Subsequent commutation failure suppression method and system for adaptively compensating turn-off angle vacancy

Abstract

The invention discloses a subsequent commutation failure suppression method and system for adaptively compensating turn-off angle vacancy. Firstly, the influence of electrical quantity and control quantity changes on a turn-off angle is researched on the basis of an interaction mechanism between the electrical quantity and the control quantity; secondly, decoupling of the electrical quantity and the control quantity is achieved through a Taylor series expansion method, and a single expression between the turn-off angle variable quantity and the lead trigger angle variable quantity is deduced and established; on the basis, a follow-up commutation failure risk coefficient KSCFRF is defined, and suppression of follow-up commutation failure and risk assessment are achieved through the single relation established by the KSCFRF and the advance trigger angle variable quantity. For an area with high subsequent commutation failure risk, the method comprehensively considers the influence of the strong coupling characteristic of the electrical quantity and the control quantity on the turn-off angle, adaptive compensation can be carried out according to the vacancy of the turn-off angle at different moments, and the commutation margin is increased.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of line commutated converter based high-voltage direct current (LCC-HVDC), and particularly relates to a method and system for inhibiting subsequent commutation failure by self-adaptive compensation of missing extinction angle. BACKGROUND

[0002] Line commutated converter based high-voltage direct current (LCC-HVDC) has advantages of large transmission capacity, long transmission distance, and small system loss, and can effectively solve the problem of "reverse distribution" of energy and load in China, meet the urgent needs of large-scale new energy development and utilization, load center power supply, and construction of "new power system". Commutation failure is one of the common faults of LCC-HVDC. During the commutation failure recovery process, if the electrical quantities and control quantities interact improperly, subsequent commutation failure is easily triggered, and in severe cases, the DC system is even locked, which greatly threatens the safe and stable operation of the power system. Moreover, the strong coupling characteristics between electrical quantities and between electrical quantities and control quantities aggravate the difficulty of risk assessment of subsequent commutation failure, resulting in limited effect of the inhibition strategy. Therefore, the analysis of subsequent commutation failure under multi-factor interaction coupling and the research on inhibition strategy can not only effectively assess the risk of subsequent commutation failure under multi-factor interaction coupling, but also improve the inhibition effect and perfect the subsequent commutation failure inhibition strategy system.

[0003] For the research on the mechanism of subsequent commutation failure, mainly includes improper interaction of controllers, insufficient commutation area, and severe fluctuation of electrical quantities under DC control. From the perspective of controller switching in the commutation failure recovery process, improper coordination between controllers is the main reason for the occurrence of subsequent commutation failure. Based on the commutation area theory, comparing the required commutation area in the commutation process with the area that can be provided by the AC system, it can be concluded that insufficient commutation area is a direct factor leading to subsequent commutation failure. The existing technology uses voltage dependent current order limiter (VDCOL) to analyze the variation characteristics of the extinction angle in the power operating range, and on this basis, considering the recovery characteristics of DC current and converter bus voltage, the mechanism of subsequent commutation failure under small disturbance is revealed. The multi-angle research on the mechanism of subsequent commutation failure does not consider the interaction coupling between electrical quantities and control quantities, the reason is that there are many factors affecting the extinction angle and it cannot be analyzed in transient state, it is difficult to establish the mathematical relationship between the extinction angle and a single variable, resulting in unclear variation trend of the extinction angle under multi-factor interaction coupling and unknown risk of subsequent commutation failure.

[0004] Research on strategies to mitigate subsequent commutation failures has primarily focused on adding relevant equipment, modifying converter topologies, and optimizing DC control. Among these, optimized DC control has attracted widespread attention due to its stable control effects and ease of implementation.

[0005] Currently, optimizing DC control mainly includes two aspects. The first is to improve VDCOL based on the fault recovery process. Existing technology research includes:

[0006] 1. Start by improving the starting voltage threshold and the slope of the dynamic adjustment curve to reduce electrical quantity mutations and improve the system's fault perception capability.

[0007] 2. Based on the mechanism of continuous commutation failure, and further considering the changes in DC electrical quantities, a restrictive low-voltage current-limiting control strategy was proposed. However, due to the limitations of VDCOL itself, this strategy for improving VDCOL only works on DC current. Dynamically adjusting the control variable based on changes in DC current inevitably reduces control effectiveness during the feedback control process. A second approach is to focus on the changing characteristics of electrical quantities and dynamically adjust the corresponding control variable.

[0008] 3. Based on the steady-state operating range of DC current and reactive power, a turn-off angle compensation control strategy is proposed. When the DC electrical quantity does not match the trigger angle command, the inverter is at high risk of subsequent commutation failure. Reducing the trigger angle deviation can effectively suppress subsequent commutation failure. Further research on asymmetric faults reveals that switching point hysteresis in the inverter controller under the influence of negative-sequence current and harmonic currents increases the risk of subsequent commutation failure. Based on this, a fixed turn-off angle acceleration control scheme is proposed.

[0009] The above research mainly suppresses subsequent commutation failure by optimizing DC control and adjusting DC electrical quantities, but ignores the direct effect of the control quantity on the turn-off angle, which will cause controller misjudgment and make it difficult to ensure the suppression effect. Summary of the Invention

[0010] Purpose of the invention: To solve the above problems, the present invention provides a method for suppressing subsequent commutation failure by adaptively compensating for the cut-off angle deficiency. Based on the method, the present invention also provides a control system for subsequent commutation failure by adaptively compensating for the cut-off angle deficiency. The system includes a subsequent commutation failure risk coefficient K SCFRF The calculation module.

[0011] Technical solution: A method for suppressing subsequent commutation failure by adaptively compensating for the turn-off angle shortfall, the method includes establishing a subsequent commutation failure risk coefficient K SCFRF and the turn-off angle compensation Δγ m The single relationship between them, and then by measuring the corresponding electrical quantities and control quantities to determine the K at different times SCFRF The value of K SCFRFWhen it is a negative value, the cut-off angle compensation is applied;

[0012] The subsequent commutation failure risk factor K SCFRF It is calculated from the LCC-HVDC system parameters, inverter-side electrical quantities, and control quantities. First, based on the interaction mechanism between electrical quantities and control quantities, the impact of changes in electrical quantities and control quantities on the shutdown angle is analyzed. Then, the Taylor series expansion method is used to decouple electrical quantities and control quantities, thereby deriving a single expression for the change in the shutdown angle and the change in the advance trigger angle:

[0013] Δγ=K SCFRF Δβ

[0014] When the trend and degree of the overdue trigger angle change Δβ are determined, the subsequent commutation failure risk coefficient K SCFRF Determine the turn-off angle change Δγ and compensate for the turn-off angle shortfall at the turn-off angle error of the inverter-side CEA control. The turn-off angle compensation Δγ m Determined according to the turn-off angle change Δγ.

[0015] Furthermore, the subsequent commutation failure risk coefficient K SCFRF By measuring the LCC-HVDC system parameters, inverter side DC current I d , inverter side commutation bus voltage U Li And the control quantity β is calculated. When the system parameters are determined, the turn-off angle γ is affected by the system electrical quantity I d and U Li The influence of the control quantity β of the control system in the commutation failure recovery stage is also considered.

[0016] Subsequent commutation failure risk factor K SCFRF The conversion calculation includes:

[0017] (1) When the inverter side shutdown angle γ is less than the minimum shutdown angle γ min When , the inverter fails to commutate. According to the commutation process and principle, the turn-off angle γ is expressed as:

[0018]

[0019] Where: I d is the DC current on the inverter side, X ci is the inverter side commutation reactance; U Li is the inverter side commutation bus voltage; T i is the inverter side converter transformer ratio; β is the leading trigger angle;

[0020] The above formula is regarded as the cut-off angle γ with respect to I d 、U Liand β, and then expand it according to Taylor's formula, ignoring the second-order and higher differential terms and remainders, to obtain the approximate function of the turn-off angle γ:

[0021]

[0022] Where: γ0, I d0 、U Li0 and β0 are the values ​​of the corresponding electrical quantity and control quantity at time t0 respectively;

[0023] When the time interval Δt is very small and can be ignored, the change in the turn-off angle Δγ is converted into the following formula:

[0024]

[0025] Based on the commutation principle, I d 、U Li And β find the partial derivative:

[0026]

[0027] The above formula shows that the change of the inverter side turn-off angle γ depends not only on the size of the corresponding electrical quantity and control quantity at time t0, but also on the DC current change ΔI d , trigger angle change Δβ and inverter side commutation bus voltage change ΔU Li related;

[0028] (2) Q under commutation failure di with U Li The relationship is expressed as:

[0029]

[0030] Where: U LiN is the rated value of the inverter side commutation bus voltage; S ci is the short-circuit capacity of the AC system on the inverter side; Q aciN Q is the reactive power fed into the commutation bus by the receiving AC system in steady state; ciN Reactive power provided by the reactive compensation device at the receiving end in steady state;

[0031] In order to further clarify the changing trend of Δγ during the recovery process of commutation failure, a mathematical expression of Δγ and a single variable Δβ is established. The changing characteristics of Δγ are analyzed according to Δβ. The Taylor formula is used to expand it, ignoring the second-order and higher differential terms and remainders. ΔU Li Expressed as:

[0032]

[0033] Change in reactive power consumed by the inverter ΔQ di and ΔI d , ΔULi and the inverter side DC voltage change ΔU di The relationship is:

[0034]

[0035] to I d 、U Li and U di Find the partial derivative:

[0036]

[0037] Arranged to get ΔU di and ΔI d and ΔU di The relationship is:

[0038]

[0039] The above formula shows that ΔU di With ΔU Li and ΔI d relationship;

[0040] (3) Using Taylor series expansion, ΔU di Expressed as:

[0041]

[0042] ΔU Li , Δβ and ΔI d Taking partial derivatives we get:

[0043]

[0044] Organize U Li , Δβ and ΔI d The relationship is:

[0045] ΔU Li =K a1 ΔI d +K a2 Δβ

[0046] in:

[0047]

[0048] Δγ and ΔI d The relationship between and Δβ is expressed as:

[0049]

[0050] The above formula shows that I d with U dr and U di The relationship between the two is that within the time of Δt, when Udi When U dr cannot be adjusted in time;

[0051] (4) Perform equivalent circuit processing on the high voltage DC system, where Expand it using Taylor's formula, ignoring the second-order and higher differential terms and remainders, ΔU di It can be expressed as:

[0052]

[0053] After finishing, we can get:

[0054] ΔI d The relationship with Δβ is:

[0055]

[0056] Based on the above formula Δγ and ΔI d The relationship between Δγ and the single variable Δβ is constructed as follows:

[0057] Δγ=K SCFRF Δβ

[0058] Among them, K SCFRF Defined as the subsequent commutation failure risk factor:

[0059]

[0060] Based on the implementation of the above method, the present invention provides a subsequent commutation failure control system that adaptively compensates for the turn-off angle shortfall, and the system also includes a subsequent commutation failure risk coefficient K SCFRF The calculation module is used to perform the coefficient calculation in the subsequent commutation failure suppression method, specifically including calculating the coefficient K that satisfies the following relationship U1 , K a2 , K U2 , K U3 、R d , K U1 , K a1 , and K a2 :

[0061]

[0062] It is to be noted that the above coefficient K U1 , K a2 , K U2 , K U3 、R d , K U1 , K a1 , and Ka2 The actual physical meaning is the intermediate coefficient in the analysis of the interaction mechanism between electrical quantities and control quantities, which is used to calculate the subsequent commutation failure risk coefficient K. SCFRF .

[0063] Beneficial Effects: Compared with the prior art, the present invention analyzes the changing trends and interaction mechanisms of electrical and control variables during commutation failure recovery, and uses the Taylor series expansion method to obtain an expression for the turn-off angle variation under multi-factor interactive coupling. Based on this approach, significant effects include:

[0064] 1) Aiming at the expression of the turn-off angle with multiple factors interacting and coupling, the Taylor series expansion method is used to decouple the electrical quantity and the control quantity, and a single expression of the turn-off angle change and the advance trigger angle change is obtained. The subsequent commutation failure risk coefficient K is proposed. SCFRF , using the change in the advance firing angle and K SCFRF The change trend of the shut-off angle can be judged;

[0065] 2)K SCFRF It is related to the DC current, the DC voltage on the inverter side and the commutation bus voltage on the inverter side. K SCFRF Positive and negative, when K SCFRF When K is positive, the leading trigger angle is increased and the risk of subsequent commutation failure is reduced. SCFRF When it is negative, the leading trigger angle increases, and the risk of subsequent commutation failure increases;

[0066] 3) The subsequent commutation failure suppression method proposed by the present invention can utilize K SCFRF Calculate the size of the cut-off angle gap and compensate it, without the need to adjust K according to different working conditions. SCFRF The adjustment is more universal and can effectively suppress the occurrence of subsequent commutation failures. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is the equivalent circuit diagram of the high voltage DC system;

[0068] Figure 2 This is a typical three-phase ground fault simulation waveform;

[0069] Figure 3 is the commutation failure recovery period K SCFRF and the changes in β;

[0070] Figure 4 Is to use K SCFRF Adaptive compensation shut-off angle deficiency control block diagram;

[0071] Figure 5 shows the system parameter variation characteristics under different control schemes and fault severity;

[0072] Figure 6 is the dynamic process of increasing the influence of β on γ;

[0073] Figure 7 is a stage 4 subdivision schematic diagram;

[0074] Figure 8 is the change of the influence of β on γ in different regions (case one);

[0075] Figure 9 is the change of the influence of β on γ in different regions (case two);

[0076] Figure 10 is the increase of the influence of β on the inverter side constant current control switching to constant off angle control switching point;

[0077] Figure 11 is a system parameter change characteristic under different control schemes and SCRs, wherein Figure 11(A) corresponds to SCR=3, Figure 11(B) corresponds to SCR=4, and Figure 11(C) corresponds to SCR=5;

[0078] Figure 12 is the K SCFRF change with β;

[0079] Figure 13 is the increase of the influence of β on γ in different regions;

[0080] Figure 14 is the γ change characteristic curve under asymmetric fault in embodiment 2. DETAILED DESCRIPTION

[0081] The present application first clearly defines the change characteristics and interaction mechanisms of electrical quantities and control quantities under transient state. Secondly, the Taylor series expansion method is used to analyze the off angle change characteristics of multi-factor interaction coupling, the mathematical expression of off angle change and leading trigger angle change is derived, and the subsequent commutation failure risk coefficient K SCFRF is further proposed. The subsequent commutation failure risk is judged by using K SCFRF and the leading trigger angle change. For the region with large subsequent commutation failure risk, a subsequent commutation failure suppression method of adaptive compensation for off angle shortage is proposed. Finally, the test system is built based on the CIGRE standard model in the PSCAD / EMTDC platform, and the correctness of the theoretical analysis and the effectiveness of the proposed strategy are verified.

[0082] (1) Analysis of subsequent commutation failure influencing factors of multi-factor interaction coupling

[0083] When the inverter side off angle γ is less than the minimum off angle γ min , the inverter occurs commutation failure. According to the commutation process and principle, γ can be expressed as:

[0084]

[0085] Where: I d is the DC current; X ci is the inverter side commutation reactance; U Li is the inverter side commutation bus voltage; T i is the inverter side converter transformer ratio; β is the leading trigger angle.

[0086] Compared with the first commutation failure, the mechanism of subsequent commutation failure is more complicated. As shown in formula (1), when the system parameters are determined, the size of the turn-off angle γ is not only affected by the system electrical quantity I d and U Li The influence of changes in the control system during the commutation failure recovery phase can also determine whether a subsequent commutation failure occurs. Furthermore, during the commutation failure recovery process, the electrical and control variables change dramatically and their interaction and coupling are complex, making it difficult to assess the risk of subsequent commutation failures and limiting the effectiveness of suppression strategies.

[0087] (1.1) Interaction mechanism between DC current, inverter-side commutation bus voltage, and trigger angle

[0088] The equivalent circuit of the high voltage DC system is as follows Figure 1 As shown. dr0 with U di0 are the ideal no-load voltages on the rectifier and inverter sides, R r With R i are the equivalent resistances of the commutation reactances on the rectifier side and the inverter side, R d is the equivalent resistance of the DC transmission line, U dr with U di are the DC voltages on the rectifier and inverter sides, respectively, r is the trigger angle on the rectifier side.

[0089] Depend on Figure 1 It can be seen that I d It can be expressed as:

[0090]

[0091] According to Kirchhoff's voltage theorem, U in formula (2) di It can be expressed as:

[0092] U di =U di0 cosβ+R i I d (3)

[0093] In formula (3), U di0 It can be expressed as:

[0094]

[0095] Where: N is the number of 6-pulse converters per pole.

[0096] R i It can be expressed as:

[0097]

[0098] Substituting equations (4) and (5) into equation (3), we can obtain:

[0099]

[0100] The inverter in the HVDC transmission system consumes a lot of reactive power Q when working. di , which can be expressed as:

[0101]

[0102] Commutation failure fault Q di with U Li The relationship can be expressed as:

[0103]

[0104] Where: U LiN is the rated value of the inverter side commutation bus voltage; S ci is the short-circuit capacity of the AC system on the inverter side; Q aciN Q is the reactive power fed into the commutation bus by the receiving AC system in steady state; ciN It is the reactive power provided by the reactive compensation device at the receiving end in steady state.

[0105] The changing characteristics of electrical quantities and controlled quantities at different moments are different. Combining equations (2), (6), (7), and (8), we can see that the change of any electrical quantity will inevitably affect the change of other electrical quantities, and thus affect the change of the controlled quantity β. From equation (1), we know that the change of electrical quantities and controlled quantity β can directly affect the change of the shutdown angle γ, making it impossible to know the changing characteristics of γ under transient conditions. To clarify the changing characteristics of γ at any moment, it is necessary to decouple the electrical quantity and controlled quantity and establish a mathematical relationship between γ and a single variable.

[0106] At present, some studies have used the increase of β to suppress the subsequent commutation failure. Although the increase of β will lead to the increase of γ, it can be seen from formula (6) that the increase of β will also lead to the increase of U di Reduce, from formula (2) we know U di A decrease in I d Increase; From formula (7), we know that U di The reduction and I d Increase will jointly cause Q di The increase of Q di Increase ULi will decrease; From formula (1), we can see that U Li The reduction and I d The increase of will jointly lead to a decrease in γ.

[0107] The results of the process analysis of the effect of increasing β on γ are as follows: Figure 6 shown. Figure 6 The dynamic process of how increasing β affects γ also reveals the complex coupling relationship between electrical and control variables. Due to varying fault severity, the changing characteristics of these variables during commutation failure recovery also differ. Therefore, for commutation failures caused by varying fault severities, simply increasing β may not be sufficient to suppress subsequent commutation failures.

[0108] (1.2) Analysis of the subsequent commutation failure mechanism

[0109] In order to facilitate the analysis of the variation characteristics of γ, the present invention takes the CIGRE HVDC standard test model in PSCAD / EMTDC as an example. The model parameters are shown in Table 1.

[0110] Table 1. Model parameters of DC transmission model

[0111]

[0112]

[0113] The changing characteristics of electrical and control quantities under a typical three-phase grounding fault are as follows: Figure 2 As shown in the figure, the whole fault process is divided into Figure 2 The four stages are shown.

[0114] Phase 1: The first commutation failure occurs, and the DC voltage on the inverter side U di Drops to 0, the rectifier side DC voltage U dr The DC voltage difference (U dr -U di ) increases, from formula (2), we know that I d Increase. Due to I d The increase in I d Greater than the rectifier side current command value I dr,ref , the constant current (CC) controller on the rectifier side is activated by rapidly increasing the trigger angle α on the rectifier side r , U dr Lower. With U dr The reduction of VDCOL starts, I dr,ref Rapidly reduce to the minimum DC current command value, I d with Idr,ref The deviation is further widened, and the CC control on the rectifier side continues to increase αr to reduce U dr , in order to reduce the DC voltage difference (U dr -U di ), thereby reducing I d purpose.

[0115] Phase 2: Commutation failure recovery, the inverter resumes normal commutation, γ and U di Rapidly increases, due to the delay characteristics of the PI controller in the CC control on the rectifier side, U dr cannot be adjusted immediately, so the current voltage difference (U dr -U di ) is reduced, thereby making I d It shows a short-term downward trend. d When it decreases, the inverter consumes reactive power Q di Reduce, from formula (8) we know that U Li At this time, γ is much larger than the rated value. In order to restore γ to the rated value, the constant turn-off angle (CEA) control on the inverter side quickly reduces β CEA To reduce γ, when β CEA Less than the β of the CC control output on the inverter side CC When , the inverter side switches from CEA control to CC control.

[0116] Phase 3: Commutation failure recovery mid-term, both the rectifier and inverter sides are in constant current control, I d According to the control characteristics of the CIGRE HVDC standard model, in phase 3, I d It always shows an increasing trend. d When Q increases, di Increase, resulting in U Li As the commutation failure recovery proceeds, the β output on the inverter side gradually decreases and approaches the steady-state value.

[0117] Phase 4: At the end of commutation failure recovery, the inverter side switches from CC control to CEA control, the β output of the inverter side increases, and I d Keep rising, U Li Continue to lower.

[0118] Combining the above analysis and formula (1), we can know that the electrical quantity I in stages 1 to 4 is d 、U Li The changing trend of the control quantity β and its influence on γ are shown in Table 2.

[0119] Table 2.I d 、U LiThe changing trends of γ and β and their impact on γ (↑ and ↓ indicate the increase or decrease of the value)

[0120]

[0121] The trends in brackets in Table 2 indicate the effects of changes in electrical and control variables on γ. Since Phase 1 is a commutation failure period, the final characteristics of γ cannot be expressed by the electrical variable I d 、U Li And the control amount β is expressed as 0, and the research object of the present invention is the commutation failure recovery period I d 、U Li and β on γ, so stages 2 to 4 are the focus of this study. As can be seen from Table 1, in stage 2, I d and U Li The change of γ increases, but the effect of the change of β on γ is the same as that of I d and U Li On the contrary, the trend of the change in γ that leads to this stage is unclear. d 、U Li The same effect as the change in β on γ is that it helps to reduce γ. d 、U Li The effect on γ is opposite to that of β, and it is also difficult to explain the changes in γ during this stage.

[0122] Table 2 shows that the turn-off angle is affected by multiple factors. However, it is difficult to determine the dominant factor in the turn-off angle variation at different times based solely on Table 2. This makes it difficult to clearly define the turn-off angle variation trend, and the subsequent commutation failure risk unknown. Therefore, it is necessary to further develop a mathematical model for the turn-off angle variation that considers the interaction of these multiple factors to clarify the characteristics of the turn-off angle during commutation failure recovery.

[0123] (2) Analysis of the turn-off angle variation characteristics considering the interaction coupling of multiple factors

[0124] (2.1) Modeling method of the change in turn-off angle

[0125] In order to clarify the changing characteristics of the turn-off angle under transient conditions, Equation (1) is regarded as the relationship between γ and I d 、U Li and β, and use Equation (9) to expand the Taylor formula, ignoring the second-order and higher differential terms and remainders

[11] , the approximate functional relationship of γ can be expressed by formula (10).

[0126]

[0127] Where: γ0, I d0 、U Li0 and β0 are the values ​​of the corresponding electrical quantity and control quantity at time t0 respectively.

[0128] When the time interval Δt is very small (Δt is selected as 2 ms), the change amount Δγ of the turn-off angle can be expressed as:

[0129]

[0130] The partial derivatives of formula (1) with respect to I d , U Li and β can be obtained as:

[0131]

[0132] As can be seen from formulae (11) and (12), the change of Δγ depends not only on the values of the corresponding electrical quantities and control quantities at t0, but also on the change amount ΔI d of the direct current, the change amount Δβ of the trigger angle, and the change amount ΔU Li of the inverter-side bus voltage. To further clarify the change trend of Δγ in the recovery process of commutation failure, a mathematical expression of Δγ with respect to a single variable Δβ needs to be established, and the change characteristics of Δγ are analyzed by using Δβ.

[0133] Similarly, formula (8) is expanded by using the Taylor formula, and the second-order and higher-order differential terms and the remainder are ignored, and ΔU Li can be expressed as:

[0134]

[0135] K Qdi can be expressed as:

[0136]

[0137] Substituting formula (4) into formula (7) can obtain the relationship between Q di and I d , U Li and U di , as shown in formula (15):

[0138]

[0139] By using the same idea and method as formulae (10) and (11), the change amount ΔQ di of the reactive power consumed by the inverter can be obtained, and the relationship between ΔQ di and ΔI d , ΔU Li and the change amount ΔU di of the inverter-side direct current voltage is:

[0140]

[0141] By using formula (15), the relationship between I d , U Li and Udi The partial derivative is:

[0142]

[0143] Substitute equation (16) into equation (13), and rearrange to obtain ΔU Li and ΔI d and ΔU di are related as follows:

[0144]

[0145] Equation (6) shows the relationship between U di and U Li and I d Similarly, using the idea of Taylor series expansion, ΔU di can be expressed as:

[0146]

[0147] Taking the partial derivative of equation (6) with respect to U Li , β, and I d yields:

[0148]

[0149] Substitute equation (19) into equation (18), and rearrange to obtain the relationship between ΔU Li and ΔI d and Δβ:

[0150] ΔU Li = K a1 ΔI d + K a2 Δβ (21)

[0151] where:

[0152]

[0153] Substitute equation (21) into equation (11), and rearrange to obtain the relationship between Δγ and ΔI d and Δβ:

[0154]

[0155] Equation (2) shows the relationship between I d and U dr and U di Since Δt is very small, and the change in U dr is achieved through a series of control actions. Therefore, within the time Δt, when U di changes, U drSimilarly, using Taylor's formula to expand Equation (2), ignoring the second-order and higher differential terms and remainders, ΔU di It can be expressed as:

[0156]

[0157] Formula (19) has established ΔU di With ΔU Li , Δβ and ΔI d Substituting formula (19) into formula (24) yields ΔI d With ΔU Li The relationship between , Δβ is shown in formula (25):

[0158]

[0159] Equation (21) represents ΔU Li and ΔI d and Δβ, substituting formula (21) into formula (25), we can get ΔI d The relationship with Δβ is:

[0160]

[0161] Formula (23) shows that Δγ and ΔI d The relationship between Δγ and Δβ is obtained by substituting formula (26) into formula (23):

[0162] Δγ=K SCFRF Δβ (27)

[0163] Among them, K SCFRF It is defined as the subsequent commutation failure risk factor (SCFRF), which is as follows:

[0164]

[0165] From formula (27), we can see that in any time interval Δt during the commutation failure recovery process, when the change trend and degree of Δβ are determined, the subsequent commutation failure risk coefficient K can be used SCFRF Determine the degree of change and trend of Δγ, and then effectively evaluate the risk of subsequent commutation failure.

[0166] (2.2) Subsequent commutation failure risk assessment

[0167] by Figure 2 For example, during the commutation failure recovery period, K SCFRF The change of β over time is as follows Figure 3 shown.

[0168] Figure 3 Regions 1 and 2 correspond to Figure 2 Phases 2 to 4 are the commutation failure recovery period. Figure 2 In the region 1, the coefficient K SCFRF Greater than 0, coefficient K in region 2 SCFRF Less than 0. As shown in Table 1, the change characteristics of the turn-off angle γ in stage 2 and stage 4 are unclear. The change characteristics of γ in stage 2 can be based on Figure 3 Medium coefficient K SCFRF The change of the leading trigger angle β is obtained by combining formula (27). Figure 3 It can be seen that stage 4 spans regions 1 and 2. To further analyze the γ variation characteristics in stage 4, we use Figure 3 Based on the regional division, stage 4 is divided into Figure 7 and Figure 8 The two typical periods shown in Figure 2 are shown in Figure 2. The coefficient K in different stages is SCFRF The changes of , Δβ and Δγ are shown in Table 3.

[0169] Table 3 K at different stages SCFRF , Δβ and Δγ

[0170]

[0171] from Figure 3 As can be seen from Table 2, due to the coefficient K of stage 2 and stage 4.1 SCFRF is greater than 0, Δβ is less than 0. From formula (27), we can see that Δγ is less than 0, that is, in stage 2 and stage 4.1, as β decreases, γ tends to decrease; in stage 4.2, the coefficient K SCFRF Less than 0, Δβ greater than 0. From Equation (27), we can see that Δγ is less than 0, that is, in stage 4.2, as β increases, γ tends to decrease. Therefore, the characteristics of the turn-off angle variation under the multi-factor interaction coupling in Table 2 are clear, that is, during the commutation failure recovery period, as β changes, γ generally shows a gradually decreasing characteristic.

[0172] Since the characteristics of the turn-off angle change under the interaction of multiple factors in transient state have been clarified, Figure 6 The problem of whether increasing β can suppress subsequent commutation failure can be solved. According to the coefficient K in Table 3 SCFRF The characteristics of (27) show that in region 1 (K SCFRF >0) can increase γ and reduce the risk of subsequent commutation failure. SCFRF <0), increasing β can reduce γ, but the risk of subsequent commutation failure increases.

[0173] (3) Subsequent commutation failure suppression strategy

[0174] According to the analysis of the subsequent commutation failure mechanism above, the design of the subsequent commutation failure suppression strategy should focus on how to reduce the decrease of the turn-off angle. For this purpose, a subsequent commutation failure control strategy is proposed to adaptively compensate for the shortage of the turn-off angle. The specific steps are as follows: SCFRF The subsequent commutation failure control strategy for adaptively compensating for the shortage of the turn-off angle. The specific steps are as follows:

[0175] 1) Calculate the subsequent commutation failure risk coefficient K SCFRF and the turn-off angle compensation amount. Wherein K SCFRF is calculated by the system parameters, the electrical quantities I d , U Li at the inverter side, and the control quantity β through equations (12)-(26), so when the system parameters are determined, the values of K SCFRF at different times can be determined by measuring the corresponding electrical quantities and control quantities. In the area with a high risk of subsequent commutation failure, the shortage of the turn-off angle is compensated, and the turn-off angle compensation amount Δγ m is determined by equation (27).

[0176] 2) Determine the turn-off angle compensation time period. From Figure 2 and Table 2, it can be seen that without other control, the turn-off angle gradually decreases, the commutation margin decreases, and the risk of subsequent commutation failure gradually increases, i.e. the time period with a high risk of subsequent commutation failure is stage 4.2. In stages 2-4.1, the turn-off angle is large and the risk of subsequent commutation failure is low, so if the turn-off angle compensation strategy is applied in the corresponding time period to increase the turn-off angle, it will be difficult to effectively restore the system current and power. Therefore, the turn-off angle compensation time period is stage 4.2, and the turn-off angle compensation strategy is applied in the corresponding time period, which will neither affect the system recovery rate nor effectively reduce the risk of subsequent commutation failure. (This embodiment only takes the typical fault shown in Figure 2 as an example to illustrate the turn-off angle compensation time period, which aims to reveal that when K SCFRF is negative, the application of the turn-off angle compensation strategy has the best transient characteristics of the system.)

[0177] 3) Determine the position of compensation. According to the control characteristics of the CIGRE HVDC standard test model, the leading trigger angle output at the inverter side can be expressed as

[0178]

[0179] In the formula: β CEA , β CC are the leading trigger angles of the CEA control and the CC output at the inverter side, respectively, and the larger value of the two is taken as the output at the inverter side; β m , β n are the initial values of β CEA , β CC ; k p , ki are the proportional and integral coefficients of the PI controller respectively; Δe γ , Δe I They are the turn-off angle error of CEA control and the current error of CC control. γ Can represent:

[0180] Δe γ =Δγ CEC +Δγ ord +Δγ m (29)

[0181] Where: Δe γ is the turn-off angle tracking error; Δγ ord is the difference between the DC value of the turn-off angle and the actual turn-off angle; Δγ CEC is the turn-off angle deviation output by the current deviation control. Since the strategy proposed in this invention is to compensate for the turn-off angle deficiency, it is sufficient to compensate for the turn-off angle error of the CEA control on the inverter side, using K SCFRF The control strategy of adaptively compensating the cut-off angle deficiency is as follows: Figure 4 shown.

[0182] Example 1: In order to verify the correctness of the present invention and the effectiveness of the proposed suppression strategy, the mechanism analysis and the proposed suppression strategy were simulated and verified based on the CIGRE HVDC standard test model. The relevant parameters of the standard test model are shown in Table 2.

[0183] Verification of the subsequent commutation failure risk assessment method: The analysis (2) above, which shows that increasing β has different effects on γ in different regions, is verified. Regions 1 and 2 represent regions where increasing β results in an increase or decrease in γ, and a decrease or increase in the subsequent commutation failure risk, respectively.

[0184] Case 1: A three-phase inductance ground fault is set at the inverter side AC system commutation busbar. The fault occurrence time is 1.0s, the fault duration is 0.2s, and the ground inductance is 0.6H. Increasing β in area 1 and area 2, the change of γ is as follows: Figure 8 (Area 1 and region 2 refer to K SCFRF >0 and K SCFRF <0)

[0185] Figure 8 In (a), the constant Δβ means that the β value has not changed, that is, the γ change curve obtained under the original control strategy. Figure 8 As can be seen from (a), compared with the original control strategy, increasing β in region 1 will increase the minimum value of γ accordingly. From equations (27) and (29), it can be seen that increasing β in the time range corresponding to region 1 will result in a turn-off angle tracking error Δe γ becomes larger; From formula (28), we can see that Δe γThe increase of will make the β of the inverter side CEA control output CEA Increase, the inverter side switches to the turn-off angle control in advance, providing a larger turn-off angle adjustment margin, thereby reducing the risk of subsequent commutation failure. Figure 8 (b) The effect of increasing β in region 1 on the switching point from CC control to CEA control on the inverter side is shown in Figure 2. Figure 9 shown.

[0186] Figure 9 Scheme 1 is the advanced trigger angle β obtained under the control of the CIGRE standard model, and Scheme 2 is Figure 8 (a) β obtained by increasing β control in region 1. Figure 10 As shown in Figure 1, increasing β in region 1 advances the switching point between the constant current and the fixed turn-off angle on the inverter side from ① to ②. The fixed turn-off angle control on the inverter side regains control, strengthens the control over the turn-off angle, and reduces the risk of subsequent commutation failure.

[0187] For the convenience of Figure 8 (b) The change of γ is explained. Figure 8 (b) Divide out ① ～ ⑤ Typical time segments are divided based on the fact that γ decreases significantly during these time segments. ① is the first commutation failure stage and is not necessary to discuss. Figure 8 As can be seen in Figure (b), in region 2, increasing β decreases γ, and the time period when γ is equal to 0 is advanced from ③ to ②, shortening the time interval for subsequent commutation failures. Moreover, the changes in γ corresponding to time periods ④ and ⑤ show that the degree of γ in time segment ④ is smaller than that in ⑤ under the original control strategy, indicating that when subsequent commutation failures are recovered, there is still a high probability of continuous commutation failures.

[0188] To further verify the correctness of the theoretical analysis, a second case is set to change the severity of the inverter-side fault. It is verified whether increasing β in different areas will increase or decrease γ when only a single commutation failure occurs in the system.

[0189] Case 2: A three-phase inductance ground fault is set at the inverter side AC system commutation busbar. The fault occurrence time is 1.0s, the fault duration is 0.1s, and the ground inductance is 1.0H. Changes in β and γ in areas 1 and 2 Figure 9 (The meanings of Area 1 and Area 2 are the same as in Case 1)

[0190] from Figure 9 As can be seen in (a), Figure 8 (b) Similarly, if β is increased in region 1, the minimum value of γ will also increase accordingly, and the risk of subsequent commutation failure will be reduced. Figure 9As can be seen in the figure (b), when β is increased in region 2, the lowest point of γ changes from ③ to ②, γ is equal to 0, and the system fails to commutate again.

[0191] The simulations of Case 1 and Case 2 verify the correctness of the theoretical analysis of the continuous commutation failure mechanism of the present invention.

[0192] In order to verify the effectiveness of the post-commutation failure suppression measures proposed in this invention, a comparative analysis is conducted on the following three control schemes:

[0193] Control scheme 1: Control method using the CIGRE HVDC standard test model.

[0194] Control scheme 2: Based on the CIGRE HVDC standard test model control method, the existing subsequent commutation failure suppression method in the literature is added.

[0195] The method of the present invention adds the subsequent commutation failure suppression method proposed by the present invention to the CIGRE HVDC standard test model control method.

[0196] Different fault severities were set at the inverter-side AC system commutation busbar: Fault (A): Grounding inductance 0.6H; Fault (B): Grounding inductance 0.1H. Both (A) and (B) were three-phase inductive grounding faults with a fault onset time of 1.0s and a fault duration of 0.2s. Figure 5 shows the system parameter variations for different control schemes and fault severities.

[0197] Figure 5 The blue dotted line I in the DC current diagram drref is the current command value on the rectifier side, the blue solid line I diref is the inverter side current command value. The short circuit ratio (SCR) can be used to measure the strength of the AC system. To further verify the effectiveness of the control strategy proposed in this invention in suppressing subsequent commutation failure, the fault (A) in Figure 5 was simulated under different SCRs. The system parameter changes under different control schemes and SCRs are shown in the figure below. Figure 9 shown.

[0198] From the changes in the turn-off angle γ under different control schemes and different SCRs in Figures 5 and 11, it can be seen that when control scheme 1 is adopted, subsequent commutation failure will occur on the inverter side, and the system will suffer two shocks, which seriously affects the stability of the system. Both control scheme 2 and the control scheme of the present invention can effectively suppress the occurrence of subsequent commutation failure. The difference is that control scheme 2 introduces a virtual resistor to make VDCOL more sensitive to faults, accelerate the change of the current command value, and thus achieve the suppression of subsequent commutation failure. However, the size of the virtual resistance value needs to be determined according to the variation range of the electrical quantity in the specific example, which limits the applicability of scheme 2 under different working conditions. The control scheme of the present invention uses KSCFRF , adaptively compensate for the corresponding cut-off angle shortfall, and have stronger universality. d It can be seen from the changes in the control scheme 2 and the control scheme 1 of the present invention that d The time to recover to the steady state is the same. Taking all factors into consideration, the solution of the present invention has more advantages.

[0199] In order to fully verify the effectiveness of the control strategy proposed in this invention in suppressing subsequent commutation failure under different working conditions, the fault level f is set L To simulate the severity of the fault, the calculation formula can be expressed as:

[0200]

[0201] Where: ω is the angular frequency of the AC system; L f is the fault grounding inductance value; P dN Delivers rated power to the system.

[0202] A three-phase inductance grounding fault is set at the inverter side AC system commutation busbar, the fault time is 1.0s, and different fault levels f are set. L Table 3 shows the number of commutation failures of control scheme 1 and the control scheme proposed in the present invention under different working conditions with different fault durations Δt.

[0203] Table 4 Number of commutation failures of control scheme 1 and the control scheme of the present invention

[0204]

[0205]

[0206] As can be seen from Table 4, when the fault level and fault duration are different, the inverter-side converter has a higher probability of subsequent commutation failure under the control scheme 1. However, after applying the control scheme proposed in the present invention, the risk of subsequent commutation failure is greatly reduced, and the subsequent commutation failure is effectively suppressed.

[0207] Example 2: To further expand the scope of application of the risk assessment model and suppression strategy of the present invention, analysis and simulation verification under asymmetric faults are as follows.

[0208] The turn-off angle γ under asymmetric fault can be expressed as

[0209]

[0210] According to the sine theorem, the angle of the zero-crossing point is It can be expressed as

[0211]

[0212] Substituting equation (F2) into equation (F1) yields

[0213]

[0214] Applying the modeling method of the turn-off angle variation in the present invention to equation (F3) can decouple the factors affecting the turn-off angle variation under asymmetric faults. After simplification, the relationship between the turn-off angle variation Δγ and the advance trigger angle variation Δβ is obtained.

[0215] Δγ=K SCFRF Δβ(F4)

[0216] Among them, K SCFRF It is also defined as the subsequent commutation failure risk factor (SCFRF), which can be expressed as

[0217]

[0218] in, It can be expressed as

[0219]

[0220] The subsequent commutation failure risk coefficient K under three-phase fault in Example 1 is SCFRF In comparison, the subsequent commutation failure risk factor under asymmetric fault has an additional factor K4. Taking a single-phase grounding fault in the receiving AC system as an example, the fault inductance is 0.7H, the fault occurrence time is 1.0s, and the fault duration is 0.2s. The subsequent commutation failure risk factor under single-phase grounding fault is K SCFRF The waveform is as Figure 12 shown.

[0221] According to the subsequent commutation failure risk factor K SCFRF The positive and negative division areas, Figure 12 It is divided into two regions, K in region 1 SCFRF >0, K in region 2 SCFRF <0. The effect of increasing β on the turn-off angle in regions 1 and 2 is as follows Figure 13 shown.

[0222] Depend on Figure 13 (a) It can be seen that in region 1 (K SCFRF >0), the turn-off angle γ increases, and the risk of subsequent commutation failure is reduced; Figure 13 (b) The change of γ is explained. Figure 13(b) Figure divides ① ~ 5 typical time segments, the division basis is that γ appears a greater degree of reduction in these time segments, ① is the first commutation failure stage, does not have the necessary discussion.From the figure 11 (B) figure can be seen, in the region 3 (K SCFRF <0) increases β, γ decreases, the time period when γ is equal to 0 will be advanced from ③ to ②, the time interval of subsequent commutation failure occurs is shortened; Not only this, from the γ change situation corresponding to ④, ⑤ time period can be known, the degree of γ in time segment ④ is less than that in ⑤ under the condition that β does not change, that is, when the subsequent commutation failure recovers, there is still a greater probability of continuous commutation failure.

[0223] To verify the applicability of the subsequent commutation failure suppression strategy proposed in the application under asymmetric fault, set up the example as shown in table 5 to carry out simulation verification, the simulation results of the turn-off angle are as shown in Figure 14

[0224] Table 5. Asymmetric fault example characteristics

[0225]

[0226] From Figure 14 It can be seen that under the asymmetric fault shown in table 5, the turn-off angle γ under CIGRE control is lower than the minimum turn-off angle γ min twice, the inverter has subsequent commutation failure; After applying the subsequent commutation failure control strategy proposed in the application, the turn-off angle γ is lower than the minimum turn-off angle γ min only once, the subsequent commutation failure is effectively suppressed. From the above, it can be known that under asymmetric fault, the correctness and effectiveness of the risk assessment model derived in the application and the suppression strategy proposed can still be guaranteed.​

Claims

1. A method for suppressing subsequent commutation failure by adaptively compensating for a turn-off angle shortfall, characterized in that: The method includes establishing a subsequent commutation failure risk factor K SCFRF and the turn-off angle compensation Δγ m The single relationship between them, and then by measuring the corresponding electrical quantities and control quantities to determine the K at different times SCFRF The value of K SCFRF When it is a negative value, the cut-off angle compensation is applied; The subsequent commutation failure risk factor K SCFRF It is calculated from the LCC-HVDC system parameters, inverter-side electrical quantities, and control quantities. First, based on the interaction mechanism between electrical quantities and control quantities, the impact of changes in electrical quantities and control quantities on the shutdown angle is analyzed. Then, the Taylor series expansion method is used to decouple electrical quantities and control quantities, thereby deriving a single expression for the change in the shutdown angle and the change in the advance trigger angle: Δγ=K SCFRF Db When the trend and degree of the overdue trigger angle change Δβ are determined, the subsequent commutation failure risk coefficient K SCFRF Determine the turn-off angle change Δγ and compensate for the turn-off angle shortfall at the turn-off angle error of the inverter-side CEA control. The turn-off angle compensation Δγ m Determined according to the turn-off angle change Δγ.

2. The method for suppressing subsequent commutation failure by adaptively compensating for turn-off angle deficiency according to claim 1, characterized in that: The subsequent commutation failure risk factor K SCFRF By measuring the LCC-HVDC system parameters, inverter side DC current I d , inverter side commutation bus voltage U Li And the control quantity β is calculated. When the system parameters are determined, the turn-off angle γ is affected by I d and U Li The influence of the changes in the electrical quantities of the two systems is considered, and the influence of the control quantity β of the control system during the commutation failure recovery phase is also considered.

3. The method for suppressing subsequent commutation failure by adaptively compensating for turn-off angle deficiency according to claim 1 or 2, characterized in that: Subsequent commutation failure risk factor K SCFRF The conversion calculation includes: (1) When the inverter side shutdown angle γ is less than the minimum shutdown angle γ min When , the inverter fails to commutate. According to the commutation process and principle, the turn-off angle γ is expressed as: Where: I d is the DC current on the inverter side, X ci is the inverter side commutation reactance; U Li is the inverter side commutation bus voltage; T i is the inverter side converter transformer ratio; β is the leading trigger angle; The above formula is regarded as the cut-off angle γ with respect to I d 、U Li and β, and then expand it according to Taylor's formula, ignoring the second-order and higher differential terms and remainders, to obtain the approximate function of the turn-off angle γ: Where: γ0, I d0 、U Li0 and β0 are the values ​​of the corresponding electrical quantity and control quantity at time t0 respectively; When the time interval Δt is very small and can be ignored, the change in the turn-off angle Δγ is converted into the following formula: Based on the commutation principle, I d 、U Li And β find the partial derivative: The above formula shows that the change of the inverter side turn-off angle γ depends not only on the size of the corresponding electrical quantity and control quantity at time t0, but also on the DC current change ΔI d , trigger angle change Δβ and inverter side commutation bus voltage change ΔU Li related; (2) Q under commutation failure di with U Li The relationship is expressed as: Where: U LiN is the rated value of the inverter side commutation bus voltage; S ci is the short-circuit capacity of the AC system on the inverter side; Q aciN Q is the reactive power fed into the commutation bus by the receiving AC system in steady state; ciN Reactive power provided by the reactive compensation device at the receiving end in steady state; In order to further clarify the changing trend of Δγ during the recovery process of commutation failure, a mathematical expression of Δγ and a single variable Δβ is established. The changing characteristics of Δγ are analyzed according to Δβ. The Taylor formula is used to expand it, ignoring the second-order and higher differential terms and remainders. ΔU Li Expressed as: Change in reactive power consumed by the inverter ΔQ di and ΔI d , ΔU Li and the inverter side DC voltage change ΔU di The relationship is: to I d 、U Li and U di Find the partial derivative: Arranged to get ΔU di and ΔI d and ΔU di The relationship is: The above formula shows that ΔU di With ΔU Li and ΔI d relationship; (3) Using Taylor series expansion, ΔU di Expressed as: ΔU Li , Δβ and ΔI d Taking partial derivatives we get: Organize U Li , Δβ and ΔI d The relationship is: D.U. Li =K a1 I d +K a2 Db in: Δγ and ΔI d The relationship between and Δβ is expressed as: The above formula shows that I d with U dr and U di The relationship between the two is that within the time of Δt, when U di When U changes dr cannot be adjusted in time; (4) Perform equivalent circuit processing on the high voltage DC system, where Expand it using Taylor's formula, ignoring the second-order and higher differential terms and remainders, ΔU di It can be expressed as: After finishing, we can get: ΔI d The relationship with Δβ is: Based on the above formula Δγ and ΔI d The relationship between Δγ and the single variable Δβ is constructed as follows: Δγ=K SCFRF Db Among them, K SCFRF Defined as the subsequent commutation failure risk factor:

4. A subsequent commutation failure control system with adaptive compensation for turn-off angle deficiency, characterized in that: The system is used to execute the subsequent commutation failure suppression method as described in any one of claims 1 to 3.

5. The subsequent commutation failure control system with adaptive compensation for turn-off angle deficiency according to claim 4, characterized in that: The system also includes a subsequent commutation failure risk factor K SCFRF A calculation module is used to perform the coefficient calculation process in the subsequent commutation failure suppression method as claimed in claim 3, including calculating the coefficient K that satisfies the following relationship U1 , K a2 , K U2 , K U3 、R d , K U1 , K a1 , and K a2 :

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