1 Introduction

In power systems, single line-ground faults are the most frequent faults. Particularly, if a single line-ground fault occurs with fault resistance, it may mal-operate the relays protecting that particular zone. Sometimes, this causes an unnecessary tripping of healthy lines, and it may lead to cascading failure. So, an extensive research is required to be done in the area of power system protection. Initially, a two end phasor estimation based line protection algorithm is introduced in [1]. Later, a fault detection index based algorithm [2,3,4] is suggested. In [5,6,7,8,9,10], synchronized voltage and current measurements obtained from the both ends of a line were used to determine the fault. Considering arcing, fault location algorithm was proposed in [11, 12]. Later, authors found that the decaying D.C. component present in transient current is having a significant effect in estimating the fault [13, 14]. So, authors propose an algorithm for removing decaying D.C component to detect faults in the transmission system accurately in [15]. After, a mimic filter is designed to remove the D.C. offset [16]. A method based on the recursive relation between even and odd samples was proposed in [17] to develop a modified DFT algorithm to identify faults. Later, an iterative current filtering technique is suggested in [18]. Even though all these methods were accurate enough, they were compromised with time because of their complexity. Moreover, they haven't suggested any idea to improve the immunity of protection algorithm to the resistance involved faults. Later, [19, 20] outline a fault detection method for resistance faults by compensating resistance calculated from the power at relaying point. Next, high-resistance faults are identified by differentiating the active power flow [21]. Recently, by calculating the real power drawn by the fault resistance the in-line fault has been found [22]. Authors [23, 24] have improved the immunity of protection by adjusting the relay setting values. But, all the above methods haven't used the voltage phasor data for their analysis even though they have succeeded in detecting the ground faults involving fault resistance.

Very recently, a line protection method is proposed by comparing the voltage phasors [25]. But significantly, this method has not considered synchronized data for its estimation. The synchrophasor measurement data enhances the transmission line protection to very greater extent [26,27,28,29]. Unlike above methods, the proposed paper aims at identifying the ground faults involving high fault resistance using synchronized voltage phasor data from the relaying point. This scheme calculates the phase difference between relay point voltage and fault point voltage based on the relation between negative sequence of relay point current and fault point current. After, to identify fault existence in the line, the calculated phase difference between relay point voltage and fault point voltage will be compared with the set point voltage phase referred from relay point voltage phase.

The paper is well organized as stion II gives the clear idea about the fault identification methodology. Stion III discusses the effectiveness of this technique by showing the results. Stion IV concludes the papers.

2 Proposed Phase Comparison Technique

2.1 Single-Sourced System

Let us consider the system as shown in Fig. 1. Eg is the source voltage estimated by the PMU placed at relay point r. And, zg is the source impedance, zset is the set-point (or zone) impedance which is for the portion of the line Rs, zline is the total line impedance.

Fig. 1
figure 1

Test system

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For a single-phase to ground fault at a point f, the sequence network becomes as shown in Fig. 2. As shown in Fig. 2, the fault sequence currents if1, if2, if0 starts flowing through their respective sequence networks with zg1, zg2, zg0 as sequence impedances of the source, and zline1, zline2, zline0 as sequence impedances of the complete line. Parameter x represents the distance to the fault point from the relay end and is expressed as the percentage of the complete line length. Hence, the phase difference between the relay point voltage and fault point voltage can be given as,

$$\begin{aligned} \theta_{rf} & = \arg \left( {\frac{{\overline{E}_{r} }}{{\overline{E}_{f} }}} \right) \\ & = \arg \left( {\frac{{\overline{E}_{r} }}{{\overline{i}_{f} }}} \right) \\ \end{aligned}$$
(1)
Fig. 2
figure 2

Sequence network

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As, during the fault, the phase of negative sequence current at fault point is same as that of the negative sequence current at relaying point [30] and the phase of fault current is same as that of fault point sequence current, the phase of fault point current is equivalent to that of sequence current at relaying point. So, this paper uses the phase of negative sequence (ir2) current at relaying point instead of the phase of fault point current. So, the proposed method which is a phase comparison-based technique, it requires only the phases of the Relay end voltage, fault point voltage and set point voltage to be measured.

$$= \arg \left( {\frac{{\overline{E}_{r} }}{{\overline{i}_{r2} }}} \right)$$
(2)

Here \(\overline{E}_{r}\) and \(\overline{i}_{r}\) are the synchronized voltage and current phasors measured at relaying point r. Similarly, \(\overline{E}_{f}\) and \(\overline{i}_{f}\) are the fault voltage and fault current at point f. For different values of Rf at point f, \(\overline{E}_{f}\) moves along the arc.

If \(\overline{E}_{s}\) is the set point voltage, the phase difference between relay point voltage and set point voltage can be given as,

$$\theta_{rs} = \arg \left( {\frac{{\overline{E}_{r} }}{{\overline{E}_{s} }}} \right)$$
(3)

where

$$\overline{E}_{s} = (\overline{E}_{r} - \overline{i}_{r} .z_{set} )$$
(4)

So,

$$\theta_{rs} = \arg \left( {\frac{{\overline{E}_{r} }}{{(\overline{E}_{r} - \overline{i}_{r} .z_{set} )}}} \right)$$
(5)

2.2 Double-Sourced System

In a double-sourced system, if a single phase to ground fault occurs, the fault point voltage \(\overline{E}_{f}\) lags behind \(\overline{i}_{r}\). This is due to the contribution of current from the other source. This causes an angular difference between \(\overline{i}_{r}\) and \(\overline{{\mathrm{i} }_{\mathrm{f}}}\) \(\overline{i}_{f}\). Now, the phase difference between the relay point voltage, \(\overline{\mathrm{E}}\mathrm{r }\) \(\overline{E}_{r}\) and fault point voltage, \(\overline{E}_{f}\) becomes,

$$\begin{gathered} = \arg \left( {\frac{{\overline{E}_{r} }}{{\overline{i}_{r} }}} \right) + \arg \left( {\frac{{\overline{i}_{r} }}{{\overline{i}_{f} }}} \right) \hfill \\ = \arg \left( {\frac{{\overline{E}_{r} }}{{\overline{i}_{r} }}} \right) + \arg \left( {\frac{{\overline{i}_{r} }}{{\overline{i}_{r2} }}} \right) \hfill \\ \end{gathered}$$
(6)

It says that the effect of load/source current from the sond source will be accounted by means of the sond term in the above Eq. (6).

3 Condition for Fault Detection

Under the no-load condition, when a single-phase to ground fault occurs in between relay point and set-point, the position of fault current phasor \(\overline{{\mathrm{i} }_{\mathrm{f}}}\) \(\overline{i}_{f}\) will be same as relay point current phasor \(\overline{{\mathrm{i} }_{\mathrm{r}}}\) \(\overline{i}_{r}\). Hence, unlike in Fig. 3, the phasor \(\overline{E}_{f}\) will be in-phase with \(\overline{{\mathrm{i} }_{\mathrm{r}}}\) \(\overline{i}_{r}\). Then the estimated set point voltage \(\overline{{\mathrm{E} }_{\mathrm{s}}}\) \(\overline{E}_{s}\) will lag behind \(\overline{{\mathrm{i} }_{\mathrm{r}}}\) \(\overline{i}_{r}\). But under loaded condition, the phasor \(\overline{E}_{f}\) lags behind \(\overline{{\mathrm{i} }_{\mathrm{r}}}\) \(\overline{i}_{r}\). As shown in Fig. 3, whenever a single-phase to ground fault occurs at point f, then the fault voltage lags immediately behind the relay point voltage \(\overline{E}_{r}\). So, the condition for the existence of fault inside set point s is,

$$\theta_{rf} \le \theta_{rs}$$
(7)
Fig. 3
figure 3

Voltage phasor diagram during phase-ground fault

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If the fault is beyond the set point, then \(\overline{E}_{f}\) lags immediately behind the set point voltage \(\overline{{\mathrm{E} }_{\mathrm{s}}}\) \(\overline{E}_{s}\). So, the condition becomes,

$$\theta_{rf} > \theta_{rs}$$
(8)

Finally, the fault protection criterion is as given below:

Condition 1: θ≤ θrf r, if fault is in-between relay and set points

Condition 2: θ> θrf r, if fault is beyond set points

4 Results and Discussions

The simulation was carried out in EMTDC/PSCAD environment. The detailed parameters for the simulated system model are given below.

Source impedance: 0.1 Ω,

TLine model: frequency dependent (phase) model,

Voltage: 230 kV,

Line length: 100 km,

Tower: 3L1,

Conductor name: chukar,

Conductor_configuration: 3wire, unsymmetrical,

Height of conductor: 30 m,

Horizontal spacing between conductors: 10 m,

Conductor_radius: 0.0203454 m,

Line_resistance: 0.140696 E-03 [ohm/m],

Line_reactance: 0.783171 E-03 [ohm/m],

Shunt_conductance: 1.0E-11 [mho/m].

The proposed scheme, as described in Fig. 4, after calculating the synchronized voltage and current phasors at the master relay point, it determines the change in current. Based on the tolerance value it calculates the phase angles of the negative sequence current, relay point voltage and zone-point voltage. Then, it identifies the existence of zone fault. The fault is simulated at 1 s. The zone is selected as 80 kms of the line rt.

Fig. 4
figure 4

Flow chart of the proposed protection scheme

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4.1 Under Different Fault Resistances

The increase in fault resistance makes the relay to be under reach. It also affects the directional feature of mho relay. This effect may be less significant if the fault location comes closer to relay point. At a certain value of fault resistance, some of the mho elements become non- directional.

For a single phase-ground fault at different locations in the line rt, the simulation results obtained for different fault resistances under different system conditions are presented below. Under no-load, the fault identification results for different fault resistances at different locations considering phase angle variations at end r are given in Tables 1 and 2. The simulation results considering RL-load are given in Tables 3, 4 and 5. From the tables, it is understood that whenever fault lies after 80 kms (which is the set point for the zone), the phase difference between the relay point voltage and fault point voltage (θrf) is becoming greater than the phase difference between relay point voltage and set point voltage (θrs). The correctness of the suggested technique can be seen from Figs. 5, 6 and 7. These results show that the algorithm identifies the fault within 14.6 ms irrespective of the fault resistance.

Table 1 Performance of proposed methodology for the fault resistance of 100 Ω under no-load
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Table 2 Performance of proposed methodology for the fault resistance of 1000 Ω under no-load
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Table 3 Performance of proposed methodology for the fault resistance of 100 Ω under RL-load, with r-side phase angle of 30°
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Table 4 Performance of proposed methodology for the fault resistance of 500 Ω under RL-load, with r-side phase angle of 30°
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Table 5 Performance of proposed methodology for the fault resistance of 100 Ω under RL-load, with r-side phase angle of 30°, fault inception angle of 15°
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Fig. 5
figure 5

Results for No-load and 100 Ω fault resistance at a 10 kms, b 30 kms, c 60 kms, d 90 kms

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Fig. 6
figure 6

Results for No-load and 1000 Ω fault resistance at a 10 kms, b 30 kms, c 60 kms, d 90 kms

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Fig. 7
figure 7

Results for RL-load and 1000 Ω fault resistance at a 10 kms, b 30 kms, c 60 kms, d 90 kms

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As the occurrence of the fault is to be checked, the condition Δi ≥ 0.1I is checked first. Here, Δi is the jump in the current sampling, 0.1I is the threshold value of the current jump.

4.2 Under Different Fault Resistances Considering Double-Sourced System

If the angle δ =  + 100, the line end r becomes sending end, and for δ = -− 100 the same end becomes receiving end. Line loading depends on the phasor difference between the two line ends. More the phasor difference heavily loaded the line is. Tables 6, 7, 8 and 9 gives the performance of the proposed algorithm considering a double-sourced system under different fault resistances and system conditions. From the Figs. 8 and 9, it is clear that the proposed algorithm could detect the fault in any double-sourced system independently with the fault resistance.

Table 6 Performance of proposed methodology for the double sourced system with fault resistance of 100 Ω, with r-side phase angle of − 20°
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Table 7 Performance of proposed methodology for the double sourced system with fault resistance of 100 Ω, with r-side phase angle of 20°
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Table 8 Performance of proposed methodology for the double sourced system with fault resistance of 500 Ω, with r-side phase angle of − 20°
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Table 9 Performance of proposed methodology for the double sourced system with fault resistance of 500 Ω, with r-side phase angle of 20°
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Fig. 8
figure 8

Results for Double-sourced, 100 Ω fault resistance and δ1 = 200, δ2 = 00 at a 10 kms, b 30 kms, c 60 kms, d 90 kms

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Fig. 9
figure 9

Results for Double-sourced, 100 Ω fault resistance and δ1 = -200, δ2 = 200 at a 10 kms, b 30 kms, c 60 kms, d 90 kms

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4.3 Under Different Fault Resistances Considering Double-Sourced System and Fault Inception

The worst fault-induced transient condition in both voltages and currents in SLG faults corresponds to the fault striking in the voltage peak. The fault-induced transients are more severe for the fault inception angles 300, 900 and 1500. As, the severity of fault-induced transients depends on point of fault striking in the voltage peak and the Synchronized phasor data is an accurate measure of the phase information of the voltage wave, the proposed phase-angle based fault detection algorithm detects the fault independently with fault-inception angle under any fault resistances. The accuracy of this technique for different fault resistances considering fault-inception at 150 is given in Fig. 10.

Fig. 10
figure 10

Results for Double-sourced, 100 Ω fault resistance, Fault inception angle: 150 and δ1 = 200, δ2 = 00 at a 10 kms, b 30 kms, c 60 kms, d 90 kms

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Since the distance protection is highly sensitive to the fault and/or source impedance, it may either not operate for the faults within the zone of protection or mal-operate for the faults outside zone. But, the proposed method makes, if it is applied in-conjunction with distance relay, the distance protection scheme immune to the source and/or fault resistance.

5 Conclusion

In this paper, a novel scheme of voltage phase comparison based single line-ground fault detection is proposed based on synchronized phasor data. The simulation results mean that the proposed scheme has following advantages:

It is highly immune to fault resistance. It differentiates the in-zone fault from out-zone faults irrespective of fault resistance. So, the problem of relay mal-operation caused by fault resistance is answered.

The fault identification is unaffected by the system operation and load conditions. It means the algorithm works satisfactorily under any load and/or power flow direction.

Finally, the reduction in the time of fault identification significantly improves the transient stability of the system. It is highly significant in power system protection practices.