A new algorithm of distance protection based on the change in phase angle of the voltage

doi:10.21203/rs.3.rs-1633861/v1

Download PDF

Research Article

A new algorithm of distance protection based on the change in phase angle of the voltage

https://doi.org/10.21203/rs.3.rs-1633861/v1

This work is licensed under a CC BY 4.0 License

Journal Publication

published 05 Jul, 2023

Read the published version in Electric Power Systems Research →

Version 1

posted

You are reading this latest preprint version

The paper presents a new algorithm of distance protection based on the change in phase angle of the voltage. As input signals, the algorithm uses measured voltages at the beginning of the line and auxiliary voltages. Auxiliary voltages were calculated using measured currents and voltages at the beginning of the line and known line parameters. The algorithm compares the instantaneous values of the measured and calculated auxiliary voltages and, based on the change in the phase angle of the voltage, detects a fault on the line. The testing of the presented algorithm was performed with signals obtained by computer simulations of line faults and recordings of faults taken from protective devices from the real network. The obtained results showed good performance of the presented algorithm.

distance protection

fault detection

phase angle

Distance protection is widely applied in transmission networks with the task of fast and selective fault detection. The distance protection is based on the linear dependence between the distance to the fault location and the impedance calculated by the relay. Algorithms implemented in distance relays calculate the impedance between the relay and the fault location. Based on the calculated impedance, the relay identifies the fault as internal or external in relation to the set protection zone. Measured voltage and current values at the relay location are used to calculate the impedance. To increase the reliability and safety of fault detection, over the years, digital relays have undergone many modifications and improvements compared to electromechanical and static relays.

Traditional methods of distance protection are based on the phasor estimation of currents and voltages. Based on the estimation of the phasor, the impedance and the distance to the fault location are estimated. Commercial phasor estimation algorithms most often use digital filters that implement discrete Fourier transform (DFT) and have the advantage of filtering higher harmonics. Although reliable and commonly used, these methods have a delay that is directly proportional to the size of the data window. To overcome this disadvantage, other methods have been proposed for phasor estimation based on modified DFT [1–3], least squares method [4, 5], discrete Wavelet transformation (DWT) [6–10], Taylor-Kalman-Fourier filter application [11], etc. In addition to the above methods, which use measured signals at the relay location for phasor estimation, methods based on remote synchrophasors can be found [12, 13]. Although the reliability of methods based on phasor estimation is quite good, many of these methods have high sensitivity on noise and DC component, and this requires appropriate pre-filters.

Some authors propose methods in the time domain. The application of digital phase comparison for the realization of the MHO operating characteristic in the time domain is shown in [14]. In [15], the authors propose a method that is based on line differential equations. The realization of distance protection using the conic section general equation is shown in [16]. A method based on fast Stockwell transformation in the time-frequency domain is shown in [17]. The authors in [18] propose distance protection based on the increment of the instantaneous values of the input signals. Methods in the time domain directly use current and voltage samples and significantly reduce the fault detection time.

The application of intelligent methods in the field of distance protection is also significant. Methods based on the application of artificial neural networks (ANN) [19, 20], fuzzy logic [21], adaptive neuro fuzzy inference system (ANFIS) [22], support vector machine (SVC) [23], decision tree (DT) [24], etc. can be highlighted here. The intelligent methods presented in [19–24] require a large number of data necessary for training. This can be a complex and time-consuming process, thus making it difficult to apply them in practice.

In recent years, solutions based on traveling waves have been proposed [25, 26]. This method is characterized by a high-speed fault detection. However, it has not yet reached a sufficient level of reliability and safety, so it has not entered in commercial use.

This paper presents an algorithm of distance protection based on a phase comparison of instantaneous values of input signals.

It is starting from Fig. 1 when forming the criteria on which the operation of the algorithm is based. Figure 1 shows a three phase line where two fault locations are considered. The impedance of the three phase line is Z. F1 fault corresponds to a location inside the length of the line (Z_F1<Z), while F2 fault corresponds to a location outside the length of the line (Z _F2>Z).

If we assume that there was the phase to phase fault in the line, based on Fig. 1, equations for auxiliary voltages can be written at the beginning of the line for faults a-b, b-c, and c-a, respectively:

$${\underset{\_}{U}}_{ab}^{\text{'}}={\underset{\_}{U}}_{a}-{\underset{\_}{U}}_{b}-\underset{\_}{Z}\left({\underset{\_}{I}}_{a}-{\underset{\_}{I}}_{b}\right)$$

$${\underset{\_}{U}}_{bc}^{\text{'}}={\underset{\_}{U}}_{b}-{\underset{\_}{U}}_{c}-\underset{\_}{Z}\left({\underset{\_}{I}}_{b}-{\underset{\_}{I}}_{c}\right)$$

$${\underset{\_}{U}}_{ca}^{\text{'}}={\underset{\_}{U}}_{c}-{\underset{\_}{U}}_{a}-\underset{\_}{Z}\left({\underset{\_}{I}}_{c}-{\underset{\_}{I}}_{a}\right)$$

The previous equations can be written in reduced form:

$${\underset{\_}{U}}_{ab}^{\text{'}}={\underset{\_}{U}}_{ab}-\varDelta {\underset{\_}{U}}_{ab}$$

$${\underset{\_}{U}}_{bc}^{\text{'}}={\underset{\_}{U}}_{bc}-\varDelta {\underset{\_}{U}}_{bc}$$

$${\underset{\_}{U}}_{ca}^{\text{'}}={\underset{\_}{U}}_{ca}-\varDelta {\underset{\_}{U}}_{ca}$$

At the occurrence of phase to phase fault a-b, the following equations apply for currents:

$${\underset{\_}{I}}_{c}=0$$

$${\underset{\_}{I}}_{a}+{\underset{\_}{I}}_{b}=0$$

$${\underset{\_}{I}}_{ab}={\underset{\_}{I}}_{a}-{\underset{\_}{I}}_{b}={2\underset{\_}{I}}_{a}$$

thus reaching the equations:

$${\underset{\_}{I}}_{bc}=-\frac{{\underset{\_}{I}}_{ab}}{2}$$

$${\underset{\_}{I}}_{ca}=-\frac{{\underset{\_}{I}}_{ab}}{2}$$

Figure 2 shows the vector diagram of the voltages in case of phase to phase fault a-b. From the figure, it is observed that for faults outside the line (Z_F2>Z), the direction of voltage ${\underset{\_}{U}}_{ab}^{\text{'}}$ remains unchanged relative to ${\underset{\_}{U}}_{ab}$. When there is the fault on the line (Z_F1<Z), there is a change in the direction of the voltage ${\underset{\_}{U}}_{ab}^{\text{'}}$. Phase to phase voltages ${\underset{\_}{U}}_{bc}^{\text{'}}$ and ${\underset{\_}{U}}_{ca}^{\text{'}}$ do not change direction, regardless of the fault position.

Similarly, equations for auxiliary voltages for the single phase to ground fault of phases a, b and c, respectively, can be written:

$${\underset{\_}{U}}_{a}^{\text{'}}={\underset{\_}{U}}_{a}-\underset{\_}{Z}\left({\underset{\_}{I}}_{a}+{k}_{0}{\underset{\_}{I}}_{0}\right)$$

$${\underset{\_}{U}}_{b}^{\text{'}}={\underset{\_}{U}}_{b}-\underset{\_}{Z}\left({\underset{\_}{I}}_{b}+{k}_{0}{\underset{\_}{I}}_{0}\right)$$

$${\underset{\_}{U}}_{c}^{\text{'}}={\underset{\_}{U}}_{c}-\underset{\_}{Z}\left({\underset{\_}{I}}_{c}+{k}_{0}{\underset{\_}{I}}_{0}\right)$$

The previous equations can be written in abbreviated form:

$${\underset{\_}{U}}_{a}^{\text{'}}={\underset{\_}{U}}_{a}-\varDelta {\underset{\_}{U}}_{a}$$

$${\underset{\_}{U}}_{b}^{\text{'}}={\underset{\_}{U}}_{b}-\varDelta {\underset{\_}{U}}_{b}$$

$${\underset{\_}{U}}_{c}^{\text{'}}={\underset{\_}{U}}_{c}-\varDelta {\underset{\_}{U}}_{c}$$

At the occurrence of the single phase to ground fault in phase a, the following terms apply for currents:

$${\underset{\_}{I}}_{a}=3{\underset{\_}{I}}_{0}$$

$${\underset{\_}{I}}_{b}={\underset{\_}{I}}_{c}=0$$

In Fig. 3, the vector diagram of the voltages in the case of the fault in phase a is shown. It can be seen from the figure that in the case of an internal fault (Z_F1<Z), the voltage ${\underset{\_}{U}}_{a}^{\text{'}}$ changes direction concerning U_a, while in the case of an external fault, the direction remains unchanged. Voltages in healthy phases ${\underset{\_}{U}}_{b}^{\text{'}}$ and ${\underset{\_}{U}}_{c}^{\text{'}}$ do not change direction, regardless of the fault position.

Based on the conducted analysis, it can be concluded that the angle δ in phases with fault will have the value of approximately 180°, while the angle δ in healthy phases ranges from 0° to approximately 30°. To increase the sensitivity and speed of fault detection, a value of 120° can be adopted instead of the threshold angle of 180°, without compromising the safety of the protection operation.

Table 1 summarizes the criteria for the operation of the proposed algorithm.

Table 1

Threshold angles for detecting different faults types
Phase	Threshold angles
Phase	δ_a	δ_b	δ_c	δ_ab	δ_bc	δ_ca
a-G	120^o	/	/	/	/	/
b-G	/	120^o	/	/	/	/
c-G	/	/	120^o	/	/	/
a-b	/	/	/	120^o	/	/
a-b-G	120^o	120^o	/	120^o	/	/
b-c	/	/	/	/	120^o	/
b-c-G	/	120^o	120^o	/	120^o	/
c-a	/	/	/	/	/	120^o
c-a-G	120^o	/	120^o	/	/	120^o
a-b-c	120^o	120^o	120^o	120^o	120^o	120^o
a-b-c-G	120^o	120^o	120^o	120^o	120^o	120^o

Based on the previous analysis, the input signals of the algorithm can be formed. To get the fastest possible response, a procedure in the time domain is proposed below. A phasor domain could also been used completely equally.

3.1 Single phase ground fault

The equations for auxiliary voltages for the single phase to ground fault of phases a, b, and c, written in the time domain, take the following form:

$${u}_{a}^{\text{'}}={u}_{a}-R\left({i}_{a}+{{k}_{R}i}_{0}\right)-L\left(\frac{{di}_{a}}{dt}+{k}_{L}\frac{{di}_{0}}{dt}\right)$$

$${{u}_{b}^{\text{'}}=u}_{b}-R\left({i}_{b}+{{k}_{R}i}_{0}\right)-L\left(\frac{{di}_{b}}{dt}+{k}_{L}\frac{{di}_{0}}{dt}\right)$$

$${u}_{c}^{\text{'}}={u}_{c}-R\left({i}_{c}+{{k}_{R}i}_{0}\right)-L\left(\frac{{di}_{c}}{dt}+{k}_{L}\frac{{di}_{0}}{dt}\right)$$

where k_R =(R₀-R)/R and k_L = (L₀-L)/L are zero-current compensation coefficients.

The following approximate equation can be used to solve the current derivative ${di}_{a}/dt$:

$$\varDelta {i}_{a}=\frac{{i}_{a(n+1)}-{i}_{a(n-1)}}{2{T}_{s}}$$

where T_s is sampling period.

By analogy, the derivatives of the other currents ${di}_{b}/dt$, ${di}_{c}/dt$, and ${di}_{0}/dt$ can be calculated.

The corresponding phase voltages measured at the beginning of the line are used as the reference voltages at the occurrence of single phase to ground fault. However, in a close fault, the phase voltage of the phase affected by the fault may have the value close to zero. Since the phase voltages are used as the reference signals, in this case, it is not possible to perform the phase comparison of the measured phase voltages u_a, u_b, and u_c with the calculated phase voltages u’_a, u’_b, and u’_c. The above mentioned problem is overcome by using a memory, i.e. a delay of one period is introduced into the original signals of the measured phase voltages. With this modification the amplitude of the phase voltages does not change. The equations describing the memorized phase voltages take the following form:

$${u}_{a}^{{\prime \prime }}={u}_{a}(n-k)$$

$${u}_{b}^{{\prime \prime }}={u}_{b}(n-k)$$

$${u}_{c}^{{\prime \prime }}={u}_{c}(n-k)$$

 where k is the delay corresponding to one period of the input signal.

If a sampling frequency of 3 kHz is adopted, the delay of k = 60 samples corresponds to one period of the input signal.

It should be noted that phase voltages also exist in equations (20)-(22). However, in these equations there is no need to introduce delays into the phase voltages. In the case of a near fault, if the phase voltages in the first part of equations (20)-(22) fall to zero, information on the occurrence of the fault will be obtained from the second and third part.

Thus, equations (24)-(26) represent reference signals, while equations (20)-(22) contain information about the occurrence of the ground fault, and based on them the ground fault is detected at the appropriate phase.

3.2 Phase to phase fault

By analogy, the equations for auxiliary voltages applicable to phase to phase faults can be written:

$${u}_{ab}^{\text{'}}={u}_{ab}-R\left({i}_{a}-{i}_{b}\right)-L\left(\frac{{di}_{a}}{dt}-\frac{d{i}_{b}}{dt}\right)$$

$${u}_{bc}^{\text{'}}={u}_{bc}-R\left({i}_{b}-{i}_{c}\right)-L\left(\frac{{di}_{b}}{dt}-\frac{d{i}_{c}}{dt}\right)$$

$${u}_{ca}^{\text{'}}={u}_{ca}-R\left({i}_{c}-{i}_{a}\right)-L\left(\frac{{di}_{c}}{dt}-\frac{d{i}_{a}}{dt}\right)$$

Corresponding phase to phase voltages, measured at the beginning of the line, are used as reference signals at the occurrence of phase to phase faults. To make these voltages usable in the case of near faults, they have to be memorized:

$${u}_{ab}^{{\prime \prime }}={u}_{ab}(n-k)$$

$${u}_{bc}^{{\prime \prime }}={u}_{bc}(n-k)$$

$${u}_{ca}^{{\prime \prime }}={u}_{ca}(n-k)$$

The algorithm uses the angle change between the input signals as the fault detection criterion. Instantaneous voltage values measured at the beginning of the line and calculated instantaneous values of auxiliary voltages are used as input signals. The operation of the algorithm is based on the application of digital phase comparison (DPC) in the time domain [27–33]. DPC is based on the calculation of the product of the instantaneous values of input signals at interval equal to the half period of the input signal. In general, when currents and voltages are used as input signals, the product of the instantaneous values of the input signals represents the instantaneous power. If the input signals are in phase, their product will be positive. On this basis, the integral of such a product will also be positive. In contrast, if the input signals are phase-shifted by an angle of 180°, their product will be negative, and accordingly the integral of the product of such a signal will be negative. The limit angle of this comparator is 90°. In this case, the integral of the input signals product will be 0. An algorithm based on the application of DPC does not directly calculate the angle between the input signals but evaluates that angle based on the calculation of integral of the product of the instantaneous values of the input signals. The integration interval is the half period of the input signals, since the frequency of the product of the input signals is two times the frequency of the input signals.

As an indicator of a fault, a fault index (FI) is introduced. FI for the phase to ground fault of phase a, b and c can be written as follows:

$${FI}_{aG}=\frac{\frac{2}{m}{\sum }_{n=1}^{m/2}{u}_{a}^{\text{'}}\left(n\right){u}_{a}^{{\prime \prime }}\left(n\right)}{{U}_{a}^{\text{'}}{U}_{a}^{{\prime \prime }}}$$

$${FI}_{bG}=\frac{\frac{2}{m}{\sum }_{n=1}^{m/2}{u}_{b}^{\text{'}}\left(n\right){u}_{b}^{{\prime \prime }}\left(n\right)}{{U}_{b}^{\text{'}}{U}_{b}^{{\prime \prime }}}$$

$${FI}_{cG}=\frac{\frac{2}{m}{\sum }_{n=1}^{m/2}{u}_{c}^{\text{'}}\left(n\right){u}_{c}^{{\prime \prime }}\left(n\right)}{{U}_{c}^{\text{'}}{U}_{c}^{{\prime \prime }}}$$

where m is the number of samples in a basic period of the input signal.

FI for phase to phase faults can be defined as follows:

$${FI}_{ab}=\frac{\frac{2}{m}{\sum }_{n=1}^{m/2}{u}_{ab}^{\text{'}}\left(n\right){u}_{ab}^{{\prime \prime }}\left(n\right)}{{U}_{ab}^{\text{'}}{U}_{ab}^{{\prime \prime }}}$$

$${FI}_{bc}=\frac{\frac{2}{m}{\sum }_{n=1}^{m/2}{u}_{bc}^{\text{'}}\left(n\right){u}_{bc}^{{\prime \prime }}\left(n\right)}{{U}_{bc}^{\text{'}}{U}_{bc}^{{\prime \prime }}}$$

$${FI}_{ca}=\frac{\frac{2}{m}{\sum }_{n=1}^{m/2}{u}_{ca}^{\text{'}}\left(n\right){u}_{ca}^{{\prime \prime }}\left(n\right)}{{U}_{ca}^{\text{'}}{U}_{ca}^{{\prime \prime }}}$$

Dividing the FI by the RMS value of the input signals, normalization of this index was performed. In this way, the FI value is limited to a range of ± 1. The RMS values of the voltages can be calculated using the mean value method [27]:

$$U=\frac{\pi }{\sqrt{2}\bullet m}\sum _{n=1}^{m/2}\left|u\left(n\right)\right|$$

Based on equations (33)-(38) it can be seen that FI≅cos(δ) is valid. Table 2 shows the threshold values for FI, obtained for the limit angle of 120^o.

In normal operating mode, the signals to be compared are in phase, so FI will have the value of 1. At the occurrence of the fault, the signals corresponding to the phase with the fault will be of the opposite sign, and accordingly, FI will have the value of -1. In this way, the algorithm will detect the fault based on the value of the corresponding FI.

The algorithm defined in this way is also sensitive for phase to phase faults with ground. For example, in case of fault of phase a-b-G, the fault information is obtained via the fault index for the phase to ground fault and the fault index for phase to phase fault, i.e. FI_aG, FI_bG, and FI_ab.

Table 2

Threshold values for different fault types
Phase	Threshold
a-G	-0.5 > FI_aG
b-G	-0.5 > FI_bG
c-G	-0.5 > FI_cG
a-b	-0.5 > FI_ab
a-b-G	-0.5 > FI_aG,bG,ab
b-c	-0.5 > FI_bc
b-c-G	-0.5 > FI_bG,cG,bc
c-a	-0.5 > FI_ca
c-a-G	-0.5 > FI_a,c,ca
a-b-c a-b-c-G	-0.5 > FI_{a,b,c,ab,bc,ca}

In this part, the testing of the presented algorithm was performed. The algorithm testing can be divided into two parts. The first part includes testing with signals obtained by computer simulations. In the second part, testing was performed with fault recordings taken from protective devices from the real network.

Modeling of the test network was performed in the software package MATLAB/Simulink. Figure 4 shows the network model. The 110 kV line connecting the two active networks was analysed. The distance protection algorithm requires knowledge of positive and zero resistance and inductance of the line. The protection zone of the relay is set to 85% of the line length. The various faults are simulated inside the set protection zone (F1) and outside the set protection zone (F2 and F3). Fault F1 is simulated at 5% and 50% of line length. The fault location F2 is at 90% of the line length, while the fault F3 is simulated at the location between the active network 1 and the distance relay (DR).

Figure 5 shows the results of the algorithm testing for single phase to ground fault inside the relay protection zone. Fault of phase a was simulated at 5% of the line length and it was detected after 5.3 ms (Fig. 5a). The algorithm also successfully detected the single phase to ground fault of phase b at 50% of the line length after 9 ms (Fig. 5b). The test results for the single phase to ground fault of phase a at locations outside the protection zone are shown in Figs. 5c and 5d. Figure 5c shows the results of algorithm testing for the close fault, at the location between the active network 1 and the distance relay. Figure 5d shows the results of the algorithm testing for the fault at 90% of the line length. In both cases, the algorithm did not generate the trip signal, as expected.

The results of the algorithm testing for phase to phase faults without ground are shown in Fig. 6. Faults a-b and c-a are simulated at 50% of the line length. From Fig. 6a it can be seen that the phase to phase fault a-b was detected after 6.3 ms, while the fault between phases c-a was detected after 9 ms, as can be seen in Fig. 6b. Figures 6c and 6d show the results of the algorithm testing for phase to phase fault a-b at locations outside the protection zone (F2 and F3). In both cases, the algorithm trips fast and selectively.

Figure 7 shows the results of the algorithm testing for phase to phase faults with ground. Two phase to ground faults (F1) are simulated at 50% of the line length. As in previous cases, the algorithm successfully detected two phase to ground faults inside the protection zone. Fault a-b-G was detected after 9 ms, fault b-c-G after 9.9 ms, and detection time of fault c-a-G is 9.3 ms. Also, in the case of faults outside the protection zone, the algorithm did not generate the trip signal. This conclusion is confirmed by the results that can be seen in Fig. 7d for the b-c-G fault simulated at 90% line length.

In the next test, the influence of the DC component in the fault current was analysed. The single phase to ground fault of phase a was simulated at 5% of the line length. The fault was simulated at the instant 0.1s, i.e. at the moment when the DC component has the maximum value. Figure 8 shows the instantaneous values of currents and voltages measured at the relay location, as well as the value of the DC component and the fault index. Based on the obtained results, it can be seen that the DC component has no significant impact on FI, which leads to the conclusion that the presented algorithm does not require additional filtering of input signals.

The influence of line load on the algorithm operation was verified by simulating faults for the load angle in the range of -25°≤θ ≤ 25^O. In this way, it was verified how the algorithm operation is affected by the direction of energy, as well as the operation of the algorithm at light and heavy load. Based on the obtained results shown in Fig. 9, it can be seen that all faults were detected within the interval of less than 10 ms and that the line load and the energy direction do not have a significant influence on the operation of the algorithm.

An active network via the SIR factor can have a significant impact on the operation of distance protection. In this section faults for different SIR values were simulated. Figure 10 shows the results obtained for the single phase to ground fault of phase a. Based on the obtained results, it can be seen that the reduction of SIR affects the reduction of the fault detection time. In other words, the stronger the network, the shorter the fault detection time. It can also be observed that the fault detection time increases with increasing distance to the fault location. The algorithm is the fastest for near faults, while the detection time is the longest for faults at the end of the protection zone.

To cover actual fault cases, testing of the algorithm was performed with recordings of faults taken from protective devices from the actual network. In this way, all factors that can bring an error into the algorithm operation are included. Here, we primarily refer to errors in measuring transformers, A/D conversion error, interference, etc.

This section presents the results of the algorithm testing with fault recordings taken from the protective device on the 220 kV line. The considered 220 kV line is 145 km long and connects two active networks. The algorithm of distance protection is set following the parameters of the considered 220 kV line, and the protection zone of the algorithm is set at 85% of the line length. Figure 11a shows the results of the algorithm testing for the single phase to ground fault a-G at 75.2% of the line length. From Fig. 11a, it can be seen that the algorithm successfully detected the fault after 9 ms. Figure 11b shows the test results for a-G fault at 91.3% of the line length, which corresponds to a location outside the protection zone. The obtained results show that the algorithm did not detect the fault, as expected.

The paper presents a new algorithm of distance protection based on the change in phase angle of voltage. The algorithm uses instantaneous values of currents and voltages, measured at the relay location. Since these are standard input signals of commercial relays, the algorithm can be easily implemented in multifunctional relay protection devices. The presented algorithm uses basic mathematical operations, which makes it easy to implement.

The algorithm testing was first performed by computer simulations for various fault cases. The algorithm showed good reliability and selectivity when simulating different types of faults inside and outside the protection zone. The presence of the DC component in the fault current has no significant effect on the operation of the algorithm. Also, the algorithm showed good results when changing the operating conditions of the line, as well as when changing the parameters of the active network. The algorithm testing was also performed with fault recordings taken from protective devices. The obtained results confirmed the good properties of the presented algorithm and in that way, the practical application was enabled.

The advantage of the presented algorithm over commercial solutions is that the operation characteristic is directed and sensitive, whether the faults are near or remote. Also, the algorithm does not require additional filtering of DC component, which gives it another essential advantage.

Conflict of interest

The authors declare that they have no conflict of interests.

Kang SH, Lee DG, Nam SR, Crossley PA, Kang YC (2009) Fourier transform-based modified phasor estimation method immune to the effect of the DC offsets. IEEE Trans Power Deliv 24(3):1104–1111
Lee DG, Oh YJ, Kang SH, Han BM (2009) Distance Relaying Algorithm Using a DFT-based Modified Phasor Estimation Method. IEEE Bucharest Power Tech 2009, Bucharest, Romania, June 2009, pp 1–6
Yu CS, Huang YS, Jiang JA (2010) A full- and half-cycle DFT-based technique for fault current filtering. IEEE Int. Conf. Industrial Technology (ICIT), Via del Mar, Chile, May 2010, pp. 859–864
Morais AP, Cardoso G Jr, Mariotto L, Ferreira GD (2011) Numerical distance relaying algorithm based on Mathematical Morphology and Least-Squares Curve Fitting method. Electr Power Syst Res 81(5):1144–1150
Liu S, Jin X, Gokaraju R (2016) High speed distance relaying using least error squares method and testing with FPGA. IET Gener Transm Distrib 13(16):3591–3600
Liang F, Jeyasurya B (2004) Transmission line distance protection using wavelet transform algorithm. IEEE Trans Power Deliv 19(2):545–553
Osman AH, Malik OP (2004) Transmission line distance protection based on wavelet transforms. IEEE Trans Power Deliv 19(2):515–523
Silva KM, Neves WLA, Souza BA (2010) Distance protection using a wavelet-based filtering algorithm. Electr Power Syst Res 80(1):84–90
Zubić S, Balcerek P, Zeljković Č (2017) Speed and security improvements of distance protection based on Discrete Wavelet and Hilbert transform. Electr Power Syst Res 148:27–34
Liang Y, Li W, Lu Z, Xu G, Wang C (2020) A new distance protection scheme based on improved virtual measured voltage. IEEE Trans Power Deliv 35(2):774–786
Zamora-Mendez A, Paternina MRA, Vazquez EM, Ramirez JM, la Serna O JA (2016) Distance relays based on the Taylor–Kalman-Fourier filter. IEEE Trans Power Deliv 31(3):928–935
Al-Emadi NA, Ghorbani A, Mehrjerdi H (2016) Synchrophasor-based backup distance protection of multi-terminal transmission lines. IET Gener Transm Distrib 10(13):3304–3313
Ivanković I, Brnobić D (2021) Distance Protection Based on the Synchrophasor Data in Control Room..9th Eur. Conf. Ren. Energy Sys., Istanbul, Turkey, April 2021, pp. 1–6
Zubić SJ, Djurić MB (2012) A distance relay algorithm based on the phase comparison principle. Electr Power Syst Res 92:20–28
Wen M, Chen D, Yin X (2014) A Novel Fast Distance Relay for Long Transmission Line. Int J Electr Power Energy Syst 63:681–686
Vianna PL, Junior GM (2022) Time-domain distance protection of transmission lines based on the conic section general equation. Electr Power Syst Res 205:107740
Chavez JJ, Popov M, López D, Azizi S, Terzija V (2021) S-Transform based Fault Detection Algorithm for Enhancing Distance Protection Performance. Int J Electr Power Energy Syst 130:106966
Chen Y, Wen M, Wang Z, Yin X (2022) A novel instantaneous value based incremental quantities distance protection for AC transmission lines. Int J Electr Power Energy Syst 135:107385
Sanaye-Pasand M, Khorashadi-Zadeh H (2006) An extended ANN-based high speed accurate distance protection algorithm. Int J Electr Power Energy Syst 28(6):387–395
Santos RC, Senger EC (2011) Transmission lines distance protection using artificial neural networks. Int J Electr Power Energy Syst 33(3):721–730
Das B, Reddy JV (2005) Fuzzy-logic-based fault classification scheme for digital distance protection. IEEE Trans Power Deliv 20(2):609–616
Khorashadi-Zadeh H, Li Z (2007) Transmission line distance protection using ANFIS and positive sequence components. Bulk Power Syst. Dyn. and Control-VII. Revit. Operat. Reliab. iREP Symp., Charleston, SC, USA, August 2007, pp. 1–9
Samantaray SR, Dash PK, Panda G (2007) Distance relaying for transmission line using support vector machine and radial basis function neural network. Int J Electr Power Energy Syst 29(7):551–556
Mohanty SK, Karn A, Banerjee S (2020) Decision Tree Supported Distance relay for Fault Detection and Classification in a series compensated line. Proc. of 2020 IEEE Int. Conf. on Power Electr. Smart Grid and Ren. Energy (PESGRE2020), Cochin, India, April 2020, pp. 1–6
Vázquez E, Castruita J, Chacón OL, Conde A (2007) A New Approach Traveling Wave Distance Protection - Part I: Algorithm. IEEE Trans Power Deliv 22(2):795–800
Franca RLS, Junior FCS, Honorato TS, Ribeiro JPG, Costa FB, Lopes FV, Strunz K (2021) Traveling wave-based transmission line earth fault distance protection. IEEE Trans Power Deliv 36(2):544–553
Stojanović ZN, Djurić MB (2011) The algorithm for directional element without dead tripping zone based on digital phase comparator. Electr Power Syst Res 81(2):377–383
Stojanović ZN, Djurić MB (2013) An algorithm for directional earth fault relay with no voltage inputs. Electr Power Syst Res 96:144–149
Krstivojević JP, Djurić MB (2014) A new method of improving transformer restricted earth fault protection. Adv Electr Comput Eng 14(3):41–48
Ostojić MM, Djurić MB (2018) Out-of-step protection of synchronous generators based on a digital phase comparison in the time domain. IET Gener Transm Distrib 12(4):873–879
Ostojić M, Djurić M (2018) The algorithm for the detection of loss of excitation of synchronous generators based on a digital-phase comparator. Electr Eng 100(2):1287–1296
Ostojić MM, Djurić MB (2018) The algorithm with synchronized voltage inputs for islanding detection of synchronous generators. Int J Electr Power Energy Syst 103:431–439
Ostojić MM, Stojanović ZN (2021) An algorithm with voltage inputs for detecting conductor breaks in radial distribution networks. Int Trans Electr Energ Syst 31(12):e13195

Download PDF

Journal Publication

published 05 Jul, 2023

Read the published version in Electric Power Systems Research →

Version 1

posted

You are reading this latest preprint version

A new algorithm of distance protection based on the change in phase angle of the voltage

Status:

Journal Publication

Version 1

Abstract

Figures

1. Introduction

2. Algorithm Formation Criteria

3. Formation Of The Input Signals

3.1 Single phase ground fault

3.2 Phase to phase fault

4. The Proposed Algorithm

5. Testing Of The Algorithm

6. Conclusion

Declarations

References

Status:

Journal Publication

Version 1