current is 3.5A, line34 The reference current is 4.0A, and the contribution of different damping types to oscillation is tested. 12 =1.2W, controlled resistance R c =1.2W, change the autonomous resistance R o Then keep the line resistance R 12 =1.2W, autonomous resistance R o =1.2W, change the controlled resistance R c .from Fig.13 and Fig.14 It can be seen that when the autonomous resistance and the controlled resistance are reduced by the same value, the main state variable i caused by the reduction of the autonomous resistance is L with u C2 The larger the transient oscillation, the longer the oscillation time, which means that under the same resistance change, the autonomous circuit resistance R a The change of has a greater impact on transient oscillation.

[0158] Then, we conducted experiments on the contribution of different injection power types to the oscillation. 1 =1500W, controlled power P 3 =1500W, change the autonomous power P 2 Then maintain the autonomous power P 2 =1500W, controlled power P 3 =1500W, change the controlled power P 1 .from Fig.15 and Fig.16 It can be seen that when the autonomous power and the controlled power are reduced by the same power respectively, the main state variable i caused by the reduction of the autonomous power is L with u C2 The larger the transient oscillation, the longer the oscillation time. This means that under the same power change condition, the change of autonomous power has a greater impact on the transient oscillation.

[0159] The present invention also provides a symmetrical current three-wire shared inductor DC power flow control transient analysis system. The symmetrical current three-wire shared inductor DC power flow control transient analysis system can be implemented by executing the process steps of the symmetrical current three-wire shared inductor DC power flow control transient analysis method, that is, those skilled in the art can understand the symmetrical current three-wire shared inductor DC power flow control transient analysis method as a preferred implementation of the symmetrical current three-wire shared inductor DC power flow control transient analysis system.

[0160] Specifically, a symmetrical current three-wire shared inductor DC power flow control transient analysis system includes:

[0161] Module M1: Establish the modal space model of the symmetrical current controlled three-line shared inductor DC power flow controller;

[0162] Module M2: Dynamic segmentation method is used for the modal space model to obtain the transfer function matrix of the autonomous system;

[0163] Module M3: Use singular value analysis to analyze the transient oscillation characteristics of the autonomous system and output the analysis results.

[0164] Also includes:

[0165] Module M4: Analyze the impact of different types of parameters on the contribution of transient oscillations.

[0166] The module M1 comprises:

[0167] Perform transient analysis on the shared inductor L and obtain the current differential equation in its switching sub-mode;

[0168] Perform transient analysis on the line inductance and capacitance respectively, and obtain the current differential equation of the line inductance and the voltage differential equation across the capacitor;

[0169] The transient analysis of the capacitor in the VSC is performed to obtain the differential equation of the voltage across the capacitor, and the modal space model is constructed using the differential equation.

[0170] The module M2 comprises:

[0171] The small signal model of the three-line DC power flow controller is dynamically divided according to whether it is completely controlled by the PI double-loop control, and the controllable system and the autonomous system are obtained.

[0172] Construct the state space equations of the controllable system and the autonomous system, and obtain the small signal model of the autonomous system;

[0173] Convert the small signal model of the autonomous system into a transfer function matrix.

[0174] The module M3 comprises:

[0175] Decompose the transfer function matrix of the autonomous system into a series of feature spaces based on singular value decomposition;

[0176] According to the different frequency characteristics presented in different feature spaces, the maximum singular value of the oscillation amplitude of the reaction state variable under different transient oscillation frequencies is extracted.

[0177] The module M4 comprises:

[0178] Change the resistance of the autonomous line and the controlled line respectively, keep the resistance of other lines unchanged, and observe the change of the maximum singular value of the system;

[0179] The autonomous injection power and the controlled injection power are changed respectively, and the changes of the maximum singular value of the system are observed.

[0180] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0181] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A transient analysis method for symmetrical current three-wire shared inductor DC power flow control, characterized in that: include: Step S1: establishing a modal space model of a symmetrical current controlled three-line shared inductor DC power flow controller; Step S2: Using a dynamic segmentation method on the modal space model to obtain the transfer function matrix of the autonomous system; Step S3: Use the singular value analysis method to analyze the transient oscillation characteristics of the autonomous system and output the analysis results.

2. The transient analysis method for symmetrical current three-wire shared inductor DC power flow control according to claim 1 is characterized in that: Also includes: Step S4: Analyze the influence of different types of parameters on the contribution of transient oscillation.

3. The transient analysis method for symmetrical current three-wire shared inductor DC power flow control according to claim 1 is characterized in that: The step S1 comprises: Perform transient analysis on the shared inductor L and obtain the current differential equation in its switching sub-mode; Perform transient analysis on the line inductance and capacitance respectively, and obtain the current differential equation of the line inductance and the voltage differential equation across the capacitor; The transient analysis of the capacitor in the VSC is performed to obtain the differential equation of the voltage across the capacitor, and the modal space model is constructed using the differential equation.

4. The transient analysis method for symmetrical current three-wire shared inductor DC power flow control according to claim 3 is characterized in that: The step S2 comprises: The small signal model of the three-line DC power flow controller is dynamically divided according to whether it is completely controlled by the PI double-loop control, and the controllable system and the autonomous system are obtained. Construct the state space equations of the controllable system and the autonomous system, and obtain the small signal model of the autonomous system; Convert the small signal model of the autonomous system into a transfer function matrix.

5. The transient analysis method for symmetrical current three-wire shared inductor DC power flow control according to claim 4 is characterized in that: The step S3 comprises: Decompose the transfer function matrix of the autonomous system into a series of feature spaces based on singular value decomposition; According to the different frequency characteristics presented in different feature spaces, the maximum singular value of the oscillation amplitude of the reaction state variable under different transient oscillation frequencies is extracted.

6. The transient analysis method for symmetrical current three-wire shared inductor DC power flow control according to claim 2 is characterized in that: The step S4 comprises: Change the resistance of the autonomous line and the controlled line respectively, keep the resistance of other lines unchanged, and observe the change of the maximum singular value of the system; The autonomous injection power and the controlled injection power are changed respectively, and the changes of the maximum singular value of the system are observed.

7. A symmetrical current three-wire shared inductor DC power flow control transient analysis system, characterized in that: include: Module M1: Establish the modal space model of the symmetrical current controlled three-line shared inductor DC power flow controller; Module M2: Dynamic segmentation method is used for the modal space model to obtain the transfer function matrix of the autonomous system; Module M3: Use singular value analysis to analyze the transient oscillation characteristics of the autonomous system and output the analysis results.

8. The symmetrical current three-wire shared inductor DC power flow control transient analysis system according to claim 7, characterized in that: Also includes: Module M4: Analyze the impact of different types of parameters on the contribution of transient oscillations.

9. The symmetrical current three-wire shared inductor DC power flow control transient analysis system according to claim 7, characterized in that: The module M1 comprises: Perform transient analysis on the shared inductor L and obtain the current differential equation in its switching sub-mode; Perform transient analysis on the line inductance and capacitance respectively, and obtain the current differential equation of the line inductance and the voltage differential equation across the capacitor; The transient analysis of the capacitor in the VSC is performed to obtain the differential equation of the voltage across the capacitor, and the modal space model is constructed using the differential equation.

10. The symmetrical current three-wire shared inductor DC power flow control transient analysis system according to claim 9, characterized in that: The module M2 comprises: The small signal model of the three-line DC power flow controller is dynamically divided according to whether it is completely controlled by the PI double-loop control, and the controllable system and the autonomous system are obtained. Construct the state space equations of the controllable system and the autonomous system, and obtain the small signal model of the autonomous system; Convert the small signal model of the autonomous system into a transfer function matrix.

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