Accurate Impedance Based Fault Location

Algorithm Using Communication between

Protective Relays
Cezary Dzienis, Marie Washer
Yilmaz Yelgin Jean-Claude Maun
EM EA PRO D École Polytechnique de Bruxelles
Siemens AG Université Libre de Bruxelles
Berlin, Germany Brussels, Belgium
cezary.dzienis@siemens.com marie.washer@ulb.ac.be

Abstract— The reactance method with fault resistance the faulty loop’s reactance, which is linearly proportional to
separation has been developed in order to determine as precisely the distance to the fault.
as possible the impedance of a fault loop in a transmission or
distribution power system line. This method has commonly been
used for impedance calculation in case of a single phase-to-earth
fault in diverse power system protection applications. New
developments in this area have shown that the extension of the
method to multi-phase faults is not only possible but also of
practical relevance. This research consists in an improvement of
this calculation method using data from both the own and the
remote line end. This approach uses communication between two Figure 1. Fault with transition resistance in a double side supplied line
measurement units e.g. protection relays, which have the
advantage of not requiring a precise synchronization with each
A faulty doubly in-fed line is first considered in the form of a
other. The additional time invariant parameters of the power
system, acquired by each device and transferred to the remote single-phase system (Fig. 1). For the short circuit, a purely
end, allow an exact computation of the fault reactance and fault resistive fault is adopted. If the faulty loop includes a fault
resistance. In this paper, the derivation of this novel approach as resistance RF, it is not possible to calculate the exact reactance
well as experimental results in a fault location application are value using only the measurements from one side A or B.
presented. Indeed, the unknown fault current IF is necessary for the
calculation. Applying Kirchhoff’s Voltage Law (KVL) to the
Keywords— Fault Location, Impedance Measurement, Power system from the point of view of side A results in (1), which is
System Protection, Transmission / Distribution Line the base to extract the fault reactance and resistance:

I. INTRODUCTION U A, Ph  Z Fault  I A, Ph  RF  I F (1)

Fault location algorithms give an estimation of the distance
between the point of measurement at the device (mostly In order to eliminate from (1) the unknown voltage drop on
protective relay) and the point of a short circuit (fault) in a the transition resistance, which depends on the fault current,
transmission or distribution line. The maintenance effort of the the so called load decoupled compensation quantity IA,Cmp and
line after an already cleared temporary fault and the recovery compensation factor δA,B are introduced. IA,Cmp corresponds to
time of the line after a permanent fault both depend on the the fault current as it is seen from side A, and δA,B is an
accuracy of the fault location. As a result, the fault location extension factor for the double in-fed line. The factor δA,B
function contributes indirectly to an improvement in quality corresponds to the phase shift due to the consideration of the
and availability of electrical energy. Accuracy of the fault remote end and is therefore the most influent term of the
location depends on the chosen algorithm and hypothesis for compensation. The product of these two quantities gives an
the calculation itself, as well as on the complexity of the estimation of the fault current IF. Therefore, it is considered
power system and on fault conditions. that this term has the same electric phase angle and magnitude
This paper focuses on the double-ended impedance based fault as the fault current IF. Equation (1) is multiplied by the
location algorithm, which is derived from the reactance conjugate of these combined quantities. The term reflecting
method with fault resistance separation. The fault location the resistive voltage drop in (1) becomes a pure real number
method described in this paper is based on the computation of and can be eliminated by considering only the imaginary part.
 Im[U A, Ph  I A,Cmp  
* *
A, B ] measured on one network side, appropriate compensation
(2) factors must be introduced.
Im[ Z Fault  I A, Ph  I A,Cmp  
* *
A, B ]
A B

ZA,1 mZL,1 (1-m)ZL,1 ZB,1

positive seq.
Introducing the line’s angle φ and thereby isolating the
reactance XFault from the fault impedance Zfault, equation (3) is I1
obtained. This result is proportional to the fault location. IF/3
ZA,2 mZL,2 (1-m)ZL,2 ZB,2
3RF
sin   Im[U A, Ph  I A,Cmp   A, B ]
* *
negative seq.
X Fault 
Im[e j  I A, Ph  I A, Cmp   A, B ]
* *
(3) I2

The compensation quantity and extension factor can further be ZA,0 mZL,0 (1-m)ZL,0 ZB,0
used to determine the fault’s resistance RF. Replacing the fault zero seq.

current by the product of these two quantities in (1), and

I0
multiplying by the conjugated product of the fault impedance
and phase current ZFault* IA,Ph*, the voltage drop on the fault Figure 2. Single phase-to-earth fault with fault resistance (representation in
impedance can be eliminated and the fault resistance can be symmetrical components – double side supplied line)
extracted:
This compensation factor can be derived from the system
Im[U A,Ph  e  j
I
*
] impedances. Applying the KVL for the zero sequence circuit,
RF   j
A,Ph
the following expression can be obtained:
Im[ I A,Cmp   A,B  e
*
I
A,Ph ] (4)
Z A,0  m Z L,0  I A,0  (1 m)  Z L,0  Z B,0  I B,0 (7)
II. IMPEDANCE MEASUREMENT IN POWER SYSTEMS
From the sequence equivalent circuit one can conclude:
Each fault type in the symmetrical electrical power system can
be described with symmetrical components. The zero-, I F  3  ( I A, 0  I B , 0 ) (8)
negative- and delta-positive- sequence components are
independent from the load flow. This property is used to Describing the unknown current IB,0 of the opposite side with
introduce compensation quantities and thereby to eliminate the the measured current IA,0 of the own side (7) and substituting it
voltage drop on the fault resistance in order to achieve a into (8), the following expression can be written:
precise reactance value. The previously introduced extension
factor is calculated based on the symmetrical components  Z A, 0  m  Z L , 0 
I F  3I A, 0   1
 (1  m)  Z  Z  
equivalent circuit as well.
The phase voltage UA,Ph and phase current IA,Ph respectively  L,0 B ,0  (9)
represent the voltage and current in the considered single- I F  I A,Cmp  A, B
phase fault loop. In the case of a phase-to-earth fault, the earth
compensation factor k0 is introduced, similarly to the As a result, the compensation factor A,B and compensation
conventional fault location algorithm, to take into account the current IA,Cmp=3IA,0 can be identified. An analogue
earth return path, as shown in (5)-(6). consideration can be carried out for the negative and delta-
positive components.
sin   Im[U A,Ph  E  I A,Cmp   A,B ]
* * For phase-to-phase faults, the voltage and current to take into
X Fault  account consist in the voltage (respectively current) difference
Im[e j  I A, Ph  k 0 I A,E  I A,Cmp   A, B ] (5)
* *
between the two concerned phases. This method can be
Im[U A, Ph  e j  I A, Ph  k 0 I A, E  ]
* generalized for phase-to-phase faults with earth [6], [7]. The
RF  (6) corresponding reactance and resistance are given in (10) and
Im[ I A,Cmp   A, B  e j  I A, Ph ]
*
(11).
sin   Im[U A,Ph1Ph 2  I A,Cmp   A,B ]
* *
In Fig. 2, the single phase to earth fault in symmetrical X Fault  (10)
Im[e j  I A,Ph1 Ph 2  I A,Cmp   A, B ]
* *
components is represented. It can be concluded that the fault
current IF can be reflected by positive, negative or zero
sequence current. Since the negative and zero sequence Im[U A,Ph1Ph 2  e  j  I A,Ph1 Ph 2 ]
*

currents are independent from the load flow, both these RF 

Im[I A,Cmp   A,B  e  j  I A,Ph1 Ph 2 ]
*
components can be used as compensation quantities. In order (11)
to estimate the fault current IF using the sequence current
 sin   Im[U A,1  I A,Cmp   A, B ]
* *

X Fault  j
Im[e  I A,1  I
*
A , Cmp 
*
A, B ] (13)

Im[U A,1  e  j  I A,1 ]

*

RF  (14)
Im[ I A,Cmp   A,B  e  j  I A,1 ]
*

For the calculation of the compensation factor, the approach

with superimposed components must be used (Fig. 4). The
compensation quantity is the difference between the current in
pre-fault and fault condition, in positive sequence. This
current will further be called delta current. It is also assumed
that the fault is symmetrical, with a resistance RF between
each phase and the star point.
Depending on the type of fault and implicated phases, the
quantity and compensation factor can be determined using the
adapted symmetrical components.

Figure 3. Phase-phase-to-earth fault with fault resistance (representation in

symmetrical components)

Figure 4. Three phase fault with symmetrical fault resistance (superposition

principle)

Fig. 3 presents the phase-to-phase fault with earth in

symmetrical components. It is assumed that the fault
resistance between phases 2RF is split symmetrical by the
earth fault resistance RF0. Expressing the fault current as the
difference between both phase currents flowing into the fault,
the following generalization can be made:

 A, B , 2  (12)
I F , Ph1  I F , Ph 2  I F  I A, Cmp , 2  I A,Cmp ,0   
 A, B , 0  Figure 5. Meshed power system with fault on the line between busbars A and
B a) network during fault; b) sequence network; c) reduced sequence network
Since in case of a phase-to-phase fault, the zero sequence
current is zero, the formulation from (12) is still valid. The line data used in the computation of the compensation
For three phase faults, the positive sequence current and factors is available in the relay device. However, the source
voltage are used: impedances are not parameterized in common protection
devices. These network parameters can be computed using the
measurements made by the protection relays during the fault
transient. Considering the equivalent circuits in symmetrical Data exchange makes it possible to determine the system’s
components, it can be concluded that based on the measured state. Moreover, the parameter m (fault location) can be
voltages and currents, in case of the fault on the line, the real calculated using an iterative procedure. Equation (5) is divided
source impedance can be simply calculated: by the reactance per unit length x’, which is a constant
parameter of the line, in order to obtain the fault location.
U A, 0 U A, 2 Introducing Gauss’ method, (20) is obtained:
Z A,0   , Z A, 2   ,
I A, 0 I A, 2
sin   Im[U A, Ph  I A, Cmp   A, B ( mn )]
* *
U A,1 (15) mn  1  ,
Z A,1   x ' Im[e j  I A, Ph  I A,Cmp   A, B ( mn )]
* *
(16)
 I A,1
m  mn 1 if mn  1  mn  
This method can also be used in meshed networks however in
that case, the calculated impedances do not reflect the real
source impedances. As a proof, the power system from Fig. 5a where  is a condition for the last iteration step. With this
can be used. Each meshed system can be replaced by the condition, if iterations do not contribute to any improvement
system given in Fig. 5a, so that this network can be considered of the result, the fault location m is adopted. Considering (16),
as an equivalent for any meshed power system. Taking this it can be noted that after some reformulations, a quadratic
network into account in a symmetrical or superimposed form for almost all fault types can be derived as well. An
component representation, each sequence network can be analytic equation of the third order only appears in the case of
considered separately like shown in Fig 5b. As presented in a phase-to-phase fault with earth. The analytical solution of
Fig. 2-5 the connection type of the sequence network depends such an equation is much more complex than the iterative
on the fault type only. The meshed system can be reduced to approach. As a result, the iteration approach was chosen as
the system from Fig. 5c. with two busbars using the general solution for the implementation of each fault type.
commonly known wye-delta transform. During the reduction After a successful estimation of the fault location, the fault
process, a fictive parallel line without mutual coupling appears resistance as minor product is computed.
between busbar A and B. In order to prove that this parallel IV. EXPERIMENTAL RESULTS
line does not impact the calculation procedure for the
compensation factors and compensation quantities, the wye- After implementing the algorithm in protection devices,
delta transform can be used. It can be noted that the calculated tests were performed for different network structures and fault
impedances applied to compute the compensation factors types represented by simulation models. The parameters used
depend on the fault location. This does not limit the approach for the network model are typical for high voltage overhead
lines. The test environment, shown in Fig. 6, is made of two
presented in this paper. However, using the estimated source
test devices to which three phase currents and voltages are
impedances presumes that the fault occurs on the line between provided by current and voltage amplifiers [8], [9]. A
busbars A and B. communication interface without synchronization was
implemented between the two devices, enabling the data
III. ACCURACY IMPROVEMENT exchange. The fault locator function was triggered after the
pick up of the protection function [10], [11], for which
The compensation quantity introduced in section A-C distance protection was used.
corresponds to the fault current seen from side A and is
deduced from the measured values on this side (ZA,0, ZA,1 or
ZA,2). However, the compensation factor depends on the Device 1: m=59.9%
network homogeneity degree as well as on the fault location
m. Therefore, the compensation factors require an equivalent Device 2: m=39.7%
of source impedance from side B in symmetrical components
(ZB,0, ZB,1 or ZB,2), and the fault location m. The impedance
parameters are a priori unknown because they depend on the Current-Voltage Amplifier
short circuit power of the remote side and on the network
configuration, which are not available to the relay. However,
they can easily be obtained by implementing data exchange Voltage Amplifier
between both devices. This data exchange procedure offers
several advantages:
 It makes network states available to each relay in
order to calculate the fault current. Figure 6. Test environment
 It only requires the exchange of a limited number of
parameters. The behavior of the fault locator algorithm for various fault
 It does not require synchronization of the exchanged locations has been tested for each fault type. As an example,
data, as opposed to other two-side based algorithms. the calculated fault location for a phase-to-earth, phase-to-
phase (without and with earth) and a three-phase fault are
plotted in Fig. 7 for locations every 5% of the fault line. The as the impedances calculated with the measurements from the
fault resistance is equal to 5Ω. The representation focuses on protection relays gave an equivalent of the meshed network.
several points, which present the greatest observed deviance.
8
As shown in Fig. 7, the maximum error attained is of 0.8%, Fault L1L2
Fault L2L3
although the simulated system contains significant load flow 6 Fault L3L1
(different short circuit power and phase shift between both
4
voltage sources from Fig. 1) and inhomogeneous network.
2

Error in %
0

-2

-4

-6

-8
0 20 40 60 80 100
Exact Fault Location (% of line length)

Figure 8. Calculated fault location determined with protection devices as a

function of the exact fault location for each phase-to-phase fault without earth
– transposed line with concentrated parameters

2.5
Fault L1E
2 Fault L2E
Fault L3E
1.5

0.5
Error in %

-0.5

-1

-1.5

-2

-2.5
0 20 40 60 80 100
Exact Fault Location (% of line length)

Figure 9. Calculated fault location determined with protection devices as a

function of the exact fault location for each phase-to-earth fault – transposed
line with concentrated parameters

15
Fault L1L2
Fault L2L3
10 Fault L3L1

5
Figure 7. Calculated fault location determined with protection devices as a
Error in %

function of the exact fault location for each fault type L1E, L1L2, L1L2E and
L1L2L3 respectively 0

The implemented algorithm shows very satisfying results, as it -5

calculates precise values not only for the fault location but
also for the fault resistance. The tests have been performed for -10
various fault resistance values ranging from 1Ω to 100Ω,
giving similar results as the ones presented in Fig. 7. The -15
0 20 40 60 80 100
results showed no influence of the fault resistance on the fault Exact Fault Location (% of line length)
location as opposed to the conventional impedance method.
Moreover, tests with meshed networks also provided accurate Figure 10. Calculated fault location determined with protection devices as a
results for faults located on the line between the two bus bars, function of the exact fault location for each phase-to-phase fault without earth
– transposed line with distributed parameters
 parameters (Fig. 8-9). This confirms that the proposed method
5
Fault L1E is also applicable for long lines.
4 Fault L2E
Fault L3E
3 V. SUMMARY
2 This paper focuses on the explanation of the method and
1 its theoretical background. It has been shown that the
Error in %

0
developed algorithm efficiently calculates the faulty loop’s
impedance in fault location applications. Successful
-1 experimental results were obtained, also when considering
-2 typical influent factors such as load flow, fault resistance and
-3
system homogeneity degree. A significant improvement in
precision of fault location is therefore achieved. The
-4 advantage of the algorithm is an elimination of the numerous
-5
0 20 40 60 80 100
aspects regarding synchronization accuracy and availability of
Exact Fault Location (% of line length) the stable communication interface between devices. The
weakness of the method is its dependency on the line
Figure 11. Calculated fault location determined with protection devices as a parameters, which can show through the residual factor k0 or
function of the exact fault location for each phase-to-earth fault – transposed the mutual coupling of the parallel line kM. The line geometry
line distirbuted parameters
and transposition schema can also influence the results of the
fault location. Moreover, the faulty loop must be provided to
For the transmission of power on long distances, transposed fault location algorithm in order to calculate the correct fault
lines are used. Depending on the voltage level and on the line location and fault resistance. Nevertheless, this method can be
length, different transposition schemas can be applied. In successful used in combination with other fault location
order to further investigate this method, a single line from the algorithms and in a lot of cases guarantees a very good
Mexican power system (from the transmission system operator accuracy.
CFE) was considered. This line has three main sections that
are transposed to each other. The line is fed in from both sides
with a heavy load. Different fault types with fault resistances
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