New energy transmission line fault location method based on Pearson correlation coefficient

The access of new energy power source makes the traditional transmission line structure become complex, and due to the influence of power electronic device control strategy, the fault characteristics have been fundamentally changed, resulting in the traditional transmission line fault localization method can not be applied to the new energy sending line. To address the above problems, this paper analyzes the transient current characteristics of different power supply faults, and learns that there are obvious differences in the transient currents on both sides of the fault point inside and outside the transmission line area, and then proposes a new energy transmission line fault localization method based on the Pearson correlation coefficient, which determines the fault location by calculating the correlation coefficients of the fault waveforms of the neighboring monitoring points. Finally, comparative experiments are carried out under different fault types and fault locations to further verify the applicability of the proposed method.


Introduction
With the rapid development of renewable energy, more and more large-scale new energy power stations are integrated into the power grid, due to the unique control strategy of power electrical devices such as converters and other impacts of the fault current presents unequal positive and negative impedance, restricted amplitude, controlled phase angle, frequency is non-industrial frequency and other characteristics [1][2], so that the traditional fault localization methods can not be directly applied to renewable energy power station sending out lines.Therefore, how to accurately locate the faults in the transmission lines of renewable energy power stations is of great significance.Inverter-type power supply fault current is affected by inverter control strategy and system access capacity and other factors [3][4], and the fault current presents completely different characteristics from synchronous generator, which makes the traditional line protection and fault localization methods have greater limitations.Therefore, some scholars have proposed protection methods applicable to new energy grid-connected lines.Literature [5][6][7] proposed a protection method based on the frequency difference between DFIG and system-side fault current, but this method cannot be applied to gridconnected lines containing inverter-type power supply; Literature [8][9][10] proposed a localization

Analysis of transient fault characteristics of different power sources
The wiring of the new energy field station sending line is shown in Figure 1, and the whole new energy grid-connected system consists of three parts: new energy power station, sending line and external system.This paper first analyzes the transient fault characteristics of different power sources, and proposes the basis for judging fault sections according to the different characteristics of each power source.

Inverter type new energy power supply
Inverter type new energy power supply is mainly connected to the grid through the inverter, completely isolated from the grid.Therefore, the fault characteristics of inverter-type power supplies are determined by the inverter and its control strategy.In actual working conditions, when a line fault occurs, the input of the inverter control system will change; before the system enters the fault steady state, the control system is always in the dynamic regulation process.Therefore, no matter how the system structure and parameters are set, there is always a transient current in the fault process.At the same time, due to the structure of the control system, parameters, different fault traversal requirements, the strong randomness of the fault conditions, resulting in the inverter-type power supply fault transient current can not give a clear mathematical expression, in order to facilitate the understanding of this paper, the fault transient current is expressed as: Where, denotes some functional relationship; F indicates the fault condition.S represents the control strategy; P indicates a system parameter.From equation (1), it can be seen that the inverter-type power supply is affected by the dynamic behavior of the control system strategy switching, the fault current in the transient process waveform changes irregularly, and no longer present the exponential decay of the frequency sine wave.

Inverter type new energy power supply
In order to avoid overcurrent damage to the converter, doubly-fed wind turbines are protected by crowbar circuits in the rotor-side converter, and the input of crowbar circuits depends on the degree of voltage drop at the machine end.In order to better obtain the fault transient characteristics of doubly-fed wind turbines, this paper analyzes the high and low degree of voltage drop at the machine end, respectively.Doubly-fed wind turbines are affected by the low-penetration control strategy and crowbar circuit casting, and their short-circuit currents will show phase characteristics:  In the first stage, the system failure resulted in a severe voltage drop at the machine end and short-circuit currents in both the stator and the rotor. In the second stage, in order to avoid overcurrent damage to the arrester, the crowbar circuit will act with shorting the rotor side arrester, and after the crowbar circuit is put into operation, the fault current of the doubly-fed wind turbine consists of three parts: steady-state industrial frequency component, attenuated rotational speed frequency component, and attenuated DC wind speed.Among them, the attenuation speed frequency component of fault current accounts for the highest proportion, and the steady state component of the industrial frequency accounts for a smaller proportion; and due to the control strategy of the wind turbine, the rotor speed will change in the range of 0.7-1.3times the synchronous speed according to the wind speed, which usually deviates from the synchronous speed, resulting in the rotational speed deviation from the industrial frequency. In the third stage, in order to achieve low-voltage ride-through, the crowbar circuit is withdrawn after a few tens of milliseconds and the converter is put back into operation.

Inverter type new energy power supply
According to the above analysis, it can be seen that different types of power supply fault transient waveform characteristics are different, this paper according to the different fault location, the fault transient current analysis is divided into three parts, the specific analysis is as follows:

Intra-area failure
When the sending line has an in-area fault, according to the above analysis, the transient current on the system side will show synchronous generator characteristics, and the fault waveform will be gradually attenuated to an industrial frequency sinusoidal waveform; the transient current characteristics on the station side will be determined by the type of new energy power source, and according to the above analysis, the fault transient current will be shown as a non-industrial frequency sinusoidal waveform or an irregular waveform.When an intra-area fault occurs in a new energy sending line, the fault current waveforms at the two ends of the fault point differ greatly, i.e., the fault current waveforms at the three collection points A, B, and C are similar, the fault currents at E, F, and G are similar, but the degree of difference between the fault waveforms at the points C and D is large, which can be relied upon as the basis for intra-area fault localization.

Out-of-area faults on the station side.
When an intra-area fault occurs on the sending line close to the field station side, the fault current characteristic of the left side of fault point F, i.e., collection point A, is determined by the new energy field station.The fault current characteristics of the right side of fault point F, i.e. collection points B-G, are determined by the external system.When an out-of-area fault occurs on the field station side of a new energy transmission line, the fault current waveform at A differs greatly from the fault waveforms collected at points B, C, D, E and G, which can be used as the basis for locating the out-of-area fault on the field station side.

Out-of-area faults on the station side.
When an intra-area fault occurs on the sending line close to the field station side, the fault current characteristics of the left side of fault point F, i.e. the five collection points A-E, are determined by the new energy field station.The fault current characteristics of the right side of the fault point F, i.e., the collection point G, are determined by the external system.When an out-of-area fault occurs on the field station side of the new energy transmission line, the fault current waveform at A-E differs greatly from the fault waveform collected at point G, which can be used as the basis for locating the out-of-area fault on the system side.

Pearson correlation coefficient
Waveform similarity algorithm has been widely used in power systems in recent years, due to its high recognition of detail features, not affected by the amplitude of the characteristics of this paper to meet the requirements of the fault waveform similarity identification.Pearson correlation coefficient of the two groups of waveforms centered on the basis of the similarity of the data processing, can be a better measure of similarity of the details of the two groups of waveforms, and its calculation formula is as follows: Where, (, ) is the Pearson correlation coefficient; x, and y are the two sets of waveform data; x i and 1，2，3，. . .， are the data x and y the ith data in the data; n is the number of samples.When (, ) = 1 When meansx When the waveforms of the two groups are exactly the same, the positive correlation is strong, y The two groups of waveforms have the same pattern of change and strong positive correlation, when (, ) =− 1 , and The two groups of waveforms have completely opposite patterns of change, strong negative correlation, when (, ) = 0 the waveforms of the two groups are in the opposite pattern, the negative correlation is strong, y The two groups of waveforms change the law of large differences, weak correlation.

New energy transmission line fault localization method based on waveform similarity
The steps of the fault localization method proposed in this paper are as follows:  The correlation coefficients of each two neighboring collection points in the six collection points A, B, C, D, E, and G are calculated by equation ( 2) to obtain five correlation coefficients 1 , 2 , 3 , 4 , 5 . Judging the correlation coefficients r 1 and r 5 , if there is a value of 0 in both, it proves that an out-of-area fault occurs; whenr 1 = 0 and other correlation coefficients are not 0, a field station side out-of-area fault occurs and the fault zone is E-G; when r 5 = 0 and other correlation coefficients are not 0, system-side out-of-area fault occurs, and the fault section is E-G; if neither of them is 0, it proves that in-area fault occurs. When it is judged that an in-zone fault occurs, the correlation coefficient is judged 2 , 3 , 4 If there is a value of 0, it is determined that the fault point is in the zone.

Simulation verification
In this paper, the simulation model is built in PSCAD/EMTDC according to Fig. 1, and set up on the field station side outside the sending line area, 5km, 15km, 25km inside the sending line area, and the system side outside the sending line area 1 , 2 , 3 , 4 , 5 five fault points.Different fault classes were set for each fault point, and the correlation coefficients between adjacent monitoring points were calculated respectively, as shown in Table 1.  1, it can be observed that under different fault types, positions, and other conditions, the method proposed in this paper is capable of determining the fault location by evaluating the correlation coefficient of fault currents between adjacent monitoring points.Furthermore, this method is computationally simple and suitable for different types of new energy power sources.

conclusion
This paper presents a novel fault location method for outgoing lines of new energy power plants, which addresses the challenge of difficult fault localization.The method utilizes the similarity of fault transient current waveform and conducts separate analyses based on different types of new energy stations.By calculating the similarity of fault current waveforms between two monitoring points using the Pearson correlation coefficient, the fault location is achieved.Finally, through comparative experiments considering various factors such as different fault types and positions, the reliability of the proposed method is validated.

Figure 1 .
Figure 1.Wiring diagram of new energy station.

Table 1 .
Correlation coefficient of two renewable energy power sources in different fault locations and fault types.