# Ultra-High-Speed Travelling Wave Protection of Transmission Line Using Polarity Comparison Principle Based on Empirical Mode Decomposition

Authors: Dong Wang; Houlei Gao; Sibei Luo; Guibin Zou
Journal: Mathematical Problems in Engineering
 (2015)

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## Abstract

The traditional polarity comparison based travelling wave protection, using the initial wave information, is affected by initial fault angle, bus structure, and external fault. And the relationship between the magnitude and polarity of travelling wave is ignored. Because of the protection tripping and malfunction, the further application of this protection principle is affected. Therefore, this paper presents an ultra-high-speed travelling wave protection using integral based polarity comparison principle. After empirical mode decomposition of the original travelling wave, the first-order intrinsic mode function is used as protection object. Based on the relationship between the magnitude and polarity of travelling wave, this paper demonstrates the feasibility of using travelling wave magnitude which contains polar information as direction criterion. And the paper integrates the direction criterion in a period after fault to avoid wave head detection failure. Through PSCAD simulation with the typical 500 kV transmission system, the reliability and sensitivity of travelling wave protection were verified under different factors’ affection.


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## Body

## 1. Introduction

According to the protection principle, travelling wave protection methods include travelling wave differential protection, travelling wave distance protection, travelling wave amplitude comparison protection, and travelling wave polarity comparison protection [1, 2].Travelling wave differential protection principle is simple and clear. But travelling wave has attenuation characteristic. There may be large unbalance current in the transmission line to cause wrong operation. And it is also affected by the bus structure [3–5]. Travelling wave distance protection cannot protect the whole line and does not have direction discrimination ability. Same with differential protection, it is affected by bus structure, too [6–9]. Travelling wave amplitude comparison protection principle has improved much compared to other protection principles. But it is affected by the bus structures, fault inception angles, and different thresholds, too. The traditional travelling wave polarity comparison protection principle has a lot of advantages: high operation speed, clear direction discrimination, and simple protection principle. But it is also affected by some things: fault initial angles, different bus structures, different fault locations, and even threshold. If those disadvantages can be overcome, a new travelling wave protection principle can be got [10–12].The traditional travelling wave protection principle’s application is limited by the transformer technology. The traditional current transformer (CT) and voltage transformer (VT) cannot transfer the travelling wave signal correctly. Currently, Rogowski based electronic current transformer (R-ECT) and capacitive divider electronic voltage transformer (C-EVT) have been able to transfer current travelling wave and voltage travelling wave accurately. And the output of C-EVT and R-ECT is the differential signal of the input. By integration circuit, the original signal can be regained exactly. So there is no transformer technology limit in the travelling wave protection principle anymore [13–16].This paper compares the polarity relationship between voltage travelling wave and current travelling wave with different fault directions. Combined with empirical mode decomposition algorithm (EMD), the new travelling wave polarity comparison protection principle based on the integration of amplitude is derived. It not only uses the initial travelling wave but also uses the travelling wave after fault happens. So it is a reliable protection principle with obvious direction discrimination. By the way, this new protection principle is not affected by different initial angles, different grounding resistance, different bus structures, and different fault locations. To verify the characteristics of the new principle, a simulation based on PSCAD/EMTDC is carried on. And the PSCAD simulation proved that this new protection principle has the characteristics mentioned above indeed.The high operation speed is a very important advantage for travelling wave protection. Considering the different parts of the new travelling wave’s operation time, the new protection principle can determine if the fault is internal or external in 5 ms. Then it can send the signal to breaker to operate. So, it can be called an ultra-high-speed travelling wave protection.


## 2. Traditional Travelling Wave Polarity Comparison Protection

The direction element of the protection principle is a polarity comparison relay. It detects the initial voltage travelling wave and current travelling wave as comparison objects. When the voltage travelling wave and current travelling wave have opposite polarities of both sides, the internal fault can be determined. When the voltage travelling wave and current travelling wave have same polarities of any side, the external fault can be determined. The schematic of protection is shown in Table1. (Superimposed voltage in the table appears at the moment that fault happens. It has same value and opposite polarity with the voltage on the transmission line just before the fault moment. And it is the voltage source in the circuit of the table indeed.)Table 1
Analysis of travelling wave polarity comparison protection.
Fault location
Superimposed voltage polarity
M side
N side
Schematic of fault superimposed state circuit
Voltage
Current
Voltage
Current
Internal fault
+−
+−
−+
+−
−+
External fault
+−
+−
−+
+−
+−
External fault
+−
+−
+−
+−
−+


## 3. Empirical Mode Decomposition

The empirical mode decomposition algorithm can distinguish the different scale fluctuations or trends in the signal gradually. And the result of EMD is a series of different characteristic scales data called intrinsic mode functions (IMF) [17–19].The result of EMD can be described as(1)St=∑i=1NIMFit+Rt,where S(t) is the EMD result, IMFi(t) is i order intrinsic mode function, and R(t) is trends signal.Intrinsic mode function is a single component signal and it must meet the following two conditions: (1) difference between the number of extreme points and zero crossing points is not more than one over the entire length of the signal; (2) the envelope of IMF is symmetry about time axis.The processes of EMD are described as the following steps.(1) Find all the maxima of the original signalS(t). Then the maxima envelope E+(t) can be calculated based on cubic spline interpolation. Similarly, the minimum envelope E-(t) can also be calculated. Then, the average envelope M(t) can be defined as(2)Mt=E+t+E-t2.(2) LetS(t) be minus M(t) to get a new signal H11(t):(3)H11t=St-Mt.Then check if the following condition can be met:(4)∑H1kt-H1k-1t2∑H1k-1t2≤ε,where k is the cycle number and the value of ε is between 0.2 and 0.3. This paper selects 0.3.If (4) cannot be met, return to step (1).If (4) can be met after k cycles, then IMF1(t) can be defined as(5)IMF1t=H1kt.(3) Let original signal be minusIMF1(t) to get a residual signal R(t) as(6)Rt=St-IMF1t.Repeat steps (1) to (3) to get another intrinsic mode functionIMF2(t). Repeat steps (1) to (3) until residual signal R(t) is small enough or monotonic function.Based on EMD, the first IMF of voltage travelling wave and current travelling wave can be calculated as Figure1. The first figure and second figure are the voltage and current travelling wave before EMD, respectively. The third figure and fourth figure are the voltage and current travelling wave after EMD, respectively. As we can see, the similarity of the voltage and current travelling wave using EMD is more obvious than before. So it is more convenient to construct a protection principle using intrinsic mode function.Figure 1
The comparison of travelling wave and travelling wave after EMD.


## 4. New Travelling Wave Polarity Comparison Protection

### 4.1. Derivation of Direction Criterion

As shown in Figure2, fault component voltage appears between the fault location F in transmission line and the earth at time t=0. Then, the transmission line will be charged. After a short time Δt, a short length of transmission line Δx is charged to ΔQ=Cu0Δx (C is the capacitance value per unit length of transmission line). An electrical field E will appear surrounding this short transmission line. And the flow of current will form a magnetic field around the line. If Δx is small enough, the current i0 can be described as(7)i0=limΔx→0⁡ΔQΔt=limΔx→0⁡Cu0ΔxΔt=Cu0v,where v is the speed of the wave and C is the capacitance value per unit length of transmission line.Figure 2
Equivalent circuit of single phase line.Now the magnetic flux aroundΔx is ΔΦ=LiΔx. According to the law of electromagnetic induction, the electromotive force is described as(8)E=limΔx→0⁡ΔΦΔt=limΔx→0⁡LCu0vΔxΔt=LCu0v2,where v is the speed of the wave, C is the capacitance value per unit length of transmission line, and L is the inductance value per unit length of transmission line.Because the voltage on capacitance cannot change suddenly andΔx is small enough, E equals voltage u0. Then the wave speed will be(9)v=1LC.Take (9) to (7) to get(10)u0i0=LC.As we can see, the ratio of voltage and current is a constant value called wave impedance.Define voltage amplitude conditioning factork:(11)k=iu.And the value ofk is approximately equal toC/L.Considering the initial polarity of voltage and current travelling wave, define a factorλ to identify the fault direction:(12)λ=∫t=tFtF+dkutitdt∫t=tFtF+di2tdt,where tF is the arrival point of the travelling wave, d is the length of the integration time, and k is the voltage amplitude conditioning factor defined above.The discretization of (12) can be described as(13)λ=∑t=tFtF+dkutit∑t=tFtF+di2t.Considering different fault directions, the value ofλ can be calculated.(1) If the fault happens as Figure2 shows, it will be forward fault type for R1. Assume the transmission line is lossless. When the travelling wave arrived, the travelling wave signal of R1 will be(14)u=u++u-=1+kufu-,i=i++i-=1+kifi-,where u is the voltage travelling wave, i is the current travelling wave, u+ is the forward voltage travelling wave, u- is the reverse voltage travelling wave, i+ is the forward current travelling wave, i- is the reverse current travelling wave, kuf is the voltage reflection coefficient at the bus, and kif is the current reflection coefficient at the bus. And the inequality relationship will be 0≤kuf,kif≤1.Now the amplitude conditioning factor can be calculated:(15)k=itut=1+kif1+kufi-tu-t.Because it is a forward direction fault for R1, the reverse voltage and current travelling wave have different polarities. So (15) can be simplified as(16)k=-1+kif1+kufi-tu-t.Take (14) and (16) to (13):(17)λ=∑t=tFtF+dkutit∑t=tFtF+di2t=-1.As we can see, the value ofλ is a constant number −1 when it is a forward direction fault. And it is not affected by the reflection coefficient and the construction of the bus.(2) If the fault happens as Figure2 shows, it will be reverse fault type for R2. Assume the transmission line is lossless. When the travelling wave arrived, the travelling wave signal of R2 will be(18)u=u+′=kuzu-,i=i+′=kizi-,where u is the voltage travelling wave, i is the current travelling wave, u+′ is the forward voltage travelling wave at R2, i+′ is the forward current travelling wave at R2, u- is the reverse voltage travelling wave at R1, i- is the reverse current travelling wave at R1, kuz is the voltage refractive coefficient at bus, and kiz is the current refractive coefficient at bus. And there is an inequality relationship kuz,kiz≥0.Now the amplitude conditioning factor can be calculated:(19)k=itut=kizi-tkuzu-t.Because it is a reverse direction fault for R2 and also a forward direction fault for R1, the reverse voltage and current travelling wave have different polarities. And the forward direction of R2 is opposite to R1. So (19) can be simplified as(20)k=itut=kizkuzi-tu-t.Take (18) and (20) to (13):(21)λ=∑t=tFtF+dkutit∑t=tFtF+di2t=1.As we can see, the value ofλ is a constant number 1 when it is a reverse direction fault. And it is not affected by the reflection coefficient and the construction of the bus.Taking a variety of errors in the actual system into account, the fault direction discrimination schematic is shown in Figure3. When forward fault happens, the value of λ is less than zero. When reverse fault happens, the value of λ is greater than zero. If two fault direction discrimination results of both ends are forward fault, an internal fault can be determined. If one of the fault direction discrimination results of both ends is reverse fault, an external fault can be determined.Figure 3
Fault direction discrimination schematic.


### 4.2. Protection Scheme

The protection scheme is shown in Figure4. First of all, the three-phase voltage and current should be decoupled using Clark transformation. Then amplitude conditioning factor, defined above, can be calculated point by point in d length of time. After that, the value of λ can be calculated. Because the other end of the transmission line needs the value of λ to identify the fault section, the value of λ should send to another end though fiber path. Then the value of factor λ can be checked to identify the external fault type. If it is a forward fault for the relay, the value of factor λ′ from another end will be received and checked to identify the external fault. If λ and λ′ are both less than zero, an internal fault can be determined. At last, the breaker will clear the transmission line fault.Figure 4
Flow chart of travelling wave protection.


## 4.1. Derivation of Direction Criterion

As shown in Figure2, fault component voltage appears between the fault location F in transmission line and the earth at time t=0. Then, the transmission line will be charged. After a short time Δt, a short length of transmission line Δx is charged to ΔQ=Cu0Δx (C is the capacitance value per unit length of transmission line). An electrical field E will appear surrounding this short transmission line. And the flow of current will form a magnetic field around the line. If Δx is small enough, the current i0 can be described as(7)i0=limΔx→0⁡ΔQΔt=limΔx→0⁡Cu0ΔxΔt=Cu0v,where v is the speed of the wave and C is the capacitance value per unit length of transmission line.Figure 2
Equivalent circuit of single phase line.Now the magnetic flux aroundΔx is ΔΦ=LiΔx. According to the law of electromagnetic induction, the electromotive force is described as(8)E=limΔx→0⁡ΔΦΔt=limΔx→0⁡LCu0vΔxΔt=LCu0v2,where v is the speed of the wave, C is the capacitance value per unit length of transmission line, and L is the inductance value per unit length of transmission line.Because the voltage on capacitance cannot change suddenly andΔx is small enough, E equals voltage u0. Then the wave speed will be(9)v=1LC.Take (9) to (7) to get(10)u0i0=LC.As we can see, the ratio of voltage and current is a constant value called wave impedance.Define voltage amplitude conditioning factork:(11)k=iu.And the value ofk is approximately equal toC/L.Considering the initial polarity of voltage and current travelling wave, define a factorλ to identify the fault direction:(12)λ=∫t=tFtF+dkutitdt∫t=tFtF+di2tdt,where tF is the arrival point of the travelling wave, d is the length of the integration time, and k is the voltage amplitude conditioning factor defined above.The discretization of (12) can be described as(13)λ=∑t=tFtF+dkutit∑t=tFtF+di2t.Considering different fault directions, the value ofλ can be calculated.(1) If the fault happens as Figure2 shows, it will be forward fault type for R1. Assume the transmission line is lossless. When the travelling wave arrived, the travelling wave signal of R1 will be(14)u=u++u-=1+kufu-,i=i++i-=1+kifi-,where u is the voltage travelling wave, i is the current travelling wave, u+ is the forward voltage travelling wave, u- is the reverse voltage travelling wave, i+ is the forward current travelling wave, i- is the reverse current travelling wave, kuf is the voltage reflection coefficient at the bus, and kif is the current reflection coefficient at the bus. And the inequality relationship will be 0≤kuf,kif≤1.Now the amplitude conditioning factor can be calculated:(15)k=itut=1+kif1+kufi-tu-t.Because it is a forward direction fault for R1, the reverse voltage and current travelling wave have different polarities. So (15) can be simplified as(16)k=-1+kif1+kufi-tu-t.Take (14) and (16) to (13):(17)λ=∑t=tFtF+dkutit∑t=tFtF+di2t=-1.As we can see, the value ofλ is a constant number −1 when it is a forward direction fault. And it is not affected by the reflection coefficient and the construction of the bus.(2) If the fault happens as Figure2 shows, it will be reverse fault type for R2. Assume the transmission line is lossless. When the travelling wave arrived, the travelling wave signal of R2 will be(18)u=u+′=kuzu-,i=i+′=kizi-,where u is the voltage travelling wave, i is the current travelling wave, u+′ is the forward voltage travelling wave at R2, i+′ is the forward current travelling wave at R2, u- is the reverse voltage travelling wave at R1, i- is the reverse current travelling wave at R1, kuz is the voltage refractive coefficient at bus, and kiz is the current refractive coefficient at bus. And there is an inequality relationship kuz,kiz≥0.Now the amplitude conditioning factor can be calculated:(19)k=itut=kizi-tkuzu-t.Because it is a reverse direction fault for R2 and also a forward direction fault for R1, the reverse voltage and current travelling wave have different polarities. And the forward direction of R2 is opposite to R1. So (19) can be simplified as(20)k=itut=kizkuzi-tu-t.Take (18) and (20) to (13):(21)λ=∑t=tFtF+dkutit∑t=tFtF+di2t=1.As we can see, the value ofλ is a constant number 1 when it is a reverse direction fault. And it is not affected by the reflection coefficient and the construction of the bus.Taking a variety of errors in the actual system into account, the fault direction discrimination schematic is shown in Figure3. When forward fault happens, the value of λ is less than zero. When reverse fault happens, the value of λ is greater than zero. If two fault direction discrimination results of both ends are forward fault, an internal fault can be determined. If one of the fault direction discrimination results of both ends is reverse fault, an external fault can be determined.Figure 3
Fault direction discrimination schematic.


## 4.2. Protection Scheme

The protection scheme is shown in Figure4. First of all, the three-phase voltage and current should be decoupled using Clark transformation. Then amplitude conditioning factor, defined above, can be calculated point by point in d length of time. After that, the value of λ can be calculated. Because the other end of the transmission line needs the value of λ to identify the fault section, the value of λ should send to another end though fiber path. Then the value of factor λ can be checked to identify the external fault type. If it is a forward fault for the relay, the value of factor λ′ from another end will be received and checked to identify the external fault. If λ and λ′ are both less than zero, an internal fault can be determined. At last, the breaker will clear the transmission line fault.Figure 4
Flow chart of travelling wave protection.


## 5. Simulation Analysis

### 5.1. Simulation Model in PSCAD

The 500 kV power transmission system is constructed in PSCAD/EMTDC as shown in Figure5. The system includes three transmission lines whose lengths are 100 km, 200 km, and 100 km, respectively. R1 and R2 are two relays on the middle line. Now the new travelling wave polarity comparison protection can be studied by different fault locations and different fault types.Figure 5
Model of 500 kV power transmission system.The transmission line uses frequency-dependent model and has uniform transposition. The transmission line parameters for per km length are shown in Table2. The bus stray capacitance to ground is set to CS = 0.01 μF. Taking the past studies into account, the sampling rate is set to 1 MHz. The integration time d is 0.1 ms.Table 2
Transmission line parameters.
R
X
G
B
(Ω/km)
(Ω/km)
(S/km)
(S/km)
Positive sequence
0.01798
0.29278
1 × 108
3.93905 × 10−6
Negative sequence
0.01798
0.29278
1 × 108
3.93905 × 10−6
Zero sequences
0.28662
1.08210
1 × 108
2.43767 × 10−6


### 5.2. Typical Fault Examples

In order to verify the protection principle’s operating characteristics, A phase to ground fault is set located at F3. The initial fault angle is45∘ and the ground resistance is 50Ω. Using empirical mode decomposition algorithm, the first-order intrinsic mode function of voltage and current travelling wave of both sides can be calculated.Takeku and i data in Figure 6 to (13) to calculate the λ=-0.8710. Then the forward fault of R1 can be determined.Figure 6
Comparison chart ofku and i of M side.Takeku and i data in Figure 7 to (13) to calculate the λ=0.9811. Then the reverse fault of R2 can be determined.Figure 7
Comparison chart ofku and i of N side.As we can see, the fault discrimination results of R1 and R2 are corrected. Taking the protection scheme of Figure4 into account, an external fault type can be determined.


### 5.3. Relater Factors

#### 5.3.1. Different Fault Location

Based on some different fault locations at F1 and F2, the fault discrimination factorλ of both M and N side is calculated.Table3 is the simulation results for different fault locations. The fault distance in the table is from the bus of M side to fault location. As can be seen, the fault principle based on EMD can identify fault direction correctly. Even at the beginning or end of the transmission line, it can still identify fault direction correctly.Table 3
Simulation results for different fault locations.
Fault location
Fault distance/km
M side
N side
Results
λ
Direction
λ
Direction
F1
10
−0.8160
Forward
−0.5732
Forward
Internal
100
−0.8763
Forward
−0.4071
Forward
Internal
190
−0.9378
Forward
−0.7965
Forward
Internal
F2
10
0.9972
Reverse
−0.9603
Forward
External
50
0.9980
Reverse
−0.3843
Forward
External
90
0.9972
Reverse
−0.9603
Forward
External


#### 5.3.2. Grounding Resistance

Based on some different grounding resistance at F1 (100 km away from the bus of M side) and F2 (10 km away from the bus of M side), the fault discrimination factorλ of both M and N side is calculated.Table4 is the simulation results for different grounding resistance. As can be seen, the fault principle based on EMD can identify fault direction correctly. With the increasing of grounding resistance, protection’s sensitivity will not change.Table 4
Simulation results for different grounding resistance.
Fault location
Grounding resistance/Ω
M side
N side
Results
λ
Direction
λ
Direction
F1
1
−0.4944
Forward
−0.8818
Forward
Internal
100
−0.4829
Forward
−0.8802
Forward
Internal
300
−0.4984
Forward
−0.8839
Forward
Internal
F2
1
0.9978
Reverse
−0.9438
Forward
External
100
0.9963
Reverse
−0.8730
Forward
External
300
0.8522
Reverse
−0.9033
Forward
External


#### 5.3.3. Fault Initial Angle

Based on some different fault initial angel at F1 (100 km away from the bus of M side) and F2 (10 km away from the bus of M side), the fault discrimination factorλ of both M and N side is calculated.Table5 is the simulation results for different fault initial angles. As can be seen, the fault principle based on EMD can identify fault direction correctly. Even with small fault angles, it can still identify fault direction correctly. And, with the decreasing of fault initial angle, protection’s sensitivity will reduce slowly.Table 5
Simulation results for different fault angles.
Fault location
Initial angle/°
M side
N side
Results
λ
Direction
λ
Direction
F1
1
−0.3884
Forward
−0.3256
Forward
Internal
45
−0.4291
Forward
−0.8732
Forward
Internal
90
−0.4944
Forward
−0.8818
Forward
Internal
F2
1
0.9972
Reverse
−0.2356
Forward
External
45
0.9997
Reverse
−0.9687
Forward
External
90
0.9997
Reverse
−0.9700
Forward
External


#### 5.3.4. Different Fault Types

Based on some different fault types at F1 (100 km away from the bus of M side) and F2 (10 km away from the bus of M side), the fault discrimination factorλ of both M and N side is calculated.Table6 is the simulation results for different fault types. As can be seen, the fault principle based on EMD can identify fault direction correctly.Table 6
Simulation results for different fault types.
Fault location
Fault type
M side
N side
Results
λ
Direction
λ
Direction
F1
AG
−0.4944
Forward
−0.8818
Forward
Internal
AC
−0.9600
Forward
−0.9602
Forward
Internal
ABG
−0.4471
Forward
−0.8804
Forward
Internal
ABCG
−0.9664
Forward
−0.7452
Forward
Internal
F2
AG
0.9972
Reverse
−0.9700
Forward
External
AC
0.9991
Reverse
−0.6022
Forward
External
ABG
0.8275
Reverse
−0.4659
Forward
External
ABCG
0.9997
Reverse
−0.9586
Forward
External


#### 5.3.5. Sampling Rate

Based on some different sampling rate and AG fault at F1 (100 km away from the bus of M side) and F2 (10 km away from the bus of M side), the fault discrimination factorλ of both M and N side is calculated.Table7 is the simulation results for different sampling rate. As can be seen, the fault principle based on EMD can identify fault direction correctly with the change of sampling rate.Table 7
Simulation results for different sampling rate.
Fault location
Sampling rate/Hz
M side
N side
Results
λ
Direction
λ
Direction
F1
100 k
−0.9794
Forward
−0.6816
Forward
Internal
500 k
−0.7345
Forward
−0.9637
Forward
Internal
1 M
−0.5018
Forward
−0.8825
Forward
Internal
F2
100 k
0.9751
Reverse
−0.9807
Forward
External
500 k
0.9994
Reverse
−0.9055
Forward
External
1 M
0.9979
Reverse
−0.9684
Forward
External


#### 5.3.6. Bus Structure

Traditional travelling wave protection principle is affected by the number of transmission lines connected to the bus. To verify the new EMD based protection principle, a new power transmission system is constructed in PSCAD as Figure8.Figure 8
Model of 500 kV power transmission system with different bus structures.Table8 is the simulation results for different fault locations. As can be seen, the fault principle based on EMD can identify fault direction correctly with different bus structure.Table 8
Simulation results for different fault locations.
Fault location
M side
N side
Results
λ
Direction
λ
Direction
F1
−0.9731
Forward
−0.9603
Forward
Internal
F2
0.9980
Reverse
−0.9779
Forward
External
F3
−0.9718
Forward
0.9992
Reverse
External


## 5.1. Simulation Model in PSCAD

The 500 kV power transmission system is constructed in PSCAD/EMTDC as shown in Figure5. The system includes three transmission lines whose lengths are 100 km, 200 km, and 100 km, respectively. R1 and R2 are two relays on the middle line. Now the new travelling wave polarity comparison protection can be studied by different fault locations and different fault types.Figure 5
Model of 500 kV power transmission system.The transmission line uses frequency-dependent model and has uniform transposition. The transmission line parameters for per km length are shown in Table2. The bus stray capacitance to ground is set to CS = 0.01 μF. Taking the past studies into account, the sampling rate is set to 1 MHz. The integration time d is 0.1 ms.Table 2
Transmission line parameters.
R
X
G
B
(Ω/km)
(Ω/km)
(S/km)
(S/km)
Positive sequence
0.01798
0.29278
1 × 108
3.93905 × 10−6
Negative sequence
0.01798
0.29278
1 × 108
3.93905 × 10−6
Zero sequences
0.28662
1.08210
1 × 108
2.43767 × 10−6


## 5.2. Typical Fault Examples

In order to verify the protection principle’s operating characteristics, A phase to ground fault is set located at F3. The initial fault angle is45∘ and the ground resistance is 50Ω. Using empirical mode decomposition algorithm, the first-order intrinsic mode function of voltage and current travelling wave of both sides can be calculated.Takeku and i data in Figure 6 to (13) to calculate the λ=-0.8710. Then the forward fault of R1 can be determined.Figure 6
Comparison chart ofku and i of M side.Takeku and i data in Figure 7 to (13) to calculate the λ=0.9811. Then the reverse fault of R2 can be determined.Figure 7
Comparison chart ofku and i of N side.As we can see, the fault discrimination results of R1 and R2 are corrected. Taking the protection scheme of Figure4 into account, an external fault type can be determined.


## 5.3. Relater Factors

### 5.3.1. Different Fault Location

Based on some different fault locations at F1 and F2, the fault discrimination factorλ of both M and N side is calculated.Table3 is the simulation results for different fault locations. The fault distance in the table is from the bus of M side to fault location. As can be seen, the fault principle based on EMD can identify fault direction correctly. Even at the beginning or end of the transmission line, it can still identify fault direction correctly.Table 3
Simulation results for different fault locations.
Fault location
Fault distance/km
M side
N side
Results
λ
Direction
λ
Direction
F1
10
−0.8160
Forward
−0.5732
Forward
Internal
100
−0.8763
Forward
−0.4071
Forward
Internal
190
−0.9378
Forward
−0.7965
Forward
Internal
F2
10
0.9972
Reverse
−0.9603
Forward
External
50
0.9980
Reverse
−0.3843
Forward
External
90
0.9972
Reverse
−0.9603
Forward
External


### 5.3.2. Grounding Resistance

Based on some different grounding resistance at F1 (100 km away from the bus of M side) and F2 (10 km away from the bus of M side), the fault discrimination factorλ of both M and N side is calculated.Table4 is the simulation results for different grounding resistance. As can be seen, the fault principle based on EMD can identify fault direction correctly. With the increasing of grounding resistance, protection’s sensitivity will not change.Table 4
Simulation results for different grounding resistance.
Fault location
Grounding resistance/Ω
M side
N side
Results
λ
Direction
λ
Direction
F1
1
−0.4944
Forward
−0.8818
Forward
Internal
100
−0.4829
Forward
−0.8802
Forward
Internal
300
−0.4984
Forward
−0.8839
Forward
Internal
F2
1
0.9978
Reverse
−0.9438
Forward
External
100
0.9963
Reverse
−0.8730
Forward
External
300
0.8522
Reverse
−0.9033
Forward
External


### 5.3.3. Fault Initial Angle

Based on some different fault initial angel at F1 (100 km away from the bus of M side) and F2 (10 km away from the bus of M side), the fault discrimination factorλ of both M and N side is calculated.Table5 is the simulation results for different fault initial angles. As can be seen, the fault principle based on EMD can identify fault direction correctly. Even with small fault angles, it can still identify fault direction correctly. And, with the decreasing of fault initial angle, protection’s sensitivity will reduce slowly.Table 5
Simulation results for different fault angles.
Fault location
Initial angle/°
M side
N side
Results
λ
Direction
λ
Direction
F1
1
−0.3884
Forward
−0.3256
Forward
Internal
45
−0.4291
Forward
−0.8732
Forward
Internal
90
−0.4944
Forward
−0.8818
Forward
Internal
F2
1
0.9972
Reverse
−0.2356
Forward
External
45
0.9997
Reverse
−0.9687
Forward
External
90
0.9997
Reverse
−0.9700
Forward
External


### 5.3.4. Different Fault Types

Based on some different fault types at F1 (100 km away from the bus of M side) and F2 (10 km away from the bus of M side), the fault discrimination factorλ of both M and N side is calculated.Table6 is the simulation results for different fault types. As can be seen, the fault principle based on EMD can identify fault direction correctly.Table 6
Simulation results for different fault types.
Fault location
Fault type
M side
N side
Results
λ
Direction
λ
Direction
F1
AG
−0.4944
Forward
−0.8818
Forward
Internal
AC
−0.9600
Forward
−0.9602
Forward
Internal
ABG
−0.4471
Forward
−0.8804
Forward
Internal
ABCG
−0.9664
Forward
−0.7452
Forward
Internal
F2
AG
0.9972
Reverse
−0.9700
Forward
External
AC
0.9991
Reverse
−0.6022
Forward
External
ABG
0.8275
Reverse
−0.4659
Forward
External
ABCG
0.9997
Reverse
−0.9586
Forward
External


### 5.3.5. Sampling Rate

Based on some different sampling rate and AG fault at F1 (100 km away from the bus of M side) and F2 (10 km away from the bus of M side), the fault discrimination factorλ of both M and N side is calculated.Table7 is the simulation results for different sampling rate. As can be seen, the fault principle based on EMD can identify fault direction correctly with the change of sampling rate.Table 7
Simulation results for different sampling rate.
Fault location
Sampling rate/Hz
M side
N side
Results
λ
Direction
λ
Direction
F1
100 k
−0.9794
Forward
−0.6816
Forward
Internal
500 k
−0.7345
Forward
−0.9637
Forward
Internal
1 M
−0.5018
Forward
−0.8825
Forward
Internal
F2
100 k
0.9751
Reverse
−0.9807
Forward
External
500 k
0.9994
Reverse
−0.9055
Forward
External
1 M
0.9979
Reverse
−0.9684
Forward
External


### 5.3.6. Bus Structure

Traditional travelling wave protection principle is affected by the number of transmission lines connected to the bus. To verify the new EMD based protection principle, a new power transmission system is constructed in PSCAD as Figure8.Figure 8
Model of 500 kV power transmission system with different bus structures.Table8 is the simulation results for different fault locations. As can be seen, the fault principle based on EMD can identify fault direction correctly with different bus structure.Table 8
Simulation results for different fault locations.
Fault location
M side
N side
Results
λ
Direction
λ
Direction
F1
−0.9731
Forward
−0.9603
Forward
Internal
F2
0.9980
Reverse
−0.9779
Forward
External
F3
−0.9718
Forward
0.9992
Reverse
External


## 5.3.1. Different Fault Location

Based on some different fault locations at F1 and F2, the fault discrimination factorλ of both M and N side is calculated.Table3 is the simulation results for different fault locations. The fault distance in the table is from the bus of M side to fault location. As can be seen, the fault principle based on EMD can identify fault direction correctly. Even at the beginning or end of the transmission line, it can still identify fault direction correctly.Table 3
Simulation results for different fault locations.
Fault location
Fault distance/km
M side
N side
Results
λ
Direction
λ
Direction
F1
10
−0.8160
Forward
−0.5732
Forward
Internal
100
−0.8763
Forward
−0.4071
Forward
Internal
190
−0.9378
Forward
−0.7965
Forward
Internal
F2
10
0.9972
Reverse
−0.9603
Forward
External
50
0.9980
Reverse
−0.3843
Forward
External
90
0.9972
Reverse
−0.9603
Forward
External


## 5.3.2. Grounding Resistance

Based on some different grounding resistance at F1 (100 km away from the bus of M side) and F2 (10 km away from the bus of M side), the fault discrimination factorλ of both M and N side is calculated.Table4 is the simulation results for different grounding resistance. As can be seen, the fault principle based on EMD can identify fault direction correctly. With the increasing of grounding resistance, protection’s sensitivity will not change.Table 4
Simulation results for different grounding resistance.
Fault location
Grounding resistance/Ω
M side
N side
Results
λ
Direction
λ
Direction
F1
1
−0.4944
Forward
−0.8818
Forward
Internal
100
−0.4829
Forward
−0.8802
Forward
Internal
300
−0.4984
Forward
−0.8839
Forward
Internal
F2
1
0.9978
Reverse
−0.9438
Forward
External
100
0.9963
Reverse
−0.8730
Forward
External
300
0.8522
Reverse
−0.9033
Forward
External


## 5.3.3. Fault Initial Angle

Based on some different fault initial angel at F1 (100 km away from the bus of M side) and F2 (10 km away from the bus of M side), the fault discrimination factorλ of both M and N side is calculated.Table5 is the simulation results for different fault initial angles. As can be seen, the fault principle based on EMD can identify fault direction correctly. Even with small fault angles, it can still identify fault direction correctly. And, with the decreasing of fault initial angle, protection’s sensitivity will reduce slowly.Table 5
Simulation results for different fault angles.
Fault location
Initial angle/°
M side
N side
Results
λ
Direction
λ
Direction
F1
1
−0.3884
Forward
−0.3256
Forward
Internal
45
−0.4291
Forward
−0.8732
Forward
Internal
90
−0.4944
Forward
−0.8818
Forward
Internal
F2
1
0.9972
Reverse
−0.2356
Forward
External
45
0.9997
Reverse
−0.9687
Forward
External
90
0.9997
Reverse
−0.9700
Forward
External


## 5.3.4. Different Fault Types

Based on some different fault types at F1 (100 km away from the bus of M side) and F2 (10 km away from the bus of M side), the fault discrimination factorλ of both M and N side is calculated.Table6 is the simulation results for different fault types. As can be seen, the fault principle based on EMD can identify fault direction correctly.Table 6
Simulation results for different fault types.
Fault location
Fault type
M side
N side
Results
λ
Direction
λ
Direction
F1
AG
−0.4944
Forward
−0.8818
Forward
Internal
AC
−0.9600
Forward
−0.9602
Forward
Internal
ABG
−0.4471
Forward
−0.8804
Forward
Internal
ABCG
−0.9664
Forward
−0.7452
Forward
Internal
F2
AG
0.9972
Reverse
−0.9700
Forward
External
AC
0.9991
Reverse
−0.6022
Forward
External
ABG
0.8275
Reverse
−0.4659
Forward
External
ABCG
0.9997
Reverse
−0.9586
Forward
External


## 5.3.5. Sampling Rate

Based on some different sampling rate and AG fault at F1 (100 km away from the bus of M side) and F2 (10 km away from the bus of M side), the fault discrimination factorλ of both M and N side is calculated.Table7 is the simulation results for different sampling rate. As can be seen, the fault principle based on EMD can identify fault direction correctly with the change of sampling rate.Table 7
Simulation results for different sampling rate.
Fault location
Sampling rate/Hz
M side
N side
Results
λ
Direction
λ
Direction
F1
100 k
−0.9794
Forward
−0.6816
Forward
Internal
500 k
−0.7345
Forward
−0.9637
Forward
Internal
1 M
−0.5018
Forward
−0.8825
Forward
Internal
F2
100 k
0.9751
Reverse
−0.9807
Forward
External
500 k
0.9994
Reverse
−0.9055
Forward
External
1 M
0.9979
Reverse
−0.9684
Forward
External


## 5.3.6. Bus Structure

Traditional travelling wave protection principle is affected by the number of transmission lines connected to the bus. To verify the new EMD based protection principle, a new power transmission system is constructed in PSCAD as Figure8.Figure 8
Model of 500 kV power transmission system with different bus structures.Table8 is the simulation results for different fault locations. As can be seen, the fault principle based on EMD can identify fault direction correctly with different bus structure.Table 8
Simulation results for different fault locations.
Fault location
M side
N side
Results
λ
Direction
λ
Direction
F1
−0.9731
Forward
−0.9603
Forward
Internal
F2
0.9980
Reverse
−0.9779
Forward
External
F3
−0.9718
Forward
0.9992
Reverse
External


## 6. Operation Time of Protection

The operation time of the travelling wave protection using polarity comparison principle based on EMD includes three parts: algorithm time, detection time, and propagation time. This new travelling wave protection principle can determine if the fault is inside or outside of the protection region in 5 ms. Then it can send the signal to breaker to operate. So it can be called ultra-high-speed travelling wave protection. The following is the introduction and analysis of the three parts.


### 6.1. Algorithm Time

Algorithm time includes two parts: the integration time and calculation time of the principle. In this paper, integration time length (the factord in (12) and (13)) is 0.1 ms. Considering the computing power of the protection unit now, the calculation time of algorithm is not longer than 0.5 ms. So, the algorithm time is not longer than 1 ms.


### 6.2. Detection Time

Detection time is the time difference of two sides’ travelling wave arrival point. As we can see, the fault may happen everywhere in the transmission line. Then the arrival times of two sides are different, except that the fault happens in the middle of the line. As a protection principle which needs two sides’ information to decide the operation of breaker, the time difference will delay the operation time. As shown in Figure9, tf, tm, and tn are the fault time, M side’s arrival time, and N side’s arrival time, respectively. And the time difference can be described as(22)Δt=tm-tn=L1-L2v.Figure 9
Schematic diagram of detection time.Andv is the travelling wave speed.Because the transmission line is generally several hundred kilometers, this time is obviously not longer than 2 ms.


### 6.3. Propagation Time

After the direction discrimination of one side, as shown in Figure10, the value of λ should transfer to another side. Propagation time is the time from one side to another side. As the length of transmission line is generally several hundred kilometers, propagation time is no longer than 2 ms.Figure 10
Schematic diagram of propagation time.


## 6.1. Algorithm Time

Algorithm time includes two parts: the integration time and calculation time of the principle. In this paper, integration time length (the factord in (12) and (13)) is 0.1 ms. Considering the computing power of the protection unit now, the calculation time of algorithm is not longer than 0.5 ms. So, the algorithm time is not longer than 1 ms.


## 6.2. Detection Time

Detection time is the time difference of two sides’ travelling wave arrival point. As we can see, the fault may happen everywhere in the transmission line. Then the arrival times of two sides are different, except that the fault happens in the middle of the line. As a protection principle which needs two sides’ information to decide the operation of breaker, the time difference will delay the operation time. As shown in Figure9, tf, tm, and tn are the fault time, M side’s arrival time, and N side’s arrival time, respectively. And the time difference can be described as(22)Δt=tm-tn=L1-L2v.Figure 9
Schematic diagram of detection time.Andv is the travelling wave speed.Because the transmission line is generally several hundred kilometers, this time is obviously not longer than 2 ms.


## 6.3. Propagation Time

After the direction discrimination of one side, as shown in Figure10, the value of λ should transfer to another side. Propagation time is the time from one side to another side. As the length of transmission line is generally several hundred kilometers, propagation time is no longer than 2 ms.Figure 10
Schematic diagram of propagation time.


## 7. Conclusion

Comparing with the traditional polarity comparison travelling wave protection, the new travelling wave protection combines the relationship between amplitude and polarity. Based on empirical mode decomposition, the derivation of the direction criterion is finished. And this protection criterion not only uses the initial travelling wave front but also uses short time’s (0.1 ms in the paper) travelling wave information after the initial travelling wave front. Through the integration of travelling wave, it can avoid the failure of the travelling wave’s detection. So it can increase the reliability of the protection principle.To verify the new protection principle, a simulation based on PSCAD is carried on. Taking the simulation results into account, this new protection principle is not affected by different fault locations, different fault types, different initial angels, different grounding resistance, and different bus structures. So it is a reliable travelling wave protection.Operation speed is an important advantage for travelling wave protection. Because the new protection principle can send the operation signal to breaker in 5 ms, it can be called ultra-high-speed travelling wave protection.



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*Source: 195170-2015-10-11.xml*