Modular Small-Signal Modeling Method and System for Four-Terminal DC Transmission with DC Power Flow Controller

Abstract

This invention provides a modular small-signal modeling method and system for four-terminal DC transmission with a DC power flow controller, comprising: Step 1: performing small-signal modeling on three sending-end constant-power controlled voltage source converters (VSCs); Step 2: performing small-signal modeling on one receiving-end constant-voltage controlled voltage source converter (VSC4); Step 3: performing small-signal modeling on the DC power flow controller (DCPFC); Step 4: constructing a total system small-signal model by modularly combining the three sending-end VSC modules, one receiving-end VSC4 module, and the DCPFC module; wherein the sending-end VSC modeling includes phase-locked loop dynamic characteristics, and the DCPFC modeling includes dual-loop proportional-integral (PI) dynamic characteristics. This invention significantly reduces the modeling complexity of multi-port coupled systems by constructing a complete small-signal model through modular combination.

Description

Technical Field

[0001] This invention relates to the field of electrical engineering technology, and more specifically, to a modular small-signal modeling method and system for four-terminal DC transmission with DC power flow controller. Background Technology

[0002] In recent years, with the large-scale integration of power electronic devices such as wind, solar, and energy storage into the power grid and the widespread application of DC transmission technology, the structure of the power system has undergone profound changes. Traditional transmission technologies, due to insufficient technical adaptability, are unable to meet the operational requirements of a high proportion of new energy sources integrated into the grid. Flexible DC transmission technology, with its active / reactive power decoupling, strong controllability, no need for reactive power compensation, and small footprint, has broad application prospects in areas such as new energy transmission. Its flexible adjustment capability can effectively improve system stability by relying on the frequency support function of the sending-end converter station, and it has now become a key technology supporting the development of new power systems.

[0003] Flexible DC transmission technology based on voltage source converters provides an effective solution for power transmission. However, in a ring-shaped DC grid, multiple lines exist between converter stations, resulting in a transmission line number greater than or equal to the number of converter stations. This makes it impossible to effectively regulate line power flow solely through voltage and power control at the converter stations. In this situation, some line power flows may become overloaded due to ineffective control, threatening the safe and efficient operation of the system. Therefore, it is urgent to effectively introduce a DC power flow controller (DCPFC) to address the power flow control problem in ring-shaped DC grids. The power flow controller can achieve precise regulation of line power flow by changing the equivalent resistance or equivalent voltage connected in series in the lines. Regarding the stability study of the DC power flow controller, this proposal presents a modular small-signal modeling method for four-terminal DC transmission that considers the small-signal model of a complete voltage source converter station (VSC). This method can effectively reflect the impact of parameters of each component of a multi-terminal DC transmission system containing a DC power flow controller on the overall system stability.

[0004] The literature (Meng Yifei, Wang Shanshan, Sun Yuanyuan, et al. Small-signal stability analysis of grid-connected flexible DC-DC systems considering internal dynamic characteristics [J / OL]. High Voltage Engineering, 1-17 [2025-07-07].) proposes a 40th-order detailed small-signal model considering the internal dynamics of the MMC, revealing the mechanism of subsynchronous oscillation caused by the mismatch of circulating current suppression parameters, and verifying the applicability of the simplified model under weak grid conditions. However, the model does not include the dynamic characteristics of the DC power flow controller (DCPFC) and the influence of multi-terminal collaborative interaction, and the error mechanism of the simplified model under strong grid or DCPFC access scenarios is not yet clear. In contrast, this scheme optimizes the stability boundary quantization capability of multi-terminal systems by modularly integrating the dynamics of DCPFC and the VSC control coupling of weak grids. The literature (Liu Xin, Yuan Yi, Wang Litong, et al. Three-port hybrid parameter modeling and stability analysis of flexible DC transmission system [J]. Journal of Electrical Engineering, 2024, 39(16): 4968-4984.) proposes a small-signal modeling method for MMC converter stations based on a three-port hybrid parameter model. It avoids the limitations of traditional impedance stability analysis by using the generalized Nyquist criterion and designs a damping control strategy to suppress DC-side oscillations. However, its model does not cover the dynamic characteristics of the DC power flow controller (DCPFC) and the collaborative interaction of multiple converter stations, and the damping control is not adapted to the multi-terminal system scenario containing DCPFC. In contrast, this scheme discusses the impact of the internal dynamics of the weak network VSC on the stability of DC transmission systems containing DCPFC by modularly integrating the dynamics of DCPFC and the coupling mechanism of the weak network VSC, and accurately characterizes all dynamics of the four-terminal DC transmission system.

[0005] Patent application CN116799809A discloses a hierarchical control method and system based on a DC power flow controller, including: performing small-signal modeling of the DC power flow controller and writing out the small-signal state-space equations; designing PI control parameters based on the established small-signal modeling and the transfer function of the n-line inter-modular capacitive DC power flow controller, and controlling the DC power flow controller; and performing power flow analysis at the centralized control layer to obtain the analysis results. However, this patent cannot completely solve the existing technical problems, nor can it meet the needs of this invention. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this invention is to provide a modular small-signal modeling method and system for four-terminal DC transmission with DC power flow controller.

[0007] The modular small-signal modeling method for four-terminal DC transmission with DC power flow controller provided by the present invention includes: Step 1: Perform small-signal modeling for the three voltage source converters (VSCs) with constant power control at the sending end; Step 2: Perform small-signal modeling for a voltage source converter VSC4 controlled by a fixed-terminal voltage. Step 3: Perform small-signal modeling of the DC power flow controller (DCPFC); Step 4: Construct a small-signal model of the overall system by modularly combining the three sending-end VSC modules, one receiving-end VSC4 module, and the DCPFC module; The VSC modeling at the sending end includes phase-locked loop dynamic characteristics, and the DCPFC modeling includes dual-loop proportional-integral (PI) dynamic characteristics.

[0008] Preferably, step 1 includes: Establish the dq-axis dynamic equations for the circuit at the sending end VSC1:

[0009]

[0010]

[0011]

[0012]

[0013]

[0014] in, i cd1 , i cq1 These represent the d-axis and q-axis currents of the filter inductor, respectively. u cd1 , u cq1 These represent the d-axis and q-axis voltages on the AC side of the rectifier, respectively. u od1 , u oq1 These represent the d-q axis voltages of the filter capacitor, respectively. i od1 , i oq1 These represent the d-axis and q-axis currents of the AC mains inductor, respectively. u gd1 , u gq1 These represent the dq-axis voltages of the AC weak network, respectively. L Pf1 , C Pf1 , L pg1 , R Pf1 The filter inductor, filter capacitor, AC weak grid inductor, and filter resistor for the VSC1 circuit section of the constant power control at the sending end. The angular frequency of the AC system; Establish the dynamic equation for the DC-side capacitor of the sending end VSC1:

[0015] in, C s1 It is the DC-side capacitor of the converter station. u 1 represents the DC-side voltage of the converter station. i 1 represents the DC-side output current of the converter station. P 1 represents the AC power of the converter station; Establish the dynamic equations for the control section of the sending end VSC1:

[0016]

[0017]

[0018]

[0019] in, P 1ref This is the VSC1 output power reference value. i cd1ref This is the reference value for the d-axis current of the filter inductor in the control section. i cd1pll To control the d-axis current of part of the filter inductor, u o1ref This is the reference value for the filter capacitor voltage. u o1pll To control the voltage of the filter capacitor in the control layer. i cq1ref This is the reference value for the q-axis current of the filter inductor. i cq1pll To control the q-axis current of the filter inductor in the control layer, It is the integral state quantity of the d-axis PI power loop. It is the integral state quantity of the d-axis PI current loop. It is the integral state quantity of the q-axis PI current loop. It is the integral state quantity of the q-axis PI voltage loop.

[0020] Preferably, the variables dynamically related to the VSC1 control section include the d-axis voltage of the rectifier AC side in the control section. u cd1pll Control section rectifier AC side q-axis voltage u cq1pll Control section filter capacitor d-axis voltage u od1pll Control section filter capacitor q-axis voltage u oq1pll Control section filter inductor q-axis current i cq1pll The equations for these variables are expressed as follows:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] in, k p1 It is the d-axis PI power loop proportional coefficient. k i1 It is the d-axis PI power loop integral coefficient. k p2 It is the d-axis PI current loop proportional coefficient. k i2 It is the integral coefficient of the d-axis PI current loop. To control certain angular frequencies, k p3 It is the q-axis PI voltage loop proportional coefficient. k i3 It is the q-axis PI voltage loop proportional coefficient. k p4 It is the q-axis PI current loop proportional coefficient. k i4 It is the q-axis PI current loop proportional coefficient. u o1d , u o1q It is the dq-axis voltage of the VSC1 filter capacitor. i c1d , i c1q It is the dq axis current of the VSC1 filter inductor.

[0027] Preferably, the dynamic equations related to the VSC1 phase-locked loop are as follows:

[0028]

[0029] in, The phase angle of the VSC1 phase-locked loop. For the phase angle error of VSC1 phase-locked loop, k p5 It is the proportional gain of the phase-locked loop (PI loop). k i5 These are the integral coefficients of the phase-locked loop (PIL). It is the integral state quantity of the phase-locked loop (PLL) PI loop. It is the rated angular frequency of the power grid; The coupling relationship between control dynamics and circuit dynamics in VSC1 is as follows:

[0030] in, X d1pll It is the dynamics of the circuit. X d1 The corresponding control part is dynamic. Xq1pll It is the dynamics of the circuit. X q1 The corresponding control section is dynamic.

[0031] Preferably, step 2 includes: Establish the dq-axis dynamic equations for the receiving end VSC4:

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] in, L Vf , C Vf , L Vg , R Vg The filter inductor, filter capacitor, AC weak network inductor, and filter resistor are for the VSC4 circuit section controlled by the received-end fixed voltage. i cd4 , i cq4 These represent the d-axis and q-axis currents of the VSC4 filter inductor, respectively. u cd4 , u cq4 These represent the dq-axis voltages on the AC side of the VSC4 inverter, respectively. u od4 , u oq4 These represent the dq-axis voltages of the VSC4 filter capacitor, respectively. i od4 , i oq4 These represent the d-axis and q-axis currents of the VSC4 AC mains inductor, respectively. u gd4 , u gq4 These represent the dq axis voltages of the VSC4 AC weak network, respectively. It is the reference angular frequency of VSC4; Establish the dynamic equation for the DC-side capacitor of the receiving end VSC4:

[0038] in,C s4 It is the DC-side capacitor of VSC4. u 4 is the DC side voltage of VSC4. i L This is the DC-side input current of VSC4. P 4 represents the AC side power of VSC4; Establish the dynamic equations for the control part of the receiver VSC4:

[0039]

[0040]

[0041] in, u 4ref This is the DC-side reference voltage of VSC4. u 4 represents the DC side voltage of VSC4. i cd4ref This is the reference value for the d-axis current of the filter inductor in the VSC4 control section. i cd4pll The current in the filter inductor of the VSC4 control section is the d-axis current. i cq4ref This is the reference value for the q-axis current of the filter inductor. i cq4pll To control the q-axis current of the filter inductor in the control layer, It is the integral state quantity of the DC voltage loop. It is the d-axis current loop integral state quantity. It is the q-axis current loop integral state variable.

[0042] Preferably, the variables dynamically related to the VSC4 control section include the AC side d-axis voltage of the inverter in the control section. u cd4pll Control section inverter AC side q-axis voltage u cq4pll Control section filter inductor d-axis current i cd4pll The equations for these variables are:

[0043]

[0044]

[0045]

[0046] in, k p20 It is the d-axis PI voltage loop proportional coefficient. ki20 It is the integral coefficient of the d-axis PI voltage loop. k p21 It is the d-axis PI current loop proportional coefficient. k i21 It is the integral coefficient of the d-axis PI current loop. VSC4 controls the angular frequency of the part. k p22 It is the q-axis PI current loop proportional coefficient. k i22 It is the q-axis PI current loop proportional coefficient. u od4pll , u oq4pll The voltage across the dq axis of the filter capacitor in the VSC4 control section.

[0047] Preferably, the dynamic equations related to the VSC4 phase-locked loop are as follows:

[0048]

[0049] in, The phase angle of the VSC4 phase-locked loop. For the phase angle error of the VSC4 phase-locked loop, k p23 It is the proportional gain of the phase-locked loop (PI loop). k i23 These are the integral coefficients of the phase-locked loop (PIL). It is the integral state quantity of the phase-locked loop (PLL) PI loop. This is the rated angular frequency of VSC4; The coupling relationship between control dynamics and circuit dynamics in VSC4 is as follows:

[0050] in, X d4pll It is the dynamics of the circuit. X d4 The corresponding control part is dynamic. X q4pll It is the dynamics of the circuit. X q4 The corresponding control section is dynamic.

[0051] Preferably, step 3 includes: Establish the circuit dynamic equations for DCPFC:

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] in, D 1 indicates the duty cycle of switch sub-mode 1. D 2 indicates the duty cycle of switch sub-mode 2. i L Indicates the common inductor current. u C1 , u C2 and u C3 These represent the power flow controllers. C 1. C 2 and C 3. Voltage across the terminals u 1 indicates the voltage at port VSC1. u 2 indicates the voltage at the VSC2 port. i 12 Indicates the line line 12 Current, R 12 Indicates the line line 12 resistance, u 4 indicates the voltage at port VSC4. i 14 Indicates the line line 14 Current, R 14 Indicates the line line 14 resistance, u 3 indicates the voltage at the VSC3 port. i 23 Indicates the line line 23 Current, R 23 Indicates the line line 23 resistance, i 24 Indicates the line line 24 Current, R24 Indicates the line line 24 resistance, i 34 Indicates the line line 34 Current, R 34 Indicates the line line 34 resistance, L Indicates the circuit inductance of DCPFC. L 12 Indicates the line line 12 inductance, L 14 Indicates the line line 14 inductance, L 23 Indicates the line line 23 inductance, L 24 Indicates the line line 24 inductance, L 34 Indicates the line line 34 inductance; Establish the dynamic equations for the control part of DCPFC:

[0061]

[0062]

[0063]

[0064] in, i 14ref For the line line 14 Current control reference value, i 34ref For the line line 34 Current control reference value, u C1ref Capacitor for power flow controller C 1. Voltage control reference value at both ends u C3ref Capacitor for power flow controller C 3. Reference value for voltage control at both ends. It is a line line 14 Integral state quantity of current loop It is the integral state quantity of the voltage loop of capacitor C1. It is a line line 34 Integral state quantity of current loop It is a capacitor C 3. Voltage loop integral state variables. k pC1 For capacitor C 1. Voltage loop proportional coefficient, k iC1 For capacitor C 1. Voltage loop integral coefficient, k pC2 For capacitor C 3. Voltage loop proportionality factor. k iC2 For capacitor C 3. Voltage loop integral coefficient, It is the rate of change of the integral state variable of the d-axis PI power loop. It is the rate of change of the integral state variable of the q-axis PI voltage loop.

[0065] Preferably, step 4 includes: Define the state equation of the sending end VSC1 submodule as follows:

[0066] in, A 1 is the VSC1 system matrix. B 11 It is a VSC1 input variable u 11 The corresponding input matrix, B 41 It is a VSC1 input variable u 41 The corresponding input matrix, For the sending end VSC1 state variable vector, The rate of change of the state variable VSC1 at the sending end; Define the state equation of the VSC2 submodule at the sending end as follows:

[0067] in, A 2 is the VSC2 system matrix. B 22 It is a VSC2 input variable u 22 The corresponding input matrix, B 42 It is a VSC2 input variable u 42 The corresponding input matrix, For the sending end VSC2 state variable vector, The rate of change of the state variable VSC2 at the sending end; Define the state equation of the VSC3 submodule at the sending end as follows:

[0068] in, A 3 is the VSC3 system matrix. B 33 It is a VSC3 input variable u 33 The corresponding input matrix, B 43 It is a VSC3 input variable u 43 The corresponding input matrix, For the sending end VSC3 state variable vector, The rate of change of the VSC3 state variable at the sending end; Define the state equation of the DCPFC submodule as follows:

[0069] in, A 4 is the DCPFC system matrix. B 14 It is a DCPFC input variable u 14 The corresponding input matrix, B 24 It is a DCPFC input variable u 24 The corresponding input matrix, B 34 It is a DCPFC input variable u 34 The corresponding input matrix, B 44 It is a DCPFC input variable u 44 The corresponding input matrix, B 54 It is a DCPFC input variable u 54 The corresponding input matrix, This is the DCPFC state variable vector. For DCPFC state variables, the rate of change is denoted as .

[0070] The state-space representation of the small-signal model of the overall system is as follows:

[0071] in, It is the vector of the rate of change of the state of the sending end VSC1. It is the state change rate vector of the sending end VSC2. It is the state change rate vector of the sending end VSC3. It is the DCPFC state change rate vector. It is the state change rate vector of the receiving end VSC4. It is the small perturbation state vector of the sending end VSC1. It is the small perturbation state vector of the sending end VSC2. It is the small perturbation state vector of the VSC3 at the sending end. It is the small perturbation state vector of DCPFC. It is the small perturbation state vector of the receiving end VSC4. O i×j for i OK j Column zero matrix C ij The following is a diagram of the first... i The output variables generated by each submodule are used as the first... j The output matrix corresponding to the input variables of each submodule. A 5 is the VSC4 system matrix. B 55 It is a VSC4 input matrix. u 55 It is an input variable for VSC4.

[0072] The modular small-signal modeling system for four-terminal DC transmission with DC power flow controller provided by the present invention adopts the aforementioned modular small-signal modeling method for four-terminal DC transmission with DC power flow controller.

[0073] Compared with the prior art, the present invention has the following beneficial effects: (1) The present invention is based on a system-level modeling method of functional modular division and combination. It decouples a DC transmission system with DC-CPFC into five independent modules: three sending-end VSC modules, one receiving-end VSC module, and one DC-CPFC module. By modular combination, a complete small-signal model is constructed, which significantly reduces the modeling complexity of multi-port coupled systems. (2) This invention breaks through the limitations of existing research on the simplification of VSC models, and innovatively establishes a complete small-signal model of VSC that takes into account the dynamics of the phase-locked loop and a complete model of DCPFC that takes into account the dynamics of the dual-loop PI controller, accurately depicting the dynamic interaction mechanism between VSC and DCPFC; for the first time, it discusses the impact of the internal dynamics of the weak network VSC on the stability of DC transmission systems containing DCPFC, and accurately depicts all dynamics of the four-terminal DC transmission system by modeling the coupling relationship between the dynamics of the dual-loop PI DC power flow controller, the dynamics of the DC network and the dynamics of VSC, providing a foundation for refined impedance modeling of four-terminal DC transmission. Attached Figure Description

[0074] 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: Figure 1 This is a block diagram of a four-terminal DC transmission system including VSC-DCPFC. Figure 2 Here is a block diagram of the VSC1 control section; Figure 3 This is a block diagram of the VSC4 control section; Figure 4 The block diagram of a three-wire DCPFC based on symmetrical current control is shown. Figure 5 This is a block diagram of the DCPFC control section; Figure 6 This is a block diagram of a four-terminal DC transmission system. Figure 7 Root locus diagram of VSC-DCPFC system as a function of line resistance; Figure 8 This is a simulation diagram showing the change of DCPFC line current with line resistance.

[0075] The diagram shows: P 1 represents the AC side power of the VSC1 converter station. P 2 represents the AC side power of the VSC2 converter station. P 3 represents the AC side power of the VSC3 converter station. P 4 represents the AC side power of the VSC4 converter station. u 1 indicates the voltage at port VSC1. u 2 indicates the voltage at the VSC2 port. i 12 Indicates the line line 12 Current, R 12 Indicates the line line 12 resistance, u 4 indicates the voltage at port VSC4. i 14 Indicates the line line 14 Current, R 14 Indicates the line line 14 resistance, u 3 indicates the voltage at the VSC3 port. i 23 Indicates the line line 23 Current, R 23 Indicates the line line 23 resistance, i24 Indicates the line line 24 Current, R 24 Indicates the line line 24 resistance, u C1 , u C2 and u C3 These represent the power flow controllers. C 1. C 2 and C 3. Voltage across the terminals L Pf1 , C Pf1 , L pg1 , R Pf1 The filter inductor, filter capacitor, AC weak grid inductor, and filter resistor for the VSC1 circuit section of the constant power control at the sending end. L Vf , C Vf , L Vg , R Vg The filter inductor, filter capacitor, AC weak network inductor, and filter resistor are for the VSC4 circuit section controlled by the received-end fixed voltage. k p1 It is the d-axis PI power loop proportional coefficient. k i1 It is the d-axis PI power loop integral coefficient. k p2 It is the d-axis PI current loop proportional coefficient. k i2 It is the integral coefficient of the d-axis PI current loop. To control certain angular frequencies, k p3 It is the q-axis PI voltage loop proportional coefficient. k i3 It is the q-axis PI voltage loop proportional coefficient. k p4 It is the q-axis PI current loop proportional coefficient. k i4 It is the q-axis PI current loop proportional coefficient. u o1d , u o1q It is the dq-axis voltage of the VSC1 filter capacitor. i c1d , i c1qIt is the dq-axis current of the VSC1 filter inductor. k p20 It is the d-axis PI voltage loop proportional coefficient. k i20 It is the integral coefficient of the d-axis PI voltage loop. k p21 It is the d-axis PI current loop proportional coefficient. k i21 It is the integral coefficient of the d-axis PI current loop. VSC4 controls the angular frequency of the part. k p22 It is the q-axis PI current loop proportional coefficient. k i22 It is the q-axis PI current loop proportional coefficient. u od4pll , u oq4pll This refers to the dq-axis voltage of the filter capacitor in the VSC4 control section. i 14ref For the line line 14 Current control reference value, i 34ref For the line line 34 Current control reference value, u C1ref Capacitor for power flow controller C 1. Voltage control reference value at both ends u C3ref Capacitor for power flow controller C 3. Reference value for voltage control at both ends. It is a line line 14 Integral state quantity of current loop It is the integral state quantity of the voltage loop of capacitor C1. It is a line line 34 Integral state quantity of current loop It is a capacitor C 3. Voltage loop integral state variables. k pC1 For capacitor C 1. Voltage loop proportional coefficient, k iC1 For capacitor C 1. Voltage loop integral coefficient, k pC2 For capacitor C 3. Voltage loop proportionality factor. k iC2 For capacitor C 3. Voltage loop integral coefficient, It is the rate of change of the integral state variable of the d-axis PI power loop. It is the rate of change of the integral state variable of the q-axis PI voltage loop. Detailed Implementation

[0076] 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.

[0077] Example This invention provides a modular small-signal modeling method for four-terminal DC transmission systems with DC power flow controllers, comprising four parts: small-signal modeling of the sending-end constant power control (VSC), small-signal modeling of the receiving-end constant voltage control (VSC), small-signal modeling of the DC power flow controller (DCPFC), and small-signal modeling of the overall system. Based on a four-terminal DC transmission system with a DC power flow controller, a complete small-signal model of the VSC considering phase-locked loop (PLL) dynamics and a refined model of the DCCPFC considering dual-loop PI dynamics are established, achieving complete system modeling with multi-module coupling. Based on this model, the influence of network parameters on system stability is analyzed, providing architectural design references for improving system stability margins and theoretical support for configuring parameters of high-reliability DC grids with DCCPFC.

[0078] The specific implementation methods are as follows: A. Small-signal modeling of VSC (Voltage Control System) at the sending end; The research object of this plan is as follows: Figure 1 The diagram shows a four-terminal DC transmission system including VSC-DCPFC. Power flows from the sending-end constant-power control VSC to the DCPFC, and then to the receiving-end constant-voltage control VSC. The modeling of the constant-power control VSC1 at the sending end is presented as an example, and its circuit dynamics include filter inductors. L Pf1 Filter capacitor C Pf1 AC weak network inductor L pg1 and DC side capacitor C s1 The dynamic equations of the VSC1 circuit along the dq axis are shown below: (1) (2) (3) (4) (5) (6) in,i cd1 , i cq1 These represent the d-axis and q-axis currents of the filter inductor, respectively. u cd1 , u cq1 These represent the d-axis and q-axis voltages on the AC side of the rectifier, respectively. u od1 , u oq1 These represent the d-q axis voltages of the filter capacitor, respectively. i od1 , i oq1 These represent the d-axis and q-axis currents of the AC mains inductor, respectively. u gd1 , u gq1 These represent the dq-axis voltages of the AC weak network, respectively.

[0079] DC side capacitor C s1 The dynamics are as follows: (7) in, C s1 It is the DC-side capacitor of the converter station. u 1 represents the DC-side voltage of the converter station. i 1 represents the DC-side output current of the converter station. P 1 represents the AC power of the converter station.

[0080] like Figure 2 As shown, the dynamics of the VSC1 control section include the d-axis PI power loop differential term, the d-axis PI current loop differential term, the q-axis PI voltage loop differential term, and the q-axis PI voltage loop differential term. The dq-axis dynamic equations of VSC1 are shown below: (8) (9) (10) (11) in, P 1ref This is the VSC1 output power reference value. i cd1ref This is the reference value for the d-axis current of the filter inductor in the control section. i cd1pll To control the d-axis current of the filter inductor. u o1ref This is the reference value for the filter capacitor voltage. u o1pllThis is the voltage of the control layer filter capacitor. i cq1ref This is the reference value for the q-axis current of the filter inductor. i cq1pll To control the q-axis current of the filter inductor in the control layer, It is the integral state quantity of the d-axis PI power loop. It is the integral state quantity of the d-axis PI current loop. It is the integral state quantity of the q-axis PI current loop. It is the integral state quantity of the q-axis PI voltage loop.

[0081] The variables dynamically related to the VSC1 control section include the d-axis voltage on the AC side of the rectifier in the control section. u cd1pll Control section rectifier AC side q-axis voltage u cq1pll Control section filter capacitor d-axis voltage u od1pll Control section filter capacitor q-axis voltage u oq1pll Control section filter inductor q-axis current i cq1pll These equations can be expanded as follows: (12) (13) (14) (15) (16) (17) in, k p1 It is the d-axis PI power loop proportional coefficient. k i1 It is the d-axis PI power loop integral coefficient. k p2 It is the d-axis PI current loop proportional coefficient. k i2 It is the integral coefficient of the d-axis PI current loop. To control certain angular frequencies, k p3 It is the q-axis PI voltage loop proportional coefficient. k i3 It is the q-axis PI voltage loop proportional coefficient. k p4 It is the q-axis PI current loop proportional coefficient. k i4This is the proportional coefficient of the q-axis PI current loop. The dynamic equations related to the VSC1 phase-locked loop can be expanded as follows: (18) (19) in, The phase angle of the VSC1 phase-locked loop. k p5 It is the proportional gain of the phase-locked loop (PI loop). k i5 These are the integral coefficients of the phase-locked loop (PIL). This is the integral state quantity of the phase-locked loop (PLL) PI loop. The coupling relationship between control dynamics and circuit dynamics in VSC1 can be expressed as: (20) in, X d1pll It is the dynamics of the circuit. X d1 The corresponding control part is dynamic. X q1pll It is the dynamics of the circuit. X q1 The corresponding control section is dynamic.

[0082] In summary, the state variables of VSC1 X 1. Input variables u 11 and u 41 It can be represented as follows: (twenty one) (twenty two) (twenty three) Similarly, we can obtain the state variables of VSC2 and VSC3, which are both constant power control at the sending end. X 2. X 3. Input variables u 22 , u 33 , u 42 , u 43 It can be represented as follows: (twenty four) (25) (26) (27) (28) (29) B. Small-signal modeling of VSC controlled by the received-end fixed voltage; The dynamics of the VSC4 circuit, controlled by the fixed voltage, include the filter inductor. L Vf Filter capacitor C Vf AC weak network inductor L Vg and DC side capacitor C s4 The dynamic equations for the dq axes of the VSC4 circuit are shown below: (30) (31) (32) (33) (34) (35) in, i cd4 , i cq4 These represent the d-axis and q-axis currents of the VSC4 filter inductor, respectively. u cd4 , u cq4 These represent the dq-axis voltages on the AC side of the VSC4 inverter, respectively. u od4 , u oq4 These represent the dq-axis voltages of the VSC4 filter capacitor, respectively. i od4 , i oq4 These represent the d-axis and q-axis currents of the VSC4 AC mains inductor, respectively. u gd4 , u gq4 These represent the dq axis voltages of the VSC4 AC weak network, respectively.

[0083] DC side capacitor C s4 The dynamics are as follows: (36) in, C s4 It is the DC-side capacitor of VSC4. u 4 is the DC side voltage of VSC4. i L This is the DC-side input current of VSC4. P 4 represents the AC power of VSC4.

[0084] like Figure 3 As shown, the dynamics of the VSC4 control section include the d-axis PI power loop differential term, the d-axis PI current loop differential term, and the q-axis PI current loop differential term. The dq-axis dynamic equations of VSC4 are shown below: (37) (38) (40) in, u 4ref This is the DC-side reference voltage of VSC4. u 4 represents the DC side voltage of VSC4. i cd4ref This is the reference value for the d-axis current of the filter inductor in the VSC4 control section. i cd4pll The current in the d-axis of the filter inductor in the VSC4 control section is the current. i cq4ref This is the reference value for the q-axis current of the filter inductor. i cq4pll This is for the q-axis current of the control layer filter inductor. It is the integral state quantity of the DC voltage loop. It is the d-axis current loop integral state quantity. It is the q-axis current loop integral state variable.

[0085] The variables dynamically related to the VSC4 control section include the AC side d-axis voltage of the inverter in the control section. u cd4pll Control section inverter AC side q-axis voltage u cq4pll Control section filter inductor d-axis current i cd4pll These equations can be expanded as follows: (41) (42) (43) (44) in, k p20It is the d-axis PI voltage loop proportional coefficient. k i20 It is the integral coefficient of the d-axis PI voltage loop. k p21 It is the d-axis PI current loop proportional coefficient. k i21 It is the integral coefficient of the d-axis PI current loop. VSC4 controls the angular frequency of the part. k p22 It is the q-axis PI current loop proportional coefficient. k i22 This is the q-axis PI current loop proportional coefficient. The dynamic equations related to the VSC4 phase-locked loop can be expanded as follows: (45) (46) in, The phase angle of the VSC4 phase-locked loop. k p23 It is the proportional gain of the phase-locked loop (PI loop). k i23 These are the integral coefficients of the phase-locked loop (PIL). This is the integral state quantity of the phase-locked loop (PLL) PI loop. The coupling relationship between control dynamics and circuit dynamics in VSC4 can be expressed as: (47) in, X d4pll It is the dynamics of the circuit. X d4 The corresponding control part is dynamic. X q4pll It is the dynamics of the circuit. X q4 The corresponding control section is dynamic.

[0086] In summary, the state variables of VSC4 X 5. Input variables u 55 and u 45 It can be represented as follows: (48) (49) (50) C. Small-signal modeling of DCPFC; Three-wire DC-CPFC based on symmetrical current control, such as Figure 4 As shown, DCPFC dynamics include a common inductor.L Line inductance L 12 Line inductance L 14 Line inductance L 23 Line inductance L 24 Line inductance L 34 Current controller capacitor C 1. Current controller capacitor C 2 and current controller capacitor C 3. The DCPFC variable equation can be expanded as follows: (51) (52) (53) (54) (55) (56) (57) (58) (59) in, D 1 indicates the duty cycle of switch sub-mode 1. D 2 indicates the duty cycle of switch sub-mode 2. i L Indicates the common inductor current. u C1 , u C2 and u C3 These represent the power flow controllers. C 1. C 2 and C 3. The voltage across the two ends. u 1 indicates the voltage at port VSC1. u 2 indicates the voltage at the VSC2 port. i 12 Indicates the line line 12 Current, R 12 Indicates the line line 12 resistance. u 4 indicates the voltage at port VSC4. i 14 Indicates the line line14 Current, R 14 Indicates the line line 14 resistance. u 3 indicates the voltage at the VSC3 port. i 23 Indicates the line line 23 Current, R 23 Indicates the line line 23 resistance. i 24 Indicates the line line 24 Current, R 24 Indicates the line line 24 resistance.

[0087] like Figure 5 As shown, the dynamic control part of the DCPFC includes control... i 14 PI current loop differential term, control i 14 PI voltage loop differential term, control i 34 PI current loop differential term and control i 34 The differential term of the PI voltage loop. The dynamic equations of the DCPFC control part are shown below: (60) (61) (62) (63) in, i 14ref For the line line 14 Current control reference value, i 34ref For the line line 34 Current control reference value. u C1ref Capacitor for power flow controller C 1. Voltage control reference value at both ends u C3ref Capacitor for power flow controller C 3. Reference value for voltage control at both ends.

[0088] In summary, the state variables of DCPFC X4. Input variables u 41 , u 42 , u 43 and u 44 It can be represented as follows: (64) (65) (66) (67) (68) D. Small-signal modeling of the overall system; The state variables of the VSC1 submodule can be represented as shown in equation (69): (69) in, A 1 is the VSC1 system matrix. B 11 It is a VSC1 input variable u 11 The corresponding input matrix, B 41 It is a VSC1 input variable u 41 The corresponding input matrix.

[0089] The state variables of the VSC2 submodule can be represented as shown in equation (70): (70) in, A 2 is the VSC2 system matrix. B 22 It is a VSC2 input variable u 22 The corresponding input matrix, B 42 It is a VSC2 input variable u 42 The corresponding input matrix.

[0090] The state variables of the VSC3 submodule can be represented as shown in equation (71): (71) in, A 3 is the VSC3 system matrix. B 33It is a VSC3 input variable u 33 The corresponding input matrix, B 43 It is a VSC3 input variable u 43 The corresponding input matrix.

[0091] The state variables of the DCPFC submodule can be represented as shown in equation (72): (72) in, A 4 is the DCPFC system matrix. B 14 It is a DCPFC input variable u 14 The corresponding input matrix, B 24 It is a DCPFC input variable u 24 The corresponding input matrix, B 34 It is a DCPFC input variable u 34 The corresponding input matrix, B 44 It is a DCPFC input variable u 44 The corresponding input matrix, B 54 It is a DCPFC input variable u 54 The corresponding input matrix. Input matrix u 14 , u 24 , u 34 , u 41 , u 42 , u 43 , u 45 and u 54 It can be obtained by multiplying the output matrix by the state variables, as shown below: (73) (74) (75) (76) (77) (78) (79) in, C ij The following is a diagram of the first... i The output variables generated by each submodule are used as the first... j The output matrix corresponding to the input variables of each submodule. The small-signal model of the system after merging the five submodules can be represented as follows: (80) in, O i×j for i OK j The column zero matrix, the system matrix of VSC-DCPFC, can be represented as follows: (81) In such Figure 6 The correctness of the modular small-signal modeling method and stability analysis results for a four-terminal DC transmission system with a DC power flow controller is verified in the illustrated four-terminal DC transmission system. The line resistance is set to decrease over time as shown in Table 1. It is observed whether the four-terminal DC transmission system with DC-DC power flow controller can recover to a steady state until system instability after each decrease in line resistance, thus obtaining the critical value for line resistance stability considering the VSC-DCPFC system. The changes in line resistance are shown in Table 1, and the following parameters are specified. R 14 = R 24 = R 34 =2W, R 12 = R 23 =1W is 1pu.

[0092] Table 1. Changes in line resistance

[0093] To investigate the impact of DC transmission line resistance on system stability, a root locus plot of the VSC-DCPFC system as a function of line resistance was plotted based on the eigenvalues ​​of the system matrix, as shown below. Figure 7 As shown. The stability condition of the system is that all eigenvalues ​​of matrix A have negative real parts, i.e., all eigenvalues ​​lie in the left half-plane. For example... Figure 7 As shown, when the line resistance decreases to 0.6 pu, a pair of eigenvalues ​​cross the imaginary axis and shift to the right half-plane, causing system instability. Simulation results are as follows. Figure 8As shown, at the 4th second, the line resistance decreases from 0.8 pu to 0.7 pu. The DC distribution network with hybrid energy storage remains stable. However, at the 5th second, the line resistance decreases from 0.7 pu to 0.6 pu. The system begins to become unstable, which is consistent with the theoretical analysis results.

[0094] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented 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, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0095] 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 modular small-signal modeling method for four-terminal DC transmission with DC power flow controller, characterized in that, include: Step 1: Perform small-signal modeling for the three voltage source converters (VSCs) with constant power control at the sending end; Step 2: Perform small-signal modeling for a voltage source converter VSC4 controlled by a fixed-terminal voltage. Step 3: Perform small-signal modeling of the DC power flow controller (DCPFC); Step 4: Construct a small-signal model of the overall system by modularly combining the three sending-end VSC modules, one receiving-end VSC4 module, and the DCPFC module; The VSC modeling at the sending end includes phase-locked loop dynamic characteristics, and the DCPFC modeling includes dual-loop proportional-integral (PI) dynamic characteristics.

2. The modular small-signal modeling method for four-terminal DC transmission with DC power flow controller as described in claim 1, characterized in that, Step 1 includes: Establish the dq-axis dynamic equations for the circuit at the sending end VSC1: in, i cd1 , i cq1 These represent the d-axis and q-axis currents of the filter inductor, respectively. u cd1 , u cq1 These represent the d-axis and q-axis voltages on the AC side of the rectifier, respectively. u od1 , u oq1 These represent the d-q axis voltages of the filter capacitor, respectively. i od1 , i oq1 These represent the d-axis and q-axis currents of the AC mains inductor, respectively. u gd1 , u gq1 These represent the dq-axis voltages of the AC weak network, respectively. L Pf1 , C Pf1 , L pg1 , R Pf1 The filter inductor, filter capacitor, AC weak grid inductor, and filter resistor for the VSC1 circuit section of the constant power control at the sending end. The angular frequency of the AC system; Establish the dynamic equation for the DC-side capacitor of the sending end VSC1: in, C s1 It is the DC-side capacitor of the converter station. u 1 represents the DC-side voltage of the converter station. i 1 represents the DC-side output current of the converter station. P 1 represents the AC power of the converter station; Establish the dynamic equations for the control section of the sending end VSC1: in, P 1ref This is the VSC1 output power reference value. i cd1ref This is the reference value for the d-axis current of the filter inductor in the control section. i cd1pll To control the d-axis current of part of the filter inductor, u o1ref This is the reference value for the filter capacitor voltage. u o1pll To control the voltage of the filter capacitor in the control layer. i cq1ref This is the reference value for the q-axis current of the filter inductor. i cq1pll To control the q-axis current of the filter inductor in the control layer, It is the integral state quantity of the d-axis PI power loop. It is the integral state quantity of the d-axis PI current loop. It is the integral state quantity of the q-axis PI current loop. It is the integral state quantity of the q-axis PI voltage loop.

3. The modular small-signal modeling method for four-terminal DC transmission with DC power flow controller as described in claim 2, characterized in that, The variables dynamically related to the VSC1 control section include the d-axis voltage on the AC side of the rectifier in the control section. u cd1pll Control section rectifier AC side q-axis voltage u cq1pll Control section filter capacitor d-axis voltage u od1pll Control section filter capacitor q-axis voltage u oq1pll Control section filter inductor q-axis current i cq1pll The equations for these variables are expressed as follows: in, k p1 It is the d-axis PI power loop proportional coefficient. k i1 It is the d-axis PI power loop integral coefficient. k p2 It is the d-axis PI current loop proportional coefficient. k i2 It is the integral coefficient of the d-axis PI current loop. To control certain angular frequencies, k p3 It is the q-axis PI voltage loop proportional coefficient. k i3 It is the q-axis PI voltage loop proportional coefficient. k p4 It is the q-axis PI current loop proportional coefficient. k i4 It is the q-axis PI current loop proportional coefficient. u o1d , u o1q It is the dq-axis voltage of the VSC1 filter capacitor. i c1d , i c1q It is the dq axis current of the VSC1 filter inductor.

4. The modular small-signal modeling method for four-terminal DC transmission with DC power flow controller as described in claim 3, characterized in that, The dynamic equations related to the VSC1 phase-locked loop are: in, The phase angle of the VSC1 phase-locked loop. For the phase angle error of VSC1 phase-locked loop, k p5 It is the proportional gain of the phase-locked loop (PLL). k i5 These are the integral coefficients of the phase-locked loop (PLL) PI loop. It is the integral state quantity of the phase-locked loop (PLL) PI loop. It is the rated angular frequency of the power grid; The coupling relationship between control dynamics and circuit dynamics in VSC1 is as follows: in, X d1pll It is the dynamics of the circuit. X d1 The corresponding control part is dynamic. X q1pll It is the dynamics of the circuit. X q1 The corresponding control section is dynamic.

5. The modular small-signal modeling method for four-terminal DC transmission with DC power flow controller as described in claim 4, characterized in that, Step 2 includes: Establish the dq-axis dynamic equations for the receiving end VSC4: in, L Vf , C Vf , L Vg , R Vg The filter inductor, filter capacitor, AC weak network inductor, and filter resistor are for the VSC4 circuit section controlled by the received-end fixed voltage. i cd4 , i cq4 These represent the d-axis and q-axis currents of the VSC4 filter inductor, respectively. u cd4 , u cq4 These represent the dq-axis voltages on the AC side of the VSC4 inverter, respectively. u od4 , u oq4 These represent the dq-axis voltages of the VSC4 filter capacitor, respectively. i od4 , i oq4 These represent the d-axis and q-axis currents of the VSC4 AC mains inductor, respectively. u gd4 , u gq4 These represent the dq-axis voltages of the VSC4 AC weak network, respectively. It is the reference angular frequency of VSC4; Establish the dynamic equation for the DC-side capacitor of the receiving end VSC4: in, C s4 It is the DC-side capacitor of VSC4. u 4 is the DC side voltage of VSC4. i L This is the DC-side input current of VSC4. P 4 represents the AC side power of VSC4; Establish the dynamic equations for the control part of the receiver VSC4: in, u 4ref This is the DC-side reference voltage of VSC4. u 4 represents the DC side voltage of VSC4. i cd4ref This is the reference value for the d-axis current of the filter inductor in the VSC4 control section. i cd4pll The current in the filter inductor of the VSC4 control section is the d-axis current. i cq4ref This is the reference value for the q-axis current of the filter inductor. i cq4pll To control the q-axis current of the filter inductor in the control layer, It is the integral state quantity of the DC voltage loop. It is the d-axis current loop integral state quantity. It is the q-axis current loop integral state variable.

6. The modular small-signal modeling method for four-terminal DC transmission with DC power flow controller as described in claim 5, characterized in that, The variables dynamically related to the VSC4 control section include the AC side d-axis voltage of the inverter in the control section. u cd4pll Control section inverter AC side q-axis voltage u cq4pll Control section filter inductor d-axis current i cd4pll The equations for these variables are: in, k p20 It is the d-axis PI voltage loop proportional coefficient. k i20 It is the integral coefficient of the d-axis PI voltage loop. k p21 It is the d-axis PI current loop proportional coefficient. k i21 It is the integral coefficient of the d-axis PI current loop. VSC4 controls the angular frequency of the part. k p22 It is the q-axis PI current loop proportional coefficient. k i22 It is the q-axis PI current loop proportional coefficient. u od4pll , u oq4pll The voltage across the dq axis of the filter capacitor in the VSC4 control section.

7. The modular small-signal modeling method for four-terminal DC transmission with DC power flow controller as described in claim 6, characterized in that, The dynamic equations related to the VSC4 phase-locked loop are: in, The phase angle of the VSC4 phase-locked loop. For the phase angle error of the VSC4 phase-locked loop, k p23 It is the proportional gain of the phase-locked loop (PLL). k i23 These are the integral coefficients of the phase-locked loop (PLL) PI loop. It is the integral state quantity of the phase-locked loop (PLL) PI loop. This is the rated angular frequency of VSC4; The coupling relationship between control dynamics and circuit dynamics in VSC4 is as follows: in, X d4pll It is the dynamics of the circuit. X d4 The corresponding control part is dynamic. X q4pll It is the dynamics of the circuit. X q4 The corresponding control section is dynamic.

8. The modular small-signal modeling method for four-terminal DC transmission with DC power flow controller as described in claim 7, characterized in that, Step 3 includes: Establish the circuit dynamic equations for DCPFC: in, D 1 indicates the duty cycle of switch sub-mode 1. D 2 indicates the duty cycle of switch sub-mode 2. i L Indicates the common inductor current. u C1 , u C2 and u C3 These represent the power flow controllers. C 1. C 2 and C 3. Voltage across the terminals u 1 indicates the voltage at port VSC1. u 2 indicates the voltage at the VSC2 port. i 12 Indicates the line line 12 Current, R 12 Indicates the line line 12 resistance, u 4 indicates the voltage at port VSC4. i 14 Indicates the line line 14 Current, R 14 Indicates the line line 14 resistance, u 3 indicates the voltage at the VSC3 port. i 23 Indicates the line line 23 Current, R 23 Indicates the line line 23 resistance, i 24 Indicates the line line 24 Current, R 24 Indicates the line line 24 resistance, i 34 Indicates the line line 34 Current, R 34 Indicates the line line 34 resistance, L Indicates the circuit inductance of DCPFC. L 12 Indicates the line line 12 inductance, L 14 Indicates the line line 14 inductance, L 23 Indicates the line line 23 inductance, L 24 Indicates the line line 24 inductance, L 34 Indicates the line line 34 inductance; Establish the dynamic equations for the control part of DCPFC: in, i 14ref For the line line 14 Current control reference value, i 34ref For the line line 34 Current control reference value, u C1ref Capacitor for power flow controller C 1. Voltage control reference value at both ends u C3ref Capacitor for power flow controller C 3. Reference value for voltage control at both ends. It is a line line 14 Integral state quantity of current loop It is the integral state quantity of the voltage loop of capacitor C1. It is a line line 34 Integral state quantity of current loop It is a capacitor C 3. Voltage loop integral state variables. k pC1 For capacitor C 1. Voltage loop proportional coefficient, k iC1 For capacitor C 1. Voltage loop integral coefficient, k pC2 For capacitor C 3. Voltage loop proportionality factor. k iC2 For capacitor C 3. Voltage loop integral coefficient, It is the rate of change of the integral state variable of the d-axis PI power loop. It is the rate of change of the integral state variable of the q-axis PI voltage loop.

9. The modular small-signal modeling method for four-terminal DC transmission with DC power flow controller as described in claim 8, characterized in that, Step 4 includes: Define the state equation of the sending end VSC1 submodule as follows: in, A 1 is the VSC1 system matrix. B 11 It is a VSC1 input variable u 11 The corresponding input matrix, B 41 It is a VSC1 input variable u 41 The corresponding input matrix, For the sending end VSC1 state variable vector, The rate of change of the state variable VSC1 at the sending end; Define the state equation of the VSC2 submodule at the sending end as follows: in, A 2 is the VSC2 system matrix. B 22 It is a VSC2 input variable u 22 The corresponding input matrix, B 42 It is a VSC2 input variable u 42 The corresponding input matrix, For the sending end VSC2 state variable vector, The rate of change of the VSC2 state variable at the sending end; Define the state equation of the VSC3 submodule at the sending end as follows: in, A 3 is the VSC3 system matrix. B 33 It is a VSC3 input variable u 33 The corresponding input matrix, B 43 It is a VSC3 input variable u 43 The corresponding input matrix, For the sending end VSC3 state variable vector, The rate of change of the VSC3 state variable at the sending end; Define the state equation of the DCPFC submodule as follows: in, A 4 is the DCPFC system matrix. B 14 It is a DCPFC input variable u 14 The corresponding input matrix, B 24 It is a DCPFC input variable u 24 The corresponding input matrix, B 34 It is a DCPFC input variable u 34 The corresponding input matrix, B 44 It is a DCPFC input variable u 44 The corresponding input matrix, B 54 It is a DCPFC input variable u 54 The corresponding input matrix, This is the DCPFC state variable vector. The rate of change of the DCPFC state variable; The state-space representation of the small-signal model of the overall system is as follows: in, It is the vector of the rate of change of the state of the sending end VSC1. It is the state change rate vector of the sending end VSC2. It is the state change rate vector of the sending end VSC3. It is the DCPFC state change rate vector. It is the state change rate vector of the receiving end VSC4. It is the small perturbation state vector of the sending end VSC1. It is the small perturbation state vector of the sending end VSC2. It is the small perturbation state vector of the VSC3 at the sending end. It is the small perturbation state vector of DCPFC. It is the small perturbation state vector of the receiving end VSC4. O i×j for i OK j Column zero matrix, C ij The following is a diagram of the first... i The output variables generated by each submodule are used as the first... j The output matrix corresponding to the input variables of each submodule. A 5 is the VSC4 system matrix. B 55 It is a VSC4 input matrix. u 55 It is an input variable for VSC4.

10. A modular small-signal modeling system for four-terminal DC transmission with a DC power flow controller, characterized in that, The method described in any one of claims 1 to 9 is a modular small-signal modeling method for four-terminal DC transmission with a DC power flow controller.

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