The influence of the abnormal data (Figure 1 and Figure 2) can be described by five parameters: uniformity degree, phase, error value, alternative degree and duration time. Limited by the thesis’ length, the analysis process is omitted. The conclusion is as following.

1) Uniformity degree describes the difference of the gap between two adjacent abnormal data. The higher the uniformity degree is, the more the abnormal data influences the relay protection system.

2) Phase describes the phase of the abnormal data, also its position. If the abnormal data occurs in the peak value of the signal, it has the maximum influence; if it occurs in the zero crossing point, it has the minimum influence. In other positions, the influence is in the middle.

3) Error value describes the difference between the abnormal value and the normal value. The bigger the error value is, the bigger the influence is.

4) Alternative degree is defined as the angle difference of a pair of adjacent abnormal data whose values are in different sign. The bigger the alternative degree is, the smaller the influence is.

5) Duration time describes how long time the abnormal data lasts. The longer the duration time, the bigger the influence is.

Fourier algorithm is widely used in the relay protection, for it has the advantage of high speed, simple to realize, highly reliable and it can separate the different frequency components. The abnormal data has much influence on Fourier Algorithm.

Imagine that for the sinuous signal, there are N sampling points in each period and the amplitude of the sinuous signal equals to A. The distance of the abnormal data to the peak value is equal to M as shown in Figure 3.

is the i^th sampling value of the sinuous signal, the abnormal data occurs in the n^th point and its value equals to.

The expression of the original fundamental wave amplitude is,

The expression of fundamental wave amplitude with abnormal data is,

Suppose, then we have,

According to Fourier Algorithm, , so

So the error of signal amplitude with abnormal data is,

From Equation (6), we can see that when s becomes bigger and M becomes smaller, the error of the signal amplitude becomes bigger. It is reasonable to conclude that the bigger the error value of the abnormal data, the closer the abnormal point close to the peak, the more an abnormal data influences the result calculated by Fourier Algorithm.

In order to test the influence of abnormal data to distance protection, a simulation model is established as shown in Figure 4.

In the simulation model, the length of L₁ is 20 km, the length of L₂ is 15 km. The current on L₁ varies from 40 A to 50 A, the current on L₃ varies from 35 A to 40 A. The minimum branching factor of protection on L₁ equals to 1.7.

According to the distance protection theory, the setting value of protection is calculated by Equation (7) and Equation (8).

Z₁ is the unit length positive sequence impedance.

is the safety factor, here we put

is the safety factor, here we put

is the minimum branching factor.

In the simulation, there are 40 sampled values in each period. The amplitude of the abnormal data varies from two times the original value to five times the original value. The occurrence possibility of abnormal data on voltage signal is 0.1. The simulation result is shown in Table 1.

The theoretical boundary of protection I is 16 km. We can find that when the fault position is very close to S₁, protection I can always start normally. But when the fault position is far from S₁ especially close to the boundary of protection I (15 km to S₁), protection II may start instead of protection I. This is because when the fault is close to S₁, the calculated impedance is very small. Though the abnormal data may enlarge the calculated impedance (abnormal data on the voltage signal), it still falls in the area of protection I. But when the fault occurs close to the boundary of protection I, the calculated impedance may fall into the area of protection II with the influence of abnormal data. This extends the fault’s influence.

In order to test the influence of abnormal data to over current protection, a simulation model is established as shown in Figure 5.

The length of Line 1 equals to 20 Km. The phase-to-phase rms voltage of S₁ is 35 kv; the phase-to-phase rms voltage of S₂ is 10 kv. The rated active power of Load 1 is 20 kw and its inductive power factor equals to 0.8; the rated active power of Load 2 is 15 kw and its inductive power factor equals to 0.6. I and II are two busbars of the system. Protection A is installed very close to I and protection B is installed very close to II.

According to the theory of over current protection, the setting values of instantaneous over current protection and time delay instantaneous over current protection are calculated by Equation (10) and Equation (11).

is the safety factor of instantaneous over current protection, here we put.

is the safety factor of time delay instantaneous over current protection, here we put.

is the minimum current when there is a fault on busbar II.

and are the setting values of instantaneous over current protection in Line 1 and Line 2. is the setting value of time relay protection in Line 1.

In the simulation, there are 40 sampled values in each period. The amplitude of the ab-normal data varies from two times the original value to five times the original value. The occurrence possibility of abnormal data on current signal is 0.1. The simulation result is shown in Table 2.

The theoretical instantaneous over current protection’s boundary is 6.8 km. We can see from the simulation result that the over current protection has the possibilities of starting without fault on the line. It is because the calculated current amplitude is enlarged with the abnormal data. This is a big threat to the safety operation of power system. We also find that in some conditions (in the last two lines) the instantaneous over current protection starts instead of time delay instantaneous over current protection. But this doesn’t have much influence on the power system safety.