A dc power transmission subsequent commutation failure prediction method and optimization method based on a turn-off angle dynamic equation

Abstract

The application discloses a DC power transmission subsequent commutation failure prediction method and optimization method based on a turn-off angle dynamic equation, and the prediction method comprises the following steps: obtaining the turn-off angle of the LCC-HVDC inverter side based on the turn-off angle output characteristics of the LCC-HVDC inverter side; analyzing the process of the first commutation failure and the subsequent commutation failure of the LCC-HVDC system based on the inverter side DC current control, the low-voltage current limiting control, the fixed turn-off angle control and the current deviation control; obtaining the transient nonlinear differential equation about the turn-off angle by analyzing the dynamic characteristics of the DC current and the trigger advance angle during the first commutation failure recovery in combination with the control characteristics of the low-voltage current limiting control and the fixed turn-off angle control; and drawing the phase diagram curve of the turn-off angle under different AC voltages and AC voltage change rates based on the transient nonlinear differential equation about the turn-off angle, and obtaining the criterion for predicting the occurrence of the subsequent commutation failure by analyzing the phase diagram curve. The application improves the stability and operation reliability of the system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of high-voltage direct current transmission transient stability evaluation, in particular to a DC transmission subsequent commutation failure prediction method and optimization method based on a turn-off angle dynamic equation. BACKGROUND

[0002] Line commutated converter base high-voltage direct current (LCC-HVDC) has the advantages of long-distance large-capacity power transmission, weak synchronous oscillation characteristics and low energy loss, and is widely used in long-distance power transmission. Since LCC-HVDC uses thyristors without self-turn-off capability, when the receiving end AC power grid fails, the commutation valve lacks sufficient commutation support, and the system will experience commutation failure (CF) fault, resulting in receiving end DC blocking and large fluctuations in transmission power. When the AC system experiences a serious fault, if not properly controlled, subsequent commutation failure (SCF) will occur after the first commutation failure (FCF), causing continuous fluctuations in DC power and continuous blocking of the converter station, seriously affecting the safe operation of the power system.

[0003] The problem caused by subsequent commutation failure is more significant, and its prediction and suppression strategy has attracted widespread attention. A large number of prediction methods for commutation failure are based on finding the critical value of the commutation voltage as the prediction criterion. The suppression strategy for subsequent commutation failure can be mainly divided into three categories: adding additional reactive power compensation devices, improving the converter topology, and improving the control strategy. Improving the control strategy is more economical and less difficult to implement, so it has attracted widespread attention. At present, the research on improving the control strategy lacks analysis of the dynamic characteristics of the system, and is also faced with the problem of slow protection and control action due to complex calculation process. SUMMARY

[0004] In view of this, the present application provides a DC transmission subsequent commutation failure prediction method and optimization method based on a turn-off angle dynamic equation.

[0005] The present application discloses a DC transmission subsequent commutation failure prediction method based on a turn-off angle dynamic equation, which comprises:

[0006] Based on the off-angle output characteristics of the inverter side of the LCC-HVDC, the off-angle of the inverter side of the LCC-HVDC is obtained; based on the constant DC current control, the low-voltage current limiting control, the constant off-angle control and the current deviation control of the inverter side, the process of the first commutation failure and the subsequent commutation failure of the LCC-HVDC system is analyzed;

[0007] By combining the control characteristics of the low-voltage current limiting control and the constant off-angle control, through the analysis of the dynamic characteristics of the DC current and the trigger advance angle during the recovery of the first commutation failure, a transient nonlinear differential equation about the off-angle is obtained;

[0008] Based on the transient nonlinear differential equation of the off-angle, the phase diagram curve of the off-angle under different AC voltages and AC voltage rates of change is drawn, and the criterion for predicting the occurrence of the subsequent commutation failure is obtained by analyzing the phase diagram curve.

[0009] Further, the calculation formula of the off-angle of the inverter side of the LCC-HVDC is:

[0010]

[0011] Wherein, γ is the off-angle, β is the trigger advance angle, I dc and U L are the effective values of the DC current and the line voltage of the AC bus of the inverter side respectively; X c is the equivalent commutation reactance.

[0012] Further, the working process of the LCC-HVDC system based on the constant DC current control link, the constant off-angle control link and the current deviation control link of the inverter side includes:

[0013] The LCC-HVDC system includes a rectifier side and an inverter side; both the rectifier side and the inverter side are composed of LCC converter valves, and both the rectifier side and the inverter side are equipped with AC filters and reactive compensators at the AC bus of the converter valves;

[0014] The rectifier side adopts a constant DC current control link, and the DC current reference signal is given by the inverter side; the inverter side is equipped with a constant DC current control link, a constant off-angle control link and a current deviation control link; for the rectifier side, the controller compares the difference between the DC current instruction and the measured DC current, generates the trigger advance angle instruction β rec of the rectifier side after the PI link, and then generates the trigger angle signal α rec to control the action of the converter valve; for the inverter side, the constant DC current control and the constant off-angle control of the inverter side generate the trigger advance angle instruction β inv_C and β inv_GThe larger one of the two is taken as the actual trigger advance angle of the inverter station, and a trigger angle signal is generated to control the operation of the converter valve.

[0015] Further, when the inverter side is in the constant DC current control mode, the DC current is controlled by the controllers of the rectifier side and the inverter side, and according to the current margin principle, the reference instruction in the constant DC current control of the inverter side is lower than that of the rectifier side; the constant DC current control is used to realize the smooth transition between the constant DC current control and the constant turn-off angle control of the inverter side when the DC current instruction is not equal to the actual current;

[0016] Meanwhile, the inverter side is equipped with a low-voltage current limiting control link, which detects the voltage at the midpoint of the DC line after the DC voltage of the inverter side is superimposed with the voltage drop of the compensation resistor when the AC system of the inverter side fails, and when the voltage is reduced to the threshold value of the low-voltage current limiting control, the low-voltage current limiting control will adjust the DC current instruction to reduce the DC current to ensure the safe operation of the system.

[0017] Further, the process of analyzing the first commutation failure and the subsequent commutation failure of the LCC-HVDC system comprises:

[0018] When the AC system of the inverter side fails, the commutation voltage and the turn-off angle decrease, and when the turn-off angle decreases to the minimum turn-off angle, the first commutation failure will occur, at which time the DC side is short-circuited, the DC voltage rapidly decreases, and the DC current instantaneously increases; then the control system starts to act, the low-voltage current limiting control cooperates with the rectifier side to reduce the DC current, the trigger angle of the inverter valve of the inverter side decreases, the inverter valve restores normal commutation, and enters the first commutation failure recovery stage.

[0019] In the first commutation failure recovery stage, if the output DC current of the low-voltage current limiting control rises too fast or the speed of reducing the trigger angle by the constant turn-off angle control of the inverter side cannot adapt to the reactive power demand of the converter valve under fault, the turn-off angle continues to decrease, which will lead to the occurrence of the subsequent commutation failure.

[0020] Further, if the following conditions occur, it is considered that the first commutation failure occurs:

[0021] In the process of commutation of the LCC converter valve, if the converter valve that has just exited the commutation process has not restored the blocking capability and bears the forward voltage drop again, or the commutation process has not been completed during the bearing of the reverse voltage drop, the converter valve will be re-conducted without a trigger signal; the time corresponding to the electrical angle required for the converter valve group to restore the forward blocking capability is defined as the limit turn-off angle, also known as the minimum turn-off angle γ min If the turn-off angle of the inverter side is smaller than the minimum turn-off angle thereof, it is considered that the commutation failure occurs.

[0022] If the following conditions occur, it is considered that the subsequent commutation failure occurs:

[0023] During the recovery period after the system has experienced its first commutation failure, if the shut-off angle again falls below the minimum shut-off angle γ due to the action of the control system... min If this is the case, it is considered that a subsequent commutation failure has occurred.

[0024] Furthermore, the control characteristics combining low-voltage current limiting control and constant turn-off angle control, through analysis of the dynamic characteristics of DC current and trigger lead angle during the recovery period of the first commutation failure, yield a transient nonlinear differential equation regarding the turn-off angle, including:

[0025] The mathematical model for DC current in low-voltage current limiting control is as follows:

[0026]

[0027] in, I represents the per-unit value of the compensated DC line midpoint voltage. dh and I dl These are the upper and lower limits of the DC current, U. dl and U dh I represents the lower and upper limits of the DC voltage. dn This is the rated value of the DC current;

[0028] The DC voltage U of the LCC inverter dc Represented as:

[0029]

[0030] Among them, U L This represents the effective value of the line voltage of the AC bus on the inverter side; β and γ represent the trigger lead angle and turn-off angle, respectively; the compensated DC line midpoint voltage is:

[0031]

[0032] in, I is the compensated DC line midpoint voltage. dc I is the average of the sum of the upper and lower limits of the DC current. dn This is the rated value of the DC current;

[0033] The dynamic characteristics of direct current are expressed as:

[0034]

[0035] The turn-off angle γ, after passing through the constant turn-off angle control structure on the inverter side, yields the following mathematical expression for the trigger lead angle:

[0036] β=(k p +k i / s)(γ ref -γ)

[0037] Where β is the trigger lead angle, γ ref γ and y are the reference value and the turn-off angle, respectively, and k i and k p These are all control parameters for constant turn-off angle control on the inverter side;

[0038] The transient nonlinear differential equation concerning the shut-off angle is expressed as:

[0039]

[0040] Where γ is the shut-off angle. and C1 and C2 represent the derivatives of the turn-off angle and AC voltage, respectively, while C3 and C4 are coefficients determined by the system parameters.

[0041] Furthermore, the expressions for C3 and C4 are:

[0042]

[0043] Furthermore, the criteria for predicting subsequent commutation failures include:

[0044] Calculate C1, C2, C3, and C4 based on the system parameters, and give the effective values ​​of the AC voltage at the current time k and the previous time k-1. Calculate the rate of change of AC voltage at the current moment. Will and Substitute C SCF In the calculation expression, the subsequent commutation failure prediction criterion C is calculated in real time. SCF And determine its size; if C SCF If it is less than zero, it is considered that when the shut-off angle decreases to γ... min If the angle continues to decrease, subsequent commutation failures will occur; conversely, if the angle increases, it indicates that the shut-off angle will not decrease to γ. min The following commutation failure will not occur.

[0045] Furthermore, C SCF The calculation expression is:

[0046]

[0047] This invention also discloses an optimization method for suppressing subsequent commutation failures. Based on the aforementioned DC transmission subsequent commutation failure prediction method using the turn-off angle dynamic equation, which predicts the occurrence of subsequent commutation failures, the method suppresses subsequent commutation failures, comprising:

[0048] If a subsequent commutation failure is predicted, the compensation amount Δγ of the turn-off angle γ is superimposed on the reference value of the turn-off angle control on the inverter side, thereby changing the dynamic characteristics of the turn-off angle during the recovery period of the first commutation failure and suppressing the occurrence of subsequent commutation failures.

[0049] Furthermore, based on the criteria for subsequent commutation failure, a setting value n is obtained. Based on the setting value n, it is determined whether the LCC-HVDC system may experience subsequent commutation failure or whether it will lead to excessively low DC voltage on the inverter side, thereby reducing transmission efficiency.

[0050] Furthermore, the expression for the setting value n is:

[0051]

[0052] Where, k i and k p γ is the control parameter for constant turn-off angle control on the inverter side. ref γ is the reference value for the shut-off angle. min C3 and C4 are coefficients determined by system parameters, representing the minimum shut-off angle. This represents the effective value of the line voltage of the AC bus on the inverter side of the system in steady state.

[0053] Furthermore, the expression for the compensation amount Δγ is:

[0054]

[0055] Among them, U L AC voltage, The rate of change of AC voltage.

[0056] Because of the adoption of the above technical solution, the present invention has the following advantages:

[0057] 1. This invention proposes a prediction method for subsequent commutation failures in conventional DC transmission receiving-end systems under AC grid faults. This method fills the gap in predicting subsequent commutation failures under AC grid faults. The prediction method based on phase diagram analysis can accurately predict whether subsequent commutation failures will occur before they happen, and it has a certain degree of speed, which is beneficial for emergency protection actions of the power system.

[0058] 2. The optimized control strategy for suppressing subsequent commutation failures in conventional DC transmission receiving-end systems proposed in this invention aims to ensure the safe operation of LCC converter valves under AC grid faults and prevent successive commutation failures. The proposed optimized control strategy for subsequent commutation failures dynamically compensates for the reference value of the constant turn-off angle control on the inverter side, thereby altering the dynamic characteristics of the turn-off angle during the recovery period from the first commutation failure. This strategy effectively suppresses subsequent commutation failures under different ground fault conditions, significantly improving system stability and operational reliability.

[0059] 3. This invention first analyzes the dynamic characteristics of DC current and turn-off angle during the recovery period of subsequent commutation failure in LCC-HVDC system, thereby clarifying the mechanism of subsequent commutation failure. It then proposes a prediction method for whether subsequent commutation failure will occur and an optimized control strategy to suppress subsequent commutation failure, which is of great significance for maintaining the safe operation of high voltage DC transmission system. Attached Figure Description

[0060] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments recorded in the embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0061] Figure 1 This is a conventional high-voltage direct current transmission topology diagram provided in the embodiments of this application;

[0062] Figure 2 This is a diagram of the high-voltage direct current transmission control structure provided in an embodiment of this application;

[0063] Figure 3 This application provides a diagram illustrating the commutation failure recovery process and controller action sequence during a system fault, as shown in the embodiments of this application.

[0064] Figure 4 The control structure and its control characteristic diagram for low-voltage current limiting control provided in the embodiments of this application;

[0065] Figure 5 Phase diagram curves of the turn-off angle at different times during the fault process provided in the embodiments of this application;

[0066] Figure 6 A flowchart for subsequent commutation failure prediction provided in this application embodiment;

[0067] Figure 7 The figure shows the test results of the prediction method for three-phase ground faults provided in the embodiments of this application;

[0068] Figure 8The figure shows the test results of the prediction method for single-phase ground faults provided in the embodiments of this application.

[0069] Figure 9 This is a diagram illustrating an optimized control strategy for suppressing subsequent commutation failures provided in an embodiment of this application.

[0070] Figure 10 The figure shows the test results (transition resistance 20Ω) of the optimized control strategy proposed under three-phase ground fault provided in the embodiments of this application.

[0071] Figure 11 Test results (transition resistance 5Ω) of the optimized control strategy proposed under three-phase ground fault provided in the embodiments of this application;

[0072] Figure 12 Test results (transition resistance 50Ω) of the optimized control strategy proposed under single-phase ground fault provided in the embodiments of this application;

[0073] Figure 13 Test results (transition resistance 5Ω) of the optimized control strategy proposed under single-phase ground fault provided in the embodiments of this application. Detailed Implementation

[0074] The present invention will be further described in conjunction with the accompanying drawings and embodiments. The described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art should fall within the protection scope of the present invention.

[0075] Reference Figure 1 and Figure 2 This method provides an embodiment of a DC transmission subsequent commutation failure prediction method based on the turn-off angle dynamic equation, which includes the following steps:

[0076] S1. Based on the output characteristics of the turn-off angle on the inverter side of the LCC-HVDC, a specific calculation formula for the turn-off angle on the inverter side of the LCC-HVDC was constructed. Based on the constant extinction angle control (CEAC), voltage-dependent current order limiter (VDCOL), current error control (CEA), and constant current control (CCC) on the inverter side, the process of the first commutation failure and subsequent commutation failures of the LCC-HVDC system was analyzed. Among them, the constant extinction angle control is a control strategy that maintains the inverter side turn-off angle at a constant value by adjusting the firing angle; the voltage-dependent current order limiter is a control strategy that adjusts the output DC current command according to the DC voltage drop on the inverter side; the current error control is a control strategy that adjusts the output command to help the system achieve a smooth switching of control strategies when the DC current command is not equal to the actual DC current; and the constant DC current control is a control strategy that maintains the DC current on the inverter side at a constant value by adjusting the firing angle.

[0077] S2. Based on the analysis of the first commutation failure recovery process in step S1, it is clarified that the dominant control strategies that determine whether the system will experience subsequent commutation failures during the first commutation failure recovery process are constant turn-off angle control and low-voltage current limiting control. Combining the control characteristics of low-voltage current limiting control and constant turn-off angle control, the transient nonlinear differential equation for the turn-off angle is obtained by analyzing the dynamic characteristics of DC current and trigger lead angle during the first commutation failure recovery period.

[0078] S3. Based on the transient nonlinear differential equation of the turn-off angle established in step S2, plot the phase diagram curves of the turn-off angle under different AC voltages and AC voltage change rates. By analyzing the phase diagram curves, obtain the criteria for predicting whether subsequent commutation failure will occur.

[0079] As an example of this embodiment, refer to Figure 1 The rectifier and inverter sides of the high-voltage direct current transmission system both consist of a twelve-pulse LCC converter valve system composed of two six-pulse LCC converter valves connected in series, and are connected via a DC line. AC filters and reactive power compensators are installed at the AC bus of the converter valves on both the rectifier and inverter sides.

[0080] As another example of this embodiment, refer to Figure 2As shown, the rectifier side employs constant DC current control (CCC), with its DC current reference signal provided by the inverter side. The inverter side is equipped with constant DC current control (CCC), constant turn-off angle control (CEAC), and current deviation control (CEA). For the rectifier side, the DC current I... dc_rec After passing through a first-order filter, the difference between the current and the DC current command is calculated. Then, after passing through a PI (proportional-integral) stage, the trigger lead angle command β on the rectifier side is generated. rec This generates the firing angle signal α. rec The converter valve is controlled to operate, where G1 and T1 are parameters of the first-order filter in the constant DC current control. For the inverter side, the constant DC current control uses the inverter-side DC current I... dc_inv After passing through a first-order filter, the error between the current and the DC current command is converted into a PI (proportional-integral) converter to generate the trigger lead angle command β. inv_C Wherein, G3 and T3 are the parameters of the first-order filter in the constant DC current control on the inverter side. Simultaneously, when the inverter side is under constant DC current control, the DC current is controlled by both the rectifier and inverter side controllers. According to the current margin principle, the reference command in the constant DC control on the inverter side is lower than that on the rectifier side (here, 0.1 pu). The constant turn-off angle control compares the minimum turn-off angle measured in the previous cycle with the turn-off angle reference value γ. ref The error between them is converted into a PI (proportional-integral) signal to generate the lead angle command β. inv_G This error has a certain upper limit threshold, which is -0.544 in this case. Let β be... inv_C and β inv_G The maximum value among them is used as the actual trigger lead angle signal β. inv This generates the firing angle signal α. inv_G The converter valve is controlled to operate. The function of current deviation control is to achieve a smooth transition between constant DC control and constant turn-off angle control strategies when the DC current command is not equal to the actual current.

[0081] Meanwhile, the inverter side is equipped with low-voltage current limiting control, namely VDCOL. When a fault occurs in the AC system on the inverter side, VDCOL detects the DC voltage U. dc_inv The voltage is then filtered first-order and superimposed with the voltage drop across the compensation resistor to serve as the voltage at the midpoint of the DC line; where G2 and T2 are the parameters of the first-order filter in the low-voltage current limiting control. When this voltage drops to the threshold value of VDCOL, VDCOL will adjust the DC current command to reduce the DC current and ensure safe system operation. Compare this current command with the DC current command I under normal operation. des The smaller value in the equation is used as the actual DC current command passed to the rectifier side.

[0082] As another embodiment of the present invention, this embodiment further supplements and elaborates on the technical solution of the present invention based on the above embodiments. In this embodiment, the turn-off angle of the LCC-HVDC inverter side constructed in step S1 is related to the DC current, AC voltage, and trigger lead angle. The specific calculation formula is as follows:

[0083]

[0084] Where γ is the turn-off angle, β is the trigger lead angle, and I dc with U L These are the effective values ​​of the DC current and the line voltage of the AC bus on the inverter side, respectively; X c This is the equivalent commutation reactance.

[0085] In step S1, during the commutation process of the LCC converter valve, if the valve that has just exited the commutation process has not yet regained its blocking capability and is subjected to a forward pressure drop again, or if the commutation process is not completed while the converter valve is subjected to a reverse pressure drop, then the converter valve will be turned on again without a trigger signal. This phenomenon is called commutation failure. The electrical angle corresponding to the time required for the converter valve group to regain its forward blocking capability is defined as the limiting shut-off angle, also known as the minimum shut-off angle γ. min (Typically 7.2°). If the turn-off angle on the inverter side is less than its minimum turn-off angle, then commutation failure is considered to have occurred.

[0086] The commutation failure process described in step S1 is attached. Figure 3 As shown. When a short-circuit fault occurs in the inverter-side AC system, the commutation voltage and turn-off angle decrease accordingly. When the turn-off angle decreases to the minimum turn-off angle, an FCF (Fault-Cooled Fault) will occur. Figure 3 At time t1, a short circuit occurs on the DC side, causing a rapid decrease in DC voltage and a momentary increase in DC current. Subsequently, the control system activates, with VDCOL (typically activated within 10ms) coordinating with the rectifier side to reduce the DC current. Simultaneously, CEAC deactivates, decreasing the firing angle of the inverter-side converter valve. Under their combined action, the converter valve resumes normal commutation. Figure 3 At time t2, the shut-off angle will instantaneously rise to its maximum value γ. max Entering the recovery phase after the initial commutation failure.

[0087] During the recovery phase from the initial commutation failure, if the controller is properly coordinated, the shut-off angle will change from γ. max Gradually decrease to the reference value γ of the constant shut-off angle controller ref The system will return to stability; however, if the controller is not properly coordinated, such as the VDCOL output DC current rising too quickly or the CEAC reducing the firing angle too slowly to meet the reactive power demand of the converter valve under fault conditions, the shut-off angle will continue to decrease until it falls below γ again. min ,correspondFigure 3 At time t3, subsequent commutation failure (SCF) will occur, corresponding to... Figure 3 At time t4 in the data.

[0088] During the recovery from the initial commutation failure and the subsequent commutation failure, control mechanisms such as VDCOL and CEAC begin to operate. These control mechanisms are key factors in predicting and suppressing subsequent commutation failures. In this process, the rectifier side uses CCC (Continuous Current Control). If the inverter side also uses CCC, the magnitude of the DC current is simultaneously controlled by both the rectifier and inverter stations. Ambiguity in the control commands will lead to DC current fluctuations, exacerbating the risk of subsequent commutation failures. Therefore, it is generally not recommended to use CCC on the inverter side during the initial commutation recovery period. Thus, this invention primarily considers the influence of VDCOL and CEAC in its analysis of subsequent commutation failures.

[0089] In step S2, the control structure and control characteristics of VDCOL are as follows: Figure 4 As shown in (a) and (b) above, the mathematical model of DC current based on VDCOL is as follows:

[0090]

[0091] in, This represents the per-unit value of the midpoint voltage of the compensated DC line. dh and I dl These are the upper and lower limits of the DC current, respectively; U dl and U dh I represents the lower and upper limits of the DC voltage. dn This is the rated value of the DC current.

[0092] In step S2, for the twelve-pulse LCC inverter under study, its DC voltage can be expressed as:

[0093]

[0094] Among them, U L This represents the effective value of the line voltage of the AC bus on the inverter side; β and γ represent the trigger lead angle and turn-off angle, respectively. The compensated DC line midpoint voltage is:

[0095]

[0096] Among them, I dc I is the average of the sum of the upper and lower limits of the DC current. dn This is the rated value of the DC current.

[0097] In step S2, from the initial commutation failure to the point before subsequent commutation failures occur, the commutator valve has resumed normal commutation. The commutation voltage remains essentially constant at a relatively low value, the output of VDCOL remains essentially constant, and the change in DC current is very small. Therefore, the dynamic characteristics of the DC current can be expressed as:

[0098]

[0099] In step S2, the mathematical expression for the trigger lead angle obtained by the CEAC control structure from the turn-off angle γ is:

[0100] β=(k p +k i / s)(γ ref -γ)

[0101] Where β is the trigger lead angle, γ ref γ and y are the reference value and the turn-off angle, respectively, and k i and k p These are the control parameters for CEAC.

[0102] The transient nonlinear differential equation concerning the turn-off angle γ mentioned in step S2 specifically refers to the transient nonlinear differential equation concerning the turn-off angle γ obtained by considering the dynamic characteristics of the DC current during the recovery period of the first commutation failure, the trigger lead angle, and the influence of the trigger lead angle β on the turn-off angle γ, as well as the influence of line impedance and AC voltage on transient characteristics. It is expressed as:

[0103]

[0104] in, and These represent the derivatives of the turn-off angle and the AC voltage, respectively. C3 and C4 are coefficients determined by the system parameters, expressed as:

[0105]

[0106] As can be seen, when the shut-off angle changes to a certain specific value, its rate of change... It is determined by the system control parameters, AC voltage, and the derivative of the AC voltage. If, after recovery from the initial commutation failure, the rate of change... If the value is always less than zero, the turn-off angle will continue to decrease until it falls below the minimum turn-off angle γ required for carrier recombination in the converter valve. min This leads to subsequent commutation failure.

[0107] As another embodiment of the present invention, this embodiment further supplements and elaborates on the technical solution of the present invention based on the above embodiments. In this embodiment, the plotting of the phase diagram curve with respect to the turn-off angle specifically refers to plotting the phase diagram curve with different AC voltages and AC voltage change rates by combining the transient nonlinear differential equation of the turn-off angle γ in step S2. Curve. The specific process is as follows: Figure 5 As shown.

[0108] Figure 5 ① The solid line in the middle represents the system in steady state. The intersection of the phase diagram curve and the horizontal axis (point a) is the steady point, and the corresponding turn-off angle is γ. ref At this time, the inverter side maintains γ = γ under the action of CEAC. ref After a fault occurred in the AC system, normal commutation resumed after a brief initial commutation failure. At different times after the initial commutation failure was recovered, the system operated at... Figure 5 On the solid lines ②, ③, or ④ in the text.

[0109] Taking the solid line in ② as an example, the stable point of the system (point b) is at γ. min To the right of γ, the shut-off angle will not continue to decrease to γ. min Therefore, subsequent commutation failure will not occur. When the system operates on line ④ (solid line), its stable point (point d) is at γ. min The left side indicates that, in this case, γ will continuously decrease during the recovery process from the first commutation failure until it is less than γ. min This leads to subsequent commutation failure. From the dynamic change of the turn-off angle, if γ = γ... min Always This indicates that the turn-off angle γ will continue to decrease even when it reaches its minimum turn-off angle, and subsequent commutation failure will occur.

[0110] The criteria for predicting whether subsequent commutation failure will occur are further defined as follows:

[0111]

[0112] The γ = γ is determined by the interaction between the current AC voltage and its rate of change and the controller (VDCOL and CEAC). min The changing trend of the inverter's turn-off angle at any given time. If C SCF If the value is less than 0, subsequent commutation will fail. The specific prediction process is as follows: Figure 6 As shown.

[0113] First, calculate C1, C2, C3, and C4 based on the system parameters. Then, the measurement unit provides the effective values ​​of the AC voltage at the current time k and the previous time k-1. Calculate the rate of change of AC voltage at the current time k. Where Δf is the sampling interval time. The AC voltage at time k and its rate of change are... and Substitute C SCF In the calculation expression, the subsequent commutation failure prediction criterion C is calculated in real time. SCF And determine its size. If the calculated C SCF If it is less than zero, it is considered that when the shut-off angle decreases to γ... min If it continues to decrease, subsequent commutation failures will occur; conversely, if C... SCF If it is zero, it means that the shut-off angle will not decrease to γ. min Therefore, no subsequent commutation failure will occur.

[0114] As another embodiment of the present invention, this embodiment further supplements and elaborates on the technical solution of the present invention based on the above embodiments. This embodiment provides verification results of the proposed method under different transition resistances and different fault times in the case of a three-phase ground fault or a single-phase ground fault in AC measurement. The AC measurement faults were set to occur at 1s, 1.004s, 1.008s, 1.012s, 1.016s, and 1.20s, respectively, with a fault duration of 0.5s. The verification results are as follows. Figure 7 and Figure 8 As shown.

[0115] Figure 7 and Figure 8 In the diagram, a square with a time indicator indicates a successful prediction of subsequent commutation failures. This time represents the time margin between the proposed method's prediction of a subsequent commutation failure and the actual occurrence of the subsequent commutation failure in the system. A square without a time indicator and with a single slash indicates a successful prediction of only the first commutation failure. A square without a time indicator and with two intersecting slashes indicates that the prediction result does not match the actual result.

[0116] As can be seen, under different transition resistances and different fault times within one power frequency cycle, the proposed prediction method exhibits good predictive performance for both single-phase and three-phase grounding faults, accurately predicting whether subsequent commutation failures will occur. The prediction accuracy can reach over 90%.

[0117] See Figure 9 The present invention also provides an embodiment of an optimized method for suppressing subsequent commutation failures. Based on the prediction of subsequent commutation failures using the DC transmission subsequent commutation failure prediction method based on the turn-off angle dynamic equation described in the above embodiment, the method suppresses subsequent commutation failures by first: [The method then proceeds to] suppress the subsequent commutation failures. This includes: [The method then proceeds to] firstly, [the ... L After processing, its rate of change U is obtained. LAs mentioned above, C SCF The expression calculates the subsequent commutation failure prediction criterion C. SCF If a subsequent commutation failure is predicted, an optimized control strategy is initiated. The calculated compensation amount Δγ of the turn-off angle γ is superimposed on the reference value of the turn-off angle control on the inverter side, thereby changing the dynamic characteristics of the turn-off angle during the recovery period of the first commutation failure and suppressing the occurrence of subsequent commutation failures.

[0118] If n is too small, the improvement effect will be insignificant, and the system may still experience subsequent commutation failures; if n is too large, it will lead to excessively low DC voltage on the inverter side, reducing transmission efficiency. Considering both safety margin and energy loss, this paper takes n as the steady-state value of C. SCF 1.5 times as the setting value, that is:

[0119]

[0120] in, This represents the effective value of the line voltage of the AC bus on the inverter side of the system in steady state.

[0121] The correctness of the above embodiments will be verified through specific examples below.

[0122] A three-phase resistive ground fault occurs at AC bus M at time 1 second, lasting 0.5 seconds, with a transition resistance of 20Ω. The test results are the system's turn-off angle γ before and after optimized control is initiated, as well as the DC voltage U. dc The results are as follows: Figure 10 As shown in (a), (b), (c), and (d) in the figure; the turn-off angle γ and DC voltage U of the system with optimized control not started and with optimized control started, obtained by testing with a transition resistance of 5Ω. dc The results are as follows: Figure 11 As shown in (a), (b), (c), and (d) in the figure.

[0123] Test results show that when the original system experiences a three-phase ground fault with a transition resistance of 20Ω and 5Ω on the AC bus, subsequent commutation failures occur after the first commutation failure, leading to a reduction in the turn-off angle to 0, a DC short circuit, and a rapid drop in DC voltage to zero. However, after implementing the proposed optimized control, the system can resume stable operation in both test scenarios after the first commutation failure without subsequent commutation failures, thus verifying the effectiveness of the proposed optimized control strategy under symmetrical faults.

[0124] A single-phase resistive ground fault occurs at AC bus M at time 1 second, lasting 0.5 seconds, with a transition resistance of 50Ω. The test results show the turn-off angle γ (without optimized control) and the DC voltage U (with optimized control activated). dc The results are as follows: Figure 12As shown in (a), (b), (c), and (d) of the figure. The transition resistance is 5Ω. The measured values ​​of the system's turn-off angle γ and DC voltage U before and after optimized control are obtained. dc The results are as follows: Figure 13 As shown in (a), (b), (c), and (d) in the figure.

[0125] Test results show that when the original system experiences a single-phase ground fault with a transition resistance of 50Ω on the AC bus, multiple subsequent commutation failures will occur after the first commutation failure, causing the turn-off angle to drop to 0 multiple times and the DC voltage to fluctuate significantly multiple times. However, after starting the proposed optimized control, subsequent commutation failures will not occur, the turn-off angle will always fluctuate above the minimum turn-off angle, and the DC voltage will not drop to zero.

[0126] When the original system experienced a single-phase ground fault with a transition resistance of 5Ω on the AC bus, commutation failures occurred multiple times within a short period after the fault, causing the turn-off angle to drop to zero and the DC voltage to fluctuate continuously. However, after implementing the proposed optimized control, although the DC voltage still fluctuates, the turn-off angle does not drop to zero after the first commutation failure. This demonstrates that even with an asymmetrical fault on the AC side, the proposed optimized control strategy retains a certain degree of reliability, reducing the risk of subsequent commutation failures and improving system stability.

[0127] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for predicting subsequent commutation failure in DC transmission based on the dynamic equation of the turn-off angle, characterized in that, include: Based on the output characteristics of the turn-off angle of the LCC-HVDC inverter side, the turn-off angle of the LCC-HVDC inverter side is obtained. Based on the constant DC current control, low voltage current limiting control, constant turn-off angle control and current deviation control on the inverter side, the process of the first commutation failure and subsequent commutation failure of the LCC-HVDC system is analyzed. By combining the control characteristics of low-voltage current limiting control and constant turn-off angle control, and analyzing the dynamic characteristics of DC current and trigger lead angle during the recovery period of the first commutation failure, a transient nonlinear differential equation for the turn-off angle is obtained. Based on the transient nonlinear differential equation of the turn-off angle, phase diagram curves of the turn-off angle under different AC voltages and AC voltage change rates are plotted. By analyzing the phase diagram curves, a criterion for predicting the occurrence of subsequent commutation failure is obtained. The operation process of the LCC-HVDC system, based on constant DC current control, constant turn-off angle control, and current deviation control on the inverter side, includes: The LCC-HVDC system includes a rectifier side and an inverter side; both the rectifier side and the inverter side are composed of LCC converter valves, and AC filters and reactive power compensators are equipped at the AC bus of the converter valves on both the rectifier side and the inverter side. The rectifier side employs constant DC current control, with its DC current reference signal provided by the inverter side. The inverter side is equipped with constant DC current control, constant turn-off angle control, and current deviation control. For the rectifier side, the controller compares the difference between the DC current command and the measured DC current, and after passing through a PI controller, generates the rectifier side's trigger lead angle command β. rec This generates the firing angle signal α. rec Controlling the converter valve operation; for the inverter side, two control strategies, constant DC current control and constant turn-off angle control, respectively generate the inverter side trigger lead angle command β by passing the DC current error and turn-off angle error through a PI circuit. inv_C With β inv_G The larger of the two values ​​is taken as the actual trigger lead angle of the inverter station, and then a trigger angle signal is generated to control the operation of the converter valve.

2. The method for predicting subsequent commutation failure in DC transmission based on the dynamic equation of the turn-off angle according to claim 1, characterized in that, The formula for calculating the turn-off angle on the LCC-HVDC inverter side is as follows: Where γ is the turn-off angle, β is the trigger lead angle, and I dc with U L These are the effective values ​​of the DC current and the line voltage of the AC bus on the inverter side, respectively; X c This is the equivalent commutation reactance.

3. The method for predicting subsequent commutation failure in DC transmission based on the dynamic equation of the turn-off angle according to claim 1, characterized in that, When the inverter side is in constant DC current control mode, the DC current is controlled by the controllers on both the rectifier side and the inverter side. According to the current margin principle, the reference command in the constant DC current control on the inverter side is lower than that on the rectifier side. The function of constant DC current control is to achieve a smooth transition between the two control strategies of constant DC current control and constant turn-off angle control on the inverter side when the DC current command is not equal to the actual current. Meanwhile, the inverter side is equipped with low-voltage current limiting control. When a fault occurs in the AC system on the inverter side, the low-voltage current limiting control detects the voltage at the midpoint of the DC line after the DC voltage on the inverter side is superimposed on the voltage drop of the compensation resistor. When it drops to the threshold value of the low-voltage current limiting control, the low-voltage current limiting control will adjust the DC current command to reduce the DC current in order to ensure the safe operation of the system.

4. The method for predicting subsequent commutation failure in DC transmission based on the dynamic equation of the turn-off angle according to claim 1, characterized in that, The analysis of the initial commutation failure and subsequent commutation failure processes of the LCC-HVDC system includes: When a short-circuit fault occurs in the inverter-side AC system, the commutation voltage and turn-off angle decrease accordingly. When the turn-off angle decreases to the minimum turn-off angle, the first commutation failure will occur. At this time, the DC side is short-circuited, the DC voltage drops rapidly, and the DC current rises instantaneously. Subsequently, the control system starts to operate. The low-voltage current limiting control works in conjunction with the rectifier side to reduce the DC current and decrease the trigger angle of the inverter-side converter valve. The converter valve resumes normal commutation, and the system enters the first commutation failure recovery stage. During the recovery phase of the first commutation failure, if the output DC current of the low-voltage current limiting control rises too quickly or the rate at which the constant turn-off angle control reduces the firing angle cannot keep up with the reactive power demand of the converter valve under fault conditions, and the turn-off angle continues to decrease, it will lead to subsequent commutation failures.

5. The method for predicting subsequent commutation failure in DC transmission based on the dynamic equation of the turn-off angle according to claim 1, characterized in that, The first commutation is considered to have failed if the following occurs: During the commutation process of an LCC converter valve, if the converter valve that has just exited the commutation process has not yet regained its blocking capability and is subjected to a forward pressure drop again, or if the commutation process of the converter valve has not been completed while it is subjected to a reverse pressure drop, then the converter valve will be turned on again without a trigger signal. The electrical angle corresponding to the time required for the converter valve group to regain its forward blocking capability is defined as the limiting shut-off angle, also known as the minimum shut-off angle γ. min If the turn-off angle on the inverter side is less than its minimum turn-off angle, then commutation failure is considered to have occurred. The following conditions indicate that subsequent commutation has failed: During the recovery period after the system has experienced its first commutation failure, if the shut-off angle again falls below the minimum shut-off angle γ due to the action of the control system... min If this is the case, it is considered that a subsequent commutation failure has occurred.

6. The method for predicting subsequent commutation failure in DC transmission based on the dynamic equation of the turn-off angle according to claim 1, characterized in that, The control characteristics combining low-voltage current limiting control and constant turn-off angle control, through analysis of the dynamic characteristics of DC current and trigger lead angle during the recovery period of the first commutation failure, yield a transient nonlinear differential equation regarding the turn-off angle, including: The mathematical model for the DC current of VDCOL is: in, I represents the per-unit value of the compensated DC line midpoint voltage. dh and I dl These are the upper and lower limits of the DC current, U. dl and U dh I represents the lower and upper limits of the DC voltage. dn This is the rated value of the DC current; The DC voltage U of the LCC inverter dc Represented as: Among them, U L This represents the effective value of the line voltage of the AC bus on the inverter side; β and γ represent the trigger lead angle and turn-off angle, respectively; the compensated DC line midpoint voltage is: in, I is the compensated DC line midpoint voltage. dc I is the average of the sum of the upper and lower limits of the DC current. dn This is the rated value of the DC current; The dynamic characteristics of direct current are expressed as: The turn-off angle γ, after passing through the constant turn-off angle control structure on the inverter side, yields the following mathematical expression for the trigger lead angle: β=(k p +k i / s)(c ref -c) Where β is the trigger lead angle, γ ref γ and y are the reference value and the turn-off angle, respectively, and k i and k p These are all control parameters for constant turn-off angle control on the inverter side; The transient nonlinear differential equation concerning the shut-off angle is expressed as: Where γ is the shut-off angle. and C1 and C2 represent the derivatives of the turn-off angle and AC voltage, respectively, while C3 and C4 are coefficients determined by the system parameters.

7. The method for predicting subsequent commutation failure in DC transmission based on the dynamic equation of the turn-off angle according to claim 6, characterized in that, The expressions for C3 and C4 are:

8. The method for predicting subsequent commutation failure in DC transmission based on the dynamic equation of the turn-off angle according to claim 6, characterized in that, The criteria for predicting subsequent commutation failures include: Calculate C1, C2, C3, and C4 based on the system parameters, and give the effective values ​​of the AC voltage at the current time k and the previous time k-1. Calculate the rate of change of AC voltage at the current time k. Will and Substitute C SCF In the calculation expression, the subsequent commutation failure prediction criterion C is calculated in real time. SCF And determine its size; if C SCF If it is less than zero, it is considered that when the shut-off angle decreases to γ... min If the angle continues to decrease, subsequent commutation failures will occur; conversely, if the angle increases, it indicates that the shut-off angle will not decrease to γ. min The following commutation failure will not occur.

9. The method for predicting subsequent commutation failure in DC transmission based on the dynamic equation of the turn-off angle according to claim 8, characterized in that, C SCF The calculation expression is: Where, γ min It is the minimum shut-off angle.

10. An optimization method for suppressing subsequent commutation failure, wherein the subsequent commutation failure is predicted by the DC transmission subsequent commutation failure prediction method based on the turn-off angle dynamic equation as described in any one of claims 1-9, and subsequent commutation failure is suppressed, characterized in that, include: If a subsequent commutation failure is predicted, the compensation amount Δγ of the turn-off angle γ is superimposed on the reference value of the turn-off angle control on the inverter side, thereby changing the dynamic characteristics of the turn-off angle during the recovery period of the first commutation failure and suppressing the occurrence of subsequent commutation failures.

11. The optimized method for suppressing subsequent commutation failure according to claim 10, characterized in that, Based on the criteria for subsequent commutation failure, the setting value n is obtained. Based on the setting value n, it is determined whether the LCC-HVDC system may experience subsequent commutation failure or whether it will lead to excessively low DC voltage on the inverter side, thereby reducing transmission efficiency.

12. The optimized method for suppressing subsequent commutation failure according to claim 11, characterized in that, The expression for the setpoint n is: Where, k i and k p γ is the control parameter for constant turn-off angle control on the inverter side. ref γ is the reference value for the shut-off angle. min C3 and C4 are coefficients determined by system parameters, representing the minimum shut-off angle. This represents the effective value of the line voltage of the AC bus on the inverter side of the system in steady state.

13. The optimized method for suppressing subsequent commutation failure according to claim 12, characterized in that, The expression for the compensation amount Δγ is: Among them, U L AC voltage, The rate of change of AC voltage.

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