1. Introduction
1.1. Motivation
Distribution networks are important because of their interesting properties and conditions, such as span, dispersion, unbalanced loads, and non-homogeneity. They are also important because they are the last point of power delivery to consumers. Distribution networks are vulnerable to different faults which affect the system’s reliability, security, and quality. Therefore, maintaining system stability, minimizing interrupted consumers and damaged networks as quickly as possible are very important. Therefore, fault location techniques play a vital role in repairing and fixing system faults in the least amount of time possible [
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14].
All of the fault location methods which have been presented so far have been developed for single circuit distribution networks, and double circuit networks have unfortunately not been addressed. Past studies on fault location have usually used a short line model and neglected the effect of capacitors. However, recent papers have used more complete models, such as the medium line model (π) or the widespread line model for fault location. Needless to say, they only address single circuit lines and not double circuit lines. In double circuit lines, the mutual effects of the lines on each other and power outages are greater than single circuit lines. Because of the high amount of consumers, if power outage occurs on the lines there will be a vast amount of undistributed power (energy). Most of the double circuit lines are overhead cables with no insulator.
If a power outage occurs somewhere along the power lines, it must be considered that the fault could be in either of the adjacent lines. Thus, locating faults in double circuit lines is more complicated than in single lines. Because of the complexity and specific conditional and operational features, fault location in double circuit lines remains a challenge to this day.
1.2. Literature Review and Challenges
Since 1980, fault location algorithms have seen substantial development, particularly methods that are based on impedance. At the beginning of these developments, power systems were modeled based on symmetric geometric lines and analyzed based on symmetric parts which were specifically used for underground systems (e.g., the method used in [
1,
2]). Reference [
3] uses symmetric factors based on the line’s parallel admittance which is also used only for underground distribution networks. In [
4], the accuracy was improved significantly by considering the effect of capacitors. However, this can only be used for underground systems. In [
5], a method was proposed for determining the distance to a single-phase fault in overhead distribution cables based on the base frequency, voltage, and current at the beginning of the feeder. In this method, by using the short line model and series and parallel analysis, the impedance of different routes were evaluated. Salim [
6] proposed a new method for fault location by considering a π line model. This method uses the corrected impedance, and a quadratic equation in accordance with the fault distance is obtained. By using this method, the fault detection accuracy was improved and maximum error percentage was reported to be 1.58%. In [
7], a new and precise fault location algorithm was provided by considering the effect of capacitors. This method has a higher accuracy than previous methods. The downside of this method is that it can only be used for single circuit distribution networks.
In [
8], special attention was given to the dynamic model. In this work, the fault distance was estimated through the load amount. The load amount was calculated from the load factor and power factor. In [
9], a method was given to determine the specific fault location since there might be more than one fault in the system. As a result, two approaches were used to determine the real fault’s location. The first approach compares the measured and recorded voltage samples, and the second approach uses the voltage’s frequency spectrum.
A hybrid fault location method is presented for single line to ground fault in [
15]. At first, the possible fault locations are determined using an impedance-based fault location method. Then, the faulty section or the main fault location among the determined possible fault locations is strongminded using a voltage sag matching algorithm. In [
16], the fault location in the four-wire lines is determined by improving the algorithm presented in [
15].
A time domain technique is presented for locating faults in a power distribution network (PDN) [
17]. It uses the voltage and current at the beginning of the feeder and distributed generator DG place. Furthermore, an iterative method is presented to solve the fault location problem. The need for a high sampling rate is the drawback of this method.
The self-healing concept is used for locating faults in PDN with DG in [
18]. In this paper, the fault location algorithm requires the transient and steady state of signals, load flow algorithm, and synchronization angle.
Furthermore, the important papers in this topic are reviewed and the characteristics and details are shown in
Table 1.
1.3. Approach and Contributions
In this paper, an improved impedance-based method is proposed for fault location in double circuit power distribution networks. In the suggested method, a collection of equations are derived to prove a new quadratic equation for locating fault in double circuit lines. The method is applied using only the recorded voltage and current at the beginning of the feeder. In this method, after distinguishing the short circuit fault, the voltage and current of each section of the distribution network is calculated through Kirchhoff’s voltage law KVL and Kirchhoff’s current law (KCL) equations, and the location of the fault is determined using the proposed method. In the proposed method, the capacitor effect and the mutual effect of the lines on each other is considered. The suggested method is tested in a thirteen-node system using MATLAB simulation and the results confirm the method’s accuracy and validity. The obtained results show that the accuracy of the proposed method is very high and the sensitivity is very low in different fault conditions.
1.4. Paper Organization
The article structure is as follows:
Section 2 explains the suggested method.
Section 3 presents the developed fault location algorithm.
Section 4 uses the results from the simulation to evaluate the precision and accuracy of the proposed method.
Section 5 concludes the paper.
2. The Proposed Method
The distribution network consists of different parts. In this article, the line is considered as the part between two buses. By using a π line model,
Figure 1 shows a single-line diagram of each section for the positive, negative, and zero sequences of a double circuit network for a normal fault in point
.
This table is an extended version of the one in [
18]:
According to
Figure 1b–d and by defining by (1) to simplify by (3), positive, negative, and zero sequence voltages in fault point
are obtained, and by using Fortescue’s transformation matrix (by (2)) as (
abc) by (3) is produced:
Now, by defining
E,
G,
H, and
L,
can be obtained from Equation (5):
The most general fault model is shown in
Figure 2, which models faults such as single phase to the ground, two phases to the ground, and three phases to the ground. In this section, a quadratic equation is suggested, and it is proven that it can determine the distance of ground faults with a suitable accuracy. By using the equation below, the voltage at the point of the fault is calculated:
where
a,
b, and
c are the phases of the faults impedance
, as shown in
Figure 2. The above equation is only suitable for fault phases that have a current not equal to zero. By inserting Equation (6) in to Equation (5) for each
k-phase, we will have:
where
is the impedance and
is the current of the
k-phase.
As shown in
Figure 2,
is the fault’s current. Considering the fault’s impedance as a pure resistance and by separating Equation (7) into two parts (real and imaginary), Equation (8) is obtained:
In the above equation, index
r indicates the real part and index
i indicates the imaginary part of these variables. Equation (8) can be used for equation matching and to separate the fault resistance
from each faulted phase; thus, a group of
n equations are obtained which are independent of
and dependent on
x,
, and
.
By multiplying
to Equation (9) and completing the algebraic calculations, the below equation is obtained:
In this equation,
shows the real part,
shows the imaginary part, and
indicates the conjugate of the complex numbers. For each
k-phase, Equation (10) can be re-written:
Based on the equation below
and if we consider
as the fault’s resistance, the next equation is derived:
where
is a group of faulted phases that consist of the system’s (a), (b), and (c) phases. In a three-phase system, there are seven different states of faults, including single-phase, two-phase, and three-phase. By replacing Equation (8) into Equation (12) and by making the algebraic changes in the mentioned equation, the final fault location equation for ground-faults, named the general ground-fault equation, is obtained:
It is important to mention that this is a fault location equation, and it is used for determining the fault distance. Therefore, it needs the three-phase voltage and current in the post, line parameters (series impedance and parallel admittance), and the faults current (because the fault current cannot be determined in local station, Equation (4) is used to calculate the coefficients of Equation (13)). As a result, an equation is needed to estimate the fault current, which will be provided in
Section 3.
3. The Developed Fault Location Algorithm
The developed method in this paper considers the mutual effects of the lines on each other. It also considers the existence of central loads and the main and subsidiary branches for a double circuit. The details of the algorithm are given below:
- (1)
Fault detection.
- (2)
Determining the fault type.
- (3)
Estimation of the fault current using the equation below:
where
and
are the measured currents during and before the fault in the local relay.
- (4)
Determining the fault’s distance from the general fault location equation (Equation (13)).
- (5)
Determining the exact physical location of the fault.
- (6)
Checking the convergence of
using Equation (15):
For
> 1, the tolerance
δ is predefined and
n is the number of repetitions.
- (7)
If is convergent with the analyzed part of the last section, then is the fault’s location and go to the next step; if it is convergent with a location beyond the current location, then we update and in the system’s next bus (changing the reference bus) and return to section one.
- (8)
Calculating the fault’s point voltage by using Equation (5), , voltages and currents of the bus in the correct analyzed upstream section (k in and refers to the reference bus).
- (9)
Updating the fault’s downstream current in the faulted phases using the calculated voltage of the fault point and based on Equation (16), finally
is obtained using Fortescue’s conversion as seen in Equation (20).
In the above equation, in series state one and two, is obtained from Equation (17), in which is the impedance connected to the -bus. Additionally, for obtaining the equivalent impedance in zero series state, Equations (18) and (19) are obtained from Y-Δ and Δ-Y conversions, and finally is derived:
- (10)
Updating the faults current by using Equation (21):
where
is the upstream current of the faulted point according to
Figure 1.
is obtained using Fortescue’s conversion.
- (11)
Return to step four.
It is known that the distribution feeders are distributed in single circuit or double circuit. This depends upon the load demands and its peak. These loads can be unbalanced and distributed in the feeder. Therefore, in the proposed method, the KVL and KCL matrices are used. The symmetrical components are taken into account in the proposed method just for calculating the updated downstream current in the faulty section. From Equations (3), (6) and (13), it can be seen that the unbalanced feeder can be analyzed because its effect on the current and voltage is known. Furthermore, in practice, the phases voltage and current can be obtained from the Over Current/Earth Fault and Over/Under Voltage relay which is installed at the beginning of the feeder.
Determining a Physical Solution
The proposed equations for fault location are second-order polynomial equations in terms of x, where x represents the fault’s distance. As a result, two new distances for the fault are obtained for each iteration of the explained algorithm. One of them is a positive and is coordinated with the section under evaluation, and the other one is purely mathematical and has no physical meaning.
The fault’s distance
x is obtained from the following equations, which show the correct physical solution:
The flowchart of the proposed method is shown in
Figure 3.
5. Conclusions
Double circuit lines are gaining popularity in distribution networks, mainly due to the increasing loads and the lack of public corridors. Automatic fault location in distribution networks is challenging, and it is even more difficult in double circuits than in single circuit lines. In this paper, a new fault location algorithm for double-circuit distribution networks is presented. In the proposed algorithm, a new quadratic equation is obtained using the power system equations and KVL and KCL. In this method, the voltage and current from the beginning of the feeder are used and the new equation is proved for calculating the equivalent impedance of each section. It is calculated using two over change the Fortescue transform to abs and upside. In the presented technique, the π line model, the lines’ capacitors effect, and the mutual effect of the lines on each other are considered. To the best of our knowledge, the improved algorithm is the first of its kind which supports double-circuit distribution networks. In this method, for each section of the distribution feeder, the proposed iterative algorithm is run and the location of the fault is determined. The maximum errors recorded from the faults were in T-offs, especially at the end of the T-offs. In our study, different fault distances, different resistances, and different inception angles were considered. The simulation results show that the maximum recorded error was 0.65%, which confirms a satisfactory performance.
For the future, our focus will be on the effect of DG on fault location in double circuit power distribution networks. We will also try to obtain a new and more accurate equation for locating faults in double circuit power distribution networks.