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

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.


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][4][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][7][8][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][11][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][14][15][16].
This paper compares the polarity relationship between voltage travelling wave and current travelling wave with 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.

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 Table

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][18][19].
The result of EMD can be described as where () is the EMD result, IMF  () is  order intrinsic mode function, and () 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 signal ().Then the maxima envelope  + () can be calculated based on cubic spline interpolation.Similarly, the minimum envelope  − () can also be calculated.Then, the average envelope () can be defined as (2) Let () be minus () to get a new signal  1 1 (): Then check if the following condition can be met: where  is the cycle number and the value of  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  cycles, then IMF 1 () can be defined as (3) Let original signal be minus IMF 1 () to get a residual signal () as Repeat steps (1) to (3) to get another intrinsic mode function IMF 2 ().Repeat steps (1) to (3) until residual signal () is small enough or monotonic function.
Based on EMD, the first IMF of voltage travelling wave and current travelling wave can be calculated as Figure 1.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.Then, the transmission line will be charged.After a short time Δ, a short length of transmission line Δ is charged to Δ =  0 Δ ( is the capacitance value per unit length of transmission line).An electrical field  will appear surrounding this short transmission line.And the flow of current will form a magnetic field around the line.If Δ is small enough, the current  0 can be described as

New Travelling Wave Polarity Comparison Protection
where V is the speed of the wave and  is the capacitance value per unit length of transmission line.Now the magnetic flux around Δ is ΔΦ = Δ.According to the law of electromagnetic induction, the electromotive force is described as where V is the speed of the wave,  is the capacitance value per unit length of transmission line, and  is the inductance value per unit length of transmission line.
Because the voltage on capacitance cannot change suddenly and Δ is small enough,  equals voltage  0 .Then the wave speed will be

Bus
Bus Take ( 9) to (7) to get As we can see, the ratio of voltage and current is a constant value called wave impedance.
Define voltage amplitude conditioning factor : And the value of  is approximately equal to√/.Considering the initial polarity of voltage and current travelling wave, define a factor  to identify the fault direction: where   is the arrival point of the travelling wave,  is the length of the integration time, and  is the voltage amplitude conditioning factor defined above.The discretization of (12) can be described as Considering different fault directions, the value of  can be calculated.
(1) If the fault happens as Figure 2 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 where  is the voltage travelling wave,  is the current travelling wave,  + is the forward voltage travelling wave,  − is the reverse voltage travelling wave,  + is the forward current travelling wave,  − is the reverse current travelling wave,   is the voltage reflection coefficient at the bus, and   is the current reflection coefficient at the bus.And the inequality relationship will be 0 Now the amplitude conditioning factor can be calculated: 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 Take ( 14) and ( 16) to (13): As we can see, the value of  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 Figure 2 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 where  is the voltage travelling wave,  is the current travelling wave,   + is the forward voltage travelling wave at R2,   + is the forward current travelling wave at R2,  − is the reverse voltage travelling wave at R1,  − is the reverse current travelling wave at R1,   is the voltage refractive coefficient at bus, and   is the current refractive coefficient at bus.And there is an inequality relationship   ,   ≥ 0. Now the amplitude conditioning factor can be calculated: 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 Take ( 18) and ( 20) to ( 13): As we can see, the value of  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 Figure 3.When forward fault happens, the value of  is less than zero.When reverse fault happens, the value of  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.

Protection Scheme.
The protection scheme is shown in Figure 4. 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  length of time.After that, the value of  can be calculated.Because the other end of the transmission line needs the value of  to identify the fault section, the value of  should send to another end though fiber path.Then the value of factor  can be checked to identify the external fault type.If it is a forward fault for the relay, the value of factor   from another end will be received and checked to identify the external fault.If  and   are both less than zero, an internal fault can be determined.At last, the breaker will clear the transmission line fault.Receive the value of      2. The bus stray capacitance to ground is set to   = 0.01 F.Taking the past studies into account, the sampling rate is set to 1 MHz.The integration time  is 0.1 ms.

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 is 45 ∘ and the ground resistance is 50 Ω.Using empirical mode decomposition algorithm, the first-order intrinsic mode function of voltage and current travelling wave of both sides can be calculated.
Take  and  data in Figure 6 to (13) to calculate the  = −0.8710.Then the forward fault of R1 can be determined.
Take  and  data in Figure 7 to (13) to calculate the  = 0.9811.Then the reverse fault of R2 can be determined.
As we can see, the fault discrimination results of R1 and R2 are corrected.Taking the protection scheme of Figure 4 into account, an external fault type can be determined.

Different Fault Location.
Based on some different fault locations at F1 and F2, the fault discrimination factor  of both M and N side is calculated.
Table 3 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.

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 factor  of both M and N side is calculated.
Table 4 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.

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 factor  of both M and N side is calculated.Table 5 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.

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 factor  of both M and N side is calculated.
Table 6 is the simulation results for different fault types.As can be seen, the fault principle based on EMD can identify fault direction correctly.

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 factor  of both M and N side is calculated.
Table 7 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.

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 Figure 8.
Table 8 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.

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 factor  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.

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 Figure 9,   ,   , and   are the fault time, M side's arrival time, and N side's arrival time, respectively.And the time difference can be described as And V is the travelling wave speed.Because the transmission line is generally several hundred kilometers, this time is obviously not longer than 2 ms.

Propagation Time.
After the direction discrimination of one side, as shown in Figure 10, the value of  should transfer to another side.Propagation time is the time from one side to another side.As the length of transmission line is generally

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.

4. 1 .
Derivation of Direction Criterion.As shown in Figure 2, fault component voltage appears between the fault location  in transmission line and the earth at time  = 0.

Figure 1 :
Figure 1: The comparison of travelling wave and travelling wave after EMD.

5. 1 .
Simulation Model in PSCAD.The 500 kV power transmission system is constructed in PSCAD/EMTDC as shown

Figure 4 :
Figure 4: Flow chart of travelling wave protection.

in Figure 5 .
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.The transmission line uses frequency-dependent model and has uniform transposition.The transmission line parameters for per km length are shown in Table

Figure 7 :
Figure 7: Comparison chart of  and  of N side.

F3Figure 8 :Figure 9 :
Figure 8: Model of 500 kV power transmission system with different bus structures.

Table 1 :
Analysis of travelling wave polarity comparison protection.
. (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 3 :
Simulation results for different fault locations.

Table 4 :
Simulation results for different grounding resistance.

Table 5 :
Simulation results for different fault angles.

Table 6 :
Simulation results for different fault types.

Table 7 :
Simulation results for different sampling rate.

Table 8 :
Simulation results for different fault locations.Figure 10: Schematic diagram of propagation time.several hundred kilometers, propagation time is no longer than 2 ms.