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A
Report on
Fault Analysis of Power
Distribution Systems
Submitted
By
KALYAN RANJAN
Under the supervision of
Mr. Rajveer Singh
Assistant Professor
Department of Electrical Engineering
Jamia Millia Islamia
New Delhi
M.Tech (EPSM)
2
nd
SEMESTER
/02/2013
Contents
1. Introduction
2. Fault analysis methods
a) Classical symmetrical components,
b) Phase variable approach and
c) Complete time-domain simulations
3. Fault analysis algorithm
a) Fault resistance sub-routines and
b) Bus impedance sub-routines
4. Conclusion
5. References
CERTIFICATE
This is certify that the seminar report titled “FAULT ANALYSIS OF POWER
DISTRIBUTION SYSTEMS” submitted in partial fulfillment of requirements of the
award of the degree of Master of Technology in Electrical Power System Management
by KALYAN RANJAN (12 MEE-04) is a bonafide record of the candidate’s work
out by him under my guidance.
Mr. RAJVEER SINGH
(Assistant Professor)
Abstract
Fault resistance is a critical component of electric power systems operation due to its
stochastic nature. If not considered, this parameter may interfere in fault analysis
studies. The fault analysis of unbalanced three-phase distribution systems can be done
by an iterative fault analysis algorithm considering a fault resistance estimate. This
algorithm is composed by two sub-routines, namely the fault resistance and the bus
impedance. The fault resistance sub-routine, based on local fault records, estimates the
fault resistance. The bus impedance sub-routine, based on the previously estimated
fault resistance, estimates the system voltages and currents.
Introduction
Electric power systems are daily exposed to service interruption due to either
temporary faults or permanent faults. Fault will be take place when two or more
conductors at different potentials are touches each other or a live conductor touching
the ground either with zero resistance or with a substance of low resistance.
A fault will cause currents of high value to flow through the
network to the faulted point. The amount of current may be much greater than the
designed thermal ability of the conductors in the power lines or machines feeding the
fault. As a result, temperature rise may cause damage by annealing of conductors and
insulation failure. In addition, the low voltage in the healthy phase of the faulty
system will cause equipment to malfunction and affects system’s reliability, security,
and energy quality.
When a distribution line short circuited, very large currents flow for a
short time until a fuse or breaker or other interrupter breaks the circuit. One important
aspect of overcurrent protection is to ensure that the fault arc and fault currents do not
cause further, possibly more permanent, damage. The two main considerations are:
• Conductor annealing —
From the substation to the fault location, all conductors in the fault-current path
must withstand the heat generated by the short-circuit current. If the relaying or fuse
does not clear the fault in time, the conductor anneals and loses strength.
• Burn downs —
Right at the fault location, the hot fault arc can burn the conductor. If a circuit
interrupter does not clear the fault in time, the arc will melt the conductor until it
breaks apart. Today, three approaches are used in the industry for such analysis: classical symmetrical components, phase variable approach and time-domain simulations.
There are many causes of faults on distribution circuits such as
lightning, insulation breakdown, conductors slapping together in the wind, trees
falling across lines, insulator flashovers caused by pollution, insulator failures, broken
wires, equipment such as transformers or capacitors failures etc. The distribution of
fault causes found in the EPRI study is shown in figure below.
Fig-1: Fault causes measured in the EPRI fault study.
Types of fault
(A) Single line-to-ground fault
(B) Line-to-line fault
(C) Double line-to-ground fault
(D) Three phase fault
(E) Three phase-to-ground fault
Fig-2: Different types of fault
Distribution faults occur on one phase, on two phases, or on all three phases. Singlephase faults are the most common. Almost 80% of the faults measured involved only
one phase either in contact with the neutral or with ground.
Fault analysis methods
Fault analysis methods are an important tool used by protection engineers to
estimate power system voltages & currents during disturbances. The fault analysis of a
power system provide information for the design of switchgear like isolators, circuit
breakers, short circuit current limiting reactors, the design of settings of protective
relays, besides coordination and efficiency analysis studies. Today, three approaches
are used for such analysis,
a) Classical symmetrical components,
b) Phase variable approach and
c) Complete time-domain simulations
a) Classical symmetrical components
•
It is quite convenient and useful in cases where network itself is balanced prior
to the faults.
•
It is based on symmetrical components transformations and per unit system.
•
The solution in this case is obtained quite fast.
•
We utilize the well-known positive, negative, and zero sequence impedance
description of power system components to develop mathematical system
models in the form of impedance matrices.
•
It not provides accurate results for power distribution systems, which are
normally characterized by those asymmetries.
•
The result may be higher than actual.
b) Phase variable approach
•
It is quite convenient and useful in the cases where network itself is unbalanced
prior to the faults.
•
For example - An untransposed feeders with single-phase or double-phase
laterals.
•
It is based upon the nodal formulation.
•
The network conditions are represented by phase voltages, currents and
admittances.
•
It preserves the physical identity of the system.
•
The symmetrical components transformations and per unit system are not
needed.
•
It provides accurate results for power distribution systems.
•
It is a time consuming approach.
c) Time domain simulations
•
It is used if significant nonlinear elements are present in the system and the
system operates near designed limit.
•
It is based on mathematical system model and numerical simulation.
•
Mathematical system model:
Either a set of differential equations
or, a set of difference equations
•
Numerical simulation :
Newton-Raphson method (EMTP)
Runga-Kutta method (PSpice)
Trapezoidal method (EMTP)
•
The modeling and simulation procedure are complex.
Fault analysis algorithm
As fault resistance is stochastic in nature, typical fault analysis studies consider
the fault paths as an ideal short-circuit. To overcome this limitation, we use fault
resistance estimation algorithm. To know the fault period system voltages and currents
we may use an iterative fault analysis algorithm that considers typical distribution
system characteristics, and a fault resistance estimate. This fault analysis algorithm is
composed by two sub-routines, namely the fault resistance and the bus impedance
sub-routines. The fault resistance sub-routine is based on an iterative formulation
executed to estimate the fault resistance through one-terminal fault records. The bus
impedance sub-routine considers the estimated fault resistance values, and uses a bus
impedance matrix based formulation to estimate the fault system voltages and
currents.
Fault resistance sub-routine
Fig. 3. Single line to ground fault
Fault resistance represents the fault impedance path between phase or ground
faults. The fault resistance sub-routine uses the sending-end voltages and currents as
input data. Referring to the power system of fig. 3, the sending-end voltages are given
by equation (1), considering the steady-state fault conditions.
Where, V sfm is the phase m sending-end voltage (V);
x is the distance between the sending-end and the fault location (m);
Z mm is the phase m line self-impedance (ohm/m);
Z mn is the mutual impedance between phases m and n (ohm/m);
I sfm is the phase m sending-end current (A);
V Fm is the phase m fault location voltage (V);
m,n are the phases a, b, or c.
For the single line-to-ground fault (SLG) illustrated in Fig. 1, the faulted phase
sending end voltage can be expanded to equation (2)
Whereas ZF is the fault impedance between line-to-ground, the sub-script p represents
the faulted phase, and I Fp is the phase p fault current. Considering the fault impedance
strictly resistive and constant, equation (2) may be expanded into its real and
imaginary parts,
Where the subscripts r and i represent the real and imaginary components, RF is the
fault resistance, and:
Evaluating equation (4), the fault distance and resistance may be calculated as
function of the sending-end voltages and currents, as well as the line parameters, as
given by equation (7):
From equation (7), fault resistance and distance independent mathematical expressions
for single line-to-ground faults are obtained, given by equations (8) and (9),
respectively:
As a result of the procedure described above, the fault distance and resistance may be
estimated. To obtain such estimates, the system parameters, sending-end voltages and
currents should be known. The fault current is the only unknown variable on such
expressions and is calculated by an iterative procedure.
Fault current estimation
Referring to fig. 1, the fault current ( I Fp ) may be estimated through the
difference between the load current and the sending-end current, as given by equation
(10).
Where [ I sf ] is the sending-end three-phase current vector; [ I L ] is the three-phase load
current vector. An iterative formulation is developed to estimate the fault current as
shown in flowchart.
Where equivalent admittance matrix between the load and the line impedance between
the fault location and the receiving-end is calculated by (11) while the three-phase
load current vector is updated using the equivalent admittance matrix obtained by
equation (12).
The estimated value of fault current obtained from above iterative method would be
used in equations (8) and (9), to estimate fault location and fault resistance
respectively.
Bus impedance sub-routine
Power distribution systems are typically unbalanced, with untransposed feeders and
single-phase loads. In these conditions, the bus impedance matrix technique is the
most suitable choice available for fault system voltages and currents state estimation.
Using this method it is possible to analyze any fault type by modifying the phase
coordinate base-case impedance matrix, considering the system’s asymmetries. The
bus impedance sub-routine is described in the following subsections.
Bus impedance matrix
Three-phase admittance matrix Ybus is calculated from the three-phase submatrices feeder’s components. The diagonal sub-matrix of a hypothetical bus p is
calculated through equation (13), which represents the sum of all sub-matrices
representing the M elements adjacent to bus p.
The off-diagonal sub-matrices are obtained from equation (29), where [Yabc ] p , j is the
admittance matrix element between buses p and j.
From equations (13) and (14), 3n*3n three-phase admittance and impedance matrices
are built, as presented in equations (15) and (16), respectively.
Where, n = number of buses in the system.
Pre-fault state calculation
The bus impedance sub-routine uses a ladder based three-phase load flow
technique, considering the non-linear characteristics of the feeder to estimate the prefault voltages on each bus. For the estimated voltages convergence analysis, the threephase load flow also considers the pre-fault voltages measured at the substation on
each fault record and compares to the calculated voltages at the substation bus.
The three-phase voltages at the substation, the complex power of all of the
loads and the load model (constant complex power, constant impedance, constant
current, or a combination) are known prior to the power flow analysis of distribution
system. Sometimes the input complex power supplied to the feeder from the
substation is also known. Because a distribution feeder is radial, iterative techniques
commonly used in transmission network power-flow studies are not used because of
poor convergence characteristics. Instead, an iterative technique specifically designed
for a radial system is used.
In this iterative method, regardless of its original topology, the distribution
network is first converted to a radial network. The solution method used for radial
distribution networks is based on the direct application of the KVL and KCL. Here we
developed a branch oriented approach using an efficient branch numbering scheme to
enhance the numerical performance of the solution method.
Branch Numbering
Figure 4 shows a typical radial distribution network with n nodes, b (=n-1)
branches and a single voltage source at the root node. In this tree structure, the
node of a branch L closest to the root note is denoted by L1 and the other node
by L2. We number the branches in layers away from the root node as shown in
Figure 5. The numbering of branches in one layer starts only after all the
branches in the previous layer have been numbered.
Solution Method
Given the voltage at the root node and assuming a flat profile for the initial
voltages at all other nodes, the iterative solution algorithm consists of three steps:
1. Nodal current calculation: At iteration k, the nodal current injection, I i (k )
at network node i is calculated as,
I i (k )  ( S i / Vi (k  1)) *  YiVi (k  1) ;
i= 1, 2, …. , n.
……… (17)
Where Vi (k  1) is the voltage at node i calculated during the (k-l)th iteration
Si is the specified power injection at node i.
Yi is the sum of all the shunt elements at the node i.
2. Backward sweep: At iteration k, starting from the branches in the last layer
and moving towards the branches connected to the root node the current in
branch L, JL is calculated as:
J L (k )   I L 2   i
;
L = b, b-1, …. ,1.
……….. (18)
Where I L 2 (k ) is the current injection at node L2. This is the direct application
of the KCL.
3. Forward sweep: Nodal voltages are updated in a forward sweep starting
from branches in the first layer toward those in the last. For each branch, L, the
voltage at node L2 is calculated using the updated voltage at node L1 and the
branch current calculated in the preceding backward sweep:
VL 2 (k )  VL1 (k )  Z L J L (k ) ;
L = 1, 2, …. , b
…….. (19)
Where Z L is the series impedance of branch L. This is the direct application of
the KVL. Steps 1, 2 and 3 are repeated until convergence is achieved.
Convergence Criterion
We used the maximum real and reactive power mismatches at the network nodes as
our convergence criterion. As described in the solution algorithm, the nodal current
injections, at iteration k, are calculated using the scheduled nodal power injections and
node voltages from the previous iteration (equation (17)). The node voltages at the
same iteration are then calculated using these nodal current injections (equations (18)
and (19)). Hence, the power injection for node i at k-th iteration, is calculated as:
S i (k )  Vi (k )( I i (k )) *  Yi | Vi (k ) | 2
……….. (20)
The real and reactive power mismatches at bus i are then calculated as:
Pi (k )  Re[ S i (k )  S i ]
Qi (k )  Im[ S i (k )  S i ]
...…….. (21)
Fault calculation
For a single line-to-ground fault, Z Bus must be modified to include the fault resistance
of the path between the faulted line and ground. The fault resistance is included in the
bus impedance matrix through a fault node r. As result, a new impedance matrix Z new
of dimension (3n+3)*(3n+ 3) is obtained. For a SLG fault, the fault current may be
calculated using equation (22)
Where, VFr is the node r pre-fault voltage, and
Where RF is the fault resistance, estimated by equation (9).
The change in voltages at each bus due to the injected fault current ( I Fr ) may be
calculated using the impedance matrix Z new :
Where equation (24) can also be rewritten as,
Whereas i= from 1to (3n+ 3) represents the node index.
Adding the change in voltages to each pre-fault bus voltage ( VPF ), the fault period bus
voltages ( VF ) are estimated through equation (26):
Finally, from the three-phase bus voltages and the admittance matrix, it is possible to
calculate the three-phase currents during the fault period at each feeder ( I gh ):
Where, [Yabc ] g ,h is the admittance matrix between buses g and h,
[V Fg ] is the bus g three-phase voltage vector,
[VFh ] is the bus h three-phase voltage vector.
Where g, h = from 1to (n+ 1), in which n is the total bus number.
Conclusion
Fault resistance and fault location are stochastic in nature and hence needed to
estimate these values. To estimate these values we use an iterative fault analysis
algorithm. This fault algorithm composed by two sub-routine , one enable to estimate
fault resistance and fault location while other one enable to estimate the system
voltages and currents.
REFERENCES
[1] Filomena AD, Resener M, Salim RH, Bretas AS." Distribution systems
fault analysis considering fault resistance estimation". Int J Electrical Power
and Energy System 2011; 33(7): 1326–1335.
[2] Liao Y." Generalized fault-location methods for overhead electric
distribution systems". IEEE Trans Power Deliv 2011;26(1):53–64.
[3] Ngu EE, Krishnathevar R. "Generalized impedance-based fault location for
distribution systems". IEEE Trans Power Deliv 2012; 27(1):449–51.
[4] Javad Sadeh, Ehsan Bakhshizadeh, Rasoul Kazemzadeh: "A new fault
location algorithm for radial distribution systems using modal analysis". Int j
Electrical Power and Energy Systems 2013; 45: 271–278.
[5] Turan Gonen,"Electric Power distribution system engineering". Taylor and
Francis, CRC Press, 2010.