Predictive Commutation Failure Suppression Strategy for High Voltage Direct Current System Considering Harmonic Components of Commutation Voltage

Abstract

The commutation failure of high voltage direct current (HVDC) systems could lead to unstable operation of the alternating current/direct current (AC/DC) hybrid power grid. The commutation voltage distortion caused by harmonics is a considerable but unclear factor of commutation failure. According to the control switching process of HVDC systems, the commutation voltage-time area method is employed to analyze and reveal the influence mechanism of harmonic components of commutation voltage on first and subsequent commutation failures. Considering the distortion characteristics of AC voltage, a predictive commutation failure suppression strategy considering multiple harmonics of commutation voltage is proposed. In this strategy, the new extinction angle and the zero-crossing offset angle after voltage distortion are calculated considering the harmonic components so as to obtain the compensation margin of the lag trigger angle by combining the correction margin with the voltage change rate. Moreover, the tuning method of parameters of extinction angle and voltage prediction variables are provided. Finally, a case study based on CIGRE standard HVDC system is performed and analyzed by using power systems computer-aided design (PSCAD) software. Compared with the International Council on Large Electric systems (CIGRE) standard test model and traditional commutation failure prevention (CFPREV) control model, the results verify that the proposed strategy can effectively reduce the risk of first and subsequent commutation failures and improve the sensitivity of CFPREV control.

1. Introduction

High voltage direct current (HVDC) transmission with grid converters are widely used in long-distance power transmission, underground and submarine cable power transmission and regional power grid interconnection due to their advantages, such as long transmission distance, small transmission loss and good economy. They are an important means to solve the uneven distribution of energy load in China [1,2,3]. Semi-controlled thyristors are mostly used as the converter elements. When the AC system at the sending and receiving ends fails, it is easy to cause commutation failure [4]. The commutation failure will lead to a sharp increase in DC current and a sharp drop in DC voltage. In serious cases, it will cause a DC blocking fault, which will interrupt the DC transmission power and eventually crash the system [5,6]. If the fault is not cleared in time after the first commutation failure, it is easy to cause subsequent commutation failure. After the subsequent commutation failure, the DC voltage, current, power and other electrical quantities change dramatically, which will have multiple impacts on the AC system. When the AC system is weak, it will cause a DC blocking fault and even cascading failure, bringing great risks and challenges to the safe and stable operation of AC/DC hybrid system [7].

There are many reasons for commutation failure. Considering the fundamental voltage, the increase of DC current, the decrease of AC voltage, the increase of commutation reactance and the decrease of lead trigger angle β will lead to the decrease of extinction angle γ. When γ is less than the inherent critical trigger angle γ_min, the commutation failure will occur [8,9]. After an AC system fault, the harmonic component and phase angle offset of commutation voltage will also cause commutation failure. Therefore, voltage distortion is also an important reason for commutation failure [10]. At present, the optimal control of HVDC transmission is mostly based on the protection control modules of converter stations, including voltage dependent current order limiter (VDCOL), commutation failure prevention (CFPREV), constant extinction angle control and power coordination control. The control system has a poor response ability to commutation voltage distortion at present [11,12].

Most of the existing methods to suppress commutation failure are based on improving the converter topology or optimizing the system control strategy [13]. Connecting capacitors and inductors in series and parallel on both sides of the AC transformer and adding reactive power compensation devices to change the structure of the converter can improve the ability to suppress commutation failure to a certain extent. However, adding power electronic devices has the disadvantages of high investment cost and high operation risk [14]. VSC-HVDC uses fully controlled devices to construct converters that are not dependent on AC system commutation, which can effectively inhibit the subsequent commutation failures, but it is not economical and operable [15,16]. Therefore, the optimization control strategy comes more from improving VDCOL and CFPREV modules, with less investment and greater operability. The basic principle of CFPREV is that when an AC fault is detected, a trigger angle margin is generated as the decrease of the lag trigger angle to achieve early triggering and reduce the risk of commutation failure. The harmonic component of the converter bus in the inverter side can cause frequent fluctuation of the CFPREV output, which leads to abnormal fluctuation of DC power. By distinguishing the zero-sequence component of inrush current and AC fault, the output of CFPREV can be controlled to be constant [17]. The literature [18] points out that CFPREV can exacerbate the negative impact of the initial fault voltage angle on commutation failure. When the fault phase voltage crosses zero, the single-phase short-circuit fault will significantly delay the start of CFPREV. Based on this, a calculation method of commutation failure probability is proposed. The literature [19] designs a coordinated controller, which can change the output of CFPREV according to the change of the extinction angle of the remote inverter, so that the trigger angle can be adaptively adjusted. But the accuracy is affected by signal transmission. The existing CFPREV control module has the problems of low output margin accuracy and poor flexibility of parameter adjustment, which may aggravate the subsequent commutation failure in the actual system.

In the process of commutation failure, the control behavior of the controller is affected by many factors. Therefore, the comprehensive effect of various electrical quantities after fault should be considered in the formulation of control and protection strategies. By suppressing the drop of DC current after faults, a control strategy for optimizing VDCOL is proposed in the literature [20], which can suppress AC overvoltage to a certain extent, but the effect of commutation failure suppression needs to be verified. The literature [21] points out that the waveform distortion of commutation voltage is the main reason for commutation failure under slight fault. By considering the time-domain effects of harmonics and DC current, the literature [22] proposes a prediction method of commutation voltage and current to realize the prediction of commutation failure, but the fault suppression strategy needs further study. A trigger angle prediction algorithm is proposed in the literature [23] by using the harmonic component to calculate the extinction angle to detect whether the commutation failure occurred. The commutation-time area method can be used to analyze the influence of harmonics on the commutation process. In the literature [24], the control parameters of each harmonic are calculated by using the commutation-time area method, and an additional harmonic control module is added to VDCOL module. But it cannot suppress the first commutation failure. Based on the commutation-time area, the dynamic adjustment of the extinction angle command value is realized in the literature [25] and the virtual resistor is used to trigger VDCOL in advance, but the suppression effect for some fault scenarios needs to be verified.

In view of the above research deficiencies, this paper analyzes the influence mechanism of the harmonic component of the commutation voltage on the commutation failure and proposes a predictive commutation failure suppression strategy considering the multiple harmonics of the commutation voltage based on the variation characteristics of the AC voltage after the fault. When it is applied to different AC fault scenarios, it can reduce the risk of the first and subsequent commutation failures more sensitively by considering the harmonic component of the voltage distortion and the dynamic change of the AC voltage. Finally, the simulation comparison between the proposed strategy and the traditional CFPREV strategy shows that it can reduce the number of commutation failures.

The main contributions of this paper are summarized as follows:

• Based on the commutation-time area method, the critical commutation area of harmonic components in fault recovery process is provided. And the mechanism of first and subsequent commutation failures is analyzed in combination with the change of electrical quantity.
• A novel commutation failure suppression strategy considering multiple harmonics of commutation voltage and voltage prediction is proposed. The new extinction angle and zero-crossing offset angle after voltage distortion are given based on the harmonic components, so as to obtain the compensation margin of the lag trigger angle by combining the correction margin with the voltage change rate.
• Tuning method of parameters of extinction angle and voltage prediction variables are provided. Extensive case studies based on a CIGRE standard HVDC system are performed and analyzed and compared with a CIGRE standard test model and commutation failure prevention (CFPREV) control model. Simulation results verify that the proposed strategy can suppress the first and subsequent commutation failures and reduce the number of commutation failures effectively when different degrees of faults occur.

The rest of this paper is organized as follows: Section 2 analyzes the principle of the inverter under the influence of harmonics. In Section 3, a commutation failure suppression strategy considering harmonics and voltage prediction is proposed. Based on the strategy, the tuning method of parameters are provided in Section 4. Simulation results based on PSCAD software and discussion are presented in Section 5. Finally, we conclude this paper in Section 6.

2. Commutation Failure and Harmonic Influence

The topology of the line-commutated converter based HVDC (LCC-HVDC) system is depicted in Figure 1, including sending-end grid, rectifier station, DC transmission lines, inverter station and receiving-end grid. Semi-controlled thyristors are widely used as the converter elements in HVDC, which can easily cause commutation failure at the receiving-end grid. Commutation failure is a common fault for HVDC systems, and it is easily affected by harmonics of commutation voltage during the AC fault occurrence. Therefore, it is meaningful to investigate the principle of commutation failure affected by the harmonics.

2.1. The Principle of Commutation under the Influence of Harmonics

When the AC fault occurs in the sending and receiving end power grid, the converter station near the fault point will fail at commutation. The essence of commutation failure is that the extinction angle is smaller than the minimum extinction angle γ_min (about 7°) corresponding to the recovery blocking time of the converter valve at the reverse voltage (about 0.4 s for high-power thyristor). In engineering, the converter unit is generally a six-pulse converter. Figure 2a analyzes the commutation process of thyristor VT3 to VT5, and Figure 2b is the simplified diagram of the inverter commutation process.

Before commutation, the thyristor VT3 and VT4 are turned on to form a DC current circuit. When VT5 receives the trigger pulse, VT3 begins to convert to VT5 and the three thyristors are simultaneously turned on. Ignoring the resistance of the large capacity transformer, the default three-phase commutation inductance is equal. The positive directions of current i_a, i_b and i_c are the conduction directions of thyristor. The positive directions of voltage u_a, u_b and u_c are shown in Figure 2a. The voltage equation during the commutation from valve VT3 to valve VT5 can be written as [26]:

$$L_{\mathrm{c}}\frac{d{i}_{\mathrm{b}}}{dt}-L_{\mathrm{c}}\frac{d{i}_{\mathrm{c}}}{dt}=-u_{\mathrm{b}}+u_c$$

(1)

where L_c is the commutation inductance. The commutation voltage u_bc can be represented by the line voltage amplitude U_L on the side of the commutation valve:

$$u_{\mathrm{bc}}=U_{\mathrm{L}}\sin (\omega t)$$

(2)

Considering the effect of flat wave reactor, the DC current I_d before and after commutation is basically unchanged. By substituting i_d = i_b + i_c into Formula (1) and integrating both sides from t₁ to t₂, the expression of commutation voltage time area (S) can be obtained:

$$S=2L_{\mathrm{c}}{I}_{\mathrm{d}}={\displaystyle {\int }_{t_1}^{t_2}{u}_{\mathrm{bc}}}dt={\displaystyle {\int }_{(\pi -\beta )/\omega }^{(\pi -\gamma )/\omega }{U}_{\mathrm{L}}\sin (\omega t)}dt$$

(3)

where t₁ is the trigger time and can be expressed by (π − β)/ω; t₂ is the end time of commutation, which can be expressed by (π − γ)/ω.

By further simplification, the following formula can be obtained:

$$\gamma =\arccos \left(\cos \beta +\frac{2\omega L_{\mathrm{c}}{I}_{\mathrm{d}}}{U_{\mathrm{L}}}\right)$$

(4)

The critical extinction angle γ_min is the minimum extinction angle required for normal turn-off of the thyristor. If the extinction angle corresponding to the commutation end time t₂ is the critical extinction angle γ_min, namely (π − γ_min)/ω, the maximum commutation area that the system can provide is defined as $S_{\max }={\displaystyle {\int }_{(\pi -{\gamma }_{\min })/\omega }^{(\pi -\beta )/\omega }{U}_{\mathrm{L}}\sin (\omega t)}dt$. The required commutation area for normal commutation of the system is defined as S_need = 2L_cI_d. When the required commutation area S_need > S_max, the extinction angle γ will be less than the critical extinction angle γ_min, the system cannot provide enough of a commutation margin, and commutation failure will occur. When the commutation voltage is distorted, the voltage distortion waveform is shown in Figure 3. During normal operation of the system, the commutation voltage is U. After an AC fault, the voltage waveform is distorted, the commutation voltage changes from U to U′, the amplitude decreases and the phase angle shifts φ. According to the parameter changes in Figure 3, the commutation area before the fault is S_x + S_y. After the fault, the commutation area provided by the system is reduced to S_y due to the distortion of voltage waveform. In order to provide sufficient a commutation margin, it is necessary to increase the commutation area S_z. At this time, γ decreases to γ′. When the extinction angle is smaller than the critical extinction angle γ_min, commutation failure occurs.

After the voltage distortion occurs, the commutation voltage u_bc will contain the harmonic components:

$$u_{\mathrm{bc}}=U_{1\mathrm{L}}\sin (\omega t)+{\displaystyle \sum _{n=2}^N{U}_{n\mathrm{L}}\sin (n\omega t+{\phi }_n)}$$

(5)

Substitute Formula (5) into Formula (3) can get the following formula:

$$2L_{\mathrm{c}}{I}_{\mathrm{d}}={\displaystyle {\int }_{(\pi -\beta )/\omega }^{(\pi -\gamma )/\omega }[U_{1\mathrm{L}}\sin (\omega t)}+{\displaystyle \sum _{n=2}^N{U}_{n\mathrm{L}}\sin (n\omega t+{\phi }_n)}]dt=S_1+{\displaystyle \sum _{n=2}^N{S}_n}$$

(6)

where S₁ and S_n are defined as the commutation area provided by the fundamental voltage and the harmonic voltage, respectively, and further simplification of Formula (6) can be obtained:

$$S_1=U_{1\mathrm{L}}\left[\cos \left(\pi -\beta \right)-\cos \left(\pi -\gamma \right)\right]$$

(7)

$$S_n=\frac{U_{n\mathrm{L}}}{n}[\cos \left(n\pi -n\beta +{\phi }_n\right)-\cos \left(n\pi -n\gamma +{\phi }_n\right)]$$

(8)

The condition for the normal switching off of thyristors is as follows: the commutation area provided by the system is larger than the required commutation area. Therefore, under the influence of harmonics, the condition for the normal commutation of the system is as follows:

$$S_{\mathrm{need}}\le S_1+{\displaystyle \sum _{n=2}^N{S}_n}$$

(9)

2.2. Influence of Harmonics on Subsequent Commutation Failure

When faults occur in the AC system of the HVDC transmission system, the control system at the rectifier and inverter side switches the control blocks to increase the trigger angle and ensure a certain commutation margin. As shown in Figure 4, the basic control blocks of the inverter side of the HVDC transmission system include the voltage dependent current order limiter (VDCOL), constant current (CC), constant extinction angle (CEA) and current error control (CEC) [27].

In Figure 4, U_di and I_di are the measured values of DC voltage and DC current on the inverter side after passing through the first-order low-pass filter; I_ord1 is the DC current instruction of the upper level; when the DC voltage is lower than the low-voltage current limiting control threshold value, VDCOL starts and outputs the DC current command value I_ord; γ_min and γ_ref are the minimum measured extinction angle and the reference value of extinction angle (15°), respectively; when the DC current reaches the current deviation control starting threshold, CEC outputs Δγ_CEC, which is added to the input of CEA as an increase. In the actual control of the system, CEA and CC control are started at the same time, and output β_CEA and β_CC, respectively. The maximum values of the two angles are taken as the output of the inverter side advance trigger angle β_i, and α_i is obtained through transformation.

When a short-circuit fault occurs in the AC system on the inverter side, the second commutation failure will occur if the fault degree is deeper. Take the CIGRE standard test system as an example, the three-phase short-circuit grounding fault on the inverter side is set up. The starting time of the fault is 2 s and lasts for 0.2 s. The changes of electrical quantities during the fault process are shown in Figure 5.

On the one hand, it can be seen from Figure 5 that in the fault recovery process of the first commutation failure (process between green dotted lines), the advance trigger angle β_cc > β_CEA, and the system switches from CEA control to CC control. After the first commutation failure, the DC voltage decreases and the DC current rises sharply, which makes the inverter side enter the VDCOL control and the DC current command value decreases. When the DC current decreases to a certain extent, the system is normally commutated, and the DC current command value I_ord rises slowly. Therefore, in the process of fault recovery, the DC current I_d increases slowly with I_ord, resulting in the increase of commutation demand area S_need. On the other hand, in the process of fault recovery, AC voltage and DC current are basically restored to the standard value, but a large number of harmonic components appear at the receiving end. Therefore, it can be preliminarily judged that the subsequent commutation failure is not due to the commutation voltage drop caused by insufficient reactive power, but the commutation voltage distortion caused by harmonics. The critical area of commutation voltage time (γ is 7°) calculated by Formulas (7) and (8) in the fault process is shown in Figure 6. S₁ is the commutation area of fundamental voltage, S_1–15 and S_2–15 are the commutation areas of 1st–15th and 2nd–15th harmonic voltages, respectively. It can be seen that after the fault occurs, although the 2nd–15th harmonic commutation area increases, the fundamental voltage commutation area S₁ drops greatly, which causes the S_1–15 to drop sharply, so that the Formula (9) cannot be satisfied and the subsequent commutation failure of the system occurs. The waveforms of critical commutation area S₁ and S_1–15 before the first and subsequent commutation failure are amplified, as shown in Figure 6b,c. One can see that before the first commutation failure occurs, the harmonic deteriorates the commutation condition and the insufficient commutation margin leads to commutation failures. In the process of fault recovery after the first commutation failure, the harmonics reduce the commutation area, and, finally, the subsequent commutation failure occurs.

3. Suppression Strategy Considering Harmonics and Voltage Prediction

The key idea of CFPREV is that after the AC system fault is detected, the reduction of the output angle margin is triggered in advance to increase the extinction angle γ, so as to avoid the abnormal extinction of the thyristor and the commutation failure of the system. The basic control block diagram of CFPREV is shown in Figure 7, including zero sequence detector and abc-αβ three-phase fault detector. The traditional CFPREV has the disadvantages of single detection, insufficient prevention accuracy and lack of flexibility in parameter adjustment. Under some fault conditions, it may even aggravate the fault and cause subsequent commutation failure [28,29].

In order to alleviate the problem of poor speed and sensitivity caused by traditional CFPREV, a commutation failure suppression strategy considering harmonic and voltage prediction is proposed.

3.1. Suppression Strategy Considering Multiple Harmonics of Commutation Voltage

The commutation voltage distortion caused by harmonics will lead to voltage amplitude decrease, phase angle change and even zero-crossing offset. The three-phase short-circuit grounding fault at the inverter side is set in the CIGRE standard test system.

The fault time is 2 s and the duration is 0.2 s. The voltage distortion rate of 2nd–15th and 2nd–31st harmonics (the fundamental voltage distortion rate is 100%) can be obtained by the fast Fourier transform (FFT) decomposition of the commutation voltage, as shown in Figure 8. It can be seen that the voltage has a large harmonic distortion after the fault occurs, and the distortion rate reaches 42.4%. After the fault, the second large harmonic distortion rate appeared, reaching 26.1% at 2.24 s. The two harmonic distortions are both caused by the saturation of converter transformer caused by the substantial increase of DC current. By amplifying the waveform of Figure 8, it can be seen that there is little difference between 2nd–15th harmonic distortion rate and 2nd–31st harmonic distortion rate, the maximum is only 2.07%. Therefore, the subsequent calculation can consider the harmonic number to 15 times.

According to Formulas (7) and (8), the commutation voltage-time area corresponding to fundamental wave and each harmonic can be calculated and the total commutation area can be obtained by the summation:

$${\displaystyle \sum _{n=2}^N{S}_n}={\displaystyle \sum _{n=2}^N\frac{U_{n\mathrm{L}}}{n}[\cos \left(n\pi -n\beta +{\phi }_n\right)-\cos \left(n\pi -n\gamma +{\phi }_n\right)]}$$

(10)

The extinction angle γ can be obtained by Formula (4). Harmonics not only bring changes in the voltage amplitude and phase, but also cause zero crossing offset. If the offset angle is Δφ, the extinction angle should meet the Formula (11) to turn off normally:

$$\arccos (\cos \beta +\frac{2\omega L_{\mathrm{c}}{I}_{\mathrm{d}}}{U_{\mathrm{L}}})-\Delta \phi \ge {\gamma }_{\min }$$

(11)

It is assumed that the voltage variation vector diagram of single-phase short-circuit fault occurs on the inverter side of the AC system, as is shown in Figure 9 [18], and the harmonics distort the voltage of each phase. U_A, U_B and U_C are the three-phase voltage amplitudes before the fault; U_A′ and U_B′ are the voltage amplitudes of phase A and phase B, respectively, after fault; U_AB and U_AB′ are line voltage amplitude before and after fault; Δφ_A and Δφ_B are the voltage phase deviation of phase A and phase B before and after the fault; Δφ_AB is phase deviation of the line voltage. Expression of Δφ_AB can be obtained by cosine theorem and phasor relation:

$$\Delta {\phi }_{\mathrm{AB}}=\left|\arccos \frac{U_{\mathrm{AB}}^2+U_{\mathrm{B}}^2-U_{\mathrm{A}}^2}{2U_{\mathrm{AB}}{U}_{\mathrm{B}}}-({30}^{\circ }-\Delta {\phi }_{\mathrm{B}})\right|$$

(12)

In the same way, the formulas for calculating the phase deviation of other line voltages can be obtained:

$$\Delta {\phi }_{\mathrm{BC}}=\left|\arccos \frac{U_{\mathrm{BC}}^2+U_{\mathrm{C}}^2-U_{\mathrm{B}}^2}{2U_{\mathrm{BC}}{U}_{\mathrm{C}}}-({30}^{\circ }-\Delta {\phi }_{\mathrm{C}})\right|$$

(13)

$$\Delta {\phi }_{\mathrm{CA}}=\left|\arccos \frac{U_{\mathrm{CA}}^2+U_{\mathrm{A}}^2-U_{\mathrm{C}}^2}{2U_{\mathrm{CA}}{U}_{\mathrm{A}}}-({30}^{\circ }-\Delta {\phi }_{\mathrm{A}})\right|$$

(14)

It can be seen from Formulas (12)–(14) that the voltage distortion will cause the phase shift of the commutation voltage, which will be unfavorable to the commutation process of the converter valve. In order to ensure the normal switching off of the thyristor, it should be triggered in advance to ensure a certain commutation margin.

3.2. Compensation Correction Based on Voltage Change Rate

If the output trigger angle margin of CFPREV is too large, it will lead to an increase in the reactive power consumption of the converter at the inverter side, thus causing the voltage drop of the converter bus, which is not conducive to the recovery of the DC system [30]. If the change trend of voltage can be considered in the fault process, the CFPREV output trigger angle can be compensated and corrected, which can promote the recovery of voltage. The design of dynamic voltage prediction variable K_i is shown in Formula (15):

$$K_{\mathrm{i}}=1-\frac{d{U}_{\mathrm{aci}}}{dt}·B,\hspace{1em} B=\{\begin{array}{l}{B}_1\hspace{1em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{U}_{\mathrm{aci}}\ge U_{\mathrm{level}}\\ B_2\hspace{1em}\hspace{0.17em}\hspace{0.17em}{U}_{\mathrm{aci}}<U_{\mathrm{level}}\end{array}$$

(15)

where U_aci is the effective value of the line voltage of the AC system at the inverter side; B₁ and B₂ are correction coefficients; U_level represents the reference value of AC voltage.

When the voltage drops, the voltage change rate is negative. At this time, K_i is greater than 1, and the output trigger angle is increased, that is, the commutation margin is increased; when the voltage rises, the voltage change rate term is positive, and K_i is less than 1, which reduces the output trigger angle and promotes the voltage recovery. In the subsequent commutation failure process, the coefficient can also dynamically adjust the commutation margin according to the voltage variation trend.

3.3. Suppression Strategy Considering Harmonic and Voltage Prediction

The principle block diagram of commutation failure suppression strategy considering harmonic and voltage prediction is shown in Figure 10, which mainly includes three links: start-up block, voltage prediction block and trigger block.

Considering the start-up link of the multiple harmonics of the commutation voltage, the commutation voltage-time area corresponding to the 2nd–15th harmonics is calculated by Formula (10). Then, it is substituted into Formula (16) to obtain the calculated values γ_{ref_AB}, γ_{ref_BC} and γ_{ref_CA} corresponding to the extinction angles of each commutation voltage in the fault process, and take the minimum value of the extinction angle corresponding to each commutation voltage to obtain γ_m:

$$\gamma =\arccos \left(\cos \beta +\frac{2\omega L_{\mathrm{c}}{I}_{\mathrm{d}}-{\displaystyle \sum _{n=2}^N{S}_n}}{U_{\mathrm{L}}}\right)$$

(16)

$${\gamma }_{\mathrm{m}}=\min \left\{{\gamma }_{\mathrm{ref}\_\mathrm{AB}},{\gamma }_{\mathrm{ref}\_\mathrm{BC}},{\gamma }_{\mathrm{ref}\_\mathrm{CA}}\right\}$$

(17)

Combined with the zero-crossing offset after the distortion of the commutation voltage, the zero-crossing offset of each commutation voltage is calculated by Formulas (12)–(14), and the maximum value is taken to obtain Δφ_m. The difference between γ_m and Δφ_m is defined as the risk judgment value of commutation failure considering the distortion of commutation voltage after fault, as shown in Formula (18):

$${\gamma }_{\mathrm{m}}-\Delta {\phi }_{\mathrm{m}}<{\gamma }_{\min }$$

(18)

where γ_min is the critical extinction angle of thyristor (7°). After meeting the starting criterion, the comparator output A₁ is equal to 1, and A₂ is obtained as the starting criterion of the trigger link after broadening.

In the voltage prediction link, the effective value U_aci of the line voltage of the AC system on the inverter side is collected in real time, compares the voltage at the current time with the voltage value passing through the first-order inertia section to obtain the voltage change rate, which is substituted into Formula (15) to calculate the compensation coefficient K_i. In the actual simulation process, U_aci will have a small range of fluctuations, a low-pass filter can be used to reduce noise. When the startup criterion is established, the output of A₂ is 1, which determines that the system has the risk of commutation failure and starts the trigger link to achieve early trigger. The trigger margin Δα is shown in Formula (19), where Δγ is the compensation margin.

$$\Delta \alpha =K_{\mathrm{i}}·\left({\gamma }_{\mathrm{m}}-\Delta {\phi }_{\mathrm{m}}-\Delta \gamma \right)$$

(19)

After detection of commutation failure risk, start the trigger link and output the lag trigger angle margin Δα, as CFPREV output trigger angle reduction. The index of the proposed control strategy is more sensitive to the harmonic component generated by the commutation voltage distortion, and the response speed is faster.

4. Tuning Method of Parameters

4.1. Calculation of Reference Value of Extinction Angle

In order to determine the pre-trigger time and pre-trigger margin of this strategy, the fast Fourier transform FFT is used to decompose each commutation voltage and the U_nL and phase angle φ_n of each harmonic voltage is obtained. The commutation-time areas corresponding to 2nd–15th harmonic voltage are calculated by substituting Formula (10). The reference value γ₀ of the extinction angle here is taken as the critical value γ_min (7°). Due to the controller switching requiring a certain time, in order to achieve early trigger, the pre-trigger angle takes the actual value of the trigger angle of the previous cycle β₀.

After summing the commutation area corresponding to each harmonic, the calculated value of the corresponding extinction angle is substituted into Formula (16), where U_L takes the amplitude of the fundamental commutation voltage U_1L. The relevant formulas are shown in (20) and (21):

$${\displaystyle \sum _{n=2}^N{S}_n}={\displaystyle \sum _{n=2}^N\frac{U_{n\mathrm{L}}}{n}[\cos \left(n\pi -n{\beta }_0+{\phi }_n\right)-\cos \left(n\pi -n{\gamma }_0+{\phi }_n\right)]}$$

(20)

$$\gamma =\arccos (\cos {\beta }_0+\frac{2\omega L_{\mathrm{c}}{I}_{\mathrm{d}}-{\displaystyle \sum _{n=2}^N{S}_n}}{U_{1\mathrm{L}}})$$

(21)

4.2. Voltage Change Rate Module Parameter Tuning

Collect the effective value U_aci of the converter bus voltage in real time and make a difference between the voltage value at the current moment and the voltage value after the first-order low-pass filter [31], so as to obtain the calculated value of the change rate of the converter bus voltage, as shown in Figure 10.

The reason for the first commutation failure is that the commutation margin is insufficient due to the commutation bus voltage drop. In order to suppress the occurrence of the first commutation failure, the value of B₂ should be increased to obtain a larger trigger margin, and trigger in advance to suppress the failure. When the voltage exceeds the converter bus voltage threshold U_level, the value of B₁ is reduced to avoid too small a margin to suppress subsequent commutation failure. After the simulation test, the reference values of B₁ and B₂ are 3–10 and 11.5–18.5, respectively. The actual parameters will be adjusted according to the fault scenario. The voltage threshold U_level is 0.928 p.u.

When the fault occurs, the measurement time of FFT is 2–3 ms [32], and the calculation time of voltage change rate of the converter bus is about 1 ms. The calculation and discrimination of the advanced firing angle can be realized by a multi-core digital signal processor (DSP) with a nanoseconds processing speed [33,34]. The time scale from the fault of the converter bus to the local commutation failure is generally 6–8 ms, so the proposed control strategy can meet the requirements of the rapidity of commutation failure suppression.

5. Case Study

Based on the PSCAD/EMTDC simulation platform, the proposed suppression strategy is built on the CIGRE standard test model. The CFPREV parameters are consistent with the literature [35]. The CIGRE model parameters are shown in

Table 1. Test system parameters.

Parameter	Rectifier	Inverter
AC voltage/kV	345	230
DC voltage/kV	507	497
DC current/kA	2	2
trigger angle/(°)	20	18
DC power/MW	1014	994

.

5.1. Validation of Commutation Failure Suppression

A three phase short-circuit fault is set on the AC bus at the inverter side, the fault occurs in 2 s and lasts for 0.2 s. The aim is to compare and analyze the fault response of the following three control strategies: control strategy I: CIGRE standard test system; control strategy II: CFPREV control; control strategy III: the strategy proposed in this paper. The responses of extinction angle, AC voltage, trigger angles of inverter side, predictive variable of dynamic voltage K_i and currents at valve side of converter transformer under three strategies are shown in Figure 11.

According to the valve side currents of converter transformer in Figure 11, after a three-phase short-circuit fault in inverter side of AC system, both control strategies I and II failed to commutation failure once and the extinction angle decreased to 0. The reason for the commutation failure of the CFPREV strategy at 2.21 s is that the CFPREV output leads to the small trigger angle α at the inverter side, the increase of reactive power consumption of the converter and the voltage drop of the AC system, which deteriorate the commutation conditions. The strategy in this paper suppresses the first commutation failure and the system has no subsequent commutation failure. When the fault occurs, the voltage change rate is less than 0, the predictive variable of dynamic voltage K_i is greater than 1 and the trigger angle margin is increased to suppress the first commutation failure. By comparing the lag trigger angle of Figure 11, it can be seen that the strategy in this paper realizes the early trigger and the trigger margin is greater than the other two strategies, which can suppress commutation failure to a certain extent.

In order to further verify the adaptability of the strategy in this paper, single-phase short-circuit and three-phase short-circuit grounding faults are set on the inverter side and the electrical responses are shown in Figure 12 and Figure 13. It can be seen from Figure 12 that the single-phase short-circuit fault leads to two consecutive commutation failures in the original CIGRE system, and both CFPREV and the proposed strategy inhibit the first and subsequent commutation failures. However, the trigger angle margin of this strategy is obtained in advance compared with CFPREV strategy, and the advance trigger angle margin increases and the voltage recovery speed is faster. At the same time, in the steady state of the fault, the value of the extinction angle of the strategy in this paper does not increase, and the converter consumes less reactive power, which is conducive to the rapid recovery of the DC system. It can be seen from Figure 13 that under the three-phase short-circuit grounding fault, strategy I has two commutation failures and the CFPREV strategy has deteriorated the commutation conditions, resulting in one commutation failure. The proposed strategy realizes the early triggering and obtains a large trigger angle margin, which inhibits the first and subsequent commutation failures.

5.2. Subsequent Commutation Failure Suppression Verification

In order to fully verify the ability of the proposed strategy to suppress the first and subsequent commutation failures at different fault levels, further simulations are performed in different fault scenarios. First, it is necessary to define the fault level F_L as shown in (22). The larger the F_L value is, the more serious the fault is.

$$F_{\mathrm{L}}=\frac{U_{\mathrm{L}}^2}{\omega L_{\mathrm{f}}}\frac{1}{P_{\mathrm{dN}}}\times 100\%$$

(22)

where P_dN is the rated DC transmitted power; U_L is the AC bus voltage on the inverter side; L_f is the grounding inductance; and ω is the rated angular frequency.

Two fault scenarios of three-phase short-circuit fault and single-phase short-circuit fault are set up with different fault severity levels to compare and analyze the fault suppression capability of the strategy in this paper, the CFPREV strategy and the original CIGRE system. The results are shown in Figure 14.

The simulation results show that the CFPREV and the proposed strategy can suppress the subsequent commutation failure compared with the original CIGRE system when the three-phase short-circuit fault occurs in the inverter side AC system, but the suppression effect of the proposed strategy is better. CFPREV control and the strategy in this paper begin to fail in the first commutation when F_L is 17.9% and 23.8%, respectively. Therefore, the strategy in this paper can inhibit the first commutation failure to a certain degree of failure. When a single-phase short-circuit fault occurs, the original CIGRE system and CFPREV strategy have different degrees of single and subsequent commutation failures, while the strategy in this paper has no commutation failure below 67.28% of the fault level. When F_L exceeds 67.28%, the single-phase short-circuit fault is more serious, and the restraining ability of commutation failure of the strategy in this paper is the same as the other two strategies.

Compared with CFPREV control, the proposed strategy can track the dynamic changes of voltage in real time. When the commutation voltage drops, the compensation margin of the trigger angle is increased, so as to realize the early trigger and suppress the first commutation failure. In the stage of fault recovery, the compensation margin of the trigger angle is dynamically adjusted to reduce, which is conducive to the rapid recovery of the DC system and inhibits the occurrence of subsequent commutation failures.

6. Conclusions

In this paper, a predictive commutation failure suppression strategy considering multiple harmonics of commutation voltage is proposed combined with the first and subsequent commutation failure mechanisms in HVDC transmission. The proposed strategy comprehensively considers the harmonic component of commutation voltage distortion and the dynamic change of AC bus voltage, and triggers in advance to increase the commutation supply area. Through theoretical and simulation analyses, the conclusions are as follows:

• During the fault recovery process after the first commutation failure, the voltage distortion of the commutation bus caused by harmonics leads to a significant reduction in the commutation supply area, which is an important factor leading to the subsequent commutation failure.
• The proposed strategy calculates the extinction angle and offset angle based on the harmonic components and constructs a comparator to judge whether there is a risk of commutation failure. It is more accurate to obtain the early trigger amount in advance and improves the sensitivity of commutation failure suppression.
• The prediction module of proposed strategy considers the dynamic change rate of AC bus voltage during the process of faults and suppresses the first and subsequent commutation failures by calculating different indicators. Compared with the traditional control methods, the strategy in this paper can suppress the first commutation failure under the three-phase short-circuit fault degree of 23.8% and the subsequent commutation failure, and the first and subsequent commutation failures with single-phase short-circuit fault degree below 67.28%.

The future works will focus on interaction principle and suppression strategy of commutation failure in multi-infeed HVDC system.