Abstract
In the voltage source converter based high-voltage direct current (VSC-HVDC) grids, fast and reliable protections are the key technologies. The traditional protection schemes are easily affected by fault resistance, line distributed capacitance, etc. Meanwhile, the influence of fault current limiting strategy (FCLS) has not been fully considered. In this paper, the fault characteristics under FCLS and the feasibility of traditional travelling wave protections are analyzed. To improve the reliability and sensibility, a similarity comparison based pilot protection scheme is proposed, which focuses on the relationship between the fault characteristics and the state of the protected transmission line, with the establishment of a precise frequency-dependent transmission line model. The criteria based on the similarity comparison calculated by cross-wavelet can identify the fault effectively. Meanwhile, the protection scheme can also endure the influence of error synchronization. Finally, the protection performance is verified in the PSCAD/EMTDC under different fault conditions.
WITH the development of power electronic devices, the voltage source converter based high-voltage direct current (VSC-HVDC) technology has been extensively applied in the power system. VSC-HVDC transmission systems have outstanding advantages in the flexible integration of renewable energy and decoupling control of active and reactive power [
To suppress the development of fault currents, some fault current limiting strategies (FCLSs) based on the controllability of converters are proposed. Compared with the traditional methods such as the configuration of large current limiting reactors (CLRs) [
The travelling wave (TW) protections are extensively applied as the primary protection in VSC-HVDC grids [
For better performance, double-ended protection schemes are proposed, which use the fault direction information at both terminals to identify the fault. The traditional current differential protection can overcome the influence of fault resistance and achieve absolute selectivity [
In short, the above protection schemes highly rely on the fault characteristics, which are determined by the topology of the grid, and then the protection thresholds are usually set by simulation. Meanwhile, the electromagnetic phenomena for these protection schemes may disappear and are easily influenced by the fault resistance. Moreover, the influence of FCLS on the fault characteristics is not considered.
To solve these problems, an idea is to shift the studied object from fault characteristics at one terminal to the state of the line model. A similarity comparison based pilot protection is proposed, which can identify the faults with high reliability and sensitivity.
The rest of the paper is structured as follows. The fault characteristics under the FCLS are analyzed in Section II. Then, the principle and feasibility of traditional TW based pilot protection are presented in Section III. Similarity analysis of TW is presented in Section IV. Section V presents the scheme of similarity based pilot protection and simulation validation are given in Section VI. Finally, Section VII concludes the paper.
According to the existing FCLS by HB-MMCs, the essence is to reduce the current contribution of SM capacitors in the discharge circuit by bypassing more SM capacitors in each phase [

Fig. 1 Equivalent HB-MMC.
The output voltage of the MMC can be calculated as:
(1) |
where Udc(s) is the output voltage of MMC; Uline(s) is the voltage at the line side of CLR; Idc(s) is the DC current; and Ldc is the inductance of CLR. Then, the equation can be written according to the equivalent loop.
(2) |
where and are the sums of the SM voltages in the upper arm and lower arm, respectively; and Req and Leq are the equivalent resistance and reactance of the bridge arm, respectively. Meanwhile, the SM voltages are determined by the number of SMs inserted in the circuit and can be expressed as:
(3) |
where Udcn is the rated output voltage of MMC. Then, the DC current can be calculated by (2) and (3).
(4) |
However, km is not a constant after faults. According to the diagram of the converter control strategy in

Fig. 2 Diagram of converter control strategy.
With the increase of fault current, km will decrease to reduce the number of SMs inserted in the discharge circuit. km can be expressed as:
(5) |
where kP and kD are the scale and differential factors of the controller, respectively; and Idcn is the rated DC current of MMC. During the normal operation, Idc is approximately equal to Idcn under the double closed-loop PI controller. After the sense of rising fault current, km will decrease within the range of [0, 1).
Combining (4) and (5), km can be expressed as:
(6) |
where the coefficient . Then, Idc can be expressed as:
(7) |
Combining (1) and (7), the relationship between Udc(s) and Uline(s) is:
(8) |
where the coefficient .
According to the analysis of fault characteristics, km will be smaller than 1 during the active current limiting control in (5) and the increase of the fault current can be suppressed as shown in (4). Further, the output voltage of the converter decreases, causing the voltage at the line side of CLR to drop as indicated in (8). Therefore, the fault characteristics are changed at the same time and the converter can be no longer regarded as a constant voltage source. During the FCLS period, an additional forward TW can be equivalent to being generated by the converter and injected into the transmission line. Therefore, the traditional TW based protection should consider this influence.
For the traditional TW analysis, MMCs at two terminals of the protected line are regarded as the constant voltage sources during the initial period of faults for analysis. Therefore, the forward TW and the backward TW are defined as:
(9) |
(10) |
where Ff and Bf are the forward TW and the backward TW, respectively; Zc is the wave impedance of the line; uf is the fault component voltage; and if is the fault component current, in which the positive direction is defined from the converter to the protected line. Meanwhile, the earth-mode component is greatly affected by the line attenuation and only exists under the single phase-to-ground fault [
With the consideration of FCLS, the measured forward TW Fm and backward TW Bm are expressed as:
(11) |
(12) |
where ucon and icon are the variations of voltage and current caused by the FCLS, respectively. As a result, the forward TW and backward TW will be changed, compared with the situation without FCLS.
For the traditional TW based protection [
(13) |
where is the indicator to identify the fault direction, in which indicates the forward fault and indicates the backward fault. According to the principle of TW reflection at the boundary of the terminal, the reflection coefficient is theoretically less than 1. When a forward fault occurs, the backward TW of initial fault propagates along the transmission line and reflects at the terminal. Therefore, the calculated will be less than 1 and a forward fault can be identified. For a backward fault, the TW refracts into the protected line across the boundary. Therefore, will be larger than 1 and a backward fault can be identified. However, the additional forward TW is generated by the FCLS and the ratio of the forward TW and backward TW is no longer equal to the reflection coefficient. Therefore, it demonstrates that the sensitivity and reliability of the traditional TW based pilot protection will be affected.
To improve the performance of TW based pilot protection, the studied object is changed from the relationship between forward TW and backward TW at the local terminal to the relationship between the forward TW at the local terminal and the backward TW at the peer terminal, since the propagation characteristics of the transmission line are only related to its state, and free from the influence of converter control at terminals.
During the normal state, only the DC component exists in HVDC grids with few harmonics. However, the long transmission lines can be no longer simplified as an invariant impedance after the fault, because the characteristics of transmission line parameters will change within the whole frequency range. Therefore, building an accurate frequency-dependent transmission line model is necessary for protection. Otherwise, the sensitivity and reliability of the protection will be influenced [
In the frequency-domain, the relationships of the voltages and currents at the two terminals M and N of the line are:
(14) |
where and are the voltages at terminals N and M, respectively; and are the currents at terminals N and M, respectively; l is the length of the transmission line; is the wave impedance, and R, L, G, and C are the resistance, inductance, conductance, and capacitance, respectively; and is the propagation coefficient.
Then, the relationship between the backward TW at the terminal M and the forward TW at the terminal N can be obtained.
(15) |
where is the attenuation function. and are both frequency-dependent. Then, (15) in the frequency-domain needs to be converted to the time domain by convolution. The equivalent circuit diagram of the frequency-dependent model of the DC line is shown in

Fig. 3 Equivalent circuit of frequency-dependent model of DC line.
The controlled voltage source EM(t) in
(16) |
where is the propagation time of the TW on a full-length transmission line; and is the state in the process of recursive convolution calculation.
The recursive convolution theorem can be used to calculate the convolution of exponential function directly through the historical value, which can be expressed as:
(17) |
where , , and are the known constants; is the sampling interval; and g, c, and q are the constants calculated by h, , and T, respectively.
The convolution function can be approximated in the form of a sum of rational functions in the Laplace-domain [
(18) |
where ri and pi ) are the residues and poles of the fitting form of the characteristic impedance and attenuation constants in the frequency domain, respectively. The residues and poles are extracted by PSCAD/EMTDC. According to the deduced frequency-dependent model and recursive convolution theorem, the model of DC line in the time domain can be obtained as:
(19) |
where , , , , , and are coefficients fitted by (18). Finally, the wave impedance and attenuation function can be calculated in the time-domain by the recursive convolution theorem. Therefore, the relationship between the backward TW at terminal M and the forward TW at terminal N can be deduced.
(20) |
Similarly, the backward TW at terminal N can also be calculated accurately by the forward TW at terminal M. The electrical quantities at two terminals always satisfy (20) when the line model is sound. If the line model is changed by the fault, (20) will no longer be satisfied. Therefore, the state of the line is decoupled from the external system.
The process of the TW propagation under an external fault is shown in

Fig. 4 Diagram of TW propagation. (a) External fault. (b) Internal fault.
Since there is no fault occurring in the protected line MN, the initial TW propagates from the terminal M to the terminal N without any reflection and refraction. Then, the backward TW at the peer terminal can be calculated by the forward TW at the local terminal accurately. The analysis of TW at terminal M is taken as an example.
(21) |
where is the calculated backward TW at the terminal N; is the forward TW at the terminal M; and are the TWs generated by the fault and FCLS of the converter, respectively; and is the propagation of the line MN. Based on the precise modeling of the line, the measured backward TW is the same as the calculated backward TW . Similarly, the measured backward TW and the calculated backward TW also satisfy the relationship.
The process of the TW propagation under an internal fault is shown in
(22) |
where is the propagation function of the line section MK. Meanwhile, the forward TW is expressed as:
(23) |
where is the reflection coefficient at the terminal M. Further, the calculated backward TW at the terminal N is expressed as:
(24) |
The actual measured backward TW is:
(25) |
where is the propagation function of the line section NK. According to (24) and (25), and have different amplitudes, polarities, and natural frequencies. Meanwhile, the difference between them increases over time.
In conclusion, the measured backward TW at the peer terminal is the same as the backward TW calculated from the local forward TW under the external fault. However, there is a large difference between the measured backward TW at the peer terminal and the backward TW calculated from the local forward TW under the internal fault. The relationship between the electrical quantities at two terminals is only related to the state of the transmission line. Therefore, the impact of FCLS on the characteristics of TW can also be eliminated.
The cross-wavelet transform can be used to analyze two time series, examining their relationship by the information of correlation and phase in the time-frequency domain space.
The cross-wavelet transform of two time series xn and yn is defined as:
(26) |
where S is the smoothing operator; n is the time series; is the wavelet coefficient matrix of xn; and is the plural conjugate wavelet coefficient matrix of yn. Meanwhile, the basic wavelet uses the Morlet wavelet to extract the TW feature, with a good balance between the time and frequency localization. The expression is:
(27) |
where N is the total sampling number; is the interval of sampling points; is the Morlet wavelet function; and s is the wavelet scaling operator.
Firstly, the wavelet correlation is utilized to characterize the correlation of two time series in time-frequency domain space. The correlation coefficient is expressed as:
(28) |
Under a specific frequency, Rn is 1 if the variation trend of these two time series is the same, while Rn is 0 if the variation trend of these two time series is opposite.
Secondly, the phase difference can be utilized to characterize the relative phase of two time series in time-frequency domain space. The expression is:
(29) |
Under a specific frequency, ° means that there is no phase difference. Otherwise, the phase difference exists between these two time series.
According to the analysis of TW characteristics between the internal and external faults, there is a large difference between the measured backward TW at the local terminal and the calculated backward TW at the peer terminal under an internal fault, while the measured backward TW at the local terminal is almost the same as the calculated backward TW at peer terminal under an external fault. The cross-wavelet transform is used to describe the similarity of TWs. An internal metallic positive pole-to-ground (P-PTG) fault and an external P-PTG fault are set to occur in the simulation system. The external and internal fault characteristics are shown in Figs.

Fig. 5 External fault characteristics. (a) Waveforms. (b) Cross-wavelet transform result.

Fig. 6 Internal fault characteristics. (a) Waveforms. (b) Cross-wavelet transform result.
For the external fault, there is no difference between BNM and BN in
After the fault occurrence, the initial fault TW will propagate to terminals. The voltage at the line side of CLR will change rapidly. Therefore, the change rate of voltage is utilized to detect the fault and then start the following protection algorithm with low computation overhead and in high speed. The criterion is:
(30) |
where is the voltage at the line side of CLR; and Uset is the threshold and the setting should consider the extreme case of internal faults.
Due to the coupling relationship between the lines, the sound pole might also sense the voltage change. Then, the ratio of the energy of transient voltages between the positive and negative poles is used to identify the faulted pole. The criterion is:
(31) |
where Eratio is the ratio of transient voltage energy between the positive and negative poles, and indicates a positive pole fault, indicates a negative pole fault, and indicates a pole-to-pole fault; and the subscripts P and N represent the positive pole and the negative poles, respectively. With the consideration of the discharge of distributed capacitance and noise disturbance, Eratio is not equal to 1 strictly when the pole-to-pole (PTP) fault occurs. Then, the reliability coefficient Eset (greater than 1) is introduced.
After the fault detection and faulty pole discrimination, the voltage and current information are acquired in the data window. Then, the calculated backward TW and the measured backward TW are obtained at two terminals of the protected line. The fault identification is according to the similarity between the TWs. Meanwhile, the similarity result is constructed by the combination of correlation coefficient and phase difference. The criterion is as follows:
(32) |
where Ra is defined as the average value of the correlation coefficient within the envelope ; and is defined as the average value of the phase difference within the envelope . Under an external fault, Ra is very close to 1 and is very close to 0°, which indicate that the similarity degree between TWs is high. Otherwise, there is an internal fault with low similarity.
Besides, the synchronization error might occur during the execution of protection algorithm. For example, a 0.5 ms time-shift is set in the external fault simulated in

Fig. 7 External fault characteristics under synchronization error. (a) Waveforms. (b) Cross-wavelet transform result.
However, the phase difference between the measured TW and calculated TW is the same in the high-frequency range. The high-frequency components of the TW are determined by propagation characteristics and their frequencies are called the natural frequencies.
(33) |
where fn is the
As shown in
(34) |
where is the standard deviation; is the phase in the high-frequency region; is the average value of the phase in the high-frequency region; and is the threshold. If (34) is satisfied, it indicates that there is an external fault. Otherwise, there is an internal fault.
The process of the proposed protection scheme based on the criteria above is as follows.
1) Based on (30), once is larger than the threshold , the protection scheme is activated.
2) According to (31), the calculated Eratio determines the faulted pole and the voltage information and current information are acquired at the same time.
3) Based on the acquired voltage and current, the local backward TW is measured and the calculated backward TW is transferred to the peer terminal.
4) If (32) is satisfied, an external fault is identified. If (32) is unsatisfied, the phase difference in high-frequency region is further used to avoid the misoperation by (34).
5) If (34) is not satisfied, an internal fault can be identified.
To verify the performance of the proposed protection scheme, a kV four-terminal MMC-HVDC grid shown in

Fig. 8 Diagram of four-terminal MMC-HVDC grid.
Converter No. | No. of SMs per arm | SM capacitance (mF) | Arm inductance (mH) | CLR (mH) |
---|---|---|---|---|
MMC1 | 220 | 10 | 50 | 100 |
MMC2 | 220 | 10 | 50 | 100 |
MMC3 | 220 | 15 | 50 | 100 |
MMC4 | 220 | 15 | 50 | 100 |
Based on the criterion in Section V, the thresholds are set according to the simulation system. For the sensitivity of fault detection, the value of needs to consider the most severe internal fault with 1000 fault resistance, in which is measured as 45 kV/ms. Therefore, is set to be 22.5 kV/ms with a reliability coefficient of 0.5. For the reliability of faulty pole discrimination, is set to be 2. Considering the reliability of the protection, is set to be 0.8, and is set to be 20°. Besides, the boundary of the high-frequency region is set to be 1000 Hz and is set to be 20°.
With the setting of the fault detection criterion in Section V, the fault can be detected if the measured is larger than the threshold . The measured under different fault conditions is shown in

Fig. 9 Measured under different fault conditions.
Based on the faulty discrimination criterion in Section V, the faulted pole can be identified by the ratio of transient voltage energy between the two poles. As shown in

Fig 10 Measured Eratio under different fault conditions.
The feasibility of fault identification criterion is verified in this part. Different fault conditions are set in the MMC-HVDC grid and the occurring time of the fault is set to be 1 s. Meanwhile, all the MMCs have the function of FCLS. After the detection of the increasing fault current, MMCs will follow the instruction in
For an internal metallic P-PTG fault , the simulation results are shown in

Fig. 11 Simulation results under internal fault. (a) Current limiting effect under FCLS. (b) Forward and backward TWs at terminal M. (c) Forward and backward TWs at terminal N. (d) Comparison of measured and calculated backward TWs. (e) , , and .
For an external metallic P-PTG fault , the simulation results are shown in

Fig. 12 Simulation results under external fault. (a) Current limiting effect under FCLS. (b) Forward and backward TWs at terminal M. (c) Forward and backward TWs at terminal N. (d) Comparison of measured and calculated backward TWs. (e) and .
For the external fault, the synchronization error between the protection devices at both terminals might aftect the correct fault identification. Based on the sampling results of TWs in

Fig. 13 Simulation results under external fault with synchronization error. (a) Comparison of measured and calculated backward TWs. (b) , , and .
To verify the protection performance under the fault resistance, P-PTG faults with resistance in different locations are set and the simulation results are listed in
Fault | Fault resistance (Ω) | (°) | (°) | Fault identification | |
---|---|---|---|---|---|
f1(0%) | 1000 | 0.24 | 162.3 | 54.1 | Internal fault |
f1(50%) | 1000 | 0.23 | 157.6 | 58.4 | Internal fault |
f1(100%) | 1000 | 0.21 | 161.8 | 55.6 | Internal fault |
f2(0%) | 1000 | 0.99 | 0.2 | External fault | |
f3(0%) | 1000 | 0.99 | 0.3 | External fault |
The capability of the proposed protection scheme against the noise is also tested. The 20 dB noise is superimposed on the measured data under different fault conditions and the simulation results are listed in
Fault | Noise (dB) | (°) | (°) | Fault identification | |
---|---|---|---|---|---|
f1(0%) | 20 | 0.14 | 169.4 | 79.5 | Internal fault |
f1(50%) | 20 | 0.09 | 161.5 | 72.2 | Internal fault |
f1(100%) | 20 | 0.10 | 174.7 | 81.3 | Internal fault |
f2(0%) | 20 | 0.89 | 9.0 | External fault | |
f3(0%) | 20 | 0.88 | 9.8 | External fault |
To verify the influence of CLR, the simulation results under different CLRs are listed in
Faults | CLR (mH) | (°) | (°) | Fault identification | |||
---|---|---|---|---|---|---|---|
f1(50%) | 100 | 431 | 5.2 | 0.22 | 143.8 | 68.4 | Internal fault |
f2(0%) | 100 | 39 | 2.1 | 0.99 | 0.2 | External fault | |
f1(50%) | 200 | 432 | 5.2 | 0.27 | 134.3 | 72.5 | Internal fault |
f2(0%) | 200 | 24 | 2.3 | 0.98 | 0.3 | External fault | |
f1(50%) | 300 | 429 | 5.2 | 0.32 | 121.7 | 79.6 | Internal fault |
f2(0%) | 300 | 18 | External fault |
For the pilot protection, the operation speed is an important factor that should be considered. In this paper, the longest transmission line is 200 km. Therefore, the TW propagation time is less than 0.7 ms. Signal transferring in the dedicated optical fiber is at the speed of 200 km/ms. Therefore, the communication is less than 1 ms. Besides, the time window is set to be 2 ms. Therefore, the total time delay of operation is about 3.7 ms. Usually, the primary protections for VSC-HVDC grid are required to operate within 3 ms before the converter blocking. Owning to the FCLS of converters, the proposed protection scheme can still act as the primary protection.
In order to compare the performance of the proposed protection scheme with the existing protection scheme [
Protection | Principle of realization | Frequency-dependent parameters | Withstanding capability of noise (dB) | Withstanding capability of resistance (Ω) | Withstanding capability of synchronization error (ms) | Sampling frequency (kHz) | Operation time (ms) |
---|---|---|---|---|---|---|---|
[ | Modulus maxima | 400 | 100.0 | 3.00 | |||
[ | Haar wavelet | No | 40 | 150 | 1000.0 | 2.57 | |
[ | Cosine distance | No | 20 | 100 | 0.3 | 10.0 | 2.25 |
[ | Pearson coefficient | No | 1000 | 10.0 | 13.00 | ||
[ | Hausdorff distance | No | 10 | 1000 | 20.0 | 7.20 | |
Proposed | Yes | 20 | 1000 | 1.0 | 10.0 | 3.70 |
This paper proposes a similarity comparison based pilot protection scheme, which can be used in the VSC-HVDC grid under the FCLS. The proposed protection scheme is based on the similarity between the measured backward TW and calculated backward TW by cross-wavelet transform. The scheme is not affected by the FCLS compared with traditional TW protection schemes theoretically. The simulation results verify that the faults can be identified effectively and the protection will not operate incorrectly under external faults. Meanwhile, the feasibility and superiority of the proposed protection scheme emerge in the comparison with other similarity based algorithms. The results have confirmed that the protection scheme has the capability to endure noise disturbance, fault resistance, and synchronization error with low sampling frequency. The proposed protection scheme can act as the primary protection with the help of FCLS in the VSC-HVDC grid and can be also applied in different topologies of grids.
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