A New Principle of Fault Identification of on the Same Tower Based on Traveling Wave Reactive Powers

In order to improve the reliability of fault identification of the double-circuit transmission lines on the same tower, a new algorithm for fast protection of double-circuit transmission lines on the same tower based on the reactive powers of traveling wave is proposed. With the implementation of S-transform, the initial traveling wave reactive powers are calculated and the change characteristics of reactive power under different fault conditions are studied. The protection criterion is constructed by analyzing the ratio of the reactive powers of the same end on double-circuit transmission lines and the ratio of the reactive powers at both ends on the same line. According to the ratio of reactive power on the same side of the line and both ends of the same line, it is possible to identify whether the faults of the double-circuit line of the same tower occurred in or out of the protection zone. A large number of simulation results show that the protection performance is sensitive and reliable, and quick to respond. The criterion is simple and is basically not affected by fault initial angles, fault types, and transitional resistances.


Introduction
With the advantages of saving investment cost and effectively improving power transmission capacity, the double circuit transmission lines on the same tower have been widely used in China's high-voltage power grid in [1]. However, the distance between the double circuit transmission lines is short due to the sharing How to cite this paper: Wu, H., Ye, R.K., Dong, X.X., Yu, K.J. and Chang, Z.W. The literature [2]- [8] mainly studies the protection and the fault phase selection of the double circuit transmission lines on the same tower based on power frequency, which has a slight deficiency in the response time. In [9], a fault locating method using single-ended impedance is proposed, which has high robustness, however, when a cross-line fault of the same name occurs, the fault location accuracy rate was not high. The literature [10] uses the circuit line protection scheme of the single-ended transient main frequency to satisfy the requirement of rapidity, but its reliability depends on too many factors. The literature [11] proposed the concept of the modal differential transverse current, and quoted the concept of constructing the line fault diagnosis criterion, which can accurately identify the internal and external faults, but the ability to identify the complex faults is still insufficient. In [12], the fault current traveling wave characteristics on the double-circuit line on the same tower are analyzed, but no specific circuit protection scheme is proposed. The literature [13] used the characteristics of inconsistent traveling wave speeds when a metallic fault on the same tower occured and proposed a differential protection scheme for traveling wave on the same tower double circuit line. The sensitivity and rapidity of the scheme are relatively high.
Based on the research ideas of literature [14] [15] [16], this paper proposes a new fault identification principle based on reactive power of the traveling wave on double-circuit lines on the same tower. The S-transform is used to extract the single-frequency initial voltage and current traveling wave after the fault occurs.
The initial traveling wave reactive power is calculated using initial voltage and current traveling wave. The fault identification principle identifies the internal and external faults according to the ratio of the reactive power of the same ends of the line and both the ends of the same line. The experimental simulation results show that the program provides a quick response, high identification accuracy and sensitivity.

Fault of Single-Circuit Transmission Line in the Area
A fault occurs at point K 1 on the double-circuit line on the same tower, according to Peterson principle in [14], the fault feature can be simplified as shown in According to [14], in Peterson equivalent circuit, when the traveling wave frequency 50 -100 kHz f = , the wave impedance of the extra (ultra) high-voltage transmission line approximates to a real constant and can be equivalent to resistance R.
Therefore, the impedance in Figure 2 approximates to 1 is the ground equivalent capacitance wave impedance of the busbar. Take the direction in which the traveling wave propagates to the bus M as an example result at the equation of:   According to circuit theory, the complex power * S U I P jQ = ⋅ = +  , where P is the active power and Q is the reactive power, the traveling wave complex power obtained at the Bus M is: The corresponding initial traveling wave reactive power can be obtained as follows: According to the calculation, the ratio of reactive power of the initial traveling wave on the M side of the double-circuit transmission line of the same tower is: In other words, the reactive power ratio λ of the double circuit transmission line on the same side is a large number when the single circuit fault occurs in the fault area, and the fault can be clearly identified by utilizing this feature.  (1 ) 1

Same Name Phase Cross Line Ground Faults in the Area
( The complex power of the transmission line is: The reactive power of the same end of the double circuit line is:   Take line L 1 as an example, the reactive power ratio at both ends of the same line can be derived as: In formula (9), the value of λ is determined by the ground capacitance of busbar. Ideally, the ground capacitance of busbar at both ends of the double circuit transmission line are about the same size, so 1 λ ≈ .

Fault out the Area
When a fault occurs at point K 3 outside the protection zone, the line fault feature can be simplified to the Peterson model of Figure 4.
Each current traveling wave can be expressed as: The complex power on the line can be expressed as: 3, 4 When a fault occurs outside the protection zone, the reactive power of the The traveling wave reactive powers on the same end of the double-circuit transmission line on the same tower are approximately equal. Taking line L1 as an example, the reactive power ratio of initial travelling wave at both ends of the line is: When a fault occurs out of the protection zone, the reactive power on the bus near the fault location is approximately zero, and the reactive power of the busbar on the far side of fault location is non-zero. The reactive power ratio at both ends of the same line is a large number.
Based on the above analysis, it can be seen that when a fault occurs out of the protection zone, 1) the reactive power of traveling wave on the same side is approximately equal; 2) the ratio of reactive power of traveling wave on both ends of the same line is relatively large.

Phase Mode Transformation
There is a more complicated coupling in the double-circuit transmission line of the same tower than that of a single-circuit transmission line. There is coupling between the phases and between the lines, so the phase-mode transformation must be implemented to decouple before calculating the fault components. This paper chooses the decoupling transformation matrix resembling Clarke transformation matrix M in [2].
The relationship between the six-phase current I and the modulus current I m on the double-circuit transmission line on the same tower is:  I  I  I  I  I  I IB  IC  IIA  IIB  IIC   I  I  I  I  I  I  I  =  (17) Similarly, relationship between the corresponding six-phase voltage U and the modulus voltage U m is: In the formula, the components represented by U and U m are: In the formula, 0, α, β respectively represent the zero-modulus, α-modulus, and β-modulus components after the phase-mode transformation is implemented; subscripts I and II denote the I-circuit and the II-circuit transmission line of the double-circuit line on the same tower respectively.

S-Transform
S-transform is a method of signal time-frequency joint analysis, and it is the development of continuous wavelet transform and short-time Fourier transform. As- where T is the time interval, and the discrete Fourier When 0 n = , the discrete transformation of time series [ ] h kT is a constant, which can be derived as: In formula (23), , The rows in this matrix correspond to the sampling time of the signal and the columns correspond to discrete frequencies.
Because S-transform has good signal extraction characteristics in time-frequency analysis, this paper uses S-transform to extract fault current traveling wave and voltage traveling wave. Based on this, the corresponding complex power and reactive power are calculated.

Calculation of Initial Traveling Wave Reactive Power
Take the three-phase grounding fault occurred at point K 1 on line L 1 in Figure 1 as an example. The fault current component is detected on protection unit R 1 , and 1 i ∆ is the combined-modulus current obtained using phase-mode transformation. Discrete S-transform is performed on the current modulus 1 i ∆ according to Equations (22) and (23). One-dimensional complex phasor is obtained at selected frequency Z f [14], which can be derived as: are the amplitude and phasor of the respectively.
If at the time 1 t , the amplitude of the traveling wave head reaches a maximum value max .1 at this moment is the initial current traveling wave peak phasor at the selected frequency Z f in [16]. Similarly, the initial voltage traveling wave peak phasor can be determined. According to the calculation formula of complex frequency, the faulted initial traveling wave complex frequency on line L 1 near M terminal can be obtained as:       Figure   9 and Figure 10 respectively. Analysis of Figure 9 and Figure

Establishment of Criterion
In order to accurately identify the faults occurred double circuit transmission line on the same tower, the reactive power ratios of the traveling wave on the same side of the two lines and the traveling wave reactive power ratios of the two ends of the same line on the double-circuit line on the same tower are calculated to construct the primary criterion and secondary criterion for fault identification.

Primary Criterion for Fault Identification
Take the system of Figure 1 as an example. The initial traveling wave reactive power measured by the four traveling wave protection units R 1~R4 on the same-tower double-circuit transmission line is Q 1~Q4 , and the ratio of the initial traveling wave reactive power on the same side of double-circuit line on the same tower is:

Secondary Criterion for Fault Identification
If the ratio of the initial traveling wave reactive powers on the same end of the double-circuit line on the same-tower cannot satisfy the primary criterion, the secondary criterion is invoked. The ratio is calculated using the initial traveling wave reactive powers at both ends of the same line according to the secondary criterion:

Algorithm Flow
When a fault traveling wave occurs on the double circuit transmission line on the same tower, the α-modulus and β-modulus of the corresponding voltage and current are obtained through phase mode transformation. According to the literature [2], when the line protection device detects that the fault is a single-phase fault or two phases, same-name phases cross line grounding fault, α-modulus is selected for S-transform, and β-modulus is selected to identify other faults.
Time-frequency transformation is performed on the selected modulus with the implementation of S-transform. The single-frequency fault initial voltage traveling wave and current traveling wave corresponding to 60 kHz are selected with the implementation of S-transform in [14], and the corresponding initial traveling wave reactive power is calculated.
Primary and secondary criteria are used to achieve fault recognition of double-circuit line on the same tower, and the fault identification algorithm flow is shown in Figure 11.

Simulation Verification
In this paper, PSCAD software is used to establish the simulation model of double-circuit transmission lines on the same tower. The total length of the line   Table 1, it can be seen that a secondary criterion (29) is needed for the same-name  Using these two criteria, the algorithm will not misjudge under different types of faults.

Faults Occurred in the Protection Zone
From Table 2  It can be seen from the analysis in Table 3 that when the transitional resistance and the fault location change, the primary criterion (27) still can be met with the ratio of the traveling wave reactive power, and it hardly changes with the change of transitional resistance, that is, the algorithm is not affected by the change of transitional resistance.
The above analysis shows that with different fault initial angles, transitional resistances, fault types, and fault locations, the simulation data is consistent with the theoretical analysis results, which means the protection can accurately reflect the faults occurred in the protection zone and operate in a reliable way.  In order to fully verify the effectiveness of fault identification algorithm out of the protection zone, a lot of simulation experiments have been carried out.  Which not satisfy the secondary criterion (29) and it can be concluded that the  fault occurred out of the protection zone, and the algorithm is not affected by the initial angle of the fault. Table 6 shows that when faults occur out of the protection zone under differ- can still be used to identify the fault occurred out of the protection zone.

Faults Occurred Out of the Protection Zone
In summary, the algorithm can accurately identify faults occurred on the double-circuit line on the same tower out of the protection zone, and is not affected by initial angles of faults, transitional resistances, and types of faults. The algorithm is accurate and reliable and shows no defect or malfunction. That is to say, the test results are identical with theoretical analysis results.

Conclusions
In this paper, the protection principle of the double-circuit transmission line on the same tower based on the ratio of the initial traveling wave reactive power is