Modeling analysis method for low-frequency dynamic characteristic equivalent circuit of flexible direct-current power transmission system

Abstract

The invention relates to a modeling analysis method for a low-frequency dynamic characteristic equivalent circuit of a flexible direct-current power transmission system, which comprises the following steps of: deducing a basic transfer function between active power and a d-axis alternating current component under the influence of factors such as outer loop alternating-current voltage control and a phase-locked loop, and expanding the basic transfer function into a multi-branch transfer function model; establishing a multi-branch equivalent circuit model connected to a weak network direct-current voltage control unit after model simplification and equivalence by combining a direct-current voltage control dynamic state; based on equivalent physical circuit parameters such as equivalent resistance and equivalent inductance of the corresponding equivalent RL circuit branch, the influence degrees of multiple control links and interaction thereof, power grid strength and the like are quantitatively evaluated; a whole-system direct current side equivalent RLC circuit model is obtained by combining the dynamic states of a direct current voltage control unit and a constant power control unit, so that the low-frequency dynamic characteristic mechanism of the flexible direct current power transmission system can be clearly and intuitively seen from the perspective of an equivalent circuit, and the impedance analysis of the system can be carried out by establishing a total parallel impedance expression.

Description

[Technical Field]

[0001] This invention belongs to the field of stability modeling and analysis of flexible DC transmission systems, and particularly relates to a method for modeling and analyzing the equivalent circuit of low-frequency dynamic characteristics of flexible DC transmission systems. [Background Technology]

[0002] Flexible DC transmission systems have attracted significant attention due to their ability to enhance the integration of renewable energy sources such as photovoltaics and wind power, and their ability to flexibly control power transmission. However, operational scenarios involving large-scale, long-distance transmission of DC power from renewable sources and severe short-circuit faults will weaken the AC grid interconnected with the flexible DC transmission system. In such cases, the characteristics of the weakened grid will have a significant impact on the low-frequency, small-disturbance dynamic characteristics of the flexible DC transmission system.

[0003] Currently, impedance analysis and state-space analysis are commonly used as modeling methods for analyzing the stability of systems under small disturbances. The literature [CHENY, XU L, AGUSTI E, et al. Stability assessment and improvement of MTDC system connected with offshore wind farms[J]. IEEE Transactions on Power Delivery, 2024, 39(6):3347-3360] established an impedance model for a wind power transmission system via MMC-HVDC, and studied the system's oscillation stability mechanism using the Nyquist stability criterion and impedance amplitude-phase characteristics. The literature [Ren Bixing, Sun Rong, Li Qiang, et al. Stability analysis of outer loop control of grid-connected VSC under weak connection[J]. High Voltage Engineering, 2022, 48(02):762-771] established a state-space model of grid-connected VSC under weak connection, and analyzed the impact of outer loop control, such as DC voltage control and reactive power control, on stability using the Routh-Hurwitz criterion. The literature [Zhao Wei, Guo Chunyi, Zhang Shuwen, et al. Stability Limits and Improvement Methods of Photovoltaic Systems Transmitted via Flexible Direct Power under Weak AC Systems [J]. Electric Power Automation Equipment, 2024, 10(44):39-45] established a state-space model of a renewable energy system transmitted via flexible direct power under weak interconnection and analyzed the influence of photovoltaic output and short-circuit capacity. In addition, the literature [Li Yuguo, Yi Hao, Jiang Xin, et al. Exploration of the Mechanism of Low-Frequency Oscillation of Renewable Energy Grid-Connected Inverters under Extremely Weak Power Grids and Stability Improvement Strategies for Transient Reactive Power Overcompensation [J]. Proceedings of the CSEE, 2023, 43(02):482-496] established a simplified transfer function model of renewable energy grid-connected inverters under extremely weak power grids and analyzed the influence of multiple control loops and their interaction characteristics on the low-frequency stability of the system through frequency characteristics. However, the above modeling methods often start from the global system and can only passively observe the influence of the system's physical parameters and control parameters on the system stability through results such as root locus or Nyquist curves. That is, they analyze the key factors affecting the system stability from the perspective of phenomena, and therefore find it difficult to directly and effectively reveal the dynamic stability mechanism of DC system from the perspective of mechanism.

[0004] To this end, this invention proposes an equivalent circuit modeling and analysis method for the low-frequency dynamic characteristics of flexible DC transmission systems. This method clearly and intuitively reveals the stability mechanism of the system under small disturbances from an equivalent perspective, and quantitatively evaluates the impact of multiple control links and their interactions, as well as grid strength, through equivalent physical circuit parameters. [Summary of the Invention]

[0005] The purpose of this invention is to propose an equivalent circuit modeling and analysis method for the low-frequency dynamic characteristics of flexible DC transmission systems. This method overcomes the shortcomings of existing technologies by establishing a multi-branch equivalent circuit model of the DC voltage control unit connected to the weak network. It clearly and intuitively reveals that the equivalent LC circuit formed by the interaction between the DC voltage control unit and the power control unit is the root cause of the low-frequency small disturbance stability problem of the system. This is a simple and easy-to-implement modeling and analysis method.

[0006] The technical solution of this invention: A method for modeling and analyzing the equivalent circuit of low-frequency dynamic characteristics of a flexible DC transmission system, characterized by comprising the following steps:

[0007] (1) For the DC voltage control unit, ignoring the dynamics of the inner current loop control and linearizing it, the dynamics of the outer AC voltage control can be expressed as:

[0008]

[0009] Where "Δ" represents the small perturbation increment of the variable, v dcref and G vdc (s) represent the DC voltage reference value and transfer function for DC voltage control, respectively; v tref and G vac (s) represent the voltage reference value and transfer function for AC voltage control, respectively; Δv dc and Δv t These are the small disturbances to the VSC output DC voltage and the grid connection point voltage, respectively; where Δi d and Δi q These represent the d-axis current component and the q-axis current component in the dq reference frame, respectively.

[0010] (2) For the DC voltage control unit, the dynamics of the phase-locked loop (PLL) control can be expressed as:

[0011]

[0012] Where, Δθ pll G represents the phase angle difference obtained by the PLL from the phase-locked loop. pll (s) represents the transfer function of the PLL; Δθ represents the grid connection point voltage v. t The phase angle difference relative to the infinite grid voltage; v t0 This represents the steady-state value of the grid connection point voltage;

[0013] (3) The DQ and dq reference coordinate systems take counterclockwise rotation as the positive direction, and the Q(q) axis lags the D(d) axis by 90°. Therefore, the transformation relationship of the same physical quantity in the two reference systems is as follows:

[0014]

[0015] In the formula, x d and x q Let x represent the d-axis and q-axis components in the dq reference frame, respectively. D and x Q These represent the D and Q axis components in the DQ reference frame, respectively, and x represents the relevant voltage or current variable.

[0016] Based on the Park transformation and the coordinate transformation relationship in equation (3), the AC current of the DC voltage control unit and the voltage at the point of common coupling (PCC) satisfy the following relationships after linearization:

[0017]

[0018] Where, Δi D and Δi Q These represent the D-axis current component and the Q-axis current component, respectively; Δv D and Δv Q These represent the D-axis voltage component and the Q-axis voltage component, respectively.

[0019] (4) In the DQ reference coordinate system, the active power ΔP and reactive power ΔQ output by the voltage source converter (VSC) can be expressed as:

[0020]

[0021] In the formula, the subscript "0" represents the steady-state value of each variable;

[0022] (5) Voltage amplitude increment at grid connection point Δv t And the phase angle increment Δθ satisfies:

[0023]

[0024] Combining equations (1)-(6), the active power ΔP, phase angle increment Δθ, and AC voltage amplitude increment Δv can be expressed as follows: t The currents Δi on the d-axis and Δi respectively d and q-axis current Δi q and the PLL output phase angle Δθ pll The specific form of the coupling relationship between electrical quantities is shown in formula (7):

[0025]

[0026] In the formula, the specific expressions for the equivalent coefficients a1, a2, a3, b1, b2, c1, and c2 are as follows:

[0027]

[0028] In the formula, the subscript "0" represents the steady-state value of each variable, v g and v t Let X represent the amplitudes of the infinite grid voltage and the grid connection point voltage, respectively, and let θ represent the phase of the grid connection point voltage. g Indicates the inductance L of the AC line g The reactance value, in steady state, the phase θ0 of the grid-connected voltage is equal to the phase-locked loop angle θ. pll0 ;

[0029] Combining formulas (7) and (8), we can obtain the basic transfer function model as shown in formula (9), that is: the small disturbance increment Δi of the d-axis AC current component. d The fundamental transfer function relationship between the active power small disturbance increment ΔP and the small disturbance increment Δi of the AC current component on the d-axis. d The basic transfer function between the active power small disturbance increment ΔP and the PLL includes the equivalent transfer function H. pll (s), and the AC voltage control equivalent transfer function H vac (s) two branches, H pll (s) is Δi q With Δi d The functional relationship, H vac (s) is Δθ pll With Δi d The functional relationship; in the transfer function, ΔP is the output of the basic transfer function, Δi d The input is used in the basic transfer function, and the basic transfer function model is constructed according to formula (9);

[0030]

[0031] In the formula, G pll (s) represents the phase-locked loop controller, G vac (s) represents the controller of the AC voltage control loop;

[0032] (6) To facilitate the revelation of the impact of different control loop dynamics and interactions on system stability, based on the principle of equivalent transformation of transfer function in automatic control, the basic transfer function shown in formula (9) is further reorganized into a multi-branch transfer function form, which includes three branches: electrical loop connection T1(s), PLL control dynamic influence T2(s), and the dynamic influence of interaction between PLL and AC voltage control loop T3(s). The specific form is shown in formula (10):

[0033]

[0034] Based on the DC-side power balance relationship, the DC-side output voltage v of the DC voltage control unitdc and current i odc After linearization, we get the following:

[0035]

[0036] Furthermore, combining equations (1) and (11), the DC voltage control transfer function G is... vdc (s) and the small disturbance increment Δi of the d-axis AC current component d The multi-branch transfer functions T1(s), T2(s), and T3(s) between the active power small disturbance increment ΔP and the active power can be rearranged to obtain the equivalent DC voltage control transfer function G. vdceq The multi-branch form of (s) is shown in equation (12):

[0037]

[0038] In the formula, v dc0 G represents the steady-state value of the DC voltage output from the DC voltage control unit. i (s) represents G vdceq The equivalent transfer function of the i-th (i = 1, 2, 3) branch of (s).

[0039] At this time, the equivalent DC voltage control transfer function G vdceq The DC voltage control unit described by (s) includes three branch transfer functions: 1) G1(s) represents the direct influence of the DC voltage control loop; 2) G2(s) represents the dynamic interaction between DC voltage control and PLL; and 3) G3(s) represents the combined effect of DC voltage control, AC voltage control, and PLL.

[0040] Combining Equation (12) with the multi-branch transfer function model of the DC voltage control unit and Equation (11) with the DC-side output voltage v of the DC voltage control unit dc Current dynamics i in The DC voltage of the DC voltage control unit can be dynamically represented as follows:

[0041] Δv dc =Δv ref +Z s Δi in (13)

[0042] In the formula, Δv ref and Δv dc Z represents the small disturbance increments of the equivalent DC voltage source voltage and the output DC voltage of the DC voltage control unit, respectively. s The equivalent output impedance of the DC voltage control unit is, in specific form:

[0043]

[0044] In the formula, Δv dcref C represents the small disturbance increment of the DC voltage reference value of the DC voltage control unit. s P0 represents the output capacitor of the DC voltage control unit and the steady-state value of the AC side output active power.

[0045] To preserve the frequency characteristics near the dominant low-frequency mode, a dynamic link simplification method based on multimodal decomposition is used. The imaginary part of the dominant mode, s=jω0, is substituted into the equivalent transfer function G of the i-th (i=1,2,3) branch in formula (12). i (s), where ω0 is the dominant mode oscillation frequency, yields the following equivalent form:

[0046]

[0047] In the formula, k pueqi and k iueqi G i The equivalent proportional coefficient and integral coefficient of (s);

[0048] Combining the simplified processing methods of equation (12) and equation (15), G can be... vdceq (s) is rearranged into an equivalent PI element, as follows:

[0049]

[0050] In the formula, k pueq and k iueq G vdceq The equivalent proportional coefficient and integral coefficient of (s);

[0051] (7) Combining equations (13), (14) and (16), an equivalent multi-branch parallel circuit model of the DC voltage control unit can be established. This model includes three branches consisting of equivalent resistance, equivalent inductance and equivalent capacitance, respectively. The equivalent resistance represents the "direct influence of the DC voltage controller on the DC voltage dynamics alone", the equivalent inductance represents the "interaction between the DC voltage controller and the PLL, and their combined influence on the DC voltage dynamics", and the equivalent capacitance represents the "interaction between the DC voltage controller, the AC voltage controller and the PLL, and their combined influence on the DC voltage dynamics". The specific form of the equivalent resistance, equivalent inductance and equivalent capacitance branch circuit is as follows:

[0052]

[0053] In the formula, ΔI dcref R represents the small disturbance increment of the equivalent current source current of the DC voltage control unit; Ti L TiThese are the resistance and inductance parameters of the corresponding branch. The DC voltage control unit for weak network access includes at least two parallel RL circuit branches; where branch I represents the resistance R of branch I. T1 Inductance L of branch I T1 The parallel branch represents the direct impact of DC voltage control; branch II represents the resistance R of branch II. T2 And the inductor L of branch II T2 The parallel branch represents the dynamic interaction between DC voltage control and the phase-locked loop (PLL). Branch III represents the resistance R of branch III. T3 and the inductor L representing branch III T3 The parallel branches represent the combined effect of DC voltage control, AC voltage control, and the phase-locked loop (PLL).

[0054] The RL parallel circuit branches are not limited to two; the core logic of "at least two RL parallel circuit branches" is that the dynamic process of DC voltage control in a weak network has at least two non-mergeable characteristics: "main control dynamics" and "basic interaction dynamics with the PLL." These need to be modeled or controlled separately through two branches. This design is the minimum requirement for system stability in weak network scenarios and is also the basis for the subsequent expansion of this patent to a third branch (introducing interaction with AC voltage control). This patent derives three branches, ultimately deducing the modeling and representation of these three branches, characterizing the combined effects of DC voltage control, AC voltage control, and the phase-locked loop (PLL).

[0055] Combining equation (17), by aggregating multiple equivalent resistance branches and inductance branches, we can obtain the DC voltage control unit composed of the equivalent resistance R. s Equivalent inductance L s and equivalent capacitance C s The equivalent lumped multi-branch parallel model formed by parallel connections takes the following form:

[0056]

[0057] The constant power control unit adopts a circuit model consisting of an equivalent resistance and an output capacitor connected in parallel, as follows:

[0058]

[0059] In the formula, Z p The equivalent impedance of the constant power control unit is ΔI. pref and Δi p These represent the equivalent current source current transformation and the output current disturbance of the constant power control unit, respectively, Δv p C represents the DC voltage disturbance at the outlet. p and R p These represent the DC capacitance and equivalent resistance at the outlet, respectively. P cpl This represents the steady-state power of the constant power control unit, with the output DC bus being positive.

[0060] Combining the DC voltage control unit of equation (17) and the dynamics of the constant power control unit of equation (19), a reduced-order model of the equivalent circuit of the flexible DC transmission system can be obtained. This model is derived from the equivalent circuit model Z of the DC voltage control unit. s and constant power control unit model Z p The total parallel impedance Z formed by parallel connection all The composition is as shown in formula (20):

[0061]

[0062] Let Z all With the denominator of the expression equal to 0, we can further obtain the specific form of the second-order characteristic equation of the flexible DC transmission system as follows:

[0063]

[0064] Since the system damping coefficient is mainly affected by DC voltage control, AC inductance, PLL control, and DC transmission power, a decrease in the proportional coefficient of DC voltage control, an increase in the integral coefficient of DC voltage control, an increase in AC inductance, an increase in transmission power, and a decrease in the proportional coefficient of PLL control all lead to a decrease in the damping coefficient. Similarly, the oscillation frequency is mainly affected by DC capacitance, the integral coefficient of DC voltage control, the proportional coefficient of PLL control, AC inductance, and transmission power. An increase in DC capacitance, a decrease in the integral coefficient of DC voltage control, an increase in the proportional coefficient of PLL control, a decrease in AC inductance, and a decrease in DC transmission power all lead to a decrease in the oscillation frequency. Therefore, when the flexible DC transmission system is in an underdamped state, the damping coefficient ζ and damped oscillation frequency ω of the flexible DC transmission system, as shown in formula (22), can be used. d Two dynamic characteristic indicators are used to evaluate the stability of the system under low-frequency small disturbances. After the system is subjected to a small disturbance, whether the oscillation amplitude can quickly converge to a stable state can be used to analyze the low-frequency dynamic characteristics of the flexible DC transmission system.

[0065]

[0066] Based on the proposed reduced-order modeling method of equivalent circuit for flexible DC transmission systems, the influence of DC voltage control, AC voltage control, and phase-locked loop control dynamics and their interactions on the low-frequency dynamics of flexible DC transmission systems can be intuitively and quantitatively analyzed through equivalent resistance, equivalent inductance, and dynamic characteristic indicators. This reveals the low-frequency dynamic mechanism of flexible DC transmission systems from the perspective of equivalent circuits.

[0067] The principle of this invention:

[0068] Taking into account the influence of factors such as outer loop AC voltage control and phase-locked loop, a multi-branch equivalent circuit model of DC voltage control unit connected to weak network is established by deriving the basic transfer function, extending the basic transfer function to a multi-branch transfer function model, DC voltage dynamic modeling, and after model simplification and equivalence.

[0069] Based on the equivalent resistance, equivalent inductance and other equivalent physical circuit parameters of the corresponding equivalent RL circuit branches, the influence of multiple control links and their interactions, grid strength and other factors is quantitatively evaluated. After obtaining the equivalent RLC circuit model of the DC side of the whole system, it is revealed that the equivalent LC circuit formed by the DC voltage control unit and the power control unit through the DC network interaction is the root cause of the system's low-frequency small disturbance stability problem.

[0070] Advantages of the present invention:

[0071] (1) A multi-branch parallel circuit model of the DC voltage control unit based on equivalent resistance and equivalent inductance was established. Each circuit branch is obtained by the dynamics and interaction of multiple control loops such as DC voltage control, AC voltage control and phase-locked loop control, which facilitates the explanation of the physical meaning of multiple control links and their interaction from the perspective of equivalent circuit. Thus, a complete equivalent circuit model of the flexible DC transmission system composed of equivalent resistance, equivalent inductance and equivalent capacitance was obtained.

[0072] (2) The influence of the dynamics and interactions of multiple control loops such as AC voltage control, DC voltage control and phase-locked loop control on the low-frequency dynamic characteristics of flexible DC transmission system can be intuitively and quantitatively analyzed through equivalent resistance and equivalent inductance, revealing the low-frequency dynamic mechanism of flexible DC transmission system from the perspective of equivalent circuit. [Attached Image Description]

[0073] Figure 1 This is a schematic diagram of the core process of DC-side reduced-order modeling and analysis of the equivalent circuit modeling and analysis method for low-frequency dynamic characteristics of a flexible DC transmission system involved in this invention.

[0074] Figure 2 This is a schematic diagram of the topology of a flexible DC transmission system, which is the basis for the modeling and analysis method of the equivalent circuit of the low-frequency dynamic characteristics of a flexible DC transmission system according to the present invention.

[0075] Figure 3 This is a schematic diagram of the DC voltage control unit topology and control strategy of the equivalent circuit modeling and analysis method for low-frequency dynamic characteristics of a flexible DC transmission system involved in this invention.

[0076] Figure 4 The small disturbance increment Δi of the d-axis AC current component in the equivalent circuit modeling and analysis method for the low-frequency dynamic characteristics of a flexible DC transmission system involved in this invention. dA schematic diagram illustrating the evolution of the multi-branch transfer function model to a small disturbance increment ΔP in active power. (Whereinafter, Figure 4 -a indicates the basic model. Figure 4 -b indicates a multi-branch model.

[0077] Figure 5 This is a schematic diagram illustrating the evolution of the multi-branch transfer function model of the DC voltage control unit in the equivalent circuit modeling and analysis method for the low-frequency dynamic characteristics of a flexible DC transmission system according to the present invention. (Whereinafter, Figure 5 -a is the basic model. Figure 5 -b indicates a multi-branch model.

[0078] Figure 6 This is a schematic diagram illustrating the evolution of the equivalent circuit model of the DC voltage control unit in the equivalent circuit modeling and analysis method for low-frequency dynamic characteristics of a flexible DC transmission system according to the present invention. (Whereinafter, Figure 6 -a is the equivalent multi-branch detailed parallel circuit model. Figure 6 -b indicates an equivalent lumped multi-branch parallel model.

[0079] Figure 7 This is the equivalent circuit model of the flexible DC transmission system in the modeling and analysis method of the low-frequency dynamic characteristics of the flexible DC transmission system involved in this invention.

[0080] Figure 8 The AC voltage control proportional coefficient k in the embodiments of the present invention puac Schematic diagram of the impact on equivalent resistance, equivalent inductance and dynamic characteristic indicators (where, Figure 8 -a indicates equivalent conductance. Figure 8 -b indicates equivalent susceptance, Figure 8 -c indicates the damping coefficient. Figure 8 -d indicates the oscillation frequency.

[0081] Figure 9 The AC voltage control proportional coefficient k in the embodiments of the present invention puac A schematic diagram of the simulation results during the change.

[0082] Figure 10 The integral coefficient k for AC voltage control in the embodiments of the present invention iuac Schematic diagram of the impact on equivalent resistance, equivalent inductance and dynamic characteristic indicators (where, Figure 10 -a indicates equivalent conductance. Figure 10 -b indicates equivalent susceptance, Figure 10 -c indicates the damping coefficient. Figure 10 -d indicates the oscillation frequency.

[0083] Figure 11 The integral coefficient k for AC voltage control in the embodiments of the present invention iuacA schematic diagram of the simulation results during the change.

Detailed Implementation Methods

[0084] Example 1

[0085] A method for modeling and analyzing the equivalent circuit of low-frequency dynamic characteristics of a flexible DC transmission system, characterized by comprising the following steps:

[0086] (1) For the DC voltage control unit, ignoring the dynamics of the inner current loop control and linearizing it, the dynamics of the outer AC voltage control can be expressed as:

[0087]

[0088] Where "Δ" represents the small perturbation increment of the variable, v dcref and G vdc (s) represent the DC voltage reference value and transfer function for DC voltage control, respectively; v tref and G vac (s) represent the voltage reference value and transfer function for AC voltage control, respectively; Δv dc and Δv t These are the small disturbances to the VSC output DC voltage and the grid connection point voltage, respectively; where Δi d and Δi q These represent the d-axis current component and the q-axis current component in the dq reference frame, respectively.

[0089] (2) For the DC voltage control unit, the dynamics of the phase-locked loop (PLL) control can be expressed as:

[0090]

[0091] Where, Δθ pll G represents the phase angle difference obtained by the PLL from the phase-locked loop. pll (s) represents the transfer function of the PLL; Δθ represents the grid connection point voltage v. t The phase angle difference relative to the infinite grid voltage; v t0 This represents the steady-state value of the grid connection point voltage;

[0092] (3) The DQ and dq reference coordinate systems take counterclockwise rotation as the positive direction, and the Q(q) axis lags the D(d) axis by 90°. Therefore, the transformation relationship of the same physical quantity in the two reference systems is as follows:

[0093]

[0094] In the formula, x d and x q Let x represent the d-axis and q-axis components in the dq reference frame, respectively. D and x QThese represent the D and Q axis components in the DQ reference frame, respectively, and x represents the relevant voltage or current variable.

[0095] Based on the Park transformation and the coordinate transformation relationship in equation (3), the AC current of the DC voltage control unit and the voltage at the point of common coupling (PCC) satisfy the following relationships after linearization:

[0096]

[0097] Where, Δi D and Δi Q These represent the D-axis current component and the Q-axis current component, respectively; Δv D and Δv Q These represent the D-axis voltage component and the Q-axis voltage component, respectively.

[0098] (4) In the DQ reference coordinate system, the active power ΔP and reactive power ΔQ output by the voltage source converter (VSC) can be expressed as:

[0099]

[0100] In the formula, the subscript "0" represents the steady-state value of each variable;

[0101] (5) Voltage amplitude increment at grid connection point Δv t And the phase angle increment Δθ satisfies:

[0102]

[0103] Combining equations (1)-(6), the active power ΔP, phase angle increment Δθ, and AC voltage amplitude increment Δv can be expressed as follows: t The currents Δi on the d-axis and Δi respectively d and q-axis current Δi q and the PLL output phase angle Δθ pll The specific form of the coupling relationship between electrical quantities is shown in formula (7):

[0104]

[0105] In the formula, the specific expressions for the equivalent coefficients a1, a2, a3, b1, b2, c1, and c2 are as follows:

[0106]

[0107] In the formula, the subscript "0" represents the steady-state value of each variable, v g and v tLet X represent the amplitudes of the infinite grid voltage and the grid connection point voltage, respectively, and let θ represent the phase of the grid connection point voltage. g Indicates the inductance L of the AC line g The reactance value, in steady state, the phase θ0 of the grid-connected voltage is equal to the phase-locked loop angle θ. pll0 ;

[0108] Combining formulas (7) and (8), the basic transfer function model shown in formula (9) can be derived through the following derivation. Focusing on the system's own disturbances, the small phase disturbance Δθ of the grid voltage is... grid Δv vref It can be considered as 0. The basic transfer function model is: The d-axis AC current component has a small disturbance increment Δi. d The fundamental transfer function relationship between the active power small disturbance increment ΔP and the small disturbance increment Δi of the AC current component on the d-axis. d The basic transfer function between the active power small disturbance increment ΔP and the PLL includes the equivalent transfer function H. pll (s), and the AC voltage control equivalent transfer function H vac (s) two branches, H pll (s) is Δi q With Δi d The functional relationship, H vac (s) is Δθ pll With Δi d The functional relationship; in the transfer function, ΔP is the output of the basic transfer function, Δi d The input is used in the basic transfer function, and the basic transfer function model is constructed according to formula (9);

[0109] PLL tracking of grid phase can be dynamically simplified as follows:

[0110] Δθ pll =G pll (s)(Δθ grid -Δθ)

[0111] Combining equation (7) and eliminating Δθ, we get:

[0112]

[0113] The AC voltage is kept constant, and the dynamic process can be simplified as follows:

[0114] Δi q =G vac (s)(Δv vref -Δv t )

[0115] Combining equation (7), eliminate Δv t ,get:

[0116]

[0117] In the formula, G pll (s) represents the phase-locked loop controller, G vac (s) represents the controller of the AC voltage control loop;

[0118] (6) To facilitate the revelation of the impact of different control loop dynamics and interactions on system stability, based on the principle of equivalent transformation of transfer function in automatic control, the basic transfer function shown in formula (9) is further reorganized into a multi-branch transfer function form, which includes three branches: electrical loop connection T1(s), PLL control dynamic influence T2(s), and the dynamic influence of interaction between PLL and AC voltage control loop T3(s). The specific form is shown in formula (10):

[0119]

[0120] Based on the DC-side power balance relationship, the DC-side output voltage v of the DC voltage control unit dc and current i odc This is just... Figure 2 The definitions of output voltage and current in the equation, after linearization and adding Δ, yield the following result:

[0121]

[0122] Furthermore, combining equations (1) and (11), the DC voltage control transfer function G is... vdc (s) and the small disturbance increment Δi of the d-axis AC current component d The multi-branch transfer functions T1(s), T2(s), and T3(s) between the active power small disturbance increment ΔP and the active power can be rearranged to obtain the equivalent DC voltage control transfer function G. vdceq The multi-branch form of (s) is shown in equation (12):

[0123]

[0124] In the formula, v dc0 G represents the steady-state value of the DC voltage output from the DC voltage control unit. i (s) represents G vdceq The equivalent transfer function of the i-th (i = 1, 2, 3) branch of (s).

[0125] At this time, the equivalent DC voltage control transfer function G vdceqThe DC voltage control unit described by (s) includes three branch transfer functions: 1) G1(s) represents the direct influence of the DC voltage control loop; 2) G2(s) represents the dynamic interaction between DC voltage control and PLL; and 3) G3(s) represents the combined effect of DC voltage control, AC voltage control, and PLL.

[0126] Combining Equation (12) with the multi-branch transfer function model of the DC voltage control unit and Equation (11) with the DC-side output voltage v of the DC voltage control unit dc Current dynamics i in The DC voltage of the DC voltage control unit can be dynamically represented as follows:

[0127] Δv dc =Δv ref +Z s Δi in (13)

[0128] In the formula, Δv ref and Δv dc Z represents the small disturbance increments of the equivalent DC voltage source voltage and the output DC voltage of the DC voltage control unit, respectively. s The equivalent output impedance of the DC voltage control unit is, in specific form:

[0129]

[0130] In the formula, Δv dcref C represents the small disturbance increment of the DC voltage reference value of the DC voltage control unit. s P0 represents the output capacitor of the DC voltage control unit and the steady-state value of the AC side output active power.

[0131] To preserve the frequency characteristics near the dominant low-frequency mode, a dynamic link simplification method based on multimodal decomposition is used. The imaginary part of the dominant mode, s=jω0, is substituted into the equivalent transfer function G of the i-th (i=1,2,3) branch in formula (12). i (s), where ω0 is the dominant mode oscillation frequency, yields the following equivalent form:

[0132]

[0133] In the formula, k pueqi and k iueqi G i The equivalent proportional coefficient and integral coefficient of (s);

[0134] Combining the simplified processing methods of equation (12) and equation (15), G can be... vdceq (s) is rearranged into an equivalent PI element, as follows:

[0135]

[0136] In the formula, k pueq and k iueq G vdceq The equivalent proportional coefficient and integral coefficient of (s);

[0137] (7) Combining equations (13), (14) and (16), an equivalent multi-branch parallel circuit model of the DC voltage control unit can be established. This model includes three branches consisting of equivalent resistance, equivalent inductance and equivalent capacitance respectively. (This patent mainly simplifies and equivalences the small-signal model to form three branches. Each branch contains multiple branches with resistance, capacitance and inductance. Equivalent resistance represents the "direct influence of the DC voltage controller on the DC voltage dynamics alone", equivalent inductance represents the "interaction between the DC voltage controller and PLL, jointly affecting the DC voltage dynamics", and equivalent capacitance represents the "interaction between the DC voltage controller, AC voltage controller and PLL, jointly affecting the DC voltage dynamics"). The equivalent resistance, equivalent inductance and equivalent capacitance branch circuits are as follows:

[0138]

[0139] In the formula, ΔI dcref R represents the small disturbance increment of the equivalent current source current of the DC voltage control unit; Ti L Ti These are the resistance and inductance parameters of the corresponding branch. The DC voltage control unit for weak network access includes at least two parallel RL circuit branches; where branch I represents the resistance R of branch I. T1 Inductance L of branch I T1 The parallel branch represents the direct impact of DC voltage control; branch II represents the resistance R of branch II. T2 And the inductor L of branch II T2 The parallel branch represents the dynamic interaction between DC voltage control and the phase-locked loop (PLL). Branch III represents the resistance R of branch III. T3 and the inductor L representing branch III T3 The parallel branches represent the combined effect of DC voltage control, AC voltage control, and the phase-locked loop (PLL).

[0140] The RL parallel circuit branches are not limited to two; the core logic of "at least two RL parallel circuit branches" is that the dynamic process of DC voltage control in a weak network has at least two non-mergeable characteristics: "main control dynamics" and "basic interaction dynamics with the PLL." These need to be modeled or controlled separately through two branches. This design is the minimum requirement for system stability in weak network scenarios and is also the basis for the subsequent expansion of this patent to a third branch (introducing interaction with AC voltage control). This patent derives three branches, ultimately deducing the modeling and representation of these three branches, characterizing the combined effects of DC voltage control, AC voltage control, and the phase-locked loop (PLL).

[0141] Combining equation (17), by aggregating multiple equivalent resistance branches and inductance branches, we can obtain the DC voltage control unit composed of the equivalent resistance R. s Equivalent inductance L s and equivalent capacitance C s The equivalent lumped multi-branch parallel model formed by parallel connections takes the following form:

[0142]

[0143] The constant power control unit adopts a circuit model consisting of an equivalent resistance and an output capacitor connected in parallel, as follows:

[0144]

[0145] In the formula, Z p The equivalent impedance of the constant power control unit is ΔI. pref and Δi p These represent the equivalent current source current transformation and the output current disturbance of the constant power control unit, respectively, Δv p C represents the DC voltage disturbance at the outlet. p and R p These represent the DC capacitance and equivalent resistance at the outlet, respectively. P cpl This represents the steady-state power of the constant power control unit, with the output DC bus being positive.

[0146] Combining the DC voltage control unit of equation (17) and the dynamics of the constant power control unit of equation (19), a reduced-order model of the equivalent circuit of the flexible DC transmission system can be obtained. This model is derived from the equivalent circuit model Z of the DC voltage control unit. s and constant power control unit model Z p The total parallel impedance Z formed by parallel connection all The composition is as shown in formula (20):

[0147]

[0148] Let Z allWith the denominator of the expression equal to 0, we can further obtain the specific form of the second-order characteristic equation of the flexible DC transmission system as follows:

[0149]

[0150] Since the system damping coefficient is mainly affected by DC voltage control, AC inductance, PLL control, and DC transmission power, a decrease in the proportional coefficient of DC voltage control, an increase in the integral coefficient of DC voltage control, an increase in AC inductance, an increase in transmission power, and a decrease in the proportional coefficient of PLL control all lead to a decrease in the damping coefficient. Similarly, the oscillation frequency is mainly affected by DC capacitance, the integral coefficient of DC voltage control, the proportional coefficient of PLL control, AC inductance, and transmission power. An increase in DC capacitance, a decrease in the integral coefficient of DC voltage control, an increase in the proportional coefficient of PLL control, a decrease in AC inductance, and a decrease in DC transmission power all lead to a decrease in the oscillation frequency. Therefore, when the flexible DC transmission system is in an underdamped state, the damping coefficient ζ and damped oscillation frequency ω of the flexible DC transmission system, as shown in formula (22), can be used. d Two dynamic characteristic indicators are used to evaluate the stability of the system under low-frequency small disturbances. After the system is subjected to a small disturbance, whether the oscillation amplitude can quickly converge to a stable state can be used to analyze the low-frequency dynamic characteristics of the flexible DC transmission system.

[0151]

[0152] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below.

[0153] Example 2

[0154] A method for modeling and analyzing the equivalent circuit of low-frequency dynamic characteristics of a flexible DC transmission system, comprising the following steps:

[0155] Taking into account the influence of factors such as outer loop AC voltage control and phase-locked loop, the basic transfer function between the small disturbance increment of d-axis AC current component and the small disturbance increment of active power is derived. The basic transfer function is then extended to a multi-branch transfer function model. Combined with the dynamics of DC voltage control, after model simplification and equivalence, a multi-branch equivalent circuit model of DC voltage control unit connected to weak network is established.

[0156] The impact of multiple control links and their interactions, as well as power grid strength, is quantitatively assessed based on the equivalent physical circuit parameters such as equivalent resistance and equivalent inductance of the corresponding equivalent RL circuit branches.

[0157] By combining the dynamics of the DC voltage control unit and the constant power control unit, the equivalent RLC circuit model of the DC side of the whole system is obtained. On the one hand, it can clearly and intuitively reveal that the equivalent LC circuit formed by the interaction of the DC voltage control unit and the constant power control unit is the root cause of the system's low-frequency small disturbance stability problem. On the other hand, the system impedance analysis is carried out by establishing the total parallel impedance expression.

[0158] Example 3

[0159] The following section provides a further explanation of the scheme in Example 2, using specific calculation formulas. The core idea of ​​DC-side order reduction modeling and analysis can be found in [link to relevant documentation]. Figure 1 See the description below for details:

[0160] The flexible DC transmission system topology considered in this invention is as follows: Figure 2 As shown, the DC voltage control unit adopts DC voltage control to maintain DC voltage stability and power balance; the AC grid can be flexibly interconnected with the DC line through the adopted voltage source converter (VSC); the constant power control unit (converter #2) adopts a constant power control strategy. Figure 2 In the middle, v dc and i odc These are the DC voltage and DC current output from the DC voltage control unit (converter station #1), respectively; C s and i in These are the output capacitor of the DC voltage control unit and the DC current injected into the DC voltage control unit, respectively; C sp and i p These are the output capacitor and DC current injection on the DC side of the constant power control unit (converter station #2); Z line These are the impedances of the DC line.

[0161] DC voltage control unit topology and its control strategy, such as Figure 3 As shown. v g ∠0 and v t ∠θ represents the amplitude and phase of the infinite grid voltage and the voltage at the grid connection point, respectively; L f This represents the filter inductance; P and Q represent the active and reactive power outputs on the AC side, respectively, with the direction of flow towards the AC grid as positive. L g This represents the inductance of an AC line, whose magnitude is negatively correlated with the strength of the power grid. It can be adjusted by changing the line inductance L. g Simulates AC power grids of varying sizes and intensities. abc and i abc These represent the three-phase AC voltage and current on the AC side, respectively. The two rotating coordinate systems, DQ and dq, are both established with counterclockwise rotation as the positive direction, and the Q(q) axis lags the D(d) axis by 90°. d and v qLet i represent the voltage components along the d-axis and q-axis in the dq coordinate system, respectively. d and i q V represents the d-axis and q-axis current components in the dq-axis coordinate system, respectively. D and v Q Let i represent the voltage components along the D-axis and Q-axis in the DQ coordinate system, respectively. D and i Q These represent the current components along the D-axis and Q-axis in the DQ-axis coordinate system, respectively.

[0162] The DC voltage control unit system includes DC voltage control, AC voltage control, phase-locked loop (PLL) control, and current inner loop control. dcref and G vdc (s) represent the DC voltage reference value and the controller value, respectively, of the DC voltage control loop; v tref and G vac (s) represent the AC voltage reference value and the controller in the AC voltage control loop, respectively. The phase-locked loop control is used to obtain the phase at the grid connection point and provide a coordinate reference. G pll (s) represents the phase-locked loop controller, θ pll Indicates the phase-locked angle. i dref and i qref These are the d-axis current reference values ​​and q-axis current reference values ​​for the inner current loop control, respectively.

[0163] Reduced-order modeling of the equivalent circuit of the DC voltage control unit

[0164] Since this invention focuses on the low-frequency dynamic characteristics of flexible DC systems, the influence of the fast-dynamic inner-loop current control is ignored. Figure 3 The topology and control strategy of the DC voltage control unit are presented, and linearization is performed at the steady-state operating point to obtain the small disturbance increment Δi of the AC current component of the DC voltage control unit on the d-axis. d The basic transfer function model with small active power disturbance increment ΔP is as follows: Figure 4 -a is shown.

[0165] For the DC voltage control unit, neglecting the dynamics of the inner current loop control and linearizing it, the dynamics of the outer loop control can be expressed as:

[0166]

[0167] Where "Δ" represents the small perturbation increment of the variable, v dcref and G vdc (s) represent the DC voltage reference value and transfer function for DC voltage control, respectively; v tref and G vac (s) represent the voltage reference value and transfer function for AC voltage control, respectively.

[0168] For a DC voltage control unit, the dynamics of a phase-locked loop (PLL) can be expressed as:

[0169]

[0170] Where, Δθ pll G represents the phase angle difference obtained by the PLL from the phase-locked loop. pll (s) represents the transfer function of the PLL; Δθ represents the grid connection point voltage v. t The phase angle difference relative to the infinite grid voltage; v t0 This represents the steady-state voltage at the grid connection point.

[0171] The DQ and dq reference coordinate systems are positively rotated counterclockwise, with the Q(q) axis lagging the D(d) axis by 90°. The transformation relationship of the same physical quantity between the two reference systems is as follows:

[0172]

[0173] In the formula, x d and x q Let x represent the d-axis and q-axis components in the dq reference frame, respectively. D and x Q These represent the D and Q axis components in the DQ reference frame, respectively, and x represents the relevant voltage or current variable.

[0174] Based on the Park transformation and the coordinate transformation relationship in equation (3), the AC current of the DC voltage control unit and the voltage at the point of common coupling (PCC) satisfy the following relationships after linearization:

[0175]

[0176] Where, Δi D and Δi Q These represent the D-axis and Q-axis current components, respectively; Δi d and Δi q These represent the d-axis and q-axis current components, respectively; Δ vD and Δv Q Representing the D-axis and Q-axis voltage components respectively; θ pll This represents the phase-locked angle obtained by the PLL.

[0177] Based on the voltage and current components in the DQ reference frame, the active power ΔP and reactive power ΔQ output of the voltage source converter VSC can be expressed as:

[0178]

[0179] In the formula, the subscript "0" represents the steady-state value of each variable.

[0180] Grid connection point voltage amplitude increment Δv t And the phase angle increment Δθ satisfies:

[0181]

[0182] Combining equations (1)-(6), the active power ΔP, phase angle increment Δθ, and AC voltage amplitude increment Δv can be expressed as follows: t The currents Δi on the d-axis and Δi respectively d and q-axis current Δi q and the PLL output phase angle Δθ pll The specific form is as follows:

[0183]

[0184] In the formula, the specific expressions for the equivalent coefficients a1, a2, a3, b1, b2, c1, and c2 are as follows:

[0185]

[0186] In the formula, the subscript "0" represents the steady-state value of each variable, v g and v t Let X represent the amplitudes of the infinite grid voltage and the grid connection point voltage, respectively, and let θ represent the phase of the grid connection point voltage. g Indicates the inductance L of the AC line g The reactance value, in steady state, the phase θ0 of the grid-connected voltage is equal to the phase-locked loop angle θ. pll0 .

[0187] Combining the dynamics of the outer loop AC voltage control (1), the dynamics of the phase-locked loop control (2), and the coupling relationship between electrical quantities (7), we can obtain the basic transfer function model of equation (9), where the small disturbance increment Δi of the AC current component on the d-axis is given. d The basic transfer function relationship between the active power small disturbance increment ΔP and the active power is as follows: Figure 4 As shown in -a, the small disturbance increment Δi of the AC current component on the d-axis. d The basic transfer function between the active power small disturbance increment ΔP and the PLL includes the equivalent transfer function H. pll (s) and AC voltage control equivalent transfer function H vac (s) Two branches, ΔP is the output of the basic transfer function, Δi d This is the input in the basic transfer function. H pll (s) and H vac (s) are in the following specific forms:

[0188]

[0189] To better reveal the impact of the dynamics and interactions of different control loops on system stability, further based on the principle of equivalent transformation of transfer functions in automatic control, Δi d The transfer function between ΔP and ΔP is rearranged into a multi-branch transfer function form, containing three branches: T1(s), T2(s), and T3(s), as follows: Figure 4 As shown in -b, the specific forms of the transfer functions for the three branches T1(s), T2(s), and T3(s) are as follows:

[0190]

[0191] In equation (10), T1(s) represents the inherent electrical circuit connection, T2(s) represents the dynamic influence of PLL control, and T3(s) represents the interactive dynamic influence between PLL and AC voltage control link.

[0192] Combination Figure 3 The DC voltage control unit topology and its control strategy, based on the DC-side power balance relationship and after linearization, yield the DC-side output voltage v of the DC voltage control unit. dc Current dynamics i odc as follows:

[0193]

[0194] Combining equation (1) with the dynamic control of the outer loop DC voltage and equation (10) Δi d The transfer function between ΔP and DC voltage control unit is reorganized into a multi-branch transfer function and equation (11) to obtain the DC voltage control unit's DC side output voltage and current dynamics. This gives the basic model of the DC voltage control unit, which is the small disturbance Δv of the DC voltage reference value controlled by the DC voltage. dcref Small disturbance Δv of DC voltage at VSC output dcref The transfer function relationship between them, such as Figure 5 -a is shown.

[0195] This leads to the DC voltage control transfer function G vdc (s) and Δi d By rearranging the transfer functions (T1(s), T2(s), and T3(s)) of each branch with respect to the active power ΔP, the equivalent DC voltage control transfer function G can be obtained. vdceq The multi-branch form of (s), such as Figure 5 As shown in -b, the specific expression is as follows:

[0196]

[0197] In the formula, v dc0 G represents the steady-state value of the DC voltage output from the DC voltage control unit. i (s) represents G vdceqThe equivalent transfer function of the i-th (i = 1, 2, 3) branch of (s).

[0198] As can be seen from equation (12), there are three branch transfer functions in the DC voltage control unit: 1) G1(s) represents the direct influence of the DC voltage control link; 2) G2(s) represents the dynamic influence of the interaction between DC voltage control and PLL; 3) G3(s) represents the influence of the combined action of DC voltage control, AC voltage control and PLL.

[0199] based on Figure 5 The multi-branch transfer function model of the DC voltage control unit obtained by -b still cannot intuitively reveal the low-frequency dynamic mechanism of the flexible DC transmission system from the perspective of equivalent circuit, and the physical meaning of the impact of multiple control loops and their interactions on the low-frequency dynamics of the system is not clear. Therefore, this invention... Figure 5 Based on the model obtained from -b, the equivalent circuit model of the flexible DC system is further derived, revealing the low-frequency dynamic characteristic mechanism of the flexible DC system from the perspective of the equivalent circuit. The detailed modeling steps are as follows.

[0200] Combining the multi-branch transfer function model of the DC voltage control unit (12) and the dynamics of the DC-side output voltage and current of the DC voltage control unit (11), the dynamics of the DC voltage control unit can be expressed as follows:

[0201] Δv dc =Δv ref +Z s Δi in (13)

[0202] In the formula, Δv ref Z represents the small disturbance increment of the equivalent DC voltage source voltage of the DC voltage control unit. s The equivalent output impedance of the DC voltage control unit is, in specific form:

[0203]

[0204] In the formula, Δv dcref C represents the small disturbance increment of the DC voltage reference value of the DC voltage control unit. s P0 represents the output capacitor of the DC voltage control unit and the steady-state value of the AC side output active power.

[0205] To preserve the frequency characteristics near the dominant low-frequency mode, a dynamic link simplification method based on multimodal decomposition is used, substituting s = jω0 (the imaginary part of the dominant mode, where ω0 is the oscillation frequency of the dominant mode) into G in equation (12). i (s) yields the following equivalent form:

[0206]

[0207] In the formula, k pueqi and k iueqi G i The equivalent proportional coefficient and integral coefficient of (s).

[0208] Combining the simplified processing methods of equation (12) and equation (15), G can be... vdceq (s) is rearranged into an equivalent PI element, as follows:

[0209]

[0210] In the formula, k pueq and k iueq G vdceq The equivalent proportional coefficient and integral coefficient of (s).

[0211] Combining equations (13), (14), and (16), an equivalent multi-branch parallel circuit model of the DC voltage control unit can be established. The model includes multiple branches with equivalent resistance, equivalent inductance, and equivalent capacitance, such as... Figure 6 As shown in -a, the specific form is as follows:

[0212]

[0213] In the formula, ΔI dcref This indicates the small disturbance increment of the current in the equivalent current source of the DC voltage control unit.

[0214] Combining equation (17), by aggregating and equivalencing multiple equivalent resistance branches and inductance branches, an equivalent lumped multi-branch parallel model of the DC voltage control unit, consisting of equivalent resistance, equivalent inductance, and equivalent capacitance connected in parallel, can be obtained, as shown below. Figure 6 As shown in -b, the specific form is as follows:

[0215]

[0216] Reduced-order model of complete equivalent circuit of flexible DC transmission system

[0217] The constant power control unit adopts a circuit model consisting of an equivalent resistance and an output capacitor connected in parallel, as follows:

[0218]

[0219] In the formula, Z p The equivalent impedance of the constant power control unit is ΔI. pref and Δi p These represent the equivalent current source current transformation and the output current disturbance of the constant power control unit, respectively, Δv p C represents the DC voltage disturbance at the outlet. p and R pThese represent the DC capacitance and equivalent resistance at the outlet, respectively. P cpl This indicates the steady-state power of the constant power control unit (positive when flowing out of the DC bus).

[0220] Combining the DC voltage control unit of equation (17) and the dynamics of the constant power control unit of equation (19), a reduced-order model of the equivalent circuit of the flexible DC transmission system can be obtained, such as... Figure 7 As shown, the model consists of the equivalent circuit model Z of the DC voltage control unit. s and constant power control unit model Z p The total parallel impedance Z formed by parallel connection all Composition, total parallel impedance Z all The specific format is as follows:

[0221]

[0222] Combining equation (20), let Z all With the denominator of the expression equal to 0, the specific form of the second-order characteristic equation of the flexible DC transmission system is as follows:

[0223]

[0224] When the flexible DC transmission system is in an underdamped state, the damping coefficient ζ and the damping oscillation frequency ω of the flexible DC transmission system... d Two dynamic characteristic indices are used to evaluate the system's stability under low-frequency small disturbances, and their analytical expressions can be expressed as:

[0225]

[0226] Based on the proposed reduced-order modeling method for the equivalent circuit of flexible DC transmission systems, the impact of DC voltage control, AC voltage control, and PLL control dynamics and their interactions on the low-frequency dynamics of flexible DC transmission systems can be intuitively and quantitatively analyzed through equivalent resistance, equivalent inductance, and dynamic characteristic indices. This reveals the low-frequency dynamic mechanism of flexible DC systems from the perspective of equivalent circuits. The system damping coefficient is mainly affected by DC voltage control, AC inductance, PLL control, and DC transmission power. Decreasing the proportional coefficient of DC voltage control, increasing the integral coefficient of DC voltage control, increasing the AC inductance, increasing the transmission power, and decreasing the proportional coefficient of PLL control all lead to a decrease in the damping coefficient. The oscillation frequency is mainly affected by DC capacitance, the integral coefficient of DC voltage control, the proportional coefficient of PLL control, AC inductance, and transmission power. Increasing the DC capacitance, decreasing the integral coefficient of DC voltage control, increasing the proportional coefficient of PLL control, decreasing the AC inductance, and decreasing the DC transmission power all lead to a decrease in the oscillation frequency.

[0227] Analysis and Verification

[0228] Not generally, with Figure 2Taking the flexible DC transmission system shown as an example, analysis and verification are performed. The DC voltage control unit employs both constant DC voltage control and constant AC voltage control strategies. A detailed model of the flexible DC transmission system is built in PSCAD / EMTDC for simulation verification. The basic system parameters are shown in Table 1.

[0229] Table 1 Basic parameters of DC transmission system

[0230]

[0231] First, we analyze the influence of the AC voltage control proportional coefficient, specifically the AC voltage control proportional coefficient k. puac The effects on equivalent resistance, equivalent inductance, and dynamic characteristics are as follows: Figure 8 As shown. The corresponding time-domain simulation results are as follows. Figure 9 As shown. By Figure 8 It can be seen that, with the AC voltage control proportional coefficient k puac Increased, the equivalent conductance 1 / R is affected by the combined effects of AC voltage control, DC voltage control, and PLL. T3 Increase (see) Figure 8 -a) Total parallel conductance of DC voltage control unit 1 / R s Mainly affected by 1 / R T3 The effect increases, and the system damping increases (see...). Figure 8 -c); DC voltage control unit total parallel susceptance 1 / L s Almost unchanged (see) Figure 8 -b), the oscillation frequency decreases (see...). Figure 8 -d). By Figure 9 It can be seen that as the AC voltage control proportional coefficient increases, the DC voltage fluctuation decreases and the system damping increases, consistent with the theoretical analysis. Furthermore, the DC voltage dynamics of the proposed reduced-order model almost perfectly match the results of the detailed model, verifying the effectiveness of the proposed modeling and analysis method. Therefore, the proposed modeling and analysis method can clearly and intuitively reveal the influence path of the AC voltage control proportional coefficient on the low-frequency dynamics of the system from the perspective of the equivalent circuit. The degree of influence of changes in the AC voltage control proportional coefficient on the low-frequency dynamics of the system can be quantitatively analyzed through the equivalent resistance, equivalent inductance, damping coefficient, and oscillation frequency of the corresponding branch circuits.

[0232] Next, we analyze the influence of the integral coefficient of AC voltage control, specifically the integral coefficient k of AC voltage control. iuac The effects on equivalent resistance, equivalent inductance, and dynamic characteristics are as follows: Figure 10 As shown. The corresponding time-domain simulation results are as follows. Figure 11 As shown. By Figure 10 -a indicates that, with the AC voltage control integral coefficient k iuac Increased, the equivalent conductance 1 / R is affected by the combined effects of AC voltage control, DC voltage control, and PLL. T3As the current increases, the equivalent conductance of other pathways remains almost unchanged, and the total parallel conductance of the DC voltage control unit is 1 / R. s Mainly affected by 1 / R T3 The effect increases, and the system damping increases (see...). Figure 10 -c), the oscillation frequency decreases (see...). Figure 10 -d); Figure 10 -b indicates that the equivalent susceptance 1 / L, influenced by the combined effects of DC voltage control, reactive power control, and PLL, is... T3 Slightly increase the total parallel susceptance of the DC voltage control unit by 1 / L. s Slightly increased. From Figure 11 As can be seen, increasing the integral coefficient of AC voltage control reduces DC voltage fluctuation and enhances system damping, which is consistent with theoretical analysis and verifies the feasibility of implementing this patent.

Claims

1. A method for modeling and analyzing the equivalent circuit of low-frequency dynamic characteristics of a flexible DC transmission system, characterized in that... It includes the following steps: (1) For the DC voltage control unit, ignoring the dynamics of the inner current loop control and linearizing it, the dynamics of the outer AC voltage control can be expressed as: Where "Δ" represents the small perturbation increment of the variable, v dcref and G vdc (s) represent the DC voltage reference value and transfer function for DC voltage control, respectively; v tref and G vac (s) represent the voltage reference value and transfer function for AC voltage control, respectively; Δv dc and Δv t These are the small disturbances to the VSC output DC voltage and the grid connection point voltage, respectively; where Δi d and Δi q These represent the d-axis current component and the q-axis current component in the dq reference frame, respectively. (2) For the DC voltage control unit, the dynamics of the phase-locked loop (PLL) control can be expressed as: Where, Δθ pll G represents the phase angle difference obtained by the PLL from the phase-locked loop. pll (s) represents the transfer function of the PLL; Δθ represents the grid connection point voltage v. t The phase angle difference relative to the infinite grid voltage; v t0 This represents the steady-state voltage at the grid connection point; (3) The DQ and dq reference coordinate systems take counterclockwise rotation as the positive direction, and the Q(q) axis lags the D(d) axis by 90°. Therefore, the transformation relationship of the same physical quantity in the two reference systems is as follows: In the formula, x d and x q Let x represent the d-axis and q-axis components in the dq reference frame, respectively. D and x Q These represent the D and Q axis components in the DQ reference frame, respectively, and x represents the relevant voltage or current variable. (4) In the DQ reference coordinate system, the active power ΔP and reactive power ΔQ output by the voltage source converter VSC can be expressed as: In the formula, the subscript "0" represents the steady-state value of each variable; Δi D and Δi Q These represent the D-axis current component and the Q-axis current component, respectively; Δv D and Δv Q These represent the D-axis voltage component and the Q-axis voltage component, respectively. (5) Voltage amplitude increment at grid connection point Δv t And the phase angle increment Δθ satisfies: The active power ΔP, phase angle increment Δθ, and AC voltage amplitude increment Δv are calculated. t The d-axis current Δi d and q-axis current Δi q and the PLL output phase angle Δθ pll The specific form of the coupling relationship between electrical quantities is shown in formula (6): In the formula, the specific expressions for the equivalent coefficients a1, a2, a3, b1, b2, c1, and c2 are as follows: In the formula, the subscript "0" represents the steady-state value of each variable, v g and v t Let X represent the amplitudes of the infinite grid voltage and the grid connection point voltage, respectively, and let θ represent the phase of the grid connection point voltage. g Indicates the inductance L of the AC line g The reactance value, in steady state, the phase θ0 of the grid-connected voltage is equal to the phase-locked loop angle θ. pll0 ; Combining formulas (6) and (7), we can obtain the basic transfer function model as shown in formula (8), that is: the small disturbance increment Δi of the d-axis AC current component. d The fundamental transfer function relationship between the active power small disturbance increment ΔP and the small disturbance increment Δi of the AC current component on the d-axis. d The basic transfer function between the active power small disturbance increment ΔP and the PLL includes the PLL equivalent transfer function H. pll (s), and the AC voltage control equivalent transfer function H vac (s) Two branches, H pll (s) is Δi q With Δi d The functional relationship, H vac (s) is Δθ pll With Δi d The functional relationship; in the transfer function, ΔP is the output of the basic transfer function, Δi d The input is used in the basic transfer function, and the basic transfer function model is constructed according to formula (8); In the formula, G pll (s) represents the phase-locked loop controller, G vac (s) represents the controller of the AC voltage control loop; (6) The basic transfer function shown in formula (8) is reorganized into a multi-branch transfer function form, which includes three branches: electrical loop connection T1(s), PLL control dynamic influence T2(s), and interactive dynamic influence between PLL and AC voltage control loop T3(s). The specific form is shown in formula (10): Based on the DC-side power balance relationship, the DC-side output voltage v of the DC voltage control unit dc and current i odc After linearization, we get the following: Furthermore, combining equations (1) and (10), the DC voltage control transfer function G is... vdc (s) and the small disturbance increment Δi of the d-axis AC current component d The multi-branch transfer functions T1(s), T2(s), and T3(s) between the active power small disturbance increment ΔP and the active power can be rearranged to obtain the equivalent DC voltage control transfer function G. vdceq The multi-branch form of (s) is shown in equation (11): In the formula, v dc0 G represents the steady-state value of the DC voltage output from the DC voltage control unit. i (s) represents G vdceq The equivalent transfer function of the i-th branch of (s); Combining Equation (11) with the multi-branch transfer function model of the DC voltage control unit and Equation (10) with the DC-side output voltage v of the DC voltage control unit dc Current dynamics i in The DC voltage of the DC voltage control unit can be dynamically represented as follows: Δv dc =Δv ref +Z s Δi in (12) In the formula, Δv ref and Δv dc Z represents the small disturbance increments of the equivalent DC voltage source voltage and the output DC voltage of the DC voltage control unit, respectively. s The equivalent output impedance of the DC voltage control unit; To preserve the frequency characteristics near the dominant low-frequency mode, a dynamic link simplification method based on multimodal decomposition is used. The imaginary part of the dominant mode, s = jω0, is substituted into the equivalent transfer function G of the i-th branch in formula (11). i (s), where ω0 is the dominant mode oscillation frequency, yields the following equivalent form: In the formula, k pueqi and k iueqi G i The equivalent proportional coefficient and integral coefficient of (s); Combining the simplified processing methods of equations (12) and (13), G can be... vdceq (s) is rearranged into an equivalent PI element, as follows: In the formula, k pueq and k iueq G vdceq The equivalent proportional coefficient and integral coefficient of (s); (7) Establish an equivalent multi-branch parallel circuit model for the DC voltage control unit. This model contains three branches, each consisting of equivalent resistance, equivalent inductance, and equivalent capacitance, as shown below: In the formula, ΔI dcref R represents the small disturbance increment of the equivalent current source current of the DC voltage control unit; Ti L Ti These are the resistance and inductance parameters for the corresponding branch; Combining equation (15), by aggregating and equivalencing multiple equivalent resistance branches and inductance branches, the DC voltage control unit can be obtained from the equivalent resistance R. s Equivalent inductance L s and equivalent capacitance C s The equivalent lumped multi-branch parallel model formed by parallel connections takes the following form: The constant power control unit adopts a circuit model consisting of an equivalent resistance and an output capacitor connected in parallel, as follows: In the formula, Z p The equivalent impedance of the constant power control unit is ΔI. pref and Δi p These represent the equivalent current source current transformation and the output current disturbance of the constant power control unit, respectively, Δv p C represents the DC voltage disturbance at the outlet. p and R p These represent the outlet DC capacitance and equivalent resistance, respectively. P cpl This represents the steady-state power of the constant power control unit, with the output DC bus being positive. Combining the DC voltage control unit of equation (15) and the dynamics of the constant power control unit of equation (17), a reduced-order model of the equivalent circuit of the flexible DC transmission system can be obtained. This model is derived from the equivalent circuit model Z of the DC voltage control unit. s and constant power control unit model Z p The total parallel impedance Z formed by parallel connection all The composition is as shown in formula (18): Let Z all With the denominator of the expression equal to 0, we can further obtain the specific form of the second-order characteristic equation of the flexible DC transmission system as follows: When the flexible DC transmission system is in an underdamped state, the damping coefficient ζ and damping oscillation frequency ω of the flexible DC transmission system can be used as shown in formula (20). d Two dynamic characteristic indicators are used to evaluate the stability of the system under low-frequency small disturbances. After the system is subjected to a small disturbance, whether the oscillation amplitude can quickly converge to a stable state can be used to analyze the low-frequency dynamic characteristics of the flexible DC transmission system.

2. The method for modeling and analyzing the equivalent circuit of low-frequency dynamic characteristics of a flexible DC transmission system according to claim 1, characterized in that... Step (3) is based on the Park transformation. Combined with the coordinate transformation relationship of equation (3), the AC current of the DC voltage control unit and the PCC voltage after linearization can satisfy the following relationships: Where, Δi D and Δi Q These represent the D-axis current component and the Q-axis current component, respectively; Δv D and Δv Q These represent the D-axis voltage component and the Q-axis voltage component, respectively.

3. The method for modeling and analyzing the equivalent circuit of low-frequency dynamic characteristics of a flexible DC transmission system according to claim 2, characterized in that... The equivalent DC voltage control transfer function G in step (6) vdceq The DC voltage control unit described in (s) includes three branch transfer functions, namely: 1) G1(s) represents the direct influence of the DC voltage control loop; 2) G2(s) represents the dynamic interaction between DC voltage control and PLL; 3) G3(s) represents the combined effect of DC voltage control, AC voltage control, and PLL.

4. The method for modeling and analyzing the equivalent circuit of low-frequency dynamic characteristics of a flexible DC transmission system according to claim 3, characterized in that... In step (6), the equivalent DC voltage source voltage Δv of the DC voltage control unit ref and the equivalent output impedance Z of the DC voltage control unit s The specific form is: In the formula, Δv dcref C represents the small disturbance increment of the DC voltage reference value of the DC voltage control unit. s P0 represents the output capacitor of the DC voltage control unit and the steady-state value of the AC side output active power.

5. The method for modeling and analyzing the equivalent circuit of low-frequency dynamic characteristics of a flexible DC transmission system according to claim 3, characterized in that... The equivalent multi-branch parallel circuit model of the DC voltage control unit in step (7) specifically refers to the DC voltage control unit for weak network access containing at least two RL parallel circuit branches; where branch I represents the resistance R of branch I. T1 Inductance L of branch I T1 The parallel branch represents the direct impact of DC voltage control; branch II represents the resistance R of branch II. T2 And the inductor L of branch II T2 The parallel branch represents the dynamic interaction between DC voltage control and the phase-locked loop (PLL). Branch III represents the resistance R of branch III. T3 and the inductor L representing branch III T3 The parallel branches represent the combined effect of DC voltage control, AC voltage control, and the phase-locked loop (PLL).

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