A fast prediction method considering the risk of commutation failure caused by harmonics

Abstract

The present invention relates to a rapid prediction method considering the risk of commutation failure caused by harmonics, and belongs to the technical field of high-voltage direct current transmission operation analysis. The commutation voltage is reconstructed based on a method of virtual three-phase construction, and the separation of fundamental signal and harmonic signal is realized. The reconstructed signal is subjected to the rapid extraction of harmonic characteristic quantity by using the curve fitting method. By comparing the actual value of the harmonic with the critical value, it can be predicted whether the DC system has the risk of commutation failure. If the actual value is greater than the critical voltage, the system has the risk of commutation failure. Otherwise, the system has no risk of commutation failure. Different from the traditional method, the method of the present invention reduces the error between the actual value and the theoretical value, improves the accuracy of the prediction criterion, and realizes the rapid prediction of the risk of commutation failure caused by harmonics. The proposed method lays the foundation for the timely action of the subsequent control and protection system, and has positive significance for preventing the subsequent continuous commutation failure.

Description

Technical Field

[0001] The invention relates to a rapid prediction method considering the risk of commutation failure caused by harmonics, and belongs to the technical field of high-voltage direct current transmission operation analysis. Background Art

[0002] Line Commutated Converter Based High Voltage Direct Current (LCC-HVDC) is widely used because it is suitable for cross-regional, large-capacity, long-distance transmission and has low cost. LCC-HVDC technology enables long-distance clean energy transmission and effectively solves the problem of uneven regional distribution of energy resources. However, since conventional DC transmission systems use semi-controlled thyristors as switching devices, their inherent commutation failure problems affect the safe and stable operation of the power grid.

[0003] With the transformation from traditional power systems to new power systems, the "double high" characteristics of the power system, a high proportion of renewable energy and a high proportion of power electronic equipment, have become more prominent. The resulting grid harmonic problem has also undergone fundamental changes compared with the past. Grid harmonics present characteristics such as high frequency and wide frequency domain. The problem of commutation failure caused by grid harmonics in the AC system voltage is no longer negligible. Most of the existing commutation failure risk prediction methods only consider the role of the commutation voltage fundamental wave and ignore the influence of harmonics. With the emergence of the "double high" characteristics of the new power system, considering the influence of harmonics on the zero-crossing offset of the commutation voltage is of great significance to improving the accuracy of the commutation failure risk prediction method. Summary of the invention

[0004] In order to solve the above problems, the present invention provides a rapid prediction method considering the risk of commutation failure caused by harmonics, which can realize the rapid prediction of the risk of commutation failure caused by harmonics.

[0005] The technical solution of the present invention is as follows:

[0006] A rapid prediction method considering the risk of commutation failure caused by harmonics includes the following steps:

[0007] S1: Determine the DC transmission system to be studied, obtain the shutdown angle γ0 under normal operation of the DC system, and calculate the critical value S of the commutation voltage-time area caused by the nth harmonic voltage under different frequencies, amplitudes, and initial phase angles. n,cri And the maximum commutation area S that the nth harmonic can provide n,max ;

[0008] S2: The critical value S of the commutation voltage-time area that causes commutation failure according to the nth harmonic voltage n,criThe maximum commutation area S that can be provided by the nth harmonic n,max The minimum harmonic voltage k that causes commutation failure at this frequency is calculated. n,cri as critical value;

[0009] By inputting harmonics of different frequencies, different amplitudes, and different harmonic initial phase angles, and calculating the respective commutation voltage-time area critical value S that causes commutation failure n,cri And the maximum commutation area S that can be provided n,max , compare the critical value of the commutation voltage-time area caused by the harmonic voltage and the maximum commutation area that the nth harmonic can provide, and select the minimum harmonic voltage k that causes commutation failure at this frequency n,cri As the critical value, the minimum harmonic voltage at each frequency can be established, and the minimum harmonic voltage at each frequency is established to form a minimum harmonic voltage database;

[0010] S3: Real-time acquisition of the three-phase voltage of the AC busbar on the inverter side, and constructing virtual three-phases for the three-phase voltages respectively. The constructed symmetrical virtual three-phases are park transformed, and the AC and DC vectors are separated through a low-pass filter to extract the DC component and obtain the instantaneous value u of the harmonic voltage. n ;

[0011] S4: The instantaneous value of harmonic voltage u n Sampling is performed, and curve fitting is performed based on the nonlinear least squares algorithm of trust region reflection to extract the harmonic feature value A n ;

[0012] S5: Comparison of harmonic characteristic quantity A n With the critical value k n,cri Size, if A n Greater than k n,cri , the system has the risk of phase switching failure, otherwise, the system has no risk of phase switching failure.

[0013] First, taking into account the influence of the zero-crossing offset of the commutation voltage, the present invention proposes a dynamic critical value for the risk of commutation failure caused by harmonics taking into account the zero-crossing offset. The critical value can be dynamically adjusted according to different harmonic orders, amplitudes and phase angles. Secondly, the commutation voltage is reconstructed based on the method of virtual three-phase construction to achieve the separation of the fundamental signal and the harmonic signal. The reconstructed signal is subjected to the curve fitting method to achieve the rapid extraction of the harmonic feature quantity. Finally, in order to facilitate the rapid prediction of harmonic risks, a method based on the minimum harmonic commutation voltage k is proposed. n,criA dynamic prediction method for the risk of commutation failure caused by harmonics. By comparing the actual value of the harmonic with the critical value, it is possible to predict whether the DC system has a risk of commutation failure. If the actual value is greater than the critical voltage, the system has a risk of commutation failure; otherwise, the system has no risk of commutation failure. Different from traditional methods, the method of the present invention improves the accuracy of the prediction of the risk of commutation failure caused by harmonics, and can effectively predict the commutation failure in advance to a certain extent. Moreover, as the effective value of the harmonic decreases, the advance amount of the predicted commutation failure becomes larger, that is, the prediction method proposed in this article is more effective under minor faults, which lays the foundation for the subsequent protection control system action.

[0014] Preferably, in step S1, when the power grid is operating normally, the commutation voltage u ba Expressed as u ba Represents the line voltage between phases ba, which is the voltage provided during phase switching, called the phase switching voltage, where U1 is the effective value of the fundamental voltage, ω1 is the fundamental angular frequency, and the phase switching process satisfies the equation:

[0015]

[0016] Among them, L c represents the equivalent commutation inductance; α represents the trigger angle; μ represents the commutation angle; i m3 Indicates the current of the bridge arm where valve VT3 is located; i m1 Indicates the current of the bridge arm where valve VT1 is located;

[0017] The left side of formula (1) is defined as the commutation required area S need , expressed as

[0018]

[0019] It can be seen from formula (2) that the commutation required area S need With DC current i d and equivalent commutation inductance L c The equivalent commutation inductance is a fixed parameter of the system, and its size determines the commutation speed. Therefore, the commutation required area mainly depends on the size of the DC current during the commutation process, in which the size of the DC current determines the size of the commutation angle μ, reflecting the energy required for the current to transfer between the bridge arms. Since the size of the DC current is mainly affected by the characteristics of the DC control system, and there is a smoothing reactor on the DC side to smooth the DC fluctuations, the DC current can be regarded as a constant during the commutation process;

[0020] The right side of formula (1) is defined as the switching area S pro , expressed as

[0021]

[0022] In order to make the system commutate normally, the commutation area S is required. need The area provided by the commutation should meet the following requirements:

[0023] S need ≤S pr o,max (4)

[0024] S pro,max Represents the maximum value of the area that the commutation voltage can provide;

[0025] When harmonics exist in the receiving AC system, the commutation voltage u' ba It can be expressed as:

[0026]

[0027] Where k represents the ratio of the effective value of the harmonic voltage to the fundamental voltage, n represents the nth harmonic, and k n It represents the ratio of the effective value of the nth harmonic voltage to the fundamental voltage, θ represents the initial phase angle of the harmonic, θ n represents the initial phase angle of the nth harmonic;

[0028] When the system contains harmonics, the commutation voltage S' pro The areas provided are:

[0029]

[0030] Among them, μ' represents the commutation angle after adding harmonics;

[0031] The commutation area S provided by the nth harmonic voltage n It can be expressed as:

[0032]

[0033] When harmonic voltage exists in the system and causes the commutation voltage amplitude to decrease, in order to ensure that the provided commutation area is still equal to the commutation area required for successful commutation, the system will be forced to increase the commutation angle to expand the actual commutation area provided. However, for the shutdown process after commutation, as the commutation angle increases, the shutdown angle will inevitably decrease. Moreover, when the harmonic voltage causes the commutation voltage to move forward through the zero point, it will continue to deteriorate the commutation conditions and further reduce the shutdown angle. When the commutation angle increases or the zero point moves forward to a certain extent, making the shutdown time less than the minimum shutdown time required for successful shutdown, commutation failure will occur.

[0034] Consider the extreme case where the system fails to commutate, that is, the turn-off angle is γ min , the maximum commutation area that the system can provide is:

[0035]

[0036] in, It represents the zero-crossing deviation angle of the commutation voltage caused by harmonics, and the maximum area provided by harmonics is ∑S n,max , the critical value of the commutation voltage-time area for commutation failure caused by harmonic voltage is obtained:

[0037]

[0038] S n,cri Indicates the critical value of the commutation voltage-time area when the nth harmonic voltage causes commutation failure; where α+μ=π-γ0, γ0 is the turn-off angle during normal commutation without harmonics;

[0039] In order for the system to successfully commutate in the presence of harmonics, the following conditions must be met:

[0040] ∑S n,max ≥S n,cri (10)

[0041] Will Substituting into equation (7), the maximum commutation area that the nth harmonic can provide can be calculated as:

[0042]

[0043] The present invention can be dynamically adjusted according to different harmonic orders, amplitudes and phase angles, and the factor of zero-crossing offset of commutation voltage caused by harmonics is taken into account in the derivation process, thereby reducing the error between the actual value and the theoretical value and improving the flexibility and accuracy of the prediction criterion.

[0044] Preferably, in step S2, k n,cri =min[k n (S n,cri ,S n,max )].

[0045] Preferably, in step S3, it is assumed that the effective value of the fundamental voltage of phase a is represented by U, the fundamental angular frequency of phase a is ω, and the initial phase of the fundamental is θ0; the effective value of the nth harmonic voltage is represented by U n , the initial phase of the harmonic is θ n ,but

[0046]

[0047] Among them, U a represents the constructed virtual a phase;

[0048] Take phase a as an example to construct its virtual three-phase. a Delay 60° and reverse to get U c , according to the symmetry of the three-phase circuit U a +U b +U c=0, we can get U b =-U a -U c , where U b represents the constructed virtual b phase; U c represents the virtual c-phase of the construction;

[0049] U b , U c Respectively expressed as

[0050]

[0051] After the virtual three-phase voltage abc is transformed by Parker transformation, we can get:

[0052]

[0053] Where i represents the construction of virtual three-phase with phase i as the reference voltage, and i can be a, b, or c; U id It represents the d-axis component obtained by Park transformation after constructing virtual three-phase with i phase as reference voltage; U iq It represents the q-axis component obtained by Park transformation after constructing virtual three-phase with i phase as reference voltage; U ia The virtual phase a is constructed with phase i as the reference voltage; U ib Indicates that the virtual b phase is constructed with the i phase as the reference voltage; U ic It means that the virtual c phase is constructed with the i phase as the reference voltage;

[0054] C abc / dq The matrix is:

[0055]

[0056] Substituting equation (12) and equation (13) into equation (14), we can obtain:

[0057]

[0058] Among them, H n Represents AC harmonic components;

[0059] Substitute u in formula (16) id and u iq A low-pass filter (LPF) is used to separate the AC and DC vectors. Different cutoff frequencies, orders, and types of low-pass filters may have a great impact on the detection of harmonic currents. Since the frequency characteristics of the Butterworth filter are best near the zero point, a higher detection accuracy can be achieved when the cutoff frequency is selected to be lower. Therefore, the present invention uses a Butterworth filter to filter out the harmonic components and extract the DC components.

[0060] The extracted DC component can be calculated through formula (17) to determine the fundamental voltage effective value U and the phase jump angle θ0:

[0061]

[0062] U id0 It represents the d-axis component obtained by Park transformation after filtering with the i-phase as the reference voltage to construct the virtual three-phase; U iq0 It represents the q-axis component obtained by Park transformation after filtering by constructing virtual three-phase with i phase as reference voltage;

[0063] Combining equations (12) and (17), the actual voltage u i With fundamental component The instantaneous value of the harmonic voltage can be obtained by subtracting:

[0064]

[0065] u n Indicates the instantaneous value of the nth harmonic voltage; u i Indicates the actual AC voltage, which is measured in real time by the measuring instrument.

[0066] Preferably, the specific implementation process of step S4 is:

[0067] The instantaneous value of the harmonic voltage is sampled, and the sampled data is recorded as (t i ,y i ), i = 1, 2, ..., m; y i Indicates t i The instantaneous value of harmonic voltage at time , its fitting function is

[0068]

[0069] A n , n, θ n is the undetermined parameter, where A n Represents the harmonic characteristic quantity, recorded as the undetermined parameter matrix P:

[0070]

[0071] According to the least squares principle, the objective function RSS is constructed to minimize its value, that is,

[0072]

[0073] In order to solve the optimization problem of the objective function, we first need to construct an initial trust region, use the quadratic model to approximate the objective function in the trust region, solve the subproblem under the quadratic model, and find the next iteration point; the trust region subproblem is described as:

[0074]

[0075] Where ΔP is the increment of parameter P, is the gradient of the objective function at the current iteration point, B k is the Hessian matrix of the objective function at the current iteration point, Δk is the radius of the trust region;

[0076] According to the sub-problem solution ΔP obtained, update the iteration point: P k+1 =P k +ΔP, when the objective function satisfies |RSS k+1 -RSS k |≤ε, the value of the undetermined parameter matrix P that meets the conditions can be obtained, and the rapid extraction of harmonic characteristic quantities can be achieved; where ε represents the preset error allowable value.

[0077] The present invention proposes a method based on virtual three-phase structure to reconstruct the commutation voltage, realizes the separation of fundamental signal and harmonic signal, and uses curve fitting method to quickly extract harmonic feature quantity from the reconstructed signal. The rapid extraction of harmonic feature quantity is of great significance for improving the speed and accuracy of commutation failure prediction.

[0078] For any details not provided in the present invention, please refer to the prior art.

[0079] The beneficial effects of the present invention are:

[0080] The present invention adopts the minimum harmonic commutation voltage k n,cri The dynamic prediction method of harmonic-induced commutation failure risk takes into account the influence of different harmonic orders, amplitudes and phase angles on the zero-crossing point of the commutation voltage, reduces the error between the actual value and the theoretical value, improves the accuracy of the prediction criterion, and realizes the rapid prediction of harmonic-induced commutation failure risk. The method proposed in the present invention lays the foundation for the timely action of the subsequent control and protection system, and has positive significance for preventing subsequent continuous commutation failures. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] The drawings in the specification, which constitute a part of the present application, are used to provide further understanding of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute improper limitations on the present application.

[0082] Figure 1 The topological structure diagram of the 6-pulse Graetz bridge inverter;

[0083] Figure 2 It is a harmonic feature instantaneous extraction method based on voltage signal reconstruction;

[0084] Figure 3 A flowchart of a rapid prediction method for the risk of commutation failure caused by harmonics;

[0085] Figure 4 Wiring diagram for standard test model;

[0086] Figure 5 Inject A into the system n = 0.130pu 100Hz harmonic system electrical quantity response curve;

[0087] Figure 6 Inject A into the system n = 0.130pu 150Hz harmonic response curve of the system electrical quantity. DETAILED DESCRIPTION

[0088] In order to enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of the present invention are clearly and completely described below in conjunction with the drawings in the implementation of this specification, but are not limited to this. Anything not fully described in the present invention shall be based on the conventional technology in the art.

[0089] Figure 1 The topology diagram of the 6-pulse Graetz bridge inverter is shown in Figure 1. a 、u b 、u c Represent the three-phase voltage on the AC side, U d is the DC side voltage, L c is the equivalent commutation inductance. The 6-pulse Graetz bridge inverter consists of six thyristor valve arms, which are turned on in the order of 1-6. During normal operation, in a 60° repetitive cycle, 2 valve arms and 3 valve arms are turned on in turn. Before valve VT1 and valve VT3 commutate, valve VT1 and valve VT2 are turned on, and the DC side is connected to the two-phase AC power supply A and C, and the port voltage is u ac , DC current i d Flows through valves VT1 and VT2. When the trigger pulse of valve VT3 arrives, if the voltage u ba If it is positive, it will be turned on immediately and valve VT1 will start to switch phase to valve VT3.

[0090] Example 1

[0091] A fast prediction method considering the risk of commutation failure caused by harmonics, such as Figure 3 As shown, the following steps are included:

[0092] S1: Determine the DC transmission system to be studied, obtain the shutdown angle γ0 under normal operation of the DC system, and calculate the critical value S of the commutation voltage-time area caused by the nth harmonic voltage under different frequencies, amplitudes, and initial phase angles. n,cri And the maximum commutation area S that the nth harmonic can provide n,max ;

[0093] S2: The critical value S of the commutation voltage-time area that causes commutation failure according to the nth harmonic voltage n,cri The maximum commutation area S that can be provided by the nth harmonic n,max The minimum harmonic voltage k that causes commutation failure at this frequency is calculated. n,cri As the critical value; k n,cri =min[k n (S n,cri ,S n,max )].

[0094] By inputting harmonics of different frequencies, different amplitudes, and different harmonic initial phase angles, and calculating the respective commutation voltage-time area critical value S that causes commutation failure n,cri And the maximum commutation area S that can be provided n,max , compare the critical value of the commutation voltage-time area caused by the harmonic voltage and the maximum commutation area that the nth harmonic can provide, and select the minimum harmonic voltage k that causes commutation failure at this frequency n,cri As the critical value, the minimum harmonic voltage at each frequency can be established, and the minimum harmonic voltage at each frequency is established to form a minimum harmonic voltage database;

[0095] S3: Real-time acquisition of the three-phase voltage of the AC busbar on the inverter side, and constructing virtual three-phases for the three-phase voltages respectively. The constructed symmetrical virtual three-phases are park transformed, and the AC and DC vectors are separated through a low-pass filter to extract the DC component and obtain the instantaneous value u of the harmonic voltage. n ;

[0096] S4: The instantaneous value of harmonic voltage u n Sampling is performed, and curve fitting is performed based on the nonlinear least squares algorithm of trust region reflection to extract the harmonic feature value A n ;

[0097] S5: Comparison of harmonic characteristic quantity A n With the critical value k n,cri Size, if A n Greater than k n,cri , the system has the risk of phase switching failure, otherwise, the system has no risk of phase switching failure.

[0098] First, taking into account the influence of the zero-crossing offset of the commutation voltage, the present invention proposes a dynamic critical value for the risk of commutation failure caused by harmonics taking into account the zero-crossing offset. The critical value can be dynamically adjusted according to different harmonic orders, amplitudes and phase angles. Secondly, the commutation voltage is reconstructed based on the method of virtual three-phase construction to achieve the separation of the fundamental signal and the harmonic signal. The reconstructed signal is subjected to the curve fitting method to achieve the rapid extraction of the harmonic feature quantity. Finally, in order to facilitate the rapid prediction of harmonic risks, a method based on the minimum harmonic commutation voltage k is proposed. n,cri A dynamic prediction method for the risk of commutation failure caused by harmonics. By comparing the actual value of the harmonic with the critical value, it is possible to predict whether the DC system has a risk of commutation failure. If the actual value is greater than the critical voltage, the system has a risk of commutation failure; otherwise, the system has no risk of commutation failure. Different from traditional methods, the method of the present invention improves the accuracy of the prediction of the risk of commutation failure caused by harmonics, and can effectively predict the commutation failure in advance to a certain extent. Moreover, as the effective value of the harmonic decreases, the advance amount of the predicted commutation failure becomes larger, that is, the prediction method proposed in this article is more effective under minor faults, which lays the foundation for the subsequent protection control system action.

[0099] Example 2

[0100] A rapid prediction method considering the risk of commutation failure caused by harmonics, as described in Example 1, except that in step S1, when the power grid is operating normally, the commutation voltage u ba Expressed as u ba Represents the line voltage between phases ba, which is the voltage provided during phase switching, called the phase switching voltage, where U1 is the effective value of the fundamental voltage, ω1 is the fundamental angular frequency, and the phase switching process satisfies the equation:

[0101]

[0102] Among them, L c represents the equivalent commutation inductance; α represents the trigger angle; μ represents the commutation angle; i m3 Indicates the current of the bridge arm where valve VT3 is located; i m1 Indicates the current of the bridge arm where valve VT1 is located;

[0103] The left side of formula (1) is defined as the commutation required area S need , expressed as

[0104]

[0105] It can be seen from formula (2) that the commutation required area S need With DC current i d and equivalent commutation inductance L cThe equivalent commutation inductance is a fixed parameter of the system, and its size determines the commutation speed. Therefore, the commutation required area mainly depends on the size of the DC current during the commutation process, in which the size of the DC current determines the size of the commutation angle μ, reflecting the energy required for the current to transfer between the bridge arms. Since the size of the DC current is mainly affected by the characteristics of the DC control system, and there is a smoothing reactor on the DC side to smooth the DC fluctuations, the DC current can be regarded as a constant during the commutation process;

[0106] The right side of formula (1) is defined as the switching area S pro , expressed as

[0107]

[0108] In order to make the system commutate normally, the commutation area S is required. need The area provided by the commutation should meet the following requirements:

[0109] S need ≤S pr o,max (4)

[0110] S pro,max Represents the maximum value of the area that the commutation voltage can provide;

[0111] When harmonics exist in the receiving AC system, the commutation voltage u' ba It can be expressed as:

[0112]

[0113] Where k represents the ratio of the effective value of the harmonic voltage to the fundamental voltage, n represents the nth harmonic, and k n It represents the ratio of the effective value of the nth harmonic voltage to the fundamental voltage, θ represents the initial phase angle of the harmonic, θ n represents the initial phase angle of the nth harmonic;

[0114] When the system contains harmonics, the commutation voltage S' pro The areas provided are:

[0115]

[0116] Among them, μ' represents the commutation angle after adding harmonics;

[0117] The commutation area S provided by the nth harmonic voltage n It can be expressed as:

[0118]

[0119] When harmonic voltage exists in the system and causes the commutation voltage amplitude to decrease, in order to ensure that the provided commutation area is still equal to the commutation area required for successful commutation, the system will be forced to increase the commutation angle to expand the actual commutation area provided. However, for the shutdown process after commutation, as the commutation angle increases, the shutdown angle will inevitably decrease. Moreover, when the harmonic voltage causes the commutation voltage to move forward through the zero point, it will continue to deteriorate the commutation conditions and further reduce the shutdown angle. When the commutation angle increases or the zero point moves forward to a certain extent, making the shutdown time less than the minimum shutdown time required for successful shutdown, commutation failure will occur.

[0120] Consider the extreme case where the system fails to commutate, that is, the turn-off angle is γ min , the maximum commutation area that the system can provide is:

[0121]

[0122] in, It represents the zero-crossing deviation angle of the commutation voltage caused by harmonics, and the maximum area provided by harmonics is ∑S n,max , the critical value of the commutation voltage-time area for commutation failure caused by harmonic voltage is obtained:

[0123]

[0124] S n,cri Indicates the critical value of the commutation voltage-time area when the nth harmonic voltage causes commutation failure; where α+μ=π-γ0, γ0 is the turn-off angle during normal commutation without harmonics;

[0125] In order for the system to successfully commutate in the presence of harmonics, the following conditions must be met:

[0126] ∑S n,max ≥S n,cri (10)

[0127] Will Substituting into equation (7), the maximum commutation area that the nth harmonic can provide can be calculated as:

[0128]

[0129] The present invention can be dynamically adjusted according to different harmonic orders, amplitudes and phase angles, and the factor of zero-crossing offset of commutation voltage caused by harmonics is taken into account in the derivation process, thereby reducing the error between the actual value and the theoretical value and improving the flexibility and accuracy of the prediction criterion.

[0130] Example 3

[0131] A rapid prediction method considering the risk of commutation failure caused by harmonics, as described in Example 2, except that in step S3, Figure 2 As shown, it is assumed that the effective value of the fundamental voltage of phase a is represented by U, the fundamental angular frequency of phase a is ω, and the initial phase of the fundamental is θ0; the effective value of the nth harmonic voltage is represented by U n , the initial phase of the harmonic is θ n ,but

[0132]

[0133] Among them, U a represents the constructed virtual a phase;

[0134] Take phase a as an example to construct its virtual three-phase. a Delay 60° and reverse to get U c , according to the symmetry of the three-phase circuit U a +U b +U c =0, we can get U b =-U a -U c , where U b represents the constructed virtual b phase; U c represents the virtual c-phase of the construction;

[0135] U b , U c Respectively expressed as

[0136]

[0137] After the virtual three-phase voltage abc is transformed by Parker transformation, we can get:

[0138]

[0139] Where i represents the construction of virtual three-phase with phase i as the reference voltage, and i can be a, b, or c; U id It represents the d-axis component obtained by Park transformation after constructing virtual three-phase with i phase as reference voltage; U iq It represents the q-axis component obtained by Park transformation after constructing virtual three-phase with i phase as reference voltage; U ia The virtual phase a is constructed with phase i as the reference voltage; U ib Indicates that the virtual b phase is constructed with the i phase as the reference voltage; U ic It means that the virtual c phase is constructed with the i phase as the reference voltage;

[0140] C abc / dq The matrix is:

[0141]

[0142] Substituting equation (12) and equation (13) into equation (14), we can obtain:

[0143]

[0144] Among them, H n Represents AC harmonic components;

[0145] Substitute u in formula (16) id and u iq A low-pass filter (LPF) is used to separate the AC and DC vectors. Different cutoff frequencies, orders, and types of low-pass filters may have a great impact on the detection of harmonic currents. Since the frequency characteristics of the Butterworth filter are best near the zero point, a higher detection accuracy can be achieved when the cutoff frequency is selected to be lower. Therefore, the present invention uses a Butterworth filter to filter out the harmonic components and extract the DC components.

[0146] The extracted DC component can be calculated through formula (17) to determine the fundamental voltage effective value U and the phase jump angle θ0:

[0147]

[0148] U id0 It represents the d-axis component obtained by Park transformation after filtering and constructing virtual three-phase with i phase as reference voltage; U iq0 It represents the q-axis component obtained by Park transformation after filtering by constructing virtual three-phase with i phase as reference voltage;

[0149] Combining equations (12) and (17), the actual voltage u i With fundamental component The instantaneous value of the harmonic voltage can be obtained by subtracting:

[0150]

[0151] u n Indicates the instantaneous value of the nth harmonic voltage; u i Indicates the actual AC voltage, which is measured in real time by the measuring instrument.

[0152] Example 4

[0153] A rapid prediction method considering the risk of commutation failure caused by harmonics is as described in Example 3, except that the specific implementation process of step S4 is as follows:

[0154] The instantaneous value of the harmonic voltage is sampled, and the sampled data is recorded as (t i ,y i ), i = 1, 2, ..., m; y i Indicates t i The instantaneous value of harmonic voltage at time , its fitting function is

[0155]

[0156] A n , n, θ n is the undetermined parameter, where A n represents the harmonic characteristic quantity, θ n Represents the initial phase angle of the nth harmonic, recorded as the undetermined parameter matrix P:

[0157]

[0158] According to the least squares principle, the objective function RSS is constructed to minimize its value, that is,

[0159]

[0160] In order to solve the optimization problem of the objective function, we first need to construct an initial trust region, use the quadratic model to approximate the objective function in the trust region, solve the subproblem under the quadratic model, and find the next iteration point; the trust region subproblem is described as:

[0161]

[0162] Where ΔP is the increment of parameter P, is the gradient of the objective function at the current iteration point, B k is the Hessian matrix of the objective function at the current iteration point, Δk is the radius of the trust region;

[0163] According to the sub-problem solution ΔP obtained, update the iteration point: P k+1 =P k +ΔP, when the objective function satisfies |RSS k+1 -RSS k |≤ε, the value of the undetermined parameter matrix P that meets the conditions can be obtained, and the rapid extraction of harmonic characteristic quantities can be achieved; where ε represents the preset error allowable value.

[0164] The present invention proposes a method based on virtual three-phase structure to reconstruct the commutation voltage, realizes the separation of fundamental signal and harmonic signal, and uses curve fitting method to quickly extract harmonic feature quantity from the reconstructed signal. The rapid extraction of harmonic feature quantity is of great significance for improving the speed and accuracy of commutation failure prediction.

[0165] Method Validation:

[0166] The present invention is based on the CIGRE BENCH MARK HVDC standard test model and builds a commutation failure identification module in MATLAB / Simulink. d is 500kV, DC current i dThe wiring diagram is as follows: Figure 4 At t = 0.8s, the initial phase angle injected into the inverter AC side bus of the CIGRE model is the same. The CIGRE model was developed by the International Conference on Large Electric Systems (Conseil International des Grands Réseaux The standard model developed by CIGRE is the existing model. The effective values ​​of harmonics are A n = 100Hz, 150Hz harmonics of 0.130pu, duration is 0.4s.

[0167] When the system is injected with A n = 0.130pu 100Hz harmonic response curve of the system electrical quantity is as follows Figure 5 As shown in the figure, after the system injected 100Hz harmonics at t=0.8s, the first commutation failure occurred at t=0.824s, and the valve VT3 that should have been turned off was turned on again, and the phase reversal occurred. The critical value of the risk of commutation failure caused by 100Hz harmonics calculated based on theoretical analysis is 0.113pu. The harmonic-induced commutation failure risk prediction method proposed in the present invention successfully predicted the risk of commutation failure at t=0.806s, which was 0.018 seconds earlier than the actual occurrence time, laying the foundation for the subsequent control and protection system action, which is of great significance for preventing subsequent continuous commutation failures from occurring and causing the DC system to lock.

[0168] When the system is injected with A n = 0.130pu 150Hz harmonic system electrical quantity response curve is as follows Figure 6 As shown in the figure, after 150Hz harmonics were injected at t=0.8s, the first commutation failure from valve VT3 to valve VT5 occurred at t=0.825s. The critical value of the risk of commutation failure caused by 150Hz harmonics calculated based on theoretical analysis is 0.120pu. The prediction method proposed in the present invention successfully predicted the risk of commutation failure at t=0.806s, which was 0.019 seconds earlier than the actual occurrence time, thus gaining advance action time for the subsequent control and protection system, which is conducive to suppressing the subsequent continuous commutation failure.

[0169] The above is a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A rapid prediction method considering the risk of commutation failure caused by harmonics, characterized in that: The steps include: S1: Determine the DC transmission system to be studied, obtain the shutdown angle γ0 under normal operation of the DC system, and calculate the critical value S of the commutation voltage-time area caused by the nth harmonic voltage under different frequencies, amplitudes, and initial phase angles. n,cri And the maximum commutation area S that the nth harmonic can provide n,max ; S2: The critical value S of the commutation voltage-time area that causes commutation failure according to the nth harmonic voltage n,cri The maximum commutation area S that can be provided by the nth harmonic n,max The minimum harmonic voltage k that causes commutation failure at this frequency is calculated. n,cri as critical value; S3: Real-time acquisition of the three-phase voltage of the AC busbar on the inverter side, and constructing virtual three-phases for the three-phase voltages respectively. The constructed symmetrical virtual three-phases are park transformed, and the AC and DC vectors are separated through a low-pass filter to extract the DC component and obtain the instantaneous value u of the harmonic voltage. n ; S4: The instantaneous value of harmonic voltage u n Sampling is performed, and curve fitting is performed based on the nonlinear least squares algorithm of trust region reflection to extract the harmonic feature value A n ; S5: Comparison of harmonic characteristic quantity A n With the critical value k n,cri Size, if A n Greater than k n,cri , the system has the risk of phase-change failure, otherwise, the system has no risk of phase-change failure; In step S1, when the power grid is operating normally, the commutation voltage u ba Expressed as Where U1 is the effective value of the fundamental voltage, ω1 is the fundamental angular frequency, and the commutation process satisfies the equation: Among them, L c represents the equivalent commutation inductance; α represents the trigger angle; μ represents the commutation angle; i m3 Indicates the current of the bridge arm where valve VT3 is located; i m1 Indicates the current of the bridge arm where valve VT1 is located; The left side of formula (1) is defined as the switching required area S need , expressed as Phase change required area S need With DC current i d and equivalent commutation inductance L c is proportional to; The right side of formula (1) is defined as the switching area S pro , expressed as In order to make the system commutate normally, the commutation area S is required. need The commutation area meets the following requirements: S need ≤S pro,max (4) S pro,max Represents the maximum value of the area that the commutation voltage can provide; When harmonics exist in the receiving AC system, the commutation voltage u' ba It is expressed as: Among them, k n Indicates the ratio of the effective value of the nth harmonic voltage to the fundamental voltage, θ n represents the initial phase angle of the nth harmonic; When the system contains harmonics, the commutation voltage S' pro The areas provided are: Among them, μ' represents the commutation angle after adding harmonics; The commutation area S provided by the nth harmonic voltage n It is expressed as: Consider the extreme case where the system fails to commutate, that is, the turn-off angle is γ min , the maximum commutation area provided by the system is: in, It represents the zero-crossing deviation angle of the commutation voltage caused by harmonics, and the maximum area provided by harmonics is ΣS n,max , the critical value of the commutation voltage-time area for commutation failure caused by harmonic voltage is obtained: S n,cri Indicates the critical value of the commutation voltage-time area when the nth harmonic voltage causes commutation failure; where α+μ=π-γ0, γ0 is the turn-off angle during normal commutation without harmonics; In order for the system to successfully commutate in the presence of harmonics, the following conditions must be met: ΣS n,max ≥S n,cri (10) Will Substituting into equation (7), the maximum commutation area that can be provided by the nth harmonic is calculated as: In step S2, k n,cri =min[k n (S n,cri ,S n,max )].

2. The rapid prediction method considering the risk of commutation failure caused by harmonics according to claim 1 is characterized in that: In step S3, it is assumed that the effective value of the fundamental voltage of phase a is represented by U, the fundamental angular frequency of phase a is ω, and the initial phase of the fundamental is θ0; the effective value of the nth harmonic voltage is represented by U n , the initial phase of the harmonic is θ n ,but Among them, U a represents the constructed virtual a phase; Take phase a as an example to construct its virtual three-phase. a Delay 60° and reverse to get U c , according to the symmetry of the three-phase circuit U a +U b +U c =0, we get U b =-U a -U c , where U b represents the constructed virtual b phase; U c represents the virtual c-phase of the construction; U b , U c Respectively expressed as After the virtual three-phase voltage of abc is transformed by Parker, we get: Where i represents the construction of virtual three-phase with phase i as the reference voltage, and i can be a, b, or c; U id It represents the d-axis component obtained by Park transformation after constructing virtual three-phase with i phase as reference voltage; U iq It represents the q-axis component obtained by Park transformation after constructing virtual three-phase with i phase as reference voltage; U ia The virtual phase a is constructed with phase i as the reference voltage; U ib Indicates that the virtual b phase is constructed with the i phase as the reference voltage; U ic It means that the virtual c phase is constructed with the i phase as the reference voltage; C abc / dq The matrix is: Substituting equation (12) and equation (13) into equation (14), we obtain: Among them, H n Represents AC harmonic components; In formula (16), id and u iq The AC and DC vectors are separated by a low-pass filter, and the extracted DC component is calculated by formula (17) to determine the fundamental voltage effective value U and the phase jump angle θ0: U id0 It represents the d-axis component obtained by Park transformation after filtering with the i-phase as the reference voltage to construct the virtual three-phase; U iq0 It represents the q-axis component obtained by Park transformation after filtering by constructing virtual three-phase with i phase as reference voltage; Combining equations (12) and (17), the instantaneous value of the harmonic voltage can be obtained: u n Indicates the instantaneous value of the nth harmonic voltage; u i Indicates the actual AC voltage, which is measured in real time by the measuring instrument.

3. The rapid prediction method considering the risk of commutation failure caused by harmonics according to claim 2 is characterized in that: The specific implementation process of step S4 is: The instantaneous value of the harmonic voltage is sampled, and the sampled data is recorded as (t i ,y i ), i = 1, 2, ..., m; y i Indicates t i The instantaneous value of harmonic voltage at time , its fitting function is A n , n, θ n is the undetermined parameter, where A n Represents the harmonic characteristic quantity, recorded as the undetermined parameter matrix P: According to the least squares principle, the objective function RSS is constructed to minimize its value, that is, To solve the optimization problem of the objective function, we first construct an initial trust region, use a quadratic model to approximate the objective function in the trust region, solve the subproblem under the quadratic model, and find the next iteration point; the trust region subproblem is described as: Where ΔP is the increment of parameter P, is the gradient of the objective function at the current iteration point, B k is the Hessian matrix of the objective function at the current iteration point, Δk is the radius of the trust region; According to the sub-problem solution ΔP obtained, update the iteration point: P k+1 =P k +ΔP, when the objective function satisfies |RSS k+1 -RSS k |≤ε, the value of the undetermined parameter matrix P that meets the conditions can be obtained, and the rapid extraction of harmonic characteristic quantities can be achieved; where ε represents the preset error allowable value.

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