High-frequency oscillation suppression method and device of MMC-HVDC system

Abstract

The invention discloses a high-frequency oscillation suppression method and device of an MMC-HVDC system, and belongs to the technical field of stable control of a flexible direct-current power transmission system. In order to solve the problem of 1000-2500Hz high-frequency oscillation caused by the non-minimum phase characteristic of the MMC caused by control link delay, a system high-frequency impedance model containing delay is constructed, and an oscillation mechanism dominated by the non-minimum phase characteristic is clarified; a third-order high-pass filter is connected in parallel to a PCC point of the MMC and the alternating current power grid, parameters of the filter are optimized to enable the filter to achieve-90-degree phase compensation in a negative damping interval, and meanwhile the active power loss of fundamental waves is reduced; the impedance characteristic is researched through an impedance detection method, the high-frequency oscillation risk is judged, and the remodeling effect is verified to suppress oscillation; the negative damping characteristic of the system is eliminated fundamentally, the suppression effect is better than that of a traditional passive filter, the influence on the steady-state and transient-state characteristics of the system is small, different power grid working conditions are adapted, and the engineering practicability is high.

Description

Technical Field

[0001] This invention belongs to the field of stable control technology for flexible DC transmission systems, and relates to a method and apparatus for suppressing high-frequency oscillations in MMC-HVDC systems. Specifically, it relates to a passive damping suppression method and apparatus for high-frequency oscillations in MMC-HVDC systems caused by non-minimum phase characteristics due to control link delay. Background Technology

[0002] Modular multilevel converter high-voltage direct current (MMC-HVDC) is a core solution for realizing long-distance, large-scale grid connection of renewable energy in modern flexible DC transmission systems. With the widespread application of flexible DC projects, the potential high-frequency oscillation problem has gradually emerged, seriously threatening the safe and stable operation of the system. Therefore, research on high-frequency oscillation suppression of MMC-HVDC systems has become a key direction in the field of power systems.

[0003] In existing technologies, the suppression strategies for high-frequency oscillations in MMC-HVDC systems are mainly divided into two categories: active impedance reshaping and passive impedance reshaping. Active impedance reshaping methods achieve suppression by adding filters or control loops inside the MMC system, but they often cannot eliminate negative damping across the entire frequency band, and the system is prone to generating new oscillations when the grid operating conditions change. Passive impedance reshaping methods, such as adding high-pass filters, achieve suppression by blocking oscillations at specific frequencies, which is more robust. However, traditional passive filters introduce significant active power losses at the fundamental frequency, limiting their engineering practicality.

[0004] Research has found that the typical non-minimum phase characteristics of the MMC (such as right-half-plane zeros and phase lag) in the high-frequency range are one of the root causes of high-frequency oscillations, and this characteristic is mainly caused by the system control link delay. The control link delay makes the MMC a non-minimum phase system, and the existence of the right-half-plane zeros expands the frequency range of high-frequency oscillations, causing the MMC impedance to exhibit negative damping characteristics. When the MMC exhibits negative damping characteristics, it couples with the inductive impedance of the AC system, and the phase difference between the two exceeds 180°, which easily excites high-frequency oscillations in the 1000-2500Hz range.

[0005] Current research on high-frequency oscillation suppression in MMC-HVDC systems dominated by non-minimum phase characteristics remains insufficient. Existing suppression strategies do not fully consider the impact of non-minimum phase characteristics, making it difficult to achieve effective phase compensation and eliminate negative damping while simultaneously reducing fundamental active power loss. Furthermore, they exhibit poor adaptability to different grid operating conditions. Therefore, there is an urgent need to develop a high-frequency oscillation suppression scheme adapted to the non-minimum phase characteristics of MMC, which can effectively suppress oscillations over a wide frequency band, reduce fundamental power loss, and improve adaptability to different grid operating conditions. Summary of the Invention

[0006] To address the problems of residual negative damping, excessive fundamental active power loss, and poor adaptability to grid conditions in existing high-frequency oscillation suppression strategies for MMC-HVDC systems, this invention provides a high-frequency oscillation suppression method and apparatus for MMC-HVDC systems. The aim is to clarify the oscillation mechanism dominated by non-minimum phase characteristics from the perspective of impedance interaction, and to achieve precise phase compensation and impedance reshaping through a passive damping scheme. This effectively suppresses high-frequency oscillations while reducing fundamental active power loss, without degrading the system's steady-state power control and transient fault response.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for suppressing high-frequency oscillations in an MMC-HVDC system includes:

[0009] (1) Construct a high-frequency impedance model of the MMC-HVDC system with control link delay, study the equivalent impedance of MMC and the equivalent impedance of AC power grid through impedance detection method, clarify the high-frequency oscillation mechanism dominated by non-minimum phase characteristics, and analyze whether the MMC-HVDC system oscillates at high frequency.

[0010] (2) Connect a third-order high-pass filter in parallel at the common coupling point PCC between the MMC and the AC power grid;

[0011] (3) The parameters of the third-order high-pass filter are optimized to provide -90° phase compensation and reduce the active power loss at the fundamental frequency. The impedance transfer function of the third-order high-pass filter is verified by the Routh criterion to have no right half-plane zeros, ensuring that the third-order high-pass filter is a minimum phase system.

[0012] (4) The equivalent impedance of MMC and the equivalent impedance of AC power grid are studied by impedance detection method. The effect of the third-order high-pass filter on the reshaping effect of the equivalent impedance of MMC-HVDC system is verified, and the high-frequency oscillation of MMC-HVDC system is suppressed.

[0013] Furthermore, the construction of the high-frequency impedance model of the MMC-HVDC system including control link delay specifically includes:

[0014] Ignoring the effects of phase-locked loop, power outer loop, circulating current suppression, and current inner loop decoupling on high-frequency impedance, the control process of the MMC is simplified, and the open-loop equivalent impedance expression of the MMC is derived. and closed-loop equivalent impedance expression :

[0015] (1)

[0016] (2)

[0017] (3)

[0018] (4)

[0019] in, Let be a complex variable representing the frequency in the Laplace transform domain; MMC equivalent reactance; Transfer function for the current inner loop PI controller; This is the proportional gain of the inner current loop; This is the inner loop integral gain of the current; and These are the voltage feedforward delay and current measurement delay of the MMC-HVDC system, respectively. and These are the voltage feedforward delay and current measurement delay times for the MMC-HVDC system, respectively. is the base of the natural logarithm.

[0020] Furthermore, the study of the equivalent impedance of the MMC and the equivalent impedance of the AC power grid using impedance detection methods clarifies the high-frequency oscillation mechanism dominated by non-minimum phase characteristics and analyzes whether the MMC-HVDC system experiences high-frequency oscillations. Specifically, this includes:

[0021] Phase margin Used to evaluate the stability of the MMC-HVDC system:

[0022] (5)

[0023] in, The equivalent impedance of the AC power grid; Need to retrieve and Frequency of the intersection point of the amplitude curves; The phase of the equivalent impedance of the AC power grid; The phase of the MMC equivalent impedance;

[0024] According to the Nyquist stability criterion, when When the value is greater than 0, the MMC-HVDC system can operate stably; according to The constraints will The expression can be rewritten as the stability criterion for oscillations in an MMC-HVDC system:

[0025] (6)

[0026] As the frequency increases, The amplitude is much greater than The amplitude, therefore the MMC phase mainly depends on In the high-frequency range, it approximates pure inductive characteristics; the voltage feedforward delay is approximated using a first-order padde expansion:

[0027] (7)

[0028] The equivalent impedance ratio expression containing the zeros of the right half-plane is obtained. :

[0029] (8)

[0030] (9)

[0031] (10)

[0032] in, This refers to the internal equivalent impedance of the MMC. The non-minimum phase zero influence factor introduced for voltage feedforward delay;

[0033] The phase is determined by the phase difference between the numerator and the denominator, therefore phase Represented as:

[0034] (11)

[0035] in, The imaginary unit; Angular frequency;

[0036] The high-frequency equivalent impedance phase of the MMC has an additional phase shift due to the non-minimum phase characteristic of the MMC, which increases the equivalent impedance phase of the MMC. The explicit control link delay causes the MMC to exhibit non-minimum phase characteristics. The zero point of the right half plane expands the high-frequency oscillation frequency range. When the MMC impedance phase is greater than 90°, it exhibits negative damping characteristics. When the phase difference with the capacitive impedance of the AC grid exceeds 180°, it triggers high-frequency oscillation.

[0037] Furthermore, the parallel connection of a third-order high-pass filter at the common coupling point (PCC) between the MMC and the AC power grid specifically includes:

[0038] A third-order high-pass filter consists of two parts connected in series, including a capacitor. ,inductance ,resistance and capacitor It is connected in parallel at the common junction point PCC; the first part is a capacitor. The second part is the resistor. and capacitor Series branch and inductor Parallel connection of branches; the third-order high-pass filter is connected one-to-one in parallel to the corresponding phase high-voltage bus of PCC at the three-phase input terminals A, B, and C. The third-order high-pass filter is connected in parallel with the MMC grid-connected main circuit and the AC grid side circuit.

[0039] The third-order high-pass filter provides -90° phase cancellation. The resulting phase gain is compensated by This causes phase lead; it reduces the phase difference between the MMC and the equivalent impedance of the AC power grid to within 180°.

[0040] Furthermore, the optimization design of the parameters of the third-order high-pass filter specifically includes:

[0041] Determine the capacitor based on the reactive power requirements of the MMC-HVDC system. The value of satisfies ,in For MMC-HVDC system power frequency; This is the rated voltage for the MMC-HVDC system; For reactive power in MMC-HVDC systems;

[0042] Design inductor The value of makes the capacitor With inductance At the target tuning angular frequency Resonance at the point, satisfying , The target tuning angular frequency;

[0043] Set resistor With capacitor The impedance of a series branch at the fundamental frequency is higher than that of an inductor. The impedance satisfies , Reduce fundamental active power loss;

[0044] The Routh criterion is used to verify that the impedance transfer function of the third-order high-pass filter has no zeros in the right half-plane, ensuring that the third-order high-pass filter is a minimum-phase system. , , .

[0045] Furthermore, the capacitor The value is 3.6μF, and the inductance is... The value is 2814mH, resistance The value is greater than or equal to 1250Ω, capacitor The value is less than or equal to 3.6 μF.

[0046] Furthermore, the control link delay ranges from 400 to 600 μs, corresponding to a negative damping range of 1000 to 2500 Hz for the MMC system.

[0047] Furthermore, the impedance detection method is used to study the equivalent impedance of MMC and the AC grid impedance, and the effect of the third-order high-pass filter on the reshaping effect of the equivalent impedance of the MMC-HVDC system is verified as follows: the phase difference between the equivalent impedance of MMC and the AC grid impedance is less than 180°, eliminating the negative damping characteristics of the system and avoiding high-frequency oscillations.

[0048] An apparatus for implementing a high-frequency oscillation suppression method for an MMC-HVDC system, comprising:

[0049] The modeling and analysis module is used to construct a high-frequency impedance model of the MMC-HVDC system with control link delay, and to clarify the high-frequency oscillation mechanism dominated by non-minimum phase characteristics.

[0050] The parameter optimization module is used to optimize the parameters of the third-order high-pass filter, so that the parallel third-order high-pass filter can effectively suppress high-frequency oscillations and minimize the fundamental frequency active power loss, and verify that the impedance transfer function of the third-order high-pass filter has no right half-plane zeros.

[0051] The impedance analysis and verification module is used to study the equivalent impedance of MMC and AC power grid, analyze whether the MMC-HVDC system experiences high-frequency oscillations, and verify the reshaping effect of the third-order high-pass filter on the equivalent impedance of the MMC-HVDC system.

[0052] Furthermore, the modeling and analysis module includes a unit for constructing a high-frequency impedance model and a unit for analyzing high-frequency oscillations;

[0053] The high-frequency impedance model building unit is used to build a high-frequency impedance model of the MMC-HVDC system including control link delay.

[0054] The high-frequency oscillation analysis unit is used to study the equivalent impedance of MMC and the equivalent impedance of AC power grid through impedance detection method, clarify the high-frequency oscillation mechanism dominated by non-minimum phase characteristics, and analyze whether the MMC-HVDC system experiences high-frequency oscillation.

[0055] The parameter optimization module includes a third-order high-pass filter parameter optimization unit and a third-order high-pass filter impedance verification unit.

[0056] The third-order high-pass filter parameter optimization unit is used to optimize the parameters of the third-order high-pass filter so that the third-order high-pass filter provides -90° phase compensation in the 1000-2500Hz negative damping range, while reducing the active power loss at the fundamental frequency.

[0057] The verification unit for the impedance of the third-order high-pass filter is used to verify that the impedance transfer function of the third-order high-pass filter has no zeros in the right half-plane through the Routh criterion, thus ensuring that the third-order high-pass filter is a minimum-phase system.

[0058] The impedance analysis and verification module includes an impedance analysis unit and a verification module unit;

[0059] The impedance analysis unit is used to study the equivalent impedance of the MMC and the equivalent impedance of the AC power grid by means of impedance detection after connecting a third-order high-pass filter in parallel at the common connection point PCC between the MMC and the AC power grid.

[0060] The verification module unit is used to verify the reshaping effect of the third-order high-pass filter on the equivalent impedance of the MMC-HVDC system, thereby suppressing high-frequency oscillations in the MMC-HVDC system.

[0061] The beneficial effects of this invention are as follows:

[0062] This invention clarifies the high-frequency oscillation mechanism of the MMC-HVDC system dominated by the non-minimum phase characteristics caused by the control link delay from the perspective of impedance interaction. It reveals that the expansion of the oscillation frequency range at the right half-plane zero point and the phase difference of more than 180° between the MMC negative damping impedance and the AC grid capacitive impedance are the core reasons for the oscillation. This provides a precise theoretical basis for high-frequency oscillation suppression and solves the problem of insufficient analysis of the oscillation mechanism in existing research.

[0063] The passive damping scheme for the third-order high-pass filter designed in this invention, through... , , and The coordinated action of the two filters achieves a -90° phase compensation in the 1000-2500Hz negative damping range, effectively offsetting the phase lead caused by the non-minimum phase characteristic, pulling the MMC impedance phase back to the stable region, and making the impedance phase difference between the MMC and the AC power grid less than 180°. This fundamentally eliminates the negative damping characteristic of the MMC and achieves effective suppression of high-frequency oscillations. Compared with second-order high-pass filters and C-type filters, the suppression effect is stronger.

[0064] This invention optimizes the parameter design of a third-order high-pass filter to achieve... and The series branch exhibits high impedance characteristics at the fundamental frequency, which significantly reduces the active power loss at the fundamental frequency and solves the engineering pain point of excessive power loss in traditional passive filters. At the same time, the filter is verified as a minimum phase system by the Routh criterion, which ensures the stability of the filter itself and improves the overall robustness of the MMC-HVDC system.

[0065] The suppression method and device proposed in this invention have minimal impact on the steady-state and transient characteristics of the MMC-HVDC system. After the filter is connected, the AC voltage, current, and power step response of the system are basically the same as those without filtering. The system can still quickly recover stability under transient conditions such as three-phase short-circuit faults. Moreover, this solution has good adaptability to different control link delays and different power grid conditions, providing a low-loss and high-reliability solution for high-frequency oscillation suppression of the MMC-HVDC system. Attached Figure Description

[0066] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings:

[0067] Figure 1 This is a simplified control model diagram of the MMC high-frequency band of the present invention;

[0068] Figure 2 This is the equivalent circuit diagram for the stability analysis of the MMC-HVDC system based on impedance analysis according to the present invention.

[0069] Figure 3 The diagram shows the calculated impedance characteristics of the MMC, minimum phase MMC, and AC power grid in this invention.

[0070] Figure 4 This is a topology diagram of the third-order high-pass filter of the present invention;

[0071] Figure 5 This is a diagram showing the effect of phase superposition at different frequencies and delays according to the present invention;

[0072] Figure 6 The impedance characteristics of the third-order high-pass filter of this invention are shown in the figure.

[0073] Figure 7 This is a diagram showing the effect of the third-order high-pass filter of this invention on the A-phase voltage of the AC bus in the system.

[0074] Figure 8 This is a diagram showing the effect of the third-order high-pass filter of this invention on the A-phase current of the AC bus in the system.

[0075] Figure 9 This is a diagram showing the effect of the third-order high-pass filter of this invention on the power step of the system characteristics;

[0076] Figure 10 This is a diagram showing the effect of the third-order high-pass filter of this invention on the AC bus current under short-circuit faults in the system.

[0077] Figure 11 This is a verification diagram of the oscillation suppression effect of the present invention under AC bus voltage with a delay of 500μs;

[0078] Figure 12This is a verification diagram of the oscillation suppression effect under the FFT analysis results of the bus voltage of the present invention;

[0079] Figure 13 This is a graph showing the change in active power between a second-order high-pass filter and a C-type filter, as presented in this invention.

[0080] Figure 14 This invention presents a comparison of reactive power variations between a second-order high-pass filter and a C-type filter.

[0081] Figure 15 This is a verification diagram of the oscillation suppression effect of the third-order high-pass filter before and after its connection, based on the impedance comparison.

[0082] Figure 16 This is a diagram showing the AC voltage of the inverter-side MMC before and after applying a third-order high-pass filter during oscillation in this invention.

[0083] Figure 17 This is a flowchart of a high-frequency oscillation suppression method for an MMC-HVDC system according to the present invention. Detailed Implementation

[0084] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0085] Definitions of core terms:

[0086] MMC (Modular Multilevel Converter): A modular multilevel converter, which consists of multiple cascaded submodules with identical structures. The submodules can be classified into three types: half-H-bridge, full-H-bridge, and dual-clamped submodules.

[0087] MMC-HVDC (Modular Multilevel Converter based High Voltage DirectCurrent): A modular multilevel converter-based high voltage direct current transmission system, it is the core topology of flexible direct current transmission and is suitable for scenarios such as large-scale grid connection of renewable energy and cross-regional power transmission.

[0088] Non-minimum phase system: refers to a system with time delay or one or more zeros or poles in the right half plane. Such systems are prone to phase lag, undershoot of step response, etc., and have poor stability.

[0089] PCC (Point of Common Coupling): The common connection point refers to the connection node between the MMC converter and the AC power grid. It is the core node for realizing grid connection and electrical quantity interaction.

[0090] Third-order high-pass filter: refers to a third-order passive filter circuit that has passband characteristics for high-frequency signals and stopband characteristics for low-frequency signals. In this invention, it is used to perform phase compensation and impedance reshaping of the high-frequency impedance of MMC.

[0091] like Figure 4 As shown, the high-frequency oscillation suppression method of the MMC-HVDC system of the present invention is based on the core of connecting a third-order high-pass filter in parallel at the common connection point PCC between the MMC and the AC power grid, and using an impedance detection method to analyze the system impedance.

[0092] A third-order high-pass filter consists of two parts connected in series, including a capacitor. ,inductance ,resistance and capacitor It is connected in parallel at the common junction point PCC. The first part is a capacitor. The second part is the resistor. and capacitor Series branch and inductor Parallel connection of branches. A third-order high-pass filter is connected in parallel one-to-one with the corresponding phase high-voltage bus of the PCC at the three-phase input terminals A, B, and C of the AC power grid. The third-order high-pass filter, the MMC grid-connected main circuit, and the AC power grid side circuit are in pure parallel connection. This topology achieves high-frequency signal passband through the resonant characteristics of capacitors and inductors, and phase compensation through the damping characteristics of resistors. and The series connection reduces fundamental power loss.

[0093] The designed third-order high-pass filter can provide a -90° phase to offset the phase gain caused by the non-minimum phase characteristic, effectively compensating for phase lead. This phase compensation brings the MMC equivalent impedance back to the positive damping region, reducing the phase difference between the MMC and the AC grid equivalent impedance to within 180°, thereby mitigating the instability caused by the non-minimum phase characteristic and improving system stability.

[0094] Impedance detection method: By collecting key electrical quantity information between the MMC module and the AC power grid, including the MMC output voltage and current and the equivalent impedance of the AC power grid, the equivalent impedance of the MMC is obtained using impedance modeling and parameter calculation. and grid impedance Furthermore, by combining the phase characteristics of both components in the high-frequency band, we analyzed whether the phase difference between them exceeded 180°, assessed the risk of high-frequency oscillation in the system, and verified the suppression effect of the third-order high-pass filter on the high-frequency oscillation of the MMC-HVDC system.

[0095] like Figure 17 As shown, the high-frequency oscillation suppression method of the MMC-HVDC system of the present invention is based on the oscillation mechanism analysis of non-minimum phase characteristics and achieves impedance reshaping through passive filtering. The specific implementation steps are as follows:

[0096] 1. Construct a high-frequency impedance model with control link delay to clarify the high-frequency oscillation mechanism dominated by non-minimum phase characteristics;

[0097] (1) such as Figure 1 As shown, ignoring the effects of the phase-locked loop, power outer loop, circulating current suppression, and current inner loop decoupling on the high-frequency impedance of the MMC, the high-frequency control process of the MMC is simplified. Only the core components of current inner loop PI control, voltage feedforward delay, and current measurement delay are retained, and the open-loop impedance expression of the MMC is derived. and closed-loop impedance expression :

[0098] (1)

[0099] (2)

[0100] (3)

[0101] (4)

[0102] in, Let be a complex variable representing the frequency in the Laplace transform domain; MMC equivalent reactance; Transfer function for the current inner loop PI controller; This is the proportional gain of the inner current loop; This is the inner loop integral gain of the current; and These are the voltage feedforward delay and current measurement delay of the system, respectively; and These are the system's voltage feedforward delay and current measurement delay, respectively. is the base of the natural logarithm;

[0103] (2) such as Figure 2As shown, the equivalent circuit of MMC can be represented by a current source in parallel with a resistor. AC systems are generally equivalent to a voltage source in series with a resistor, and the connection point is the voltage at the PCC point. Impedance analysis essentially equates a complex system to a power source and a resistor connected in series and parallel. It is simple to calculate and suitable for stability analysis of complex systems. The impedance ratio expression can be used to... Stability analysis is performed; therefore, the study of high-frequency oscillations in MMC-HVDC systems focuses on the stability of the closed-loop system formed by the MMC and the AC power grid, and the phase margin. It can be used to evaluate the stability of MMC-HVDC systems:

[0104] (5)

[0105] in, The equivalent impedance of the AC power grid; Need to retrieve and Frequency of the intersection point of the amplitude curves; The phase of the equivalent impedance of the AC power grid; The phase of the MMC equivalent impedance;

[0106] According to the Nyquist stability criterion, when When the value is greater than 0, the system can operate stably; according to The constraints can The expression is rewritten as the stability criterion for oscillation in the MMC-HVDC system. When formula (6) is satisfied, the MMC-HVDC system oscillates at high frequency.

[0107] (6)

[0108] With increasing frequency The amplitude is much greater than The amplitude, therefore the MMC phase mainly depends on In the high-frequency range, it approximates pure inductive characteristics; the voltage feedforward delay is approximated using a first-order padde expansion:

[0109] (7)

[0110] The equivalent impedance ratio expression containing the zeros of the right half-plane is obtained. :

[0111] (8)

[0112] (9)

[0113] (10)

[0114] in, This refers to the internal equivalent impedance of the MMC. The non-minimum phase zero influence factor introduced for voltage feedforward delay;

[0115] (3) such as Figure 5 As shown, The phase is determined by the phase difference between the numerator and the denominator, therefore phase Represented as:

[0116] (11)

[0117] in, The imaginary unit; Angular frequency;

[0118] Combined with the target frequency, ,in Let be the frequency; =1000-2500Hz, =500μs. The calculation results show that when At 1000Hz, =115°; when At 2500Hz, =151.4°. Therefore, in the 1000-2500Hz range, the high-frequency impedance phase of the MMC exhibits an additional phase shift due to its non-minimum phase characteristic. At this point, the phase range of the MMC exceeds 90° from 115° to 151.4°, resulting in a negative damping effect. Explicitly controlling the link delay causes the MMC to exhibit non-minimum phase characteristics; the minimum phase difference between the MMC's impedance and the capacitive impedance of the AC system reaches 195°, exceeding the 180° stability threshold, thus increasing the risk of oscillation.

[0119] (4) such as Figure 3As shown, the phase angle of the AC system impedance is between ±90°. Due to the negative damping characteristic of the MMC, there is a risk of oscillation between the two. The calculated impedances of both the MMC and the minimum-phase MMC intersect the amplitude curves of the AC system's calculated impedance at multiple points. At 1100Hz, the phase difference between the MMC and AC system calculated impedances is 189.5° (>180°), while the phase difference between the minimum-phase MMC and AC system calculated impedances is 121.4° (<180°). At 2103Hz, 2230Hz, 2300Hz, and 2497Hz, the phase differences between the MMC and minimum-phase MMC calculated impedances and the AC system calculated impedances are all below 180°. Therefore, the situation at 1100Hz indicates high-frequency oscillation between the MMC and the AC system. It is worth noting that non-minimum-phase systems expand the frequency range of oscillation risk. When the MMC and AC system calculated impedances are equal, the presence of RHP zeros causes phase lag, increasing the phase difference to over 180°, thus increasing the number of instabilities. Compared to non-minimum phase MMC, minimum phase MMC is stable at 1100Hz.

[0120] 2. Parameter optimization design of a third-order high-pass filter;

[0121] like Figure 6 As shown, the parameter design of the third-order high-pass filter in this invention aims to achieve -90° phase compensation, minimum fundamental power loss, and a minimum-phase filter system in the 1000-2500Hz range. The specific design process is as follows:

[0122] (1) Determine the capacitance Designed according to the system's reactive power requirements, to meet... Among them, the system power frequency =2π×50rad / s, the rated voltage U is taken as the system nominal voltage, and the reactive power Q is the reactive power output of the filter branch allowed by the system; in this embodiment, it is taken as =3.6μF, which meets the system's reactive power requirements and does not exhibit overcompensation.

[0123] (2) Determine the inductance :make and At the target tuning frequency Resonance at the point, satisfying , , The resonant frequency, =1581Hz, calculated as follows =2814mH; after resonance The branch exhibits low impedance in the high-frequency range, enabling the passband characteristics of high-frequency signals.

[0124] (3) Determine the resistance and capacitor :set up and The impedance of a series branch at the fundamental frequency is higher than that of an inductor. The impedance satisfies , In this embodiment, we take =1250Ω, =3.6μF. At this point, the branch exhibits high impedance under the fundamental frequency, which significantly reduces the flow of the fundamental frequency current and reduces active power loss.

[0125] (4) Filter stability verification: The Routh criterion, also known as the algebraic stability criterion, determines the stability of a system by analyzing the coefficient distribution of its characteristic equation, without directly solving for the location of the roots. This method determines the number of eigenvalues ​​in the right half of the complex plane based on the sign changes of the elements in the first column of the Routh array table: if all elements in the first column are positive, the system is stable, and the number of sign changes corresponds to the number of roots in the right half-plane. Therefore, the Routh criterion is used to verify that the impedance transfer function of the third-order high-pass filter has no zeros in the right half-plane. The Routh table is constructed and verified to satisfy the criterion. , and This ensures that the filter is a minimum-phase system and has no risk of oscillation. The optimized filter parameters in this embodiment are: =3.6μF, =2814mH, =1250Ω, =3.6μF; with these parameters, the filter provides -90° phase compensation in the 1000-2500Hz range, and the fundamental active power loss is 1.19×10⁻⁶. 5 kW, which is much lower than that of a second-order high-pass filter and a C-type filter.

[0126] 3. Verification of filter connection and oscillation suppression effect;

[0127] The optimized third-order high-pass filter was connected in parallel to the PCC point of the MMC-HVDC system. The suppression effect was verified by PSCAD / EMTDC electromagnetic transient simulation and hardware-in-the-loop experiment. The system parameters for the experiment and simulation were as follows: the rated power of the MMC converter was the conventional capacity of the flexible DC project, the control link delay was 400μs, 500μs, and 600μs respectively, the AC grid line length was 110km, the simulation step size was 30μs, and the hardware-in-the-loop experiment adopted a dual-terminal MMC AC-DC-AC system, with 180 MMC sub-modules at each end and 30 sub-modules in each valve group.

[0128] Verification 1: Influence of steady-state characteristics;

[0129] like Figure 7 , Figure 8 and Figure 9 As shown, after the filter is connected, the voltage and current waveforms of phase A of the AC bus of the MMC-HVDC system are basically the same as those without filter, with no obvious distortion; the step response of the active and reactive power of the system only shows slight fluctuations, and the response speed and steady-state accuracy are not significantly different from those without filter, proving that the filter has a minimal impact on the steady-state characteristics of the system.

[0130] Verification 2: Impact of transient characteristics;

[0131] like Figure 10 As shown, a three-phase short-circuit ground fault was set at the PCC point of the AC bus at 4s, and the fault lasted for 0.02s. After the filter was connected, the AC bus current waveform of the system was only slightly different from that without the filter in the range of 4.0s-4.2s. The system could quickly recover stability after the fault, which proves that the filter does not significantly degrade the system's transient fault response.

[0132] Verification 3: High-frequency oscillation suppression effect;

[0133] (1) such as Figure 11 and Figure 12 As shown, voltage impedance analysis and voltage FFT analysis reveal that when the control link delay is 500μs, the unfiltered MMC-HVDC system exhibits significant high-frequency oscillations at 1050Hz, resulting in severe distortion of the AC bus voltage waveform. After connecting a third-order high-pass filter, the 1050Hz oscillation is effectively suppressed, and the AC bus voltage gradually recovers to its rated value.

[0134] (2) such as Figure 13 As shown, P2, PC, and P3 represent the active power of the second-order high-pass filter, the C-type filter, and the third-order high-pass filter, respectively. Comparing the active power disturbance amplitude and recovery time of the second-order high-pass filter, the C-type filter, and the third-order high-pass filter of this invention: after a three-phase short-circuit fault occurs in 4.0s, the active power disturbance amplitude of the MMC-HVDC system corresponding to the third-order high-pass filter is smaller, the recovery time is shorter, and the fluctuation of the power recovery process is much smaller than that of the other two filters, which reflects the advantage of the third-order high-pass filter of this invention having less transient impact on the MMC-HVDC system.

[0135] (3) such as Figure 14As shown, Q2, QC, and Q3 represent the reactive power of the second-order high-pass filter, the C-type filter, and the third-order high-pass filter, respectively. Comparing the reactive power disturbance amplitude and recovery time of the second-order high-pass filter, the C-type filter, and the third-order high-pass filter of this invention: after a three-phase short-circuit fault occurs in 4.0s, the reactive power disturbance amplitude of the MMC-HVDC system corresponding to the third-order high-pass filter is smaller, the recovery time is shorter, and the fluctuation of the power recovery process is much smaller than that of the other two filters, which reflects the advantage of the third-order high-pass filter of this invention having less transient impact on the MMC-HVDC system.

[0136] (4) such as Figure 15 As shown, at 1050Hz, the MMC impedance without a passive filter will produce a negative damping phenomenon, and the phase angle difference between the MMC impedance and the AC system impedance is 186.8° > 180°; however, after connecting a third-order high-pass filter, the MMC impedance does not produce a negative damping phenomenon within ±90°, and the phase angle difference between the MMC impedance and the AC system impedance is 141.6° < 180°, effectively suppressing the high-frequency oscillation phenomenon of the flexible DC transmission system.

[0137] Verification 4: Hardware-in-the-Loop (HIL) experiment.

[0138] An experimental platform for the MMC-HVDC system based on HIL was built. The experimental process is as follows:

[0139] (1) 0-1.0s: The system operates without filtering and in steady state, with the AC bus voltage remaining stable at the rated value;

[0140] (2) 1.0s: Adding a 500μs delay to the system control link causes high-frequency oscillations in the system and distortion of the AC bus voltage waveform;

[0141] (3) 2.0s: The third-order high-pass filter of the present invention is applied at the PCC point, and the oscillation gradually decays;

[0142] (4) After 2.5s: the system oscillation is completely suppressed, the AC bus voltage is restored to stability, and it continues to operate in steady state.

[0143] like Figure 16 As shown, experimental results demonstrate that the third-order high-pass filter of this invention can effectively suppress high-frequency oscillations caused by non-minimum phase characteristics in actual hardware systems, and the system operates stably.

[0144] Summary of implementation results:

[0145] This invention proposes a high-frequency oscillation suppression method for MMC-HVDC systems. By using a third-order high-pass filter with optimized parallel parameters at the PCC point, precise phase compensation is achieved in the 1000-2500Hz negative damping range, effectively eliminating the negative damping characteristics of the system and fundamentally suppressing high-frequency oscillations. Simultaneously, the fundamental active power loss of the filter is significantly reduced, with no significant impact on the steady-state and transient characteristics of the system, and it exhibits good adaptability to different control link delays and different power grid operating conditions. The mechanism analysis of this invention is precise: it clarifies the oscillation mechanism dominated by non-minimum phase characteristics from the perspective of impedance interaction, providing theoretical support for the design of suppression strategies.

[0146] Significant suppression effect: Compared with traditional passive filters, the third-order high-pass filter has a stronger oscillation suppression effect and can adapt to different MMC-HVDC system operating conditions;

[0147] High engineering practicality: It significantly reduces fundamental active power loss and solves the engineering pain points of traditional passive filters;

[0148] The system exhibits good robustness: the filter itself is a minimum-phase system, and its connection does not degrade the steady-state and transient characteristics of the system, thereby improving the overall stability of the MMC-HVDC system.

[0149] This invention provides an apparatus for suppressing high-frequency oscillations in an MMC-HVDC system, comprising:

[0150] The modeling and analysis module is used to construct a high-frequency impedance model of the MMC-HVDC system with control link delay, and to clarify the high-frequency oscillation mechanism dominated by non-minimum phase characteristics.

[0151] This module includes a high-frequency impedance model building unit and a high-frequency oscillation analysis unit. The high-frequency impedance model building unit is used to build a high-frequency impedance model of the MMC-HVDC system with control link delay. The high-frequency oscillation analysis unit is used to study the equivalent impedance of MMC and the equivalent impedance of AC power grid through impedance detection methods, clarify the high-frequency oscillation mechanism dominated by non-minimum phase characteristics, and analyze whether the MMC-HVDC system experiences high-frequency oscillation.

[0152] By constructing a high-frequency impedance model unit, the effects of phase-locked loop, power outer loop, circulating current suppression, and current inner loop decoupling on the high-frequency impedance of the MMC are ignored, simplifying the high-frequency control process of the MMC. Only the core components of current inner loop PI control, voltage feedforward delay, and current measurement delay are retained, and the open-loop impedance expression of the MMC is derived. and closed-loop impedance expression ;

[0153] The high-frequency oscillation unit is analyzed by using a first-order padde expansion to approximate the voltage feedforward delay, introducing the right half-plane zero in the impedance ratio, and analyzing that the impedance phase difference originates from the non-minimum phase characteristic, thereby clarifying the high-frequency oscillation mechanism dominated by the non-minimum phase characteristic.

[0154] The parameter optimization module is used to optimize the parameters of the third-order high-pass filter, so that the parallel third-order high-pass filter can effectively suppress high-frequency oscillations and minimize the fundamental frequency active power loss, and verify that the impedance transfer function of the third-order high-pass filter has no right half-plane zeros.

[0155] This module includes a third-order high-pass filter parameter optimization unit and a third-order high-pass filter impedance verification unit. The third-order high-pass filter parameter optimization unit optimizes the parameters of the third-order high-pass filter to provide -90° phase compensation in the 1000-2500Hz negative damping range while reducing active power loss at the fundamental frequency. The third-order high-pass filter impedance verification unit verifies that the impedance transfer function of the third-order high-pass filter has no right-half-plane zeros using the Routh criterion, ensuring that the third-order high-pass filter is a minimum-phase system. The third-order high-pass filter parameter optimization unit verifies the parameters... , , and The settings and optimizations provide phase compensation for the system in the target oscillation frequency band and reduce the risk of negative damping. The phase difference criterion calculated by the impedance detection method is used as the optimization constraint. The parameters are iteratively adjusted in combination with the frequency domain scanning and simulation verification results until the oscillation suppression effect and loss constraint requirements are met.

[0156] The impedance unit of the third-order high-pass filter was verified to suppress the filter's own resonance peak and ensure that the filter exhibits minimum phase characteristics by adjusting the parameters and injecting damping.

[0157] The impedance analysis and verification module is used to study the equivalent impedance of MMC and AC power grid, analyze whether the MMC-HVDC system experiences high-frequency oscillations, and verify the reshaping effect of the third-order high-pass filter on the equivalent impedance of the MMC-HVDC system.

[0158] This module includes an impedance analysis unit and a verification module unit. The impedance analysis unit is used to study the equivalent impedance of MMC and the equivalent impedance of AC power grid through impedance detection methods. The verification module unit is used to verify the reshaping effect of the third-order high-pass filter on the equivalent impedance of the MMC-HVDC system, thereby suppressing high-frequency oscillations in the MMC-HVDC system.

[0159] The impedance analysis unit obtained before the third-order high-pass filter was connected showed that the equivalent impedance of the MMC and the AC grid impedance may have a significant phase difference greater than 180° in the target high-frequency oscillation band, thus satisfying the negative damping formation condition and inducing the risk of high-frequency oscillation. After the filter was connected in parallel to the PCC, the filter presented low impedance and provided phase compensation in the target high-frequency band, so that the phase difference between the equivalent impedance of the MMC side and the AC grid impedance was less than 180°.

[0160] In the steady-state characteristic verification, the verification module unit compares the PCC voltage, current, and power output of the system under rated operating conditions before and after the filter is connected, checking whether the fundamental component remains stable and whether the steady-state error increases, thus proving that the filter's impact on fundamental frequency operation is controllable. In the transient characteristic verification, typical disturbances are applied, and the changes in the PCC voltage and current before and after connection are compared, verifying that the filter does not deteriorate the transient response and can improve the damping and convergence speed of the transient process. In the high-frequency oscillation suppression effect verification, frequency domain analysis is performed on the voltage and current signals for the target oscillation frequency band, comparing the peak amplitude of oscillation, oscillation duration, and energy decay rate; at the same time, the stability margin before and after connection is compared with the phase difference criterion obtained by impedance detection, proving that the filter pulls the system from the negative damping risk region back to the stable region through impedance reshaping and phase compensation, achieving high-frequency oscillation suppression. Those skilled in the art will recognize that the units and modules of the various examples described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Skilled professionals may use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0161] In the above embodiments, the various units and modules are divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be achieved; in addition, the specific names of each functional unit are only for easy differentiation and are not used to limit the scope of protection of the present invention.

[0162] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications and substitutions should be covered within the scope of the claims of the present invention. Furthermore, all content not described in detail in this specification belongs to the prior art known to those skilled in the art.

Claims

1. A method for suppressing high-frequency oscillations in an MMC-HVDC system, characterized in that, include: (1) Construct a high-frequency impedance model of the MMC-HVDC system with control link delay, study the equivalent impedance of MMC and the equivalent impedance of AC power grid through impedance detection method, clarify the high-frequency oscillation mechanism dominated by non-minimum phase characteristics, and analyze whether the MMC-HVDC system oscillates at high frequency. (2) Connect a third-order high-pass filter in parallel at the common coupling point PCC between the MMC and the AC power grid; (3) Optimize the parameters of the third-order high-pass filter to provide -90° phase compensation and reduce the active power loss at the fundamental frequency. The Routh criterion is used to verify that the impedance transfer function of the third-order high-pass filter has no zeros in the right half-plane, ensuring that the third-order high-pass filter is a minimum-phase system. (4) The equivalent impedance of MMC and the equivalent impedance of AC power grid are studied by impedance detection method. The effect of the third-order high-pass filter on the reshaping effect of the equivalent impedance of MMC-HVDC system is verified, and the high-frequency oscillation of MMC-HVDC system is suppressed.

2. The high-frequency oscillation suppression method for the MMC-HVDC system as described in claim 1, characterized in that, The construction of the high-frequency impedance model of the MMC-HVDC system including control link delay specifically includes: Ignoring the effects of phase-locked loop, power outer loop, circulating current suppression, and current inner loop decoupling on high-frequency impedance, the control process of the MMC is simplified, and the open-loop equivalent impedance expression of the MMC is derived. and closed-loop equivalent impedance expression : (1) (2) (3) (4) in, Let be a complex variable representing the frequency in the Laplace transform domain; MMC equivalent reactance; Transfer function for the current inner loop PI controller; This is the proportional gain of the inner current loop; This is the inner loop integral gain of the current; and These are the voltage feedforward delay and current measurement delay of the MMC-HVDC system, respectively. and These are the voltage feedforward delay and current measurement delay times for the MMC-HVDC system, respectively. is the base of the natural logarithm.

3. The high-frequency oscillation suppression method for the MMC-HVDC system as described in claim 2, characterized in that, The study of the equivalent impedance of the MMC and the equivalent impedance of the AC power grid using impedance detection methods aims to clarify the high-frequency oscillation mechanism dominated by non-minimum phase characteristics and analyze whether the MMC-HVDC system experiences high-frequency oscillations. Specifically, this includes: Phase margin Used to evaluate the stability of the MMC-HVDC system: (5) in, The equivalent impedance of the AC power grid; Need to retrieve and Frequency of the intersection point of the amplitude curves; The phase of the equivalent impedance of the AC power grid; The phase of the MMC equivalent impedance; According to the Nyquist stability criterion, when When the value is greater than 0, the MMC-HVDC system can operate stably; according to The constraints will The expression can be rewritten as the stability criterion for oscillations in an MMC-HVDC system: (6) As the frequency increases, The amplitude is much greater than The amplitude, therefore the MMC phase mainly depends on In the high-frequency range, it approximates pure inductive characteristics; the voltage feedforward delay is approximated using a first-order padde expansion: (7) The equivalent impedance ratio expression containing the zeros of the right half-plane is obtained. : (8) (9) (10) in, This refers to the internal equivalent impedance of the MMC. The non-minimum phase zero influence factor introduced for voltage feedforward delay; The phase is determined by the phase difference between the numerator and the denominator, therefore phase Represented as: (11) in, The imaginary unit; Angular frequency; The high-frequency equivalent impedance phase of the MMC has an additional phase shift due to the non-minimum phase characteristic of the MMC, which increases the equivalent impedance phase of the MMC. The explicit control link delay causes the MMC to exhibit non-minimum phase characteristics. The zero point of the right half plane expands the high-frequency oscillation frequency range. When the MMC impedance phase is greater than 90°, it exhibits negative damping characteristics. When the phase difference with the capacitive impedance of the AC grid exceeds 180°, it triggers high-frequency oscillation.

4. The high-frequency oscillation suppression method for the MMC-HVDC system as described in claim 1, characterized in that, The third-order high-pass filter connected in parallel at the common coupling point (PCC) between the MMC and the AC power grid specifically includes: A third-order high-pass filter consists of two parts connected in series, including a capacitor. ,inductance ,resistance and capacitor It is connected in parallel at the common junction point PCC; the first part is a capacitor. The second part is the resistor. and capacitor Series branch and inductor Parallel connection of branches; the third-order high-pass filter is connected one-to-one in parallel to the corresponding phase high-voltage bus of PCC at the three-phase input terminals A, B, and C. The third-order high-pass filter is connected in parallel with the MMC grid-connected main circuit and the AC grid side circuit. The third-order high-pass filter provides -90° phase cancellation. The resulting phase gain is compensated by This causes phase lead; it reduces the phase difference between the MMC and the equivalent impedance of the AC power grid to within 180°.

5. The high-frequency oscillation suppression method for the MMC-HVDC system as described in claim 4, characterized in that, The optimization design of the parameters of the third-order high-pass filter specifically includes: Determine the capacitor based on the reactive power requirements of the MMC-HVDC system. The value of satisfies ,in For MMC-HVDC system power frequency; This is the rated voltage for the MMC-HVDC system; For reactive power in MMC-HVDC systems; Design inductor The value of makes the capacitor With inductance At the target tuning angular frequency Resonance at the point, satisfying ; Set resistor With capacitor The impedance of a series branch at the fundamental frequency is higher than that of an inductor. The impedance satisfies , Reduce fundamental active power loss; The Routh criterion is used to verify that the impedance transfer function of the third-order high-pass filter has no zeros in the right half-plane, ensuring that the third-order high-pass filter is a minimum-phase system. , , .

6. The high-frequency oscillation suppression method for the MMC-HVDC system as described in claim 5, characterized in that, The capacitor The value is 3.6μF, and the inductance is... The value is 2814mH, resistance The value is greater than or equal to 1250Ω, capacitor The value is less than or equal to 3.6 μF.

7. The high-frequency oscillation suppression method for the MMC-HVDC system as described in claim 1, characterized in that, The control link delay ranges from 400 to 600 μs, corresponding to a negative damping range of 1000 to 2500 Hz for the MMC system.

8. The high-frequency oscillation suppression method for the MMC-HVDC system as described in claim 1, characterized in that, The method of impedance detection was used to study the equivalent impedance of MMC and the AC grid impedance. The effect of the third-order high-pass filter on the reshaping effect of the equivalent impedance of the MMC-HVDC system was verified to be: to make the phase difference between the equivalent impedance of MMC and the AC grid impedance less than 180°, to eliminate the negative damping characteristics of the system, and to avoid high-frequency oscillation.

9. An apparatus for implementing the high-frequency oscillation suppression method of the MMC-HVDC system according to any one of claims 1 to 8, characterized in that, include: The modeling and analysis module is used to construct a high-frequency impedance model of the MMC-HVDC system with control link delay, and to clarify the high-frequency oscillation mechanism dominated by non-minimum phase characteristics. The parameter optimization module is used to optimize the parameters of the third-order high-pass filter, so that the parallel third-order high-pass filter can effectively suppress high-frequency oscillations and minimize the fundamental frequency active power loss, and verify that the impedance transfer function of the third-order high-pass filter has no right half-plane zeros. The impedance analysis and verification module is used to study the equivalent impedance of MMC and AC power grid, analyze whether the MMC-HVDC system experiences high-frequency oscillations, and verify the reshaping effect of the third-order high-pass filter on the equivalent impedance of the MMC-HVDC system.

10. The apparatus according to claim 9, characterized in that: The modeling and analysis module includes a high-frequency impedance model building unit and a high-frequency oscillation analysis unit; The high-frequency impedance model building unit is used to build a high-frequency impedance model of the MMC-HVDC system including control link delay. The high-frequency oscillation analysis unit is used to study the equivalent impedance of MMC and the equivalent impedance of AC power grid through impedance detection method, clarify the high-frequency oscillation mechanism dominated by non-minimum phase characteristics, and analyze whether the MMC-HVDC system experiences high-frequency oscillation. The parameter optimization module includes a third-order high-pass filter parameter optimization unit and a third-order high-pass filter impedance verification unit. The third-order high-pass filter parameter optimization unit is used to optimize the parameters of the third-order high-pass filter so that the third-order high-pass filter provides -90° phase compensation in the 1000-2500Hz negative damping range, while reducing the active power loss at the fundamental frequency. The verification unit for the impedance of the third-order high-pass filter is used to verify that the impedance transfer function of the third-order high-pass filter has no zeros in the right half-plane through the Routh criterion, thus ensuring that the third-order high-pass filter is a minimum-phase system. The impedance analysis and verification module includes an impedance analysis unit and a verification module unit; The impedance analysis unit is used to study the equivalent impedance of the MMC and the equivalent impedance of the AC power grid by means of impedance detection after connecting a third-order high-pass filter in parallel at the common connection point PCC between the MMC and the AC power grid. The verification module unit is used to verify the reshaping effect of the third-order high-pass filter on the equivalent impedance of the MMC-HVDC system, thereby suppressing high-frequency oscillations in the MMC-HVDC system.

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