Recent Advances in Energy Planning and Environment
Program for calculation parameters of power systems during
Short-circuit
PETER JANIGA, ŽANETA ELESCHOVÁ, DOMINIK VIGLAŠ
Department of Electrical Power Engineering
Slovak University of Technology in Bratislava
Ilkovičova 3, 812 19 Bratislava
SLOVAKIA
peter.janiga@stuba.sk, http://www.fei.stuba.sk
Abstract: - This paper discusses about program created to solve a short – circuit ratios in the Power
System according to Standard IEC 60909. One of the main subject is describing short-circuit current
in system with currents without attenuation alternating component and short-circuit current in system
with currents with attenuation alternating component. It solves short-circuit ratios in complex network
with the possibility to observe a partial results. This article also brings to public a comparison of
results taken from sample examples solved by the program which gives the relevant outputs. Such
program outputs are needed for design and optimal set up of protective devices in the Power System.
Key-Words: -short-circuit impedance matrix, Power System, short-circuit current, 3-phase short-circuit
power, positive sequence short-circuit impedance matrix, negative sequence short-circuit impedance
matrix, zero sequence short-circuit impedance matrix
knowledge of the short – circuit ratios in the entire
length of the electrical circuit to the most important
background for projecting some electrical
components. Setting the switches and the circuit
breakers, respectively the protections is determined
by the tripping circuit current, the mechanical and
the thermal effects by the other constituents of short
– circuit current.
Short-circuit proportions are solved and defined in
the Standard IEC 60909, which describes universal
practical process ensuring sufficiently accurate
result with respect to degree of security. This article
is dedicated to description of short-circuit
proportions solving in energetic system according
STN IEC 60909 norm, as well as to description of
programme for solving short-circuit proportions in
user based network.
There are different methods used for calculating
short-circuits in complex networks. In most cases
these are derived from the method of node voltages
or the method of loop currents.
1 Introduction
Constantly evolving society increases its demands
on Power System. It is associated with an increasing
the amount of the consumed energy and also with
the quality a price of electricity. In consequence,
there is also increasing demand on security and
reliability of the Power System.
During operation of the power system there may
occur transient effects that appear while the system
transits from one steady-state into another with new
parameters.
One of the reasons of occurrence of these transient
events could be short-circuit. Impedance of shortcircuit is multiply decreasing which leads to
increase of current and decrease of voltage.
Duration of short-circuit is short but due to the size
it causes the mechanical and dynamic effects on
various machines.
Electrical equipments must be designed that when
exposed to short – circuit currents that may occur in
that locations not incurred a damage or deformation
of electrical, mechanical or thermal character. It is
therefore necessary, due to the dangerous effects of
short – circuit currents on electrical equipment, to
know the short – circuit ratios at the entire length of
the electrical circuit.
Due to the dangerous effects of short – circuit
currents on electricity equipments belongs the
ISBN: 978-960-474-346-9
2 Method of short-circuit impedance
matrix
For computing is necessary to make line admittance
matrix, that is diagonal. Members of matrix are
admittances of system elements.
61
Recent Advances in Energy Planning and Environment
YV 11

0
.

YV =  .

.
0

0
0
... 0
... 0
... 0
YV 22 ... 0
... 0
... 0
.
.
.
.
.
0
.
YV ii
.
.
.
.
.
... 0 YV ( n −1)( n −1) ... 0
0
0
... YV nn
... 0
Sequence of elements is free but is necessary make
the same sequence for making matrix k V .
List of common used elements is in a chapter 3.
Admittances can be calculated like inverse value of
impedance of elements.
Then for making matrix k V is necessary the system











topology.
Component
kij determine
selected
direction of current for element YV ii to node j
kij = 1 if current flows from YV ii to node j ,
kij = −1 if current flows from YV ii to node i .
Matrix k V has dimension n x m , where m is
number of nodes of system.
Short-circuit admittance matrix is then calculated:
Y = k V .Y V .k V (1)
T
For example showed on the figure 1 can matrix Y
have this form:
Fig.2 Example of matrix form
On example is showed method of making
matrixesand short-circuit matrix is computed:
−1
Z = Y (2)
Fig.1 Example of power system
On example is showed method of making matrixes
k V and Y V .
For Power System on figure 1 can be matrix
this form:
YG1

0
0
YV = 
0
0

0
0
0
0
0
YG 2
0
0
0
0
YT 1
0
0
0
0
YT 2
0
0
0
0
YV 1
0
0
0
0
ISBN: 978-960-474-346-9
Diagonal elements of short-circuit matrix Z
determines short-circuit impedance of system
elements. Element Z jj determines short-circuit
Y V in
impedance in node j .
In next step is calculated short-circuit current for
node j using this formula:


0 
0 

0 
0 

YT 3 
0
I k = c.
U
(3)
3.Z k
c - Voltage coefficient,
U - Voltage in short-circuit node before failure,
Z k - Final short-circuits impedance.
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Recent Advances in Energy Planning and Environment
3 Program for calculation of the
behaviour of Power System during the
short-circuit
This state is described in next formula:
0  Y11
  
0  Y21
.   .
  
 I k  = Y j1
.  
  .
0  Y( m−1)1
  
0  Ym1
I = Y .U (4)
 U1 


... Y2 m
Y22 ... Y2 j
 U 2 

 .
.
... .
... .


.U j 
... Y jm
Y j 2 ... Y jj


.
... .
... .

 .


Y( m−1) 2 ... Y( m−1) j ... Y( m−1) m U m−1 


 U m 
Ym 2 ... Ymj ... Ymm
Y12
... Y1 j
... Y1m
Program for calculation of the behaviour of Power
System during the short-circuit respects the
Standard IEC 60909. In calculation is used
correction coefficient for generator and power plant
block.
Input data are inserted by using main menu
(Elements).
You can choose from:
- Power network (Q)
- Motor (M)
- Transformer (T*2 – double winding, T*3 – triple
winding)
- Line (V)
- Generator (G)
or by inserting dates to main table. When dates are
inserted it is necessary to use the key (View ->Sort).
The key (Q, M, T*2, T*3, V or G) is written to the
first cell. This key determines which component is
used.
Modification of formula (4):
−1
U = Y .I (5)
U is matrix of voltages during short-circuit.
Multiplication gives us matrix ∆U :
∆U = k V .U (6)
For computation of line currents between nodes is
used next formula:
I V = Y V .∆U (7)
Matrix form of formula (7):
 IV 1  
 YV 11

 I V 21  0
 

 .
.
=.
I
 Vj  
 .
.
 

 I V n−1  0
 0

 I Vn1  
0
... 0
... 0
... 0
YV 22 ... 0
... 0
... 0
.
.
.
.
.
0
0
.
YV ii
.
.
.
.
.
... 0 YV ( n−1)( n−1) ... 0
0
... 0
... YV nn
 ∆U 1 


 ∆U 2 

 .


.∆U j 



 .
 ∆U 
  m−1 
 ∆U m 
Calculations of short-circuit currents in asymmetric
short-circuit is similar to computation of 3-phases
short-circuit. For asymmetric short-circuit is
necessary to calculate short-circuit matrix
individually for positive sequence, negative
sequence and zero sequence of impedance. We must
keep the same marking of nodes and lines in all
three parts.
ISBN: 978-960-474-346-9
Fig.3 Page of output data – three phase shortcircuit currents
63
Recent Advances in Energy Planning and Environment
too. In theoretical section is shown method for
calculation of short-circuit currents in power system
with difficult topology. It is necessary to identify
short-circuit in system with attenuation alternating
component and system without attenuation
alternating component. In the system with
attenuation alternating component is needed to
use correction coefficient. Program for calculations
of the behaviour of Power System during shortcircuit respects Standard IEC 60909. It is described
in second chapter.
Acknowledgement
Fig.4Page of output data - short-circuit
asymmetrical currents and impedance matrixes
This work was done during implementation of the
project Effective control of production and
consumption of energy from renewable resources,
ITMS code 26240220028, supported by the
Research and Development Operational Program
funded by the ERDF.
Calculated values are possible to watch in page
(Output data). There is possibility to choose shortcircuit node, format of calculated values
(goniometric form, algebraic form) and motors
which contribution will be considered in calculation.
Program does not solve the case of connection of
one phase with ungrounded node. In this case the
result is zero, because short circuit impedance is
zero.
References:
[1] Reváková, D., Eleschová, Ž., Beláň, A.,
Prechodnéjavy v elektrizačnýchsústavách, STU,
2008.
[2] Standard IEC 60909:2000, Short-circuit currents
in three-phase a.c. systems.
[3] Standard IEC 60865-1:2011, Short – circuit
currents – Calculation of effects – Part 1:
Definitions and calculation methods.
[4] Standard IEC/TS 60865-2:2011, Short – circuit
currents – Calculation of effects – Part 2:
Examples of calculation.
[5] Kvasnica, P. a kol.:Elektroenergetika, 3.diel,
Skraty
v
elektrizačnejsústave.
Príklady.
Bratislava, SVŠT 1984
[6] Kolcun, M.,Chladný, V.,Varga, L.,Beňa,
Ľ.,Ilenin,
S.,Leščinský,
P.,Mešter,
M.:
Analýzaelektrizačnejsústavy. Košice, TU 2005
[7] Neeser, D.R., "Short-circuit current ratings of
equipment," Industrial & Commercial Power
Systems Technical Conf (I&CPS), 2013
IEEE/IAS 49th , vol., no., pp.1,4, April 30 2013May 3 2013
[8] Ramos, M. J S; Bernardon, D.P.; Comassetto, L.;
Resener, M.; Daza, E.B., "Analysis of shortcircuit asymmetrical currents in power
distribution systems," Universities Power
Engineering Conference (UPEC), 2012 47th
International , vol., no., pp.1,6, 4-7 Sept. 2012
Calculated values:
- 3-phase short-circuit current,
- Part of 3-phase short-circuit current,
- Power of 3-phase short-circuit current,
-2-phase short-circuit current,
- Power of 2-phase short-circuit current,
-1-phase short-circuit current,
- Power of 1-phase short-circuit current.
Advanced values:
-Positive sequence short-circuit impedance matrix,
-Negative sequence short-circuit impedance matrix,
-Zero sequence short-circuit impedance matrix,
-Correction coefficient for positive sequence
impedance,
-Correction coefficient for negative sequence
impedance.
4 Conclusion
Calculation of the behaviour of Power System has
great application sphere in building new segments
of power system and reconstruction of old segments
ISBN: 978-960-474-346-9
64