Adaptive restart method for extra-high voltage direct current transmission system containing hybrid MMC (Modular Multilevel Converter)

Abstract

The invention provides a self-adaptive restart method for an extra-high voltage direct current transmission system containing a hybrid MMC, and the method comprises the steps: analyzing the attenuation characteristic difference of a system current aperiodic component under different fault properties through building an equivalent model of a power grid commutation converter (LCC) station and a hybrid MMC station in a restart stage; and a matrix pencil algorithm (MPM) is adopted to extract a non-periodic component to construct a fault property identification criterion, so that a self-adaptive restart strategy is formed. The strategy can sensitively and reliably identify an instantaneous fault and a high-resistance permanent fault on the premise of not depending on communication, the restart success rate of the system is effectively improved, and the operation reliability of the system is enhanced. The method is suitable for a hybrid direct current system and a pure flexible direct current system, and has remarkable technical advantages and application value.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and particularly to an adaptive restart method for a UHVDC transmission system with a hybrid modular multilevel converter (MMC), which is applicable to hybrid DC systems and pure flexible DC systems. Technical Background

[0002] Ultra-high voltage direct current (UHVDC) transmission is a key technology for large-capacity clean energy consumption across regions. At present, the commonly used converters in UHVDC systems include line-commutated converters (LCC) and modular multilevel converters (MMC). The hybrid MMC combines the advantages of full-bridge and half-bridge sub-modules, has the ability to ride through DC faults, and at the same time reduces construction costs and power losses. However, the existing fault restart strategy of the hybrid MMC judges whether the fault has disappeared by detecting whether the DC voltage can be successfully established, and it is difficult to distinguish between transient faults and high-resistance permanent faults, resulting in insufficient reliability of system restart. In addition, the existing restart method based on active injection signals relies on communication to achieve, increasing system complexity and fault risks. Summary of the Invention

[0003] The present invention proposes an adaptive restart method for a UHVDC transmission system with a hybrid MMC, aiming to analyze the equivalent models of each converter in the restart stage, reveal the attenuation characteristic differences of the aperiodic components of the system current under different fault natures, and use the matrix pencil method (MPM) to extract the aperiodic components to construct a fault nature identification criterion, so as to form an adaptive restart strategy. This strategy can sensitively and reliably identify the fault nature without relying on communication, effectively improve the restart success rate of the system, and enhance the operation reliability of the system.

[0004] To solve the above problems, the present invention provides an adaptive restart method for a UHVDC transmission system with a hybrid MMC, including the following steps:

[0005] Step 1: Establish equivalent models of the line-commutated converter (LCC) station and the hybrid MMC station in the restart stage;

[0006] Step 2: Analyze the attenuation characteristic differences of the aperiodic components of the system current under different fault natures;

[0007] Step 3: Use the matrix pencil method (MPM) to extract the aperiodic components in the current signal and construct a fault nature identification criterion;

[0008] Step 4: According to the fault nature identification result, form an adaptive restart strategy to improve the restart success rate of the system.

[0009] Further, the equivalent model of the LCC station in the restart stage described in Step 1 includes:

[0010] The equivalent resistance (Rsn) and capacitance (Csn) of the converter valve buffer circuit;

[0011] The smoothing reactor inductance (Lp);

[0012] The equivalent impedance (Zdcf) of the filter branch.

[0013] Furthermore, the equivalent model of the hybrid MMC station in the restart stage described in step one includes:

[0014] The equivalent resistance (RMMC), inductance (LMMC), and capacitance (CMMC) under the DC current control mode;

[0015] The voltage source (us) under the characteristic signal injection mode, and its voltage amplitude is 0.1 pu.

[0016] Furthermore, the fault nature identification criterion described in step three includes:

[0017] For a hybrid DC system, there is no aperiodic component in the current during a transient fault, and there is an undamped DC component in the current during a permanent fault;

[0018] For a fully flexible DC system, there is an aperiodic component with a decay coefficient of 333.6 in the current during a transient fault, and there is a DC component with a decay coefficient of 0 in the current during a permanent fault.

[0019] Furthermore, the matrix pencil method (MPM) described in step three is used to extract the aperiodic component in the current signal, and specifically includes:

[0020] Perform modal parameter identification on the collected current signal;

[0021] Extract the decay coefficient of the aperiodic component and construct a fault nature identification criterion.

[0022] Furthermore, the specific implementation steps of the adaptive restart strategy described in step four include:

[0023] For a hybrid DC system, the LCC station performs phase shift control, the hybrid MMC station switches to the DC current control mode, after 300 ms of deionization time, it switches to the characteristic signal injection mode, collects the current signal and extracts the aperiodic component, and judges the fault nature;

[0024] For a fully flexible DC system, both hybrid MMC stations switch to the DC current control mode, after 300 ms of deionization time, the inverter-side hybrid MMC station switches to the characteristic signal injection mode, collects the current signal and extracts the aperiodic component, and judges the fault nature.

[0025] Furthermore, the voltage amplitude of the characteristic signal injection mode is 0.1 pu.

[0026] Furthermore, the fault nature identification criterion in step three further includes:

[0027] For a pure VSC-HVDC system, if the minimum attenuation coefficient (α_min) is less than the set threshold (α_set), it is determined as an instantaneous fault; otherwise, it is determined as a permanent fault. The set threshold (α_set) is 166.8.

[0028] Furthermore, the restart strategy can still effectively identify the fault nature under noise interference, and the noise signal-to-noise ratio is 25 dB.

[0029] Furthermore, the restart strategy is applicable to hybrid DC systems and pure VSC-HVDC systems, where:

[0030] The rectifier side of the hybrid DC system is an LCC, and the inverter side is a hybrid MMC;

[0031] Both the rectifier side and the inverter side of the pure VSC-HVDC system are hybrid MMCs.

[0032] The specific application technical solution of the present invention is as follows:

[0033] 1 System model

[0034] 1.1 System topology structure

[0035] Taking the Mengxi - Beijing-Tianjin-Hebei ±800 kV and Gansu - Zhejiang ±800 kV UHVDC transmission projects as the background, a hybrid DC system (the rectifier side is an LCC, and the inverter side is a hybrid MMC) and a pure VSC-HVDC system (both the rectifier side and the inverter side are hybrid MMCs) are built.

[0036] The fault points are located at the head, middle, and end of the line, all of which are DC line area faults and are likely to be instantaneous faults.

[0037] 1.2 Converter parameters

[0038] LCC station:

[0039] Smoothing reactor inductance (Lp): 0.5 H.

[0040] Equivalent resistance of the buffer circuit (Rsn): 10 Ω, capacitance (Csn): 10 μF.

[0041] Hybrid MMC station:

[0042] Equivalent resistance of the bridge arm (Rarm): 0.1 Ω, inductance (Larm): 0.05 H.

[0043] DC side current-limiting inductance (Ldc): 0.1 H.

[0044] DC voltage reference value (Udcref): 1.0 pu.

[0045] Voltage amplitude (us) in the characteristic signal injection mode: 0.1 pu.

[0046] 1.3. Line parameters

[0047] Resistance per unit length (R): 0.01 Ω / km, inductance (L): 1 mH / km, capacitance (C): 10 nF / km, conductance (G): 0.

[0048] 1.4. Simulation tool

[0049] Use PSCAD / EMTDC to build a simulation model with a sampling frequency of 10 kHz.

[0050] 2 Restart method

[0051] 2.1. Phase-shifting control and equivalent model of LCC station

[0052] After a DC line fault, the line protection operates within 2 ms. The LCC station performs phase-shifting control, urgently shifting the thyristor firing angle to 120°, converting the system from the rectification state to the inversion operation to reduce the fault current. The phase-shifting operation is completed within 5 ms after fault detection. The equivalent model of the LCC station includes the smoothing reactor, buffer circuit, and equivalent impedance of the filter branch, as Figure 2 shown.

[0053] 2.2. Fault ride-through and active injection control of hybrid MMC station

[0054] The hybrid MMC station adopts the fault ride-through control strategy as Figure 3 shown. The control mode switching is achieved through switch S:

[0055] Mode I (normal operation): Switch S is placed in position 0, and the DC voltage reference value Udcref = 1.0 pu.

[0056] Mode II (DC current control): Switch S is placed in position 1, and the DC voltage adapts to the change in DC current. When a DC line fault occurs, the line protection trips on a millisecond time scale, controlling switch S to switch from position 0 to position 1, and the hybrid MMC enters the DC current control mode, reducing the DC current to 0.

[0057] Mode III (characteristic signal injection): Switch S is placed in position 2, injecting a voltage signal with an amplitude of 0.1 pu into the line. After the fault current drops to 0 and after a 300 ms deionization time, control switch S is switched from position 1 to position 2, and the hybrid MMC attempts to inject a characteristic signal into the DC line.

[0058] 3 Fault nature identification

[0059] 3.1. Matrix Pencil Method (MPM)

[0060] The non - periodic components in the current signal are extracted by MPM, and the specific steps are as follows:

[0061] Identify the modal parameters of the collected current signal.

[0062] Extract the attenuation coefficient of the non - periodic component and construct a criterion for fault nature identification.

[0063] The parameter settings are as follows:

[0064] Data window length: Collect the current signal within a 20 - ms data window after injecting the characteristic signal.

[0065] Amplitude of the characteristic signal: The amplitude of the injected voltage signal is 0.1 pu.

[0066] De - ionization time: The default is 300 ms, which can be adjusted according to the actual engineering requirements.

[0067] Noise tolerance: The proposed restart strategy can still effectively identify the fault nature under the noise interference with a signal - to - noise ratio of 25 dB.

[0068] 3.2. Fault Nature Criterion

[0069] Hybrid DC system:

[0070] For transient faults, there are no non - periodic components in the current.

[0071] For permanent faults, there is a non - decaying DC component in the current.

[0072] Pure VSC - HVDC system:

[0073] For transient faults, there is a non - periodic component with an attenuation coefficient of 333.6 in the current.

[0074] For permanent faults, there is a DC component with an attenuation coefficient of 0 in the current.

[0075] 4 Specific Implementation Steps of the Adaptive Restart Strategy

[0076] 4.1 Adaptive Restart Strategy for Hybrid DC System

[0077] S1. The LCC station performs a phase - shifting operation after receiving the line protection action signal.

[0078] S2. The hybrid MMC station switches to Mode II after receiving the line protection action signal. At the same time, set the counter n = 1, indicating that the first injection will be started.

[0079] S3. After 300 ms of deionization, the hybrid MMC on the inverter side switches to Mode III and attempts to inject a voltage signal with an amplitude of 0.1 pu into the line.

[0080] S4. Collect the current signal within a 20-ms data window after injection, and use the MPM to extract the aperiodic component.

[0081] S5. Judge the fault nature according to the attenuation characteristics of the aperiodic component: if the aperiodic component cannot be extracted, it is judged as an instantaneous fault; if a non-decaying DC component is extracted, it is judged as a permanent fault.

[0082] S6. If it is judged as an instantaneous fault, the LCC station switches back to the constant DC current control, and the hybrid MMC station switches back to the normal operation mode to restore the system power.

[0083] S7. If it is judged as a permanent fault, the counter n is incremented by 1 (nmax is the maximum restart times, default set to 3). If n < nmax, the hybrid MMC station switches back to the DC current control mode, and repeat steps 3 - 5; if n = nmax, lock the hybrid MMC station.

[0084] 4.2 Adaptive restart strategy for pure VSC-HVDC system

[0085] After receiving the line protection action signal, the hybrid MMC stations on both sides switch the control mode from Mode I to Mode II. At the same time, set the counter n = 1, indicating that the first injection will be started.

[0086] After 300 ms of deionization, the hybrid MMC on the inverter side switches to Mode III and attempts to inject a voltage signal with an amplitude of 0.1 pu into the line.

[0087] The subsequent steps are the same as steps 4 - 7 in the adaptive restart strategy of the hybrid DC system.

[0088] Compared with the existing technology, it has the following technical effects:

[0089] 1. Fault nature identification criterion

[0090] By analyzing the attenuation characteristic differences of the aperiodic components of the system current during the restart stage, a fault nature identification criterion based on the matrix pencil algorithm is constructed, which can sensitively and reliably distinguish between instantaneous faults and high-resistance permanent faults.

[0091] 2. Adaptive restart method

[0092] It does not rely on communication to achieve. By injecting characteristic signals and using the matrix pencil algorithm to extract the aperiodic components, an adaptive restart strategy is formed, effectively improving the system restart success rate.

[0093] 3. System model optimization

[0094] An equivalent model of the LCC station and the hybrid MMC station during the restart phase is established, which simplifies the computational complexity of fault nature identification and improves the real-time performance and applicability of the above method.

[0095] The adaptive restart method proposed in the present invention can sensitively and reliably identify the fault nature without relying on communication, effectively improve the restart success rate of the UHVDC transmission system, and enhance the operation reliability of the system. This strategy is applicable to the scenario of large-scale cross-region consumption of clean energy and has significant technical advantages and application value. Description of the Drawings

[0096] Figure 1 : Topological structure of the UHVDC transmission system with a hybrid MMC.

[0097] Figure 2 : Equivalent model of the LCC station during the restart phase.

[0098] Figure 3 : Fault ride-through and active injection control strategy for the hybrid MMC.

[0099] Figure 4 : Equivalent circuit of the hybrid MMC station.

[0100] Figure 5 : Equivalent model of the hybrid MMC station during the restart phase.

[0101] Figure 6 : Equivalent circuit diagram of the hybrid DC system when a transient fault occurs.

[0102] Figure 7 : Graphic method for non-periodic components of the hybrid DC system when a transient fault occurs.

[0103] Figure 8 : Graphic method for non-periodic components of the pure VSC-HVDC system when a transient fault occurs.

[0104] Figure 9 : Equivalent circuit of the hybrid DC system when a permanent fault occurs.

[0105] Figure 10 : Decay characteristics of non-periodic components of the hybrid DC system when a permanent fault occurs.

[0106] Figure 11 : Decay characteristics of non-periodic components of the pure VSC-HVDC system when a permanent fault occurs.

[0107] Figure 12 : Flow chart of the system adaptive restart strategy.

[0108] Figure 13 : Accuracy test of the equivalent model.

[0109] Figure 14 : Transient fault waveform.

[0110] Figure 15 : Permanent fault waveform.

[0111] Figure 16 Frequency-varying parameters of DC overhead lines and tower models. Specific implementation manners

[0112] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0113] The following describes the specific implementation of the present invention in detail with reference to specific embodiments.

[0114] 1 UHVDC transmission system with hybrid MMC

[0115] Taking the Mengxi - Beijing-Tianjin-Hebei ±800kV UHVDC transmission project and the Gansu - Zhejiang ±800kV UHVDC transmission project as the background, a system as shown in Figure 1 is built (only one pole is shown schematically in the figure, the line length is 600km, and the transmission power of bipolar operation is 8000MW).

[0116] According to the public information, in the Mengxi - Beijing-Tianjin-Hebei ±800kV UHVDC transmission project, LCC is planned to be used in the rectifier station and hybrid MMC is used in the inverter station, as shown in Figure 1 (a) (hereinafter referred to as the hybrid DC system). During normal operation, the control strategy of the LCC station is constant DC current control, and the control strategy of the hybrid MMC station is constant DC voltage / constant reactive power control. In the Gansu - Zhejiang ±800kV UHVDC transmission project, the rectifier station and the inverter station adopt hybrid MMC, as shown in Figure 1 (b) (hereinafter referred to as the pure flexible DC system). During normal operation, the hybrid MMC station on the rectifier side adopts constant active power / constant reactive power control, and the hybrid MMC station on the inverter side adopts constant DC voltage / constant reactive power control. In the figure, f1, f2, and f3 respectively represent that the fault point is located at the head, middle, and end of the line. These three types of faults are all DC line internal faults, and are likely to be transient faults, and the nature of the faults needs to be discriminated.

[0117] 2 Control response of the converter after DC line protection action

[0118] 2.1 Phase-shifting control of LCC station

[0119] After a DC line fault, the line protection should act quickly. For an LCC station, after the pole control system receives the line protection action signal, the thyristor trigger angle is urgently shifted to 120°. The LCC changes from the rectification state to the inversion operation, so that the fault energy in the DC system is fed back to the AC power grid, reducing the current idcR flowing into the fault point by the LCC. When idcR is reduced to close to zero, the trigger angle will be further shifted to more than 150°.

[0120] 2.2 Equivalent model of LCC station in the restart stage

[0121] According to the LCC commutation principle, no commutation valve conducts in the commutation bridge after the LCC station performs phase-shifting control. However, in actual projects, to reduce the voltage and current shocks generated during the thyristor breaking process, an RC buffer circuit is connected in parallel at both ends of the commutation valve, and a path can still be formed between the LCC station and the DC line through the commutation valve buffer circuit. Therefore, the equivalent model of the LCC station in the restart stage is as Figure 2 shown. In the figure, Zdcf is the equivalent impedance of the filter branch, Lp is the inductance of the smoothing reactor, and Rsn and Csn are the equivalent resistance and capacitance of the buffer circuit respectively.

[0122] To ensure the voltage equalization effect between valve groups, the buffer circuit structures of each phase are symmetric. If there are N six-pulse bridges in the LCC, then Rsn = R0×2N / 3 and Csn = C0×3N / 2. Among them, C0 and R0 are the buffer capacitance and resistance values of the single-phase buffer circuit in a single six-pulse bridge.

[0123] 2.3 Fault ride-through and active injection control of hybrid MMC station

[0124] The literature points out that the negative voltage output ability of the full-bridge sub-module in the hybrid MMC can be utilized to actively control the fault current by switching the control mode, so as to achieve the non-blocking fault ride-through of the hybrid MMC. On the other hand, thanks to the DC voltage regulation ability of the hybrid MMC, a small-amplitude characteristic signal can be injected into the DC line during fault restart to assist in judging whether the fault point has disappeared and avoid blind restart during the fault recovery process. To sum up, for the hybrid MMC station, the fault ride-through control strategy shown in Figure 3 is adopted in this paper. In the figure, Udcref is the DC voltage reference value; Idc and Idcref are the measured DC current and the DC current command value respectively; udiffj and ucirj are the j-phase differential-mode voltage reference value and the circulating current voltage reference value respectively (j represents the three phases A, B, and C, the same below); up(n)jref is the j-phase upper (lower) bridge arm voltage reference value.

[0125] As Figure 3 shown, the switching of the switch S makes the DC control loop present three selectable control modes. The following will explain these three control modes respectively:

[0126] Mode I: Normal operation mode. In this mode, switch S is placed at position 0, and Udcref = 1.0 pu.

[0127] Mode II: DC current control mode. After a DC line fault occurs, the line protection will operate within a time scale of milliseconds, controlling switch S to switch from position 0 to position 1, and the hybrid MMC enters the DC current control mode. In this mode, the DC voltage of the hybrid MMC will adapt to the change in DC current until the DC current reaches the preset value of 0 pu. This process is dynamically determined by the equation shown in Equation (1):

[0128]

[0129] where s is the Laplace operator, and kp and ki are the proportional and integral coefficients of the PI controller, respectively.

[0130] Mode III: Characteristic signal injection mode. After the fault current drops to 0, after a certain deionization time, control switch S is switched from position 1 to position 2, and the hybrid MMC attempts to inject a voltage signal with an amplitude of 0.1 pu into the DC line (ensuring that the converter will not lock up within the time scale for fault nature identification).

[0131] For Figure 1 the two systems shown, after the line deionizes, the hybrid MMC on the inverter side can inject characteristic signals into the line to assist in discriminating the fault nature.

[0132] 2.4 Equivalent model of the hybrid MMC station during the restart phase

[0133] The equivalent model of the hybrid MMC station during the restart phase is related to the control mode it is in. In this section, combined with the MMC equivalent circuit shown in Figure 4 and the control principle of the hybrid MMC, the equivalent models in Mode II and Mode III are derived. Figure 4 where Rac and Lac are the equivalent resistance and inductance of the AC system respectively; Rarm and Larm are the equivalent resistance and inductance of the bridge arm respectively; Ldc is the DC side current limiting inductor; idc and udc are the line outlet voltage and voltage respectively; up(n)j is the voltage of the upper (lower) bridge arm of phase j; ip(n)j is the current of the upper (lower) bridge arm of phase j.

[0134] Applying Kirchhoff's current law to Figure 4 yields Equation (2):

[0135]

[0136] Applying Kirchhoff's voltage law to Figure 4 yields Equation (3):

[0137]

[0138] Where, iphj = ipj + inj.

[0139] Summing up the three-phase differential equations in Equation (3) and substituting Equation (2), Equation (4) can be obtained:

[0140]

[0141] Where, Req = 2 / 3Rarm, Leq = 2 / 3Larm + Ldc. Considering the symmetry of the three-phase units in the MMC under DC faults, define the single-phase arm voltage uarm = upj + unj, then Equation (4) can be further expressed as:

[0142]

[0143] Performing Laplace transform on Equation (5), Equation (6) is obtained:

[0144] -(R eq + sL eq )I dc + U arm = U dc (6)

[0145] According to the modulation principle of the MMC, it can be known that if high-frequency harmonics and control delay are ignored, Uarm in Equation (6) is equal to Figure 3 Udcref output by the DC control loop in

[0146]

[0147] According to Equation (7), the equivalent model of the hybrid MMC station in Mode II during the restart phase can be obtained as Figure 5 (a) shown. In the figure, RMMC = Req + kp, LMMC = Leq, CMMC = 1 / ki.

[0148] Similarly, the equivalent model of the hybrid MMC station in Mode III during the restart phase is as Figure 5 (b) shown. Combining Section 2.3, it can be known that Figure 5 the expression of the voltage source us in (b) in the complex frequency domain is as shown in Equation (8):

[0149]

[0150] Where, UN is the rated voltage; Uarm0 is the sum of the arm capacitor voltages at the moment before the injection control switch.

[0151] 3 Analysis of the DC components of the current under different fault natures

[0152] When the hybrid MMC injects characteristic signals into the DC line, it is equivalent to applying a voltage source on the inverter side. Due to the different circuit structures under permanent faults and transient faults, the current responses will necessarily be different after applying the excitation shown in Equation (8). According to circuit theory, the complete response of a dynamic circuit is the superposition of the free response (related to the poles of the network function) and the forced response (related to the poles of the excitation function). Since the applied excitation has a step nature, there may be an aperiodic component in the free response, and the forced response should be a DC component (which can be considered as an undamped aperiodic component). The following analyzes different systems separately. When analyzing, a monopole system is taken as an example for the following reasons: ① For symmetric faults, the whole system is balanced and symmetric, and taking a monopole system is convenient for analysis; ② For asymmetric faults, although there is a coupling effect between the two-pole lines, according to Reference

[16] , for the aperiodic component concerned in this paper, the coupling coefficient between the two-pole lines is extremely small. In addition, to accurately grasp the characteristics of the DC outlet current of the hybrid MMC, the line should adopt a distributed parameter model and be analyzed using operational calculus.

[0153] 3.1 Analysis of the attenuation characteristics of the aperiodic component of the current under transient faults

[0154] 3.3.1 Hybrid DC system

[0155] 1) Aperiodic component in the free response

[0156] Based on the equivalent model of the converter station obtained in Sections 2.2 and 2.4, the system schematic diagram of the hybrid DC system when a transient fault occurs is drawn as Figure 6 shown. In the figure, l is the line length, dx is an infinitesimal element at x on the line, and R, L, C, and G are the resistance, inductance, conductance, and capacitance of the DC line per unit length, respectively. uR(I), iR(I) are the voltages and currents at the protection installation points at the beginning (end) of the line.

[0157] From Figure 2 and Figure 6 it can be seen that in the complex frequency domain, uR and iR satisfy the relationship shown in Equation (9):

[0158]

[0159] According to the line transmission equation, the relationship between the voltage ux and current ix at a distance x from the line and uI and iI in the complex frequency domain satisfies Equation (10):

[0160]

[0161] where γ is the line propagation constant; Zc is the wave impedance of the line. The expressions of γ and Zc are shown in Equations (11) and (12) respectively:

[0162]

[0163] For Equation (10), taking \(x = l\) and substituting Equation (9) into it, the equivalent impedance \(Z_{in}\) seen from the end of the line towards the start can be obtained as shown in Equation (13):

[0164]

[0165] Combined with Figure 6 , Equation (8) and Equation (13), it can be known that the Laplace transform of \(i_{I}\) is:

[0166]

[0167] As long as the roots of the characteristic equation \(f(s)=0\) can be obtained, and then the inverse Laplace transform is applied, the time-domain solution \(i_{I}(t)\) can be obtained. According to the physical meaning of the poles of the Laplace function, each real root in the characteristic equation \(f(s)=0\) corresponds to a non-periodic component in \(i_{I}(t)\), and each pair of conjugate complex roots corresponds to a frequency component in \(i_{I}(t)\). Since \(f(s)\) contains hyperbolic function terms, and this term is nested with multiple composite functions about \(s\), for the convenience of analysis, the following three simplifications are made when examining \(f(s)\): ① Considering that the resistance per unit length of the line distributed along the actual UHV transmission line is extremely small, the line is regarded as a lossless line, and there is Wave velocity Taking the speed of light. On this basis, define \(\tau = l / v\), then \(l = s\tau\)

[18] ; ② For a 12-pulse LCC, the ideal DC filter should exhibit a "zero impedance" characteristic only at the frequency points corresponding to the 12k (k = 1, 2,...) harmonics, and a large impedance value should be maintained in the remaining frequency bands. Since this section only focuses on the non-periodic components in \(i_{I}(t)\), rather than the frequency components corresponding to the 12k harmonics, let \(Z_{f}=\infty\)

[19] ; ③ Neglect the arm resistance. Substituting the above relationships into (14) gives a more concise expression of \(f(s)\), and can intuitively show the mapping relationship between \(s\) and \(f(s)\), as shown in Equation (15):

[0168]

[0169] It can be seen from Equation (15) that the characteristic equation is still essentially a transcendental equation and has no analytical solution, but the roots can be obtained offline by using the graphical method with the aid of a computer. Denote \(s = -\delta(\delta>0)\) as a real root of \(f(s)=0\), then the expression of the corresponding non-periodic component \(i_{Iap1}(t)\) is as shown in Equation (16):

[0170]

[0171] where $f'(-\delta)$ is the value of the derivative function $f'(s)$ of $f(s)$ at the point $s = -\delta$. From Equation (16), it can be seen that $\delta$ is the attenuation coefficient corresponding to this non-periodic component. Considering that the non-periodic component corresponding to the real root of $s < -500$ decays extremely fast, only the real root satisfying $f(s) = 0$ is searched for on the negative real axis interval of $s\in[-500,0)$. Substituting the parameters of this model into Equation (15) to plot the image of $f(s)$ as Figure 7 shown. Observing Figure 7 it can be seen that $f(s)>0$, indicating that there is no non-periodic component in the transient process of $iI(t)$ when the hybrid DC system has an instantaneous fault.

[0172] 2) Forced response

[0173] Theoretically, the forced response corresponding to the step response of the circuit is the DC component corresponding to $s = 0$ (the pole of the excitation function). However, $f(s)$ in Equation (15) is undefined at $s = 0$. Therefore, its forced response can be analyzed through the final value theorem, as shown in Equation (17):

[0174]

[0175] Substituting Equation (15) into Equation (17), it can be seen that the forced response is 0.

[0176] Therefore, it can be considered that there is no non-periodic component in $iI(t)$ when the hybrid DC system has an instantaneous fault.

[0177] 3.1.2 Pure flexible DC system

[0178] 1) Non-periodic component in the free response

[0179] Similarly, combining the equivalent model of the hybrid MMC station obtained in Section 2.4, the corresponding $f(s)$ when the pure flexible DC system has an instantaneous fault can be deduced as shown in Equation (18):

[0180]

[0181] Substituting the parameters of this model into Equation (18) to plot the image of $f(s)$ as Figure 8 shown. Observing Figure 8 it can be seen that when $s$ takes values in $[-500,0)$, the characteristic equation $f(s)=0$ has and only has one real root, that is, there is and only one decaying non-periodic component in the transient process of $iI(t)$ when the pure flexible DC system has an instantaneous fault, and its attenuation coefficient is 333.6.

[0182] 2) Forced response

[0183] Substituting Equation (18) into Equation (17), it can be seen that $iI(t)=0$ under steady state.

[0184] Therefore, it can be considered that in the transient process of iI(t) when a transient fault occurs in the pure HVDC system, there is an aperiodic component with a decay coefficient of 333.6, and iI(t) finally tends to 0.

[0185] 3.2 Analysis of the Characteristics of the Aperiodic Component of the Current under Permanent Fault

[0186] 3.2.1 Hybrid DC System

[0187] 1) Aperiodic Component in the Free Response

[0188] Figure 9 Figure shows the schematic diagram of a hybrid DC system when a permanent fault occurs. Among them, the fault point is at xf from the inverter side, and the transition resistance is Rf. Observation Figure 9 It can be seen that the fault point divides the line into two segments. Substituting Equation (10) into these two segments respectively, the equivalent impedance Zin seen from the end of the line to the start can be obtained, as shown in Equation (19):

[0189]

[0190] In the formula, "||" represents the parallel operation, and the expressions of A and B are as shown in Equation (20):

[0191]

[0192] Furthermore, the corresponding f(s) when a permanent fault occurs in the hybrid DC system can be deduced as shown in Equation (21):

[0193] f(s) = sZ in +s 2 L eq (21)

[0194] Substitute Equation (20) and related parameters into Equation (21), and traverse xf and Rf. It can be known that when Rf ≥ 188Ω, regardless of the value of xf, f(s) has no real roots in the interval s ∈ [-500, 0). Therefore, only the distribution of the characteristic roots of f(s) under different xf when Rf < 188Ω is plotted as Figure 10 shown. Observation Figure 10 It can be seen that when xf(Rf) is fixed, the larger Rf(xf) is, the larger the decay coefficient is, and the shorter the decay time of the aperiodic component appearing in the transient process of iI(t) is.

[0195] 2) Forced Response

[0196] Substitute Equation (21) into Equation (17) to obtain the forced response iI(t) = (0.1UN - Uarm0) / Rf. When considering the line and converter losses, the accurate forced response should be iI(t) = (0.1UN - Uarm0) / (Rf + xfR + RMMC).

[0197] 3.2.2 Pure Soft - DC System

[0198] 1) Aperiodic Component in Free Response

[0199] Similarly, when a permanent fault occurs in the pure soft - DC system, the corresponding f(s) is similar in form to Equation (21), and only need to replace ZLCC with ZMMC = kp + sLeq + ki / s. The attenuation characteristics of the aperiodic component of iI(t) under the parameters of this model are as Figure 11 shown. By traversing xf and Rf, it can be seen that when Rf < 100Ω, there are at most two decaying aperiodic components in the transient component of iI(t). When Rf ≥ 100Ω, there is at most one decaying aperiodic component in the transient component of iI(t). And when xf(Rf) is fixed, the larger Rf(xf) is, the smaller the attenuation coefficient is.

[0200] 2) Forced Response

[0201] Using the final - value theorem, the forced response iI(t) = (0.1UN - Uarm0) / Rf. When considering the line and converter losses, the accurate forced response should be iI(t) = (0.1UN - Uarm0) / (Rf + xfR + RMMC).

[0202] 4 Fault Nature Identification Criterion and Adaptive Restart Strategy

[0203] 4.1 Matrix Pencil Algorithm

[0204] As can be seen from the analysis in the previous section, the differences in different fault natures can be reflected by the characteristics of the aperiodic components in iI(t). Therefore, quickly and effectively extracting the aperiodic components in the current signal is the key to designing the fault identification criterion. Commonly used modal parameter identification methods in power systems are: matrix pencil method (MPM), Prony algorithm, eigen - system realization algorithm, etc. Among them, MPM has advantages in terms of operation efficiency and anti - noise performance. Therefore, MPM is used in this paper to extract the aperiodic components in iI(t).

[0205] 4.2 Fault Nature Identification Criterion for Hybrid DC System

[0206] As can be seen from the analysis in Sections 3.1.1 and 3.2.1, when a transient fault occurs in the hybrid DC system, there is no aperiodic component in iI(t). In theory, the MPM cannot extract the aperiodic component. When a permanent fault occurs, regardless of the values of xf and Rf, there must be an undamped aperiodic component (the DC component corresponding to the forced response) in iI(t) with an amplitude of (0.1UN - Uarm0) / (Rf + xfR + RMMC). Therefore, if the MPM cannot extract the aperiodic component, it is considered that the fault has disappeared and the power can be restored. Otherwise, it is considered that the fault has not disappeared and preparations are made to start the next round of injection or block the converter.

[0207] 4.3 Fault nature identification criterion for pure VSC-HVDC system

[0208] As can be seen from the analysis in Sections 3.1.2 and 3.2.2, when a transient fault occurs in the pure VSC-HVDC system, there is exactly one aperiodic component with a decay coefficient of 333.6 in iI(t). When a permanent fault occurs, regardless of the value of Rf, among all the aperiodic components included in iI(t), the aperiodic component with the smallest decay coefficient is the DC component with a decay coefficient of 0. To sum up, the fault nature identification criterion for the pure VSC-HVDC system based on the minimum decay coefficient shown in Equation (22) can be constructed:

[0209]

[0210] In the formula, αmin is the minimum value of the decay coefficients among all the aperiodic components extracted by the MPM; αset is the threshold value, which can be set according to Equation (25):

[0211]

[0212] In the formula, αt is the minimum decay coefficient calculated offline when a transient fault occurs in the pure VSC-HVDC system (see Section 3.1.2 for details). For the model in this paper, αt = 333.6, and αset = 166.8.

[0213] 4.4 System fault restart strategy

[0214] The adaptive restart strategies for the hybrid DC system and the pure VSC-HVDC system are as Figure 12 shown.

[0215] The specific steps of the adaptive restart strategy for the hybrid DC system are as follows:

[0216] Step 1: The LCC station performs a phase shift operation after receiving the line protection action signal. The hybrid MMC station switches to Mode II after receiving the line protection action signal. At the same time, set the counter n = 1, indicating that the first injection will be started.

[0217] Step 2: After 300 ms of deionization, the hybrid MMC on the inverter side switches to Mode III and attempts to inject a voltage signal with an amplitude of 0.1 pu into the line.

[0218] Step 3: Collect iI within the 20 ms data window after injection and extract the non-periodic component using MPM. If the non-periodic component is not extracted, it is determined as an instantaneous fault; otherwise, the discrimination result is a permanent fault. At this time, if n < nmax (nmax is the maximum restart times), then let n = n + 1, the hybrid MMC switches to Mode II, and jumps back to Step 2. If n = nmax, lock the hybrid MMC.

[0219] Step 4: When performing Steps 2 to 3, continuously judge whether uR reaches 0.9 pu. Once uR > 0.9 pu, the LCC immediately switches back to the original DC current control to restore the system current. If uR cannot exceed 0.9 pu all the time within the (nmax + 1) × 300 ms period after the protection action, lock the LCC.

[0220] The specific steps of the adaptive restart strategy for the fully flexible DC system are as follows:

[0221] Step 1: After receiving the line protection action signal, both hybrid MMC stations on both sides switch the control mode from Mode I to Mode II. At the same time, set the counter n = 1, indicating that the first injection will be started.

[0222] Step 2: After 300 ms of deionization, the hybrid MMC on the inverter side switches to Mode III and attempts to inject a voltage signal with an amplitude of 0.1 pu into the line.

[0223] Step 3: Collect iI within the 20 ms data window after injection and extract the non-periodic component using MPM. If αmin < αset is satisfied, it is determined as an instantaneous fault; otherwise, the discrimination result is a permanent fault. At this time, if n < nmax (nmax is the maximum restart times), then let n = n + 1, the hybrid MMC on the inverter side switches to Mode II, and jumps back to Step 2. If n = nmax, lock the hybrid MMC on the inverter side.

[0224] Step 4: When performing Steps 2 to 3, continuously judge whether uR reaches 0.9 pu. Once uR > 0.9 pu, the hybrid MMC on the rectifier side immediately switches back to the original active power control to restore the system power. If uR cannot exceed 0.9 pu all the time within the (nmax + 1) × 300 ms period after the protection action, lock the hybrid MMC on the rectifier side.

[0225] As described above, whether it is a hybrid DC system or a fully flexible DC system, the entire restart process does not require data interaction at both ends of the line. That is, the system can determine the nature of the fault without relying on communication and reliably restore power during transient faults.

[0226] 5 Implementation Verification

[0227] To verify the effectiveness of the proposed adaptive restart strategy, a simulation model as shown in Figure 1 is built in PSCAD. The main parameters of the two systems are shown in Table A1. The pole tower structure of the DC line is shown in Figure A1. Let all faults occur at t = 3 s, the duration of all transient faults is 0.1 s, and the sampling frequency of the measuring device is 10 kHz. Considering the fast-acting requirement of DC line protection, it is assumed that the protection on both sides of the line trips 2 ms after the fault occurs. At t = 3.302 s, the hybrid MMC on the inverter side switches from Mode II to Mode III and injects a characteristic signal into the DC line.

[0228] 5.1 Equivalent Model Verification

[0229] Taking the bipolar metallic fault as an example, Figure 13 for the transient fault occurring at the midpoint f2 of the line in the two systems, the accuracy of the equivalent model of the converter station derived in Section 2 is tested.

[0230] From Figure 13 it can be seen that the deviation between the simulation results obtained by using the detailed model and those obtained by using the equivalent model is small. The quantitative analysis results show that for the hybrid DC system, the maximum relative error within 20 ms after the characteristic signal injection is 1.64%, and the relative average deviation is 0.32%; for the fully flexible DC system, the maximum relative error within 20 ms after the characteristic signal injection is 0.77%, and the relative average deviation is 0.29%, verifying the correctness of the equivalent model in Section 2.

[0231] 5.2 Transient Fault

[0232] Taking the fault condition in Section 5.1 as an example, Figure 14 the waveforms of the non-periodic components extracted by MPM are given. As can be seen from the figure, the modes extracted by MPM can accurately fit the original signal. From Figure 14 (a), it can be seen that for the hybrid DC system, MPM cannot extract the non-periodic component, which is consistent with the analysis in Section 3.1.1; from Figure 14 (b), it can be seen that for the fully flexible DC system, MPM extracts a non-periodic component with an attenuation coefficient of 331.8, which is close to the analysis result in Section 3.1.2, and 331.8 > αset = 166.8. Combining Sections 4.2 - 4.4, it can be seen that the restart strategies of the two systems can correctly identify transient faults.

[0233] In addition, Tables 1 and 2 examine the adaptability of the proposed restart strategy under different transient fault conditions. In the tables, a "-" in the column of the minimum attenuation coefficient αmin indicates that the MPM fails to extract the aperiodic component.

[0234] Table 1 Simulation Results of the Hybrid DC System under Different Transient Fault Conditions

[0235]

[0236] Table 2 Simulation Results of the Purely Soft DC System under Different Transient Fault Conditions

[0237]

[0238] As can be seen from Table 1, for the hybrid DC system, the MPM fails to extract the aperiodic component under all transient faults. As can be seen from Table 2, for the purely soft DC system, the minimum value of αmin is 327.8, that is, αmin > αset is satisfied under all transient faults. According to the proposed restart strategy, the above faults are all judged as transient faults, and the converter will quickly switch back to the normal operation control strategy, and the system can quickly resume power supply under the regulation of the converter control action.

[0239] 5.3 Permanent Fault

[0240] Taking the fault of the positive pole grounded through a 600Ω transition resistor as an example, Figure 15 The corresponding simulation waveforms for the permanent faults occurring at f1 - f3 in the two systems are given. In the figure, the solid line represents the measured waveform of iI(t), and the dashed line represents the aperiodic component with the minimum attenuation coefficient among all the aperiodic components extracted by the MPM. Observing Figure 14 it can be seen that the waveforms of iI(t) at the three fault positions finally tend to a non-zero steady-state value, that is, the forced response caused by the step excitation on the inverter side.

[0241] For the hybrid DC system, the minimum attenuation coefficients αmin of the aperiodic components corresponding to f1 - f3 extracted by the MPM are 1.7, 2.6, and 1.1 respectively. According to the judgment logic in Section 4.2, all three faults are identified as permanent faults; for the purely soft DC system, the minimum attenuation coefficients αmin of the aperiodic components corresponding to f1 - f3 are 8.4, 10.6, and 11.7 respectively. At the three fault positions, αmin < αset, and Equation (22) has sufficient margin to ensure that it is correctly identified as a permanent fault.

[0242] Tables 3 and 4 give the simulation results under different permanent fault conditions. As can be seen from Table 3, the MPM can extract the aperiodic component. According to the proposed restart strategy, the hybrid DC system does not recover reliably. As can be seen from Table 4, αmin < αset always holds. According to the proposed restart strategy, the purely soft DC system does not recover reliably.

[0243] Table 3 Simulation Results of the Hybrid DC System under Different Permanent Fault Conditions

[0244]

[0245] Table 4 Simulation Results of the Pure VSC-HVDC System under Different Permanent Fault Conditions

[0246]

[0247] 5.4 Influence of Noise

[0248] The UHVDC transmission system has a high voltage level and strong electromagnetic interference, so the influence of noise is inevitably present during on-site sampling. To investigate the effectiveness of the proposed restart strategy in the presence of noise, consider the case where the measuring device is severely affected by noise: superimpose noise with a signal-to-noise ratio of 25 dB on the collected simulation data to simulate the actual sampling process. Tables 5 and 6 give the corresponding simulation results by traversing different fault conditions. It can be seen from Tables 5 and 6 that due to the inherent noise tolerance of the MPM, the proposed restart strategy still has sufficient margin to ensure the correct identification of the fault nature even at a noise intensity of 25 dB.

[0249] Table 5 Fault Simulation Results of the Hybrid DC System under 25 dB Noise

[0250]

[0251] Table 6 Fault Simulation Results of the Pure VSC-HVDC System under 25 dB Noise

[0252]

[0253] 6 Conclusions

[0254] Applying the hybrid MMC to a large-capacity overhead line transmission system can effectively improve the fault ride-through ability of the system, but there are still challenges in the restart after line faults. Based on the background of the UHVDC project under construction in China, giving full play to the control advantages of the hybrid MMC, aiming at improving the restart success rate of the system under high-resistance faults, an adaptive restart strategy based on the characteristics of the aperiodic component of the current is proposed. The main conclusions are as follows:

[0255] 1) In the restart stage, the LCC can be equivalent to an RC series branch; the hybrid MMC in the DC current control mode (current command is zero) can be equivalent to an RLC series branch, and when in the characteristic signal injection mode, it can be equivalent to a controlled voltage source in series with an RL branch.

[0256] 2) For a hybrid HVDC system, after injecting a characteristic voltage signal under a transient fault, there is no aperiodic component in the measured current signal; after injecting a characteristic voltage signal under a permanent fault, there must be a steady-state DC component in the measured current signal.

[0257] 3) For a fully flexible HVDC system, after injecting a characteristic voltage signal under a transient fault, there is exactly one aperiodic component with a large attenuation coefficient in the measured current signal; after injecting a characteristic signal under a permanent fault, there must be a steady-state DC component in the measured current signal.

[0258] 4) The matrix pencil algorithm can effectively extract the aperiodic component in the signal, and has a certain noise tolerance ability, which is suitable for constructing a fault nature identification criterion.

[0259] 5) The simulation results show that the proposed restart strategy can adapt to various fault conditions of the whole line, with a transition resistance tolerance of 600 Ω and can withstand noise with a signal-to-noise ratio of 25 dB. Compared with the traditional restart strategy, it effectively improves the sensitivity and reliability of fault nature detection. In addition, the proposed restart strategy does not depend on the communication system, has a low sampling frequency requirement for protection devices, and is easy to implement in engineering applications.

[0260] Appendix A

[0261] Table A1 Main parameters of the hybrid MMC station

[0262]

[0263]

[0264] The adaptive restart strategy proposed by the present invention forms an adaptive restart strategy by establishing an equivalent model of each converter during the restart stage, analyzing the attenuation characteristic differences of the aperiodic components of the system current under different fault natures, and using the matrix pencil algorithm to extract the aperiodic components to construct a fault nature identification criterion. This strategy can sensitively and reliably identify the fault nature without relying on communication, effectively improve the restart success rate of the UHVDC transmission system, and enhance the operation reliability of the system.

[0265] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

[0266] In addition, it should be understood that although this specification is described according to the embodiments, not every embodiment only contains an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. An adaptive restart method for a UHV DC transmission system containing a hybrid MMC, characterized in that: The following steps are involved: Step 1: Establish equivalent models of the grid-commutated converter (LCC) station and the hybrid MMC station during the restart phase; Step 2: Analyze the difference in attenuation characteristics of the non-periodic component of system current under different fault properties; Step 3: Use the matrix bundle algorithm (MPM) to extract the non-periodic component in the current signal and construct the fault property identification criterion; Step 4: Based on the fault nature identification results, form an adaptive restart strategy to improve the system restart success rate.

2. The adaptive restart method according to claim 1, characterized in that: The equivalent model of the LCC station in the restart phase described in step 1 includes: Equivalent resistance (Rsn) and capacitance (Csn) of the converter valve snubber circuit; Smoothing reactor inductance (Lp); Filter branch equivalent impedance (Zdcf).

3. The adaptive restart method according to claim 1, characterized in that: The equivalent model of the hybrid MMC station in the restart phase described in step 1 includes: Equivalent resistance (RMMC), inductance (LMMC) and capacitance (CMMC) in DC current control mode; The voltage source (us) in the characteristic signal injection mode has a voltage amplitude of 0.1pu.

4. The adaptive restart method according to claim 1, characterized in that: The fault nature identification criteria described in step 3 include: For a hybrid DC system, there is no non-periodic component in the current during a transient fault, and there is an undecayed DC component in the current during a permanent fault; For a pure flexible DC system, the current contains a non-periodic component with an attenuation coefficient of 333.6 during an instantaneous fault, and the current contains a DC component with an attenuation coefficient of 0 during a permanent fault.

5. The adaptive restart method according to claim 1, characterized in that: The matrix bundle algorithm (MPM) described in step 3 is used to extract the non-periodic component in the current signal, specifically including: Perform modal parameter identification on the collected current signal; The attenuation coefficient of the non-periodic component is extracted and the fault property identification criterion is constructed.

6. The adaptive restart method according to claim 1, characterized in that: The specific implementation steps of the adaptive restart strategy described in step 4 include: For the hybrid DC system, the LCC station performs phase shift control, and the hybrid MMC station switches to the DC current control mode. After a 300ms deionization time, it switches to the characteristic signal injection mode to collect the current signal and extract the non-periodic component to determine the nature of the fault; For the pure flexible DC system, the hybrid MMC stations on both sides switch to the DC current control mode. After 300ms of de-ionization time, the hybrid MMC station on the inverter side switches to the characteristic signal injection mode to collect current signals and extract non-periodic components to determine the nature of the fault.

7. The adaptive restart method according to claim 6, characterized in that: The voltage amplitude of the characteristic signal injection mode is 0.1 pu.

8. The adaptive restart method according to claim 1, characterized in that: The fault nature identification criteria described in step 3 also include: For a pure flexible DC system, if the minimum attenuation coefficient (α_min) is less than a set threshold (α_set), it is determined to be a transient fault; otherwise, it is determined to be a permanent fault, and the set threshold (α_set) is 166.

8.

9. The adaptive restart method according to claim 1, characterized in that: The restart strategy can still effectively identify the nature of the fault under noise interference, and the noise signal-to-noise ratio is 25dB.

10. The adaptive restart method according to claim 1, characterized in that: The restart strategy is applicable to hybrid DC system and pure flexible DC system, where: The rectifier side of the hybrid DC system is LCC, and the inverter side is a hybrid MMC; The rectifier and inverter sides of the pure flexible DC system are both hybrid MMCs.

Images