Journal of Modern Power Systems and Clean Energy

ISSN 2196-5625 CN 32-1884/TK

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A Similarity Comparison Based Pilot Protection Scheme for VSC-HVDC Grids Considering Fault Current Limiting Strategy  PDF

  • Keao Chen 1
  • Jinghan He 1 (Fellow, IEEE)
  • Meng Li 1
  • Yong Tang 2
  • Ming Nie 1
  • Chenguang Liang 1
1. School of Electrical Engineering, Beijing Jiaotong University, Beijing, China; 2. China Electrical Power Research Institute, Beijing, China

Updated:2023-07-24

DOI:10.35833/MPCE.2022.000107

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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.

I. Introduction

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 [

1]-[3]. Meanwhile, there is no commutation failure compared with the traditional HVDC technology [4]. However, VSC-HVDC grids usually use overhead lines, which have a high probability of line faults. Owning to the low impedance of the grid, fault currents increase rapidly, posing a huge threat to the safety of power electronic devices [5].

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) [

6], inserted current limiting devices after faults [7], and modified topologies of converters [8], [9], there is no additional cost by using converter control to suppress the rise of fault current. According to the analysis in [10], the fault current is largely contributed by the sub-module (SM) capacitors inserted in the discharge circuit. Therefore, an FCLS based on half-bridge modular-multilevel-converter (HB-MMC) has been proposed in [11]. With the coordination between HB-MMCs and DC circuit breakers (DCCBs), the faults can be handled effectively. However, the influence of FCLS on protection schemes is still an unsolved problem [12].

The travelling wave (TW) protections are extensively applied as the primary protection in VSC-HVDC grids [

13]. In real projects, TW protection schemes of ABB and SIEMENS are usually adopted, which measure the change of voltage and current at one terminal to identify faults with fast operation speed [14]. However, they suffer from some influencing factors such as noise interference and fault resistance. Some boundary-condition based protection schemes are proposed in [15], [16]. The fault characteristics across the CLR are used to identify the fault, improving the reliability and sensitivity. However, there is a requirement for the strength of boundary-condition. Besides, if the value of CLR is large, the dynamic response characteristics and stability of the grid will be influenced [17]. For the above single-ended protection schemes, the operation speed is mainly concerned. However, the FCLS further weakens the fault characteristics and then increases the possibility of maloperation. Therefore, the reliability, sensitivity, and selectivity need to be improved.

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 [

18]. However, the operation speed is severely affected by line distributed capacitance. To solve the delay problem, multiple distributed optical sensors are configured along the transmission line and the influence of line distributed capacitance can be eliminated [19]. However, the cost will increase greatly by employing the extra equipment. Then, the pilot TW protections based on the ratio of forward TW to backward TW are proposed [20], [21]. The protection schemes are independent of the boundary-condition and have a great performance in fault identification. However, the output voltage of the converter is reduced under the FCLS, which is equivalent to generating an additional TW. Then, the fault characteristics are varied and the reliability and sensitivity are influenced.

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.

II. Fault Characteristics Under FCLS

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 [

11]. The modulation factor km is introduced, which influences the proportion of inserted SMs in each phase. In the normal operation, km is 1 without any additional control. When the current rises after DC faults, km will decrease to bypass more SM capacitors to achieve fault current limiting. However, the fault characteristics will also change. The equivalent HB-MMC is shown in Fig. 1 and the fault characteristics under FCLS are analyzed as follows.

Fig. 1  Equivalent HB-MMC.

The output voltage of the MMC can be calculated as:

Udc(s)=2sLdcIdc(s)+Uline(s) (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.

Uupper(s)+Ulower(s)=(sLeq+Req)Idc(s)+Udc(s) (2)

where Uupper(s) and Ulower(s) 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:

Uupper(s)+Ulower(s)=kmUdcn (3)

where Udcn is the rated output voltage of MMC. Then, the DC current can be calculated by (2) and (3).

Idc(s)=kmUdcn-Udc(s)sLeq+Req (4)

However, km is not a constant after faults. According to the diagram of the converter control strategy in Fig. 2, the value of km is determined by FCLS. Note that variable definitions in Fig. 2 are presented in [

11].

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:

km=1-kP(Idc(s)-Idcn)-kDsIdc(s) (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:

km=1-k1(s)Udc(s)/Udcn+kPIdcn1+k1(s) (6)

where the coefficient k1(s)=Udcn(kP+kDs)/(sLeq+Req). Then, Idc can be expressed as:

Idc(s)=Udcn-(1+2k1(s))Udc(s)+kPIdcnUdcn(1+k1(s))(sLeq+Req) (7)

Combining (1) and (7), the relationship between Udc(s) and Uline(s) is:

Uline(s)=Udc(s)(1+k2(s)+2k1(s)k2(s))-Udcn(k2(s)+k2(s)kPIdcn) (8)

where the coefficient k2(s)=2sLeq/(1+k1)(sLeq+Req).

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.

III. Principle and Feasibility of Traditional TW Based Pilot Protection

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:

Ff=(Δuf+ZcΔif)/2 (9)
Bf=(Δuf-ZcΔif)/2 (10)

where Ff and Bf are the forward TW and the backward TW, respectively; Zc is the wave impedance of the line; Δuf is the fault component voltage; and Δif 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 [

22]. Therefore, the line-mode component is generally adopted for protection.

With the consideration of FCLS, the measured forward TW Fm and backward TW Bm are expressed as:

Fm=[(Δuf+Δucon)+Zc(Δif+Δicon)]/2 (11)
Bm=[(Δuf+Δucon)-Zc(Δif+Δicon)]/2 (12)

where Δucon and Δicon 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 [

23], the criterion is:

λ=Ff/Bf (13)

where λ is the indicator to identify the fault direction, in which λ<1 indicates the forward fault and λ1 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 λ 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, λ 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.

IV. Similarity Analysis of TW

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.

A. Construction of Frequency-dependent Transmission Line Model

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 [

21]. To reflect the relationship between the forward TW at the local terminal and the backward TW at the peer terminal accurately, the characteristics of TW impedance and propagation coefficient related to the frequency should be analyzed to construct an accurate frequency-dependent transmission line model.

In the frequency-domain, the relationships of the voltages and currents at the two terminals M and N of the line are:

UM(ω)IM(ω)=cosh(γ(ω)l)-Zc(ω)sinh(γ(ω)l)sinh(γ(ω)l)/Zc(ω)-cosh(γ(ω)l)UN(ω)IN(ω) (14)

where UN(ω) and UM(ω) are the voltages at terminals N and M, respectively; IN(ω) and IM(ω) are the currents at terminals N and M, respectively; l is the length of the transmission line; Zc(ω)=(R(ω)+jωL(ω))/(G(ω)+jωC(ω)) is the wave impedance, and R(ω), L(ω), G(ω), and C(ω) are the resistance, inductance, conductance, and capacitance, respectively; and γ(ω)=(R(ω)+jωL(ω))(G(ω)+jωC(ω)) is the propagation coefficient.

Then, the relationship between the backward TW BM(ω) at the terminal M and the forward TW FN(ω) at the terminal N can be obtained.

UM(ω)-Zc(ω)IM(ω)=A(ω)[UN(ω)+Zc(ω)IN(ω)]BM(ω)=A(ω)FN(ω) (15)

where A(ω)=cosh(γ(ω)l)-sinh(γ(ω)l)=e-γ(ω)l is the attenuation function. Zc(ω) and A(ω) 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, where EM(t) and EN(t) are the controlled voltage sources at terminals M and N, respectively; uM(t) and uN(t) are the measured voltages at terminals M and N, respectively; and iM(t) and iN(t) are the measured currents at terminals M and N, respectively.

Fig. 3  Equivalent circuit of frequency-dependent model of DC line.

The controlled voltage source EM(t) in Fig. 3 is the backward voltage TW at the local side, which can be expressed as:

EM(t)=BM(t)=uM(t)-τiMz(t-u)Zc(u)du (16)

where τ is the propagation time of the TW on a full-length transmission line; and iMz(t-u) 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:

s(t)=Tf(t-u)he-α(u-T)du=gs(t-Δt)+cf(t-T)+qf(t-T-Δt) (17)

where h, α, and T are the known constants; Δt is the sampling interval; and g, c, and q are the constants calculated by h, α, and T, respectively.

The convolution function f() can be approximated in the form of a sum of rational functions in the Laplace-domain [

24].

Zc(s)=r0+r1s-p1+r2s-p2++rns-pnA(s)=r1s-p1+r2s-p2++rns-pne-sτ (18)

where ri (i=0, 1,, n) and pi (i=1, 2, , n) 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:

uM(t)=EM(t)+g1iMz(t-Δt)+c1iM(t)+q1iM(t-Δt)EM(t)=g2EM(t-Δt)+c2FN(t-τ)+q2FN(t-τ-Δt) (19)

where g1, c1, q1, g2, c2, and q2 are coefficients fitted by (18). Finally, the wave impedance Zc(t) and attenuation function A(t) 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.

uM(t)-Zc(t)iM(t)=A(t)(uN(t)+zc(t)iN(t))BM(t)=A(t)FN(t) (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.

B. Characteristics of TW Under Different Faults

1) External Fault

The process of the TW propagation under an external fault is shown in Fig. 4(a).

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.

BNM(t)=AMN(t)(Ff(t)+Fcon(t))=AMN(t)FM(t) (21)

where BNM(t) is the calculated backward TW at the terminal N; FM(t) is the forward TW at the terminal M; Ff(t) and Fcon(t) are the TWs generated by the fault and FCLS of the converter, respectively; and AMN(t) is the propagation of the line MN. Based on the precise modeling of the line, the measured backward TW BN(t) is the same as the calculated backward TW BNM(t). Similarly, the measured backward TW BM(t) and the calculated backward TW BMN(t) also satisfy the relationship.

2) Internal Fault

The process of the TW propagation under an internal fault is shown in Fig. 4(b). K is the fault location in the protected line MN, where the initial fault TW f0 is generated and propagates to both terminals. The TWs will reflect and refract at the fault point and both terminals. The analysis of TW at terminal M is taken as an example and the backward TW Bf(t) is:

Bf(t)=f0(t)AMK(t) (22)

where AMK(t) is the propagation function of the line section MK. Meanwhile, the forward TW FM(t) is expressed as:

FM(t)=f0(t)AMK(t)Mrfl+Fcon(t) (23)

where Mrlf is the reflection coefficient at the terminal M. Further, the calculated backward TW BNM(t) at the terminal N is expressed as:

BNM(t)=(f0(t)AMK(t)Mrfl+Fcon(t))AMN(t) (24)

The actual measured backward TW BN(t) is:

BN(t)=f0(t)ANK(t) (25)

where ANK(t) is the propagation function of the line section NK. According to (24) and (25), BN(t) and BNM(t) 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.

C. TW Similarity Measurement Based on Cross-wavelet Transform

1) Cross-wavelet Transform

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:

WnXY(s)=S(WnX(s)×WnY*(s)) (26)

where S is the smoothing operator; n is the time series; WnX(s) is the wavelet coefficient matrix of xn; and WnY*(s) 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:

WnX(s)=n'=1Nxn'ψ0n'-nδts (27)

where N is the total sampling number; δt is the interval of sampling points; ψ0 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:

Rn(s)=S(s-1WnXY(s))2Ss-1WnX(s)2Ss-1WnY(s)2 (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:

λn(s)=arctanIm{WnXY(s)}Re{WnXY(s)} (29)

Under a specific frequency, λ=0° means that there is no phase difference. Otherwise, the phase difference exists between these two time series.

2) Extraction of TW Similarity

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 f1(50%) and an external P-PTG fault f2(0%) are set to occur in the simulation system. The external and internal fault characteristics are shown in Figs. 5 and 6.

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 Fig. 5(a). The result of the cross-wavelet transform is depicted in Fig. 5(b), where the color blocks represent the correlation degree. The higher the color saturation, the higher the correlation coefficient. The arrow direction represents the phase difference. The arrow horizontally towards the right represents 0°, which means there is no phase difference. The solid black line is the envelope and the region within the envelope is the high confidence region, where the accuracy of the calculation is not affected by wavelet edge effects. Therefore, it indicates that there is a high correlation and low phase difference under an external fault. For the simulation results of the internal fault depicted in Fig. 6(a), it can be observed that there is a large difference in amplitude, polarity, and natural frequency. Within the envelope in Fig. 6(b), most regions are blue with a low correlation. Although some regions have a high correlation, the phase difference is large. Therefore, the combination of the correlation coefficient and phase difference can be used to describe the similarity of TWs.

V. Scheme of Similarity Based Pilot Protection

A. Fault Detection

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:

duline/dt>ΔUset (30)

where uline is the voltage at the line side of CLR; and ΔUset is the threshold and the setting should consider the extreme case of internal faults.

B. Faulted Pole Discrimination

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:

uline,P2dtuline,N2dt=Eratio (31)

where Eratio is the ratio of transient voltage energy between the positive and negative poles, and Eratio>Eset indicates a positive pole fault, Eratio<1/Eset indicates a negative pole fault, and 1/EsetEratioEset 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.

C. Fault Identification

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:

Ra=R¯n(s)Csetλa=λ¯n(s)θset (32)

where Ra is defined as the average value of the correlation coefficient within the envelope R¯n(s); and λa is defined as the average value of the phase difference within the envelope λ¯n(s). Under an external fault, Ra is very close to 1 and λa 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. 5 and the results are shown in Fig. 7. The severe synchronization error will cause that Ra is smaller than the threshold Cset or λa is larger than θset, and the protection might misoperate.

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.

fn=θM+θN+2kπv4πl        k=0,±1,±2,... (33)

where fn is the nth order component of the natural frequencies of the TW; θM and θN are the reflection angles of TW at both terminals; and v is the velocity of TW. Theoretically, the reflection angle is between [0, π], which is dependent on the impedance of the terminal. The minimum main natural frequency f1 is calculated to be 750 Hz in a 200 km transmission line when θM=θN=π. Therefore, the frequency region above f1 is defined as the high-frequency region, where the phase information can be used to avoid the influence of synchronization errors.

As shown in Fig. 7(b), the arrow directions within the high-frequency region are almost the same but not horizontal. Therefore, the standard deviation is used to describe the dispersion degree and the criterion is:

α=1Ni=1Nλn,hf-λ¯n,hf2βset (34)

where α is the standard deviation; λn,hf is the phase in the high-frequency region; λ¯n,hf is the average value of the phase in the high-frequency region; and βset is the threshold. If (34) is satisfied, it indicates that there is an external fault. Otherwise, there is an internal fault.

D. Overall Process of Proposed Protection Scheme

The process of the proposed protection scheme based on the criteria above is as follows.

1) Based on (30), once duline/dt is larger than the threshold ΔUset, 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.

VI. Simulation Validation

To verify the performance of the proposed protection scheme, a ±500 kV four-terminal MMC-HVDC grid shown in Fig. 8 is constructed by PSCAD/EMTDC, in which each converter employs HB-MMC. The grid consists of four transmission lines, which use frequency-dependent models. Meanwhile, further details of the simulation system along with its parameters are listed in Table I. Meanwhile, the sampling rate is set to be 10 kHz in this paper and the data window is 2 ms. The protection unit M in line I (200 km) is taken to verify the protection performance under different fault conditions.

Fig. 8  Diagram of four-terminal MMC-HVDC grid.

Table I  Major Parameters of Simulation System
Converter No.No. of SMs per armSM 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 ΔUset needs to consider the most severe internal fault f1(100%) with 1000 Ω fault resistance, in which duline/dt is measured as 45 kV/ms. Therefore, ΔUset is set to be 22.5 kV/ms with a reliability coefficient of 0.5. For the reliability of faulty pole discrimination, Eset is set to be 2. Considering the reliability of the protection, Cset is set to be 0.8, and θset is set to be 20°. Besides, the boundary of the high-frequency region is set to be 1000 Hz and βset is set to be 20°.

A. Performance of Fault Detection

With the setting of the fault detection criterion in Section V, the fault can be detected if the measured duline/dt is larger than the threshold ΔUset. The measured duline/dt under different fault conditions is shown in Fig. 9. It shows that internal faults can be detected when the fault resistance is under 1000  Ω.

Fig. 9  Measured duline/dt under different fault conditions.

B. Performance of Faulty Pole Discrimination

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, f1(50%) is set to verify the threshold under various fault types with different fault resistances, where P-PTG, N-PTG, and PTP represent the positive pole-to-ground fault, negative pole-to-ground fault, and pole-to-pole fault, respectively. The results indicate that Eset is reliable for the protection to discriminate the faulted pole.

Fig 10  Measured Eratio under different fault conditions.

C. Performance of Fault Identification

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 Fig. 2, and decrease the number of the inserted SMs to limit the fault current.

1) Internal Fault

For an internal metallic P-PTG fault f1(25%), the simulation results are shown in Fig. 11. The effect of the FCLS is shown in Fig. 11(a), where IM and IN represent the currents limited by FCLS, respectively; and IM0 and IN0 represent the currents under the traditional control method at two terminals of the line I, respectively. The comparison indicates that the FCLS can effectively limit the fault currents. The forward and backward TWs are shown in Fig. 11(b) and (c) by the acquired voltage and current at both terminals. By comparing BM and BMN from terminal N with cross-wavelet transform, the results of correlation coefficient Ra and phase difference λa are shown in Fig. 11(e). The calculated Ra and λa are 0.12 and 172.5°, respectively, unsatisfying criterion (32). Further, the calculated α is 74.4°, which is much larger than βset. Therefore, an internal fault can be identified.

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) Ra, λa, and α.

2) External Fault

For an external metallic P-PTG fault f2(0%), the simulation results are shown in Fig. 12. By comparing BM and BMN, Ra and λa are 0.99 and 0.3°, respectively. Criterion (32) is satisfied with the high similarity and an external fault can be identified.

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) Ra and λa.

D. Influence of Synchronization Error

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. 12(d), a 1.0 ms time-shift Δt is set in Fig. 13(a). Owing to the synchronization error, Ra decreases to 0.68, and λa increases to 46.4°. It indicates that the similarity degree is affected by synchronization error. Further, the standard deviation of phases in high-frequency should be calculated. In Fig. 13(b), the calculated α is 5.8°, which is smaller than βset. Therefore, the simulation results verify that the proposed protection scheme can overcome the influence of the synchronization error.

Fig. 13  Simulation results under external fault with synchronization error. (a) Comparison of measured and calculated backward TWs. (b) Ra, λa, and α.

E. Influence of Fault Resistance

To verify the protection performance under the fault resistance, P-PTG faults with 1000  Ω resistance in different locations are set and the simulation results are listed in Table II. For external faults, since the fault resistance will not influence the TW propagation process of the protected line, the protection performance is not influenced. For internal faults, the amplitude of TW is reduced with the fault resistance. However, the fault can be still identified. The simulation results show that the proposed method can endure 1000  Ω of fault resistance.

Table II  Simulation Results with Fault Resistance
Fault

Fault

resistance (Ω)

Raλa (°)α (°)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

F. Influence of Noise Disturbance

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 Table III. For the internal faults, the similarity degree is still very small and the faults can be identified effectively. For the external faults, it shows that the proposed protection scheme will not misoperate under the 20 dB noise disturbance.

Table III  Simulation Results with Noise Disturbance
FaultNoise (dB)Raλa (°)α (°)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

G. Influence of CLR

To verify the influence of CLR, the simulation results under different CLRs are listed in Table IV. Under the internal fault, the results show that there is no influence on fault detection and faulty pole discrimination. The sensitivity of the fault identification is influenced, and Ra and α increase and λ decreases with the larger CLR. However, they still satisfy the criteria and it is also conducive to identifying the internal fault. Under the external fault, the duline/dt will be much smaller with the increasing CLR. The result shows that the protection will not be activated when the CLR is over 300 mH with the original threshold. If the protection can be activated, the value of CLR will not influence the fault identification. It can be concluded that the sensitivity of the protection is influenced under the large CLR when an internal fault occurs. But the set threshold is still robust to identify the fault. Besides, the influence of CLR under the external can be ignored.

Table IV  Simulation Results Under Different CLRs
FaultsCLR (mH)duline/dtEratioRaλa (°)α (°)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

H. Operation Speed

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.

I. Comparison and Discussion

In order to compare the performance of the proposed protection scheme with the existing protection scheme [

25]-[29], some performance indicators are listed in Table V such as frequency-dependent parameters, sampling frequency, operation time, and withstanding capability of noise, withstanding capability of resistance, and withstanding capability of synchronization error. References [25] and [26] adopt the wavelet transform to extract the high-frequency component of the fault characteristics. There is a high requirement for sampling frequency, even up to 1000 kHz. Besides, the capability of enduring the fault characteristics and noise disturbance is weak. References [27]-[29] are also based on the principle of similarity comparison. Owning to full consideration of the frequency-dependent parameters of the transmission line, the reliability of the proposed protection scheme is improved with high calculation accuracy. Meanwhile, the proposed protection scheme has advantages in enduring fault resistance and noise disturbance. In addition, the withstanding capability of synchronization error is weak or even not mentioned in other schemes. The proposed protection scheme can deal with this problem without high sampling frequency. For the operation time, most pilot protections act as the backup protections with a large delay. The operation speed of the proposed protection scheme is not faster than the traditional primary protections. However, there is a larger margin for the proposed protection scheme under the FCLS. Therefore, the proposed protection scheme is also a candidate for primary protection in the VSC-HVDC grid. If the traditional primary protections fail to identify the faults, the proposed protection scheme can also be a supplement.

Table V  Comparison with Other Protection Schemes
ProtectionPrinciple of realizationFrequency-dependent parametersWithstanding capability of noise (dB)Withstanding capability of resistance (Ω)Withstanding capability of synchronization error (ms)Sampling frequency (kHz)Operation time (ms)
[25] Modulus maxima 400 100.0 3.00
[26] Haar wavelet No 40 150 1000.0 2.57
[27] Cosine distance No 20 100 0.3 10.0 2.25
[28] Pearson coefficient No 1000 10.0 13.00
[29] Hausdorff distance No 10 1000 20.0 7.20
Proposed Yes 20 1000 1.0 10.0 3.70

VII. Conclusion

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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