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

Abstract

The application provides a symmetrical current three-wire common inductance DC power flow control transient analysis method and system, the method comprises the following steps: S1, a modal space model of a symmetrical current control three-wire common inductance type DC power flow controller is established; S2, a dynamic segmentation method is used for the modal space model to obtain a transfer function matrix of an autonomous system; S3, a singular value analysis method is used for transient oscillation characteristic analysis of the autonomous system, and an analysis result is output; and S4, the influence of different types of parameters on the contribution degree of transient oscillation is analyzed. The DC power flow controller transient analysis method based on singular value decomposition is used to obtain transient oscillation characteristics closer to multi-terminal DC power transmission in the three-wire DC power flow controller topology, and reference is provided for more comprehensive and more dimensional DC power flow transient oscillation suppression.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of electrical engineering, in particular to a symmetrical current three-wire common inductance DC power flow control transient analysis method and system, especially a three-wire common inductance type DC power flow controller transient oscillation characteristic analysis method based on symmetrical current control. BACKGROUND

[0002] To cope with climate change and accelerate clean and low-carbon energy transformation, gradually reducing and replacing fossil energy has become a driving force for clean and low-carbon energy transformation. At the same time, DC loads dominated by electric vehicles and photovoltaic storage and flexible AC transmission are also developing rapidly. New DC transmission systems are widely used due to their flexibility, controllability and efficiency. However, with the access of a large number of distributed power sources, diversified loads and high proportion of power electronic devices, new DC transmission systems face 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 new DC transmission systems.

[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, which can fully utilize the economy and flexibility of DC transmission. However, due to the mesh structure of multi-terminal DC transmission systems and the lack of power flow control means, DC transmission networks will have uneven power flow distribution and limited transmission capacity. DC power flow controllers can actively control power flow distribution to solve the problem of limited transmission capacity, and can improve the flexibility of DC transmission networks and promote overall new energy consumption. By using the three-wire common inductance type DC power flow controller transient oscillation analysis method based on symmetrical current control, the non-fault transient oscillation of the DC transmission network containing the three-wire DC power flow controller can be effectively suppressed.

[0004] The three-wire common inductance type DC power flow controller transient characteristic analysis method based on symmetrical current control mainly includes three-wire DC power flow controller modal space modeling, three-wire DC power flow controller dynamic segmentation, autonomous DC power flow controller singular value decomposition, and the contribution of different parameter types to DC power flow controller oscillation. In the construction of small signal model and transfer function matrix of three-wire DC power flow controller, existing researches mostly focus on coupled inductance type, coupled capacitance type or common capacitance type three-wire DC power flow controller analysis and modeling, and there is no small signal modeling and transfer function construction work for common inductance type three-wire DC power flow controller. In the analysis of three-wire common inductance type transient characteristics, there is no literature based on modal space segmentation method and singular value analysis method to study the contribution of different types of system parameters to DC power flow controller transient oscillation.

[0005] Liu SC, Zhu M, Zhong X, et al. Three-line DC power flow controller with dual freedom control capability[J]. Power System Automation, 2019, 43(18): 75-81. A new three-line DC power flow controller topology is proposed, and the working principle and dual-target control strategy are designed to realize dual freedom flow control, but it does not involve the modal space modeling and dynamic segmentation method considering the three-line DC power flow controller; Based on the three-line common inductance type DC power flow controller of symmetric current control, the modal space modeling based on small signal modeling and the dynamic segmentation considering state variable division are carried out, and the mathematical model of the three-line DC power flow controller is obtained in detail and comprehensively. In addition, the document does not involve the research on the transient process of the power flow controller.

[0006] Wang WY, Zhang YP, Li SH, et al. Network type flexible DC system damping controller design based on disturbance observation[J]. Power Grid Technology, 2024, 48(06): 2262-2271. A method for analyzing the oscillation characteristics of AC / DC systems based on singular value decomposition technology is proposed, and the key oscillation mode damping suppression is realized by using quadratic optimal feedback control, but it does not involve the transient oscillation characteristic analysis of the non-fault switching of the DC power flow controller; Based on the three-line common inductance type DC power flow controller of symmetric current control, the modal space modeling and dynamic segmentation method are adopted, and the non-fault transient mode of the three-line power flow controller is quantified. In addition, the document does not classify and study the parameters that may affect the transient oscillation.

[0007] The present application aims to identify the contribution of different damping types and different injection power type parameters to transient oscillation, and provide a better reference for non-fault transient oscillation suppression of DC power transmission systems containing three-line DC power flow controllers. SUMMARY

[0008] In view of the defects in the prior art, the present application aims to provide a symmetric current three-line common inductance DC power flow control transient analysis method and system.

[0009] According to the symmetric current three-line common inductance DC power flow control transient analysis method provided by the present application, the following steps are included:

[0010] Step S1: Establish the modal space model of the three-line common inductance type DC power flow controller of symmetric current control;

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

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

[0013] Preferably, it further includes:

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

[0015] Preferably, step S1 includes:

[0016] Transient analysis of the common inductor L yields the current differential equation for its switching sub-mode.

[0017] Transient analysis was performed on the line inductance and capacitance respectively to obtain the differential equation of the current of the line inductance and the differential equation of the voltage across the capacitor.

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

[0019] Preferably, step S2 includes:

[0020] Based on whether it is completely controlled by PI dual-loop, the small-signal model of the three-line DC power flow controller is dynamically segmented to obtain the controllable system and the autonomous system.

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

[0022] The small-signal model of the autonomous system is transformed into a transfer function matrix.

[0023] Preferably, step S3 includes:

[0024] Singular value decomposition is used to decompose the transfer function matrix of an autonomous system into a series of characteristic spaces.

[0025] Based on 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 includes:

[0027] Change the resistance of the autonomous line and the controlled line respectively, while keeping the resistance of other lines constant, and observe the change in the maximum singular value of the system.

[0028] Change the autonomous injection power and the controlled injection power respectively, and observe the changes in the maximum singular value of the system.

[0029] A transient analysis system for DC power flow control with a symmetrical three-wire shared inductor, provided by the present invention, includes:

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

[0031] Module M2: The modal space model is dynamically segmented to obtain the transfer function matrix of the autonomous system;

[0032] Module M3: Uses singular value analysis to analyze the transient oscillation characteristics of autonomous systems and outputs the analysis results.

[0033] Preferred options also include:

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

[0035] Preferably, the module M1 includes:

[0036] Transient analysis of the common inductor L yields the current differential equation for its switching sub-mode.

[0037] Transient analysis was performed on the line inductance and capacitance respectively to obtain the differential equation of the current of the line inductance and the differential equation of the voltage across the capacitor.

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

[0039] Preferably, the module M2 includes:

[0040] Based on whether it is completely controlled by PI dual-loop, the small-signal model of the three-line DC power flow controller is dynamically segmented to obtain the controllable system and the autonomous system.

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

[0042] The small-signal model of the autonomous system is transformed into a transfer function matrix.

[0043] Preferably, the module M3 includes:

[0044] Singular value decomposition is used to decompose the transfer function matrix of an autonomous system into a series of characteristic spaces.

[0045] Based on 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, while keeping the resistance of other lines constant, and observe the change in the maximum singular value of the system.

[0048] Change the autonomous injection power and the controlled injection power respectively, and observe the changes in the maximum singular value of the system.

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

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

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

[0052] 3. This invention applies the singular value decomposition method, which is more adaptable than the traditional modal analysis method, to the transient oscillation analysis of the autonomous three-line DC power flow controller, and provides a more comprehensive and rigorous numerical analysis of the transient oscillation characteristics of the three-line power flow controller.

[0053] 4. This 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 more dimensions of reference for the suppression of transient oscillation of multi-terminal DC power flow controller.

[0054] Other beneficial effects of the present invention will be explained in detail through the introduction of specific technical features and technical solutions in specific embodiments. Those skilled in the art should be able to understand the beneficial technical effects brought about by these technical features and technical solutions through the introduction of these technical features and technical solutions. Attached Figure Description

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

[0056] Figure 1 This is a topology diagram of the symmetrical current control three-wire shared inductor type DC power flow controller in this invention.

[0057] Figure 2 This is a schematic diagram of the working sub-mode of the DC power flow controller with three-wire shared inductor for symmetrical current control in this invention.

[0058] Figure 3 This is a schematic diagram of the working sub-mode of the DC power flow controller with three-wire shared inductor for symmetrical current control in this invention.

[0059] Figure 4 This is a schematic diagram of the working sub-mode of the three-wire shared inductor DC power flow controller with symmetrical current control in this invention.

[0060] Figure 5 The central control unit of this invention 14 The double-ring PI block diagram.

[0061] Figure 6 The central control unit of this invention 14 The internal block diagram of the double-ring PI.

[0062] Figure 7 The central control unit of this invention 34 The double-ring PI block diagram.

[0063] Figure 8 The central control unit of this invention 34 The internal block diagram of the double-ring PI.

[0064] Figure 9 This is a Bode plot corresponding to the maximum singular value of the transfer function matrix at different frequencies in this invention.

[0065] Figure 10 In this invention, R is changed respectively a R c A schematic diagram showing the change in the maximum singular value of the system while keeping the resistance of other lines constant.

[0066] Figure 11 This is a schematic diagram showing how the maximum singular value of the system changes when P1 and P2 are changed respectively in this invention.

[0067] Figure 12 This is a schematic diagram of the four-terminal ring network DC transmission system in this invention.

[0068] Figure 13 The diagram shows the waveform of the common inductor current in the experiment on the contribution of different damping types to oscillation in this invention.

[0069] Figure 14 The voltage waveform of capacitor C2 is shown in the experiment on the contribution of different damping types to oscillation in this invention.

[0070] Figure 15 The waveform of the common inductor current in the experiment on the contribution of different injected power types to oscillation in this invention is shown.

[0071] Figure 16 The voltage waveform of capacitor C2 is shown in the experiment on the contribution of different injected power types to oscillation in this invention.

[0072] Figure 17 This is a flowchart of the method of the present invention. Detailed Implementation

[0073] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0074] The technical solution of this application is a method for analyzing the transient oscillation characteristics of a three-line shared-inductance DC power flow controller based on symmetrical current control for four-terminal DC transmission. The method 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 autonomous three-line power flow controller, and analysis of the contribution of different types of parameters to transient oscillations. Modal space modeling is performed on the symmetrically current-controlled three-line shared-inductance DC power flow controller. Based on the complete three-line small-signal model, a dynamic segmentation method is used to obtain the transfer function matrix of the autonomous three-line DC power flow controller. Singular value analysis, which has better adaptability than traditional modal analysis, is used to analyze the transient oscillation characteristics of the autonomous system. The maximum singular value changes of parameters with different damping types and different injected power types are comprehensively considered to obtain the transient oscillation characteristics of the three-line shared-inductance DC power flow controller. Figure 17 As shown, the specific implementation methods are as follows:

[0075] I. Modal Space Modeling of a Three-Wire Shared Inductor DC Power Controller with Symmetrical Current Control

[0076] For reference Figure 1 The study focuses on a three-line symmetrical current control system using a shared inductive DC power flow controller. The connecting hub units Part 1, Part 2, and Part 3 can be considered as three equivalent voltage sources connected in series with the line. 14 ,line 24 and line 34 The connecting hub unit alternately exchanges energy with the energy central unit under specific switching states. Through the energy central unit, some energy can be transferred between the three DC lines to achieve DC power flow control. Symmetrical current control refers to controlling only the transmission lines at both ends of the three-line topology. 14 ,line 34 Current is controlled, but not for intermediate transmission lines. 24 The current is controlled using 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 below:

[0078] (1) Switching sub-mode 1: QA1A On / Q A2A Shutdown / Q A3A Turn off, C1-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 phase, the line current I... 14 When energy is transferred to the common inductor L, the change in current in the common inductor L increases linearly.

[0079] (2) Switching sub-mode 2: Q A1A Shutdown / Q A2A Shutdown / Q A3A When C3-D is turned on, As3A -Q A3 -LD Bs3B -Q B3B Forming loop 2, such as Figure 3 As shown. During the duration of this switching sub-mode phase, the line current I... 34 When energy is transferred to the common inductor L, the change in current in the common inductor L increases linearly.

[0080] (3) Switching sub-mode 3: Q A1A Shutdown / Q A2A On / Q A3A Turn off, at this time C2-D As2A -Q A2 -LD Bs2B -Q B2B Forming loop 3, such as Figure 4 As shown. Energy flows from the common inductor L to the line current I. 24 As the current shifts, the change in current through the shared inductor L decreases linearly.

[0081] Set switch Q A1A Q A2A and Q A3A The duty cycles are D1, D2 and (1-D1-D2), respectively.

[0082] (1) Transient analysis of common inductor L: When the switch is in sub-mode 1, i.e. in [0, D1T S During the time interval, capacitor voltage uC1 is applied across the common inductor L; in switch sub-mode 2, i.e., during [D1T]... S ,(D1+D2)T S During the time interval, capacitor voltage uC2 is applied across the common inductor L; in switch sub-mode 3, i.e., during [(D1+D2)T]... S ,(1-D1-D2)T SDuring the specified time, capacitor voltage uC3 is applied across the common inductor L. The current i in the common inductor L... L The differential equation is shown in equation (1):

[0083]

[0084] (2) Line inductance L 12 Transient analysis: line 12 The voltages at both ends are the VSC1 (voltage source converter) port voltage u1 and the VSC2 port voltage u2, respectively. The line... 12 The voltage across the resistor is i 12 R 12 Line inductance L 12 current i 12 The differential equation is shown in equation (2):

[0085]

[0086] (3) Line inductance L 14 Transient analysis: line 14 The voltages at both ends are the sum of the voltage u1 at port VSC1 and the voltage at port VSC4, and the voltage across capacitor C1 (u4 + u). C1 ), line 14 The voltage across the resistor is i 14 R 14 Line inductance L 14 current i 14 The differential equation is shown in equation (3):

[0087]

[0088] (4) Line inductance L 23 Transient analysis: line 23 The voltages at both ends are the voltage u2 at port VSC2 and the voltage u3 at port VSC3, respectively. (Line) 23 The voltage across the upper resistor is i 23 R 23 Line inductance L 23 current i 23 The differential equation is shown in equation (4):

[0089]

[0090] (5) Line inductance L 24 Transient analysis: line 24 The voltages at both ends are the sum of the voltage u2 at port VSC2 and the voltage at port VSC4, and the voltage across capacitor C2 (u4 + u). C2 ), line 24The voltage across the upper resistor is i 24 R 24 Line inductance L 24 current i 24 The differential equation is shown in equation (5):

[0091]

[0092] (6) Line inductance L 34 Transient analysis: line 34 The voltages at both ends are the sum of the voltage u3 at port VSC3 and the voltage at port VSC4, and the voltage across capacitor C3 (u4 + u). C3 ), line 34 The voltage across the upper resistor is i 34 R 34 Line inductance L 34 current i 34 The differential equation is shown in equation (6):

[0093]

[0094] (7) Transient analysis of capacitor C1: When the switch is in sub-mode 1, i.e. in [0, D1T S Within a given time period, the current flowing through capacitor C1 is the line current. 14 Current i 14 With the common inductor L current i L The difference (i) 14 -i L ); in switching sub-modes 2 and 3, i.e. in [D1T S ,T S Within a given time period, the current flowing through capacitor C1 is the line current. 14 Current i 14 The voltage u across capacitor C1 C1 The differential equation is shown in equation (7):

[0095]

[0096] (8) Transient analysis of capacitor C2: When the switch is in sub-mode 1, i.e. in [0, D1T S Within a given time period, the current flowing through capacitor C2 is the line... 24 Current i 24 ; When switching sub-mode 2, that is, in [D1T S ,(D1+D2)T S Within a given time period, the current flowing through capacitor C2 is the line... 24 Current i 24 With the common inductor L current i L The difference (i) 24 -i L); When the switching sub-mode is 3, that is, in [(D1+D2)T S ,(1-D1-D2)T S Within a given time period, the current flowing through capacitor C2 is the line... 24 Current i 24 The voltage u across capacitor C2 C2 The differential equation is shown in equation (8):

[0097]

[0098] (9) Transient analysis of capacitor C3: In switching sub-modes 1 and 2, i.e. in [0, (D1+D2)T S Within a given time period, the current flowing through capacitor C3 is the line... 34 Current i 34 ; When the switching sub-mode is 3, that is, in [(D1+D2)T S ,(1-D1-D2)T S Within a given time period, the current flowing through capacitor C3 is the line... 34 Current i 34 With the common inductor L current i L The difference (i) 34 -i L The voltage u across capacitor C3 C3 The differential equation is shown in equation (9):

[0099]

[0100] (10) Capacitor C in VSC1 s1 Transient analysis: Current flowing through capacitor C s1 The current is the theoretical current of VSC1 (P1 / u1) minus the line current. 12 With line 14 The sum of currents (i) 12 +i 14 Where P1 is the output power of VSC1. Capacitor C s1 The differential equation for the voltage u1 across the two ends is shown in equation (10):

[0101]

[0102] (11) Capacitor C in VSC2 s2 Transient analysis: Current flowing through capacitor C s2 The current is the theoretical current of VSC2 (P2 / u2) minus the line current. 23 With line 24 The sum of currents (i) 23 +i 24 ), plus the line 12Current i 12 Where P2 is the output power of VSC2. Capacitor C s2 The differential equation for the voltage u2 across the two ends is shown in equation (11):

[0103]

[0104] (12) Capacitor C in VSC3 s3 Transient analysis: Current flowing through capacitor C s3 The current is the theoretical current of VSC3 (P3 / u3) minus the line current. 34 Current i 34 In addition to the line 23 Current i 23 Where P3 represents the output power of VSC3. Capacitor C s3 The differential equation for the voltage u3 across the two ends is shown in equation (12):

[0105]

[0106] (13)Control i 14 Dynamic analysis of PI current loop: The control block diagram of the PI dual loop is as follows Figure 5 As shown, by Figure 6 It can be seen that the differential term of the current loop ( Describe the differential of ξ1, and (Equivalent) is the line 14 Current reference value i 14ref With line 14 Current i 14 The difference (i) 14ref -i 14 ). Differential term of PI current loop The differential equation is shown in equation (13):

[0107]

[0108] (14)Control i 14 Dynamic analysis of the PI voltage loop: voltage loop differential term The reference value u for the voltage across capacitor C1 C1ref The voltage u across capacitor C1 C1 The difference (u) C1ref -u C1 ), where k pC1 For PI control i 14 The proportional gain of the PI current loop, k iC1 For PI control i 14 The integral coefficient of the PI current loop. The differential term of the PI voltage loop. The differential equation is shown in equation (14):

[0109]

[0110] (15)Control i 34 Dynamic analysis of PI current loop: The control block diagram of the PI dual loop is as follows Figure 7 As shown, by Figure 8 It can be seen that the differential term of the current loop ( Describe the differential of ξ3, and (Equivalent) is the line 34 Current reference value i 34ref With line 34 Current i 34 The difference (i) 34ref -i 34 ). Differential term of PI current loop The differential equation is shown in equation (15):

[0111]

[0112] (16)Control i 34 Dynamic analysis of the PI voltage loop: voltage loop differential term The reference value u for the voltage across capacitor C3 C3ref The voltage u across capacitor C3 C3 The difference (u) C3ref -u C3 ), where k pC2 For PI control i 34 The proportional gain of the PI current loop.

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

[0114]

[0115] II. Symmetrical Current Control Three-Wire Shared Inductor Type DC Power Flow Controller Dynamic Segmentation

[0116] Based on whether it is completely controlled by a PI dual-loop, 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. Due to the state variable i... 14 i 34 u C1 u C3 If x1, x2, x3, and x4 are completely controlled by the PI double loop, then these eight state variables can be classified into a controllable system, while other state variables are classified into an autonomous system.

[0117] ΔX1=[Δi 14 Δu C1 Δi 34 Δu C3 Δξ1 Δξ2 Δξ3 Δξ4] T (17)

[0118] ΔX2=[Δi L Δi 12 Δi 23 Δi 24 Δu C2 Δu1 Δu2 Δu3] T (18)

[0119] Where DX1 represents the state variable vector of the controllable system, and DX2 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] Where A1 represents the system matrix of the controllable system, B1 represents the input matrix of the controllable system, and u1 represents the input variable vector of the controllable system. A2 represents the system matrix of the autonomous system, B2 represents the input matrix of the autonomous system, and u2 represents the input variable vector of the autonomous system.

[0122] Due to the state variable Di 14 Di 34 Du C1 Du C3 Since input variables Dd1 and Dd2 cannot be obtained from within the autonomous system, these five variables are classified as input variables of the autonomous system. That is, the input variable vector of the autonomous system can be represented as shown in equation (21):

[0123] Δu2=[Δd1 Δd2 Δi 14 Δu C1 Δi 34 Δu C3 ] T (twenty one)

[0124] Therefore, the small-signal model of the autonomous system can be represented as shown in equation (22):

[0125]

[0126] To study the impact of input variable disturbances on the oscillations of state variables 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 small signal Di of the duty cycle variable perturbation Dd1 in the input variables of the autonomous system to the common inductor current Di in the state variables of the autonomous system. L The transfer function of G. iLd2 (s) represents the duty cycle disturbance Dd2 in the input variable disturbance of the autonomous system, which is connected to the small signal Di of the common inductor current in the state variables of the autonomous system. L The transfer function of G. iLi14 (s) represents the line in the disturbance of the input variable of the autonomous system. 14 Current disturbance Di 14 The small signal Di of the shared inductor current in the state variables of the autonomous system L The transfer function of G. iLuC1 (s) represents the voltage disturbance of capacitor C1 in the input variable disturbance of the autonomous system, Du. C1 The small signal Di of the shared inductor current in the state variables of the autonomous system L The transfer function of G. iLi34 (s) represents the line in the disturbance of the input variable of the autonomous system. 34 Current Di 34 The small signal Di of the shared inductor current in the state variables of the autonomous system L The transfer function of G. iLuC3 (s) represents the voltage disturbance of capacitor C3, Du, in the input variable disturbance of the autonomous system. C3 The small signal Di of the shared inductor current in the state variables of the autonomous system L The transfer function of G. i12d1 (s) represents the disturbance Dd1 of the duty cycle variable in the input variables of the autonomous system to the line in the state variables of the autonomous system. 12 Small current signal Di 12 The transfer function of G. i23d1 (s) represents the disturbance Dd1 of the duty cycle variable in the input variables of the autonomous system to the line in the state variables of the autonomous system. 23 Small current signal Di 23 The transfer function of G. i24d1 (s) represents the disturbance Dd1 of the duty cycle variable in the input variables of the autonomous system to the line in the state variables of the autonomous system. 24 Small current signal Di 24 The transfer function of G. uC2d1 (s) represents the small signal Du of the duty cycle variable Dd1 in the input variables of the autonomous system, which is a disturbance of the voltage of capacitor C2 in the state variables of the autonomous system. C2 The transfer function of G. u1d1(s) represents the transfer function of the duty cycle 1 variable disturbance Dd1 in the input variables of the autonomous system to the small signal Du1 of the input voltage of the voltage source converter VSC1 in the state variables of the autonomous system. u2d1 (s) represents the transfer function of the duty cycle 1 variable disturbance Dd1 in the input variables of the autonomous system to the small signal Du2 of the input voltage of the voltage source converter VSC2 in the state variables of the autonomous system. u3d1 (s) represents the transfer function of the duty cycle 1 variable disturbance Dd1 in the input variables of the autonomous system to the small signal Du3 of the input voltage of the voltage source converter VSC3 in the state variables of the autonomous system.

[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 from equation (24):

[0130]

[0131] Where C2 represents the output matrix of the autonomous system, and C2(i,:), (i=1,2,3…,8) represents the i-th row vector of the output matrix of the autonomous system. s represents the Laplace operator, and I represents an 8x8 unit vector. B d1 B d2 B i14 B uC1 B i34 and B uC3 These are the 1st, 2nd, 3rd, 4th, 5th, and 6th column vectors of the input matrix of the autonomous system, respectively.

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

[0133]

[0134] Where DY2 represents the output variable of the autonomous system.

[0135] III. Singular Value Analysis of Autonomous System for Symmetrical Current-Controlled Three-Wire DC Power Flow Controller

[0136] Singular value decomposition (SVD) can decompose the transfer function matrix of an autonomous system of a symmetrically current-controlled three-wire DC power flow controller into a series of characteristic spaces. Based on the different frequency characteristics exhibited by different characteristic spaces, the maximum singular value of the oscillation amplitude of the state variable at different transient oscillation frequencies can be extracted.

[0137] G = USV T (26)

[0138] Where U and V are the left and right eigenvector matrices, respectively, and S is the diagonal matrix of singular values, whose main diagonal elements are the singular values ​​s1,...,s1 of the transfer function matrix G in descending order. n The sum of squares of s equals the eigenvalues ​​l of the transfer function matrix. The outer product of matrices U and V forms a series of subspaces, all of which constitute a complete orthogonal basis for matrix G. Therefore, matrix G can be expressed as:

[0139]

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

[0141] For an input vector v k The system's output response at frequency w can be calculated as shown in equation (28):

[0142] G(jω)v k =σ k u k (28)

[0143] Where, row vector u k With column vector v k Let s be the system's output and input vectors. k The singular value represents the system's singular value and also the magnitude gain between the input and output vectors. Therefore, the singular value can characterize the magnitude of the transient oscillation amplitude caused by input variable disturbances in the state variables of the autonomous three-wire DC power flow controller. 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 below. Figure 9 As shown, we then conduct an analysis of the contribution of different types of parameters to transient oscillations.

[0144] IV. Analysis of the Contribution of Different Types of Parameters to Transient Oscillations in Three-Line DC Power Controllers

[0145] Considering the line 23 ,line 24Current i 23 i 24 Not directly controlled by the dual-loop PI, the line 14 ,line 34 Current i 14 i 34 Directly controlled by a dual-loop PI controller. Define the line resistance R. 23 R 24 For the autonomous line resistance R a Line resistance R 14 R 34 The controlled line resistance R c , let R 14 =R 34 =R c ,R 23 =R 24 =R a ; respectively change R a R c Keeping the resistance of other lines constant and equal to 1.2W, the variation of the system's maximum singular value is as follows: Figure 10 As shown. By Figure 10 It is evident that, under the same resistance change, the change in the resistance Ra of the autonomous circuit has a greater impact on transient oscillations.

[0146] Define the output power P2 of voltage source converter VSC2 as autonomous injected power, and the output powers P1 and P3 of VSC1 and VSC3 as controlled injected power. Change P1 and P2 respectively, keeping P2 = P3 = 1500W while changing P1, and keeping P1 = P3 = 1500W while changing P2. The change in the system's maximum singular value is as follows: Figure 11 As shown. By Figure 11 It is evident that, under the same injection power variation, the change in autonomous injection power P2 has a greater impact on transient oscillations.

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

[0148] Example 1

[0149] In such Figure 12 Transient oscillation characteristics of a three-line inter-line shared inductor DC power flow controller based on symmetrical current control are analyzed in the four-terminal ring network DC transmission system shown. The three-line inter-line DC power flow controller is described as follows: Figure 12 The active control line shown is located on the VSC4 side. 14 ,line 34 Current. Change the resistance R of the autonomous circuit respectively. a Controlled line resistance R cThe autonomous injection power P2 and the controlled injection power P1 are used to verify the effectiveness of the proposed 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 Symmetrical Current Control Three-Wire DC Power Flow Controller

[0151]

[0152]

[0153] Table 2: Experimental parameters for the contribution of different damping types to oscillation.

[0154]

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

[0156]

[0157] Set line 14 The reference current is 3.5A, and the line... 34 With a reference current of 4.0A, an experiment was conducted to investigate the contribution of different damping types to oscillation. First, the line resistance R was kept constant. 12 =1.2W, controlled resistor 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 resistor R c .from Figure 13 and Figure 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 decrease in the autonomous resistance is... L with u C2 The larger the transient oscillation and the longer the oscillation time, the greater the resistance R of the autonomous circuit under the same resistance change. a Changes in [the specific element] have a greater impact on transient oscillations.

[0158] Subsequently, experiments were conducted to investigate the contribution of different injected power types to oscillation. First, the controlled power P1 = 1500W and the controlled power P3 = 1500W were kept constant, while the autonomous power P2 was changed. Then, the autonomous power P2 = 1500W and the controlled power P3 = 1500W were kept constant, while the controlled power P1 was changed. From... Figure 15 and Figure 16 It can be seen that when the autonomous power and the controlled power decrease by the same amount, the main state variable i caused by the decrease in autonomous power is... L with u C2The larger the transient oscillation, the longer the oscillation time. This indicates that, under the same power change, the change in autonomous power has a greater impact on transient oscillations.

[0159] This invention also provides a transient analysis system for DC power flow control with a symmetrical three-wire shared inductor. This system can be implemented by executing the steps of the transient analysis method for DC power flow control with a symmetrical three-wire shared inductor. That is, those skilled in the art can understand the transient analysis method for DC power flow control with a symmetrical three-wire shared inductor as a preferred embodiment of the transient analysis system for DC power flow control with a symmetrical three-wire shared inductor.

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

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

[0162] Module M2: The modal space model is dynamically segmented to obtain the transfer function matrix of the autonomous system;

[0163] Module M3: Uses singular value analysis to analyze the transient oscillation characteristics of autonomous systems and outputs the analysis results.

[0164] Also includes:

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

[0166] The module M1 includes:

[0167] Transient analysis of the common inductor L yields the current differential equation for its switching sub-mode.

[0168] Transient analysis was performed on the line inductance and capacitance respectively to obtain the differential equation of the current of the line inductance and the differential equation of the voltage across the capacitor.

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

[0170] The module M2 includes:

[0171] Based on whether it is completely controlled by PI dual-loop, the small-signal model of the three-line DC power flow controller is dynamically segmented to obtain the controllable system and the autonomous system.

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

[0173] The small-signal model of the autonomous system is transformed into a transfer function matrix.

[0174] The module M3 includes:

[0175] Singular value decomposition is used to decompose the transfer function matrix of an autonomous system into a series of characteristic spaces.

[0176] Based on 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 includes:

[0178] Change the resistance of the autonomous line and the controlled line respectively, while keeping the resistance of other lines constant, and observe the change in the maximum singular value of the system.

[0179] Change the autonomous injection power and the controlled injection power respectively, and observe the changes in the maximum singular value of the system.

[0180] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0181] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A transient analysis method for DC power flow control using a symmetrical three-wire shared inductor, characterized in that, include: Step S1: Establish the modal space model of a symmetrical current-controlled three-wire shared inductor type DC power flow controller; Transient analysis of the common inductor L yields the current differential equation for its switching sub-mode. Transient analysis was performed on the line inductance and capacitance respectively to obtain the differential equation of the current of the line inductance and the differential equation of the voltage across the capacitor. Transient analysis is performed on the capacitor in VSC to obtain the differential equation of the voltage across the capacitor. The modal space model is then constructed using the differential equation. Step S2: Apply a dynamic segmentation method to the modal space model to obtain the transfer function matrix of the autonomous system; Based on whether it is completely controlled by PI dual-loop, the small-signal model of the three-line DC power flow controller is dynamically segmented to obtain the controllable system and the autonomous system. Construct the state-space equations of the controllable system and the autonomous system to obtain the small-signal model of the autonomous system; Transform the small-signal model of the autonomous system into a transfer function matrix; Step S3: Use singular value analysis to analyze the transient oscillation characteristics of the autonomous system and output the analysis results.

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

3. The transient analysis method for DC power flow control with symmetrical current three-wire shared inductor according to claim 1, characterized in that, Step S3 includes: Singular value decomposition is used to decompose the transfer function matrix of an autonomous system into a series of characteristic spaces. Based on 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.

4. The transient analysis method for DC power flow control with symmetrical current three-wire shared inductor according to claim 2, characterized in that, Step S4 includes: Change the resistance of the autonomous line and the controlled line respectively, while keeping the resistance of other lines constant, and observe the change in the maximum singular value of the system. Change the autonomous injection power and the controlled injection power respectively, and observe the changes in the maximum singular value of the system.

5. A transient analysis system for DC power flow control using a symmetrical three-wire shared inductor, characterized in that, include: Module M1: Establish the modal space model of a symmetrical current-controlled three-wire shared inductor type DC power flow controller; Transient analysis of the common inductor L yields the current differential equation for its switching sub-mode. Transient analysis was performed on the line inductance and capacitance respectively to obtain the differential equation of the current of the line inductance and the differential equation of the voltage across the capacitor. Transient analysis is performed on the capacitor in VSC to obtain the differential equation of the voltage across the capacitor. The modal space model is then constructed using the differential equation. Module M2: The modal space model is dynamically segmented to obtain the transfer function matrix of the autonomous system; Based on whether it is completely controlled by PI dual-loop, the small-signal model of the three-line DC power flow controller is dynamically segmented to obtain the controllable system and the autonomous system. Construct the state-space equations of the controllable system and the autonomous system to obtain the small-signal model of the autonomous system; Transform the small-signal model of the autonomous system into a transfer function matrix; Module M3: Uses singular value analysis to analyze the transient oscillation characteristics of autonomous systems and outputs the analysis results.

6. The symmetrical current three-wire shared inductor DC power flow control transient analysis system according to claim 5, characterized in that, Also includes: Module M4: Analyzes the impact of different types of parameters on the contribution of transient oscillations.

Images