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Voltage Sags Assessment by an Extended Fault Positions Method
and Monte Carlo simulation
Evaluación de Hundimientos de Tensión mediante un Método
Extendido de Posiciones de Falla y Simulación de Monte Carlo
Jorge W. Sagrea, John E. Candelob & Johny H. Montañac
b
a
Grupo de Investigación en Sistemas Eléctricos de Potencia, Universidad del Norte, Barranquilla, Colombia. [email protected]
Departamento de Energía Eléctrica y Automática, Facultad de Minas Universidad Nacional de Colombia, Medellín, Colombia. [email protected]
c
Departamento de Ingeniería Eléctrica, Universidad Técnica Federico Santa María, Chile. [email protected]
Received: January 15th, 2015. Received in revised form: January 15th, 2015. Accepted: January 15th, 2015.
Abstract
To evaluate the voltage sags at specific points of the electrical power system, this article proposes an extended method of fault position
combined with Monte Carlo simulation. The proposed method allows to build the distribution function of indicator SARFI at bus bars of
interest, considering the randomness of: i) location of faults in lines; (ii) generation dispatch, and (iii) variation of the pre-fault voltage in
the bus bar at the time that the fault was produced. Voltage profiles were obtained by means of a power flow, considering changes in
generation dispatch, the load on bus bars, and the topological configuration of the system in the area of vulnerability (AOV). The method
was applied to the Atlantic Coast area of the National Interconnected Power System of Colombia. The distribution of the number of voltage
sags per year, depending on their magnitude in bus bars of the electrical system and the impact of generation on the voltage sags, was
determined. With a higher number of plants dispatched, voltage sags caused by faults were less severe, due to the robustness of the power
system and the voltage support.
Keywords: voltage sags; power quality; Monte Carlo; fault position method; electromagnetic compatibility.
Resumen
Para evaluar los hundimientos de tensión en puntos específicos del sistema eléctrico de potencia, este artículo propone un método de
posiciones de falla extendido combinado con simulación de Monte Carlo. El método propuesto permite construir la función de distribución
del indicador SARFI en las barras de interés, considerando la aleatoriedad de: i) los puntos de falla en líneas; ii) el despacho de generación;
iii) variación del perfil de tensión pre-falla en las barras al momento de ocurrir la falla que lo produce. Los perfiles de tensión se obtuvieron
por medio de un flujo de carga, considerando cambios en los despachos de generación, la carga en barras y la configuración topológica del
sistema en el área de vulnerabilidad. El método fue aplicado al área de la costa atlántica del Sistema de Potencia Interconectado Nacional
de Colombia. Se determinó la distribución del número de hundimientos de tensión al año en función de su magnitud en las barras del
sistema eléctrico y el impacto de la generación sobre los hundimientos de tensión. A mayor número de plantas despachadas, los
hundimientos de tensión ocasionados por fallas fueron menos severos, debido a la robustez del sistema y el soporte de tensión.
Palabras clave: hundimientos de tensión; calidad de potencia, Monte Carlo; método de posición de falla; compatibilidad electromagnética.
1 Introduction
The requirements of users of electricity service for better
power quality have grown increasingly since the last three
decades. The reason is the economic impact of power quality,
especially voltage sags, caused in electrical companies,
customers and manufacturers of end use equipment [1].
Several factors affect the power quality [1–3]: devices
powered by electronic converters, speed drivers and CFL, are
a source of harmonics. Distributed generation and renewable
sources can create voltage variations, flicker and harmonic
distortion. Furthermore, energy efficiency equipment are also
an important source of disturbance of power quality. In
addition to the above, all these devices are very sensitive to
© The authors; licensee Universidad Nacional de Colombia.
DYNA 81 (184), pp. 1-2. April, 2014. Medellín. ISSN 0012-7353 Printed, ISSN 2346-2183 Online
Velásquez-Henao & Rada-Tobón / DYNA 81 (184), pp. 1-2. April, 2014.
voltage sags because they are manufactured with narrow
ranges of operation for competitive reasons.
Many power quality studies have been conducted and
reported previously, for example: i) measurement techniques,
ii) evaluation of voltage sags and, iii) economic impacts of
equipment damage and losses in industrial processes.
In [4] two stochastic methods for voltage sags prediction
are compared: method of critical distance and fault positions
method. The results were presented by means of maps
showing the variation of the voltage sags (duration and
magnitude) into the network.
In [5] the application of probabilistic methods are
presented to predict and characterize the events frequency in
the power system to assess their impact, allowing to know
how often an user can be affected.
In [6] is shown an analytic method to determine the
probability density function of voltage sags caused by threephase faults. This method considers the impact of fault
positions in the transmission lines and generation dispatch.
In [7], the Monte Carlo method is used to evaluate the
voltage sags magnitude and unbalance, considering
stochastic factors.
In [8], an extended fault positions method was used to
calculate the distribution of voltage sags experienced by the
users in the Finland Electric System during one year.
In [9], an extending monitoring of bus bar unmeasured by
means of voltage sags estimation was presented. The
estimation is performed by a simulation method that
combines fault stochastic data with residual voltages during
the fault, calculated deterministically.
In [10], the impact of fault probability distribution model
of transmission lines in assessing the number of voltage sags
and their characteristic are analyzed.
In [11], the behavior of voltage sags using fault positions
and Monte Carlo method is evaluated. The results shows that
Monte Carlo method provided a better statistical description
of voltage sags, due to the fault positions method only gives
long-terms average values, whereas Monte Carlo shows the
total distribution function.
In [12], the fault positions method and Monte Carlo
simulation were compared in order to evaluate stochastically
the voltage sags behavior in a large transmission system. This
work shows that fault positions method cannot be used to
predict the behavior of a particular year, unless correction
factors are used to adjust the behavior. Whereas fault
positions method gives average values, Monte Carlo method
describe totally the frequency distribution function of voltage
sags index (SARFIX: System Average RMS Frequency Index;
average number of voltage sags per year with magnitude <
X%).
In [13], a method of Monte Carlo simulation that takes
into account the fault positions method to evaluate voltage
sags index was applied. This method considers the
randomness of the pre-fault conditions and uncertainty in
failure rates.
In [14], a method for stochastic prediction of voltage sags
generated by faults in the power system was presented.
Furthermore, in this research article a method for determining
the AOV was proposed.
In [15], the influence of generation dispatch and the
failures rates changing in time on the stochastic prediction of
voltage sags is discussed.
In [16], the fault positions method to predict
stochastically the frequency and characteristics of balanced
and unbalanced voltage sags in distributions systems was
presented.
The fault positions and Monte Carlo methods have
provided good results to evaluate the impact of generation in
voltage sags and SARFI indexes. Unfortunately, they do not
consider the random behavior of generation dispatch and flat
voltage profiles in the faulted bus bar and the bus bar of
interest when this behavior is studied.
In this paper, an extended fault positions technique and
Monte Carlo Method to evaluate the voltage sags is proposed.
Random faults, changes in generation dispatch, and load
variation are considered to evaluate different operating
conditions. The voltage profiles in bus bar are updated
continuously using the power flow. Topology changes of bus
bars and transmission lines are also considered in the
simulation. Although, voltage sags can be originated by
lightning, disconnection of large loads, etc, this work focus
only on faults in bus bars and overhead lines of the power
system.
2 Voltage sags
Voltage sag is “a decrease in r.m.s. voltage or current at
the power frequency for durations of 0,5 cycle to 1 min.
Typical values are 0,1 to 0,9 p.u.” (obtained from IEEE
1346). They are caused by events with large current flows
flowing through the network impedances as a result of a fault
in any point of the distribution or transmission system
affecting customer connection point [2,4,11,12,17].
Events that can cause voltage sags are short-circuits in the
power system, transformers energization, capacitors
disconnection, circuit breaker operations, starting of large
motors and large changes in load on the power system.
Voltage sag is characterized mainly by means of
magnitude and duration [1–3,18–21], this is shown in Figure
1. Additionally, voltage sag can be characterized by the
frequency of occurrence, phase shifting, start point in the
voltage waveform and shape and type of voltage sag.
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Figure 1. Characteristics of voltage sags.
Standard IEC 61000-4-30 [21], presents calculation of a
sliding reference voltage using a first-order filter with a 1
minute time constant. The filter is given by the expression
presented in (1).
𝑈𝑠𝑟(𝑛) = 0.9967 ∗ 𝑈𝑠𝑟(𝑛−1) + 0.0033
∗ 𝑉(10/12)𝑟𝑚𝑠
Figure 2. Flow chart of the methodology
(1)
4 Fault positions method
Fault positions method is a stochastic method to predict
the expected number of voltage sags in a specific node of the
network. This method considers faults in different places of
the network, as is shown in Figure 3. Electrical variables for
each fault is stored: residual voltage and duration on the
interest nodes, as is shown in Table 1.
Where, Usr(n) is the present value of the sliding reference
voltage, Usr(n-1) is the previous value of the sliding reference
voltage, and V(10/12)rms is the most recent 10/12 cycle r.m.s.
value.
Vrms(1/2) is computed from the voltage samples in time
domain, as shown in (2) [2,3,21].
𝑁
𝑉𝑟𝑚𝑠 (1/2)
1
= √ ∑ 𝑣𝑖2
𝑁
(2)
𝑖=1
Where, i is each sample, N is the number of samples and
vi are the voltage values in time domain. The value obtained
from the N previous samples is updated every half-cycle.
Most meters measure as voltage sag magnitude the lower
value of the Vrms(1/2) computed each half-cycle in time
domain [2]. The reason of this decision is the tolerance curve
according to which the device trips instantaneously when the
voltage drops below the threshold [2].
Figure 3. Fault points to estimate the voltage sags.
3 Methodology
The failure rate is assigned to each fault position. The
transmission lines are divided in a specific number of fixed
positions. Each position has a failure rate, which is
proportional to segment longitude. Thus, frequency,
magnitude and duration is determined for each fault position,
allowing to calculate the expected number of voltage sags per
year [4,6,8,9,11,12,14,16,22,23].
This work was made using the fault positions method
combined with Monte Carlo simulation method. Figure 2
shows the procedure to study the voltage sags in a power
system.
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Table 1.
Failure report for many points into the network.
Item Fault
Failure rate
Sags
position
magnitude
1
Bus bar 1
x faults/year
0
2
…
y faults/year
30%
.
Bus bar n
…
…
.
Line 1
…
…
.
…
…
…
n
Line n
m faults/year
75%
7. If the accumulated time is less than simulation time
selected in step 2, go to step 3. Otherwise go to step 8.
8. Analyze the results statistically.
Duration
(ms)
120
70
…
…
…
240
5.1 Statistical analysis of results
The great volume of data obtained by Monte Carlo
analysis has to be summarized by means of statistical tools.
The most important results from Monte Carlo are the longterm mean values and the frequency distribution of mean
values [2,11,12,25].
Computation of the mean values and standard deviation
of the voltage sags lower than the defined magnitudes must
be carried out. Commonly, the magnitudes are form 0.1 to 0.9
in steps of 0.1. It is also important to calculated, minimum,
maximum, median and quartiles 1, 2 and 3.
Once the deviation, mean value 𝑋̅ and standard deviation
s are known, the confidence intervals for the expected value
can be obtained, as expressed in (3) [11,12,25].
𝑠
𝑠
(3)
𝑆𝐴𝑅𝐹𝐼𝑋 ∈ [𝑋̅ − 2.05.
; 𝑋̅ + 2.05. ]
𝑛
𝑛
√
√
Where, 𝑋̅ is the mean value of voltage sags per year
computed from the simulation of n years, s is the standard
deviation of results from the simulation of n years, n is the
number of years of simulation, and the constant 2.05 is the
critic value of t-student distribution for 95% of confidence.
Unlike the conventional fault positions method, where the
fault positions are fixed, in the proposed method on this
work, the positions are randomly assigned anywhere in the
transmission line for each type of electrical fault.
5 Monte Carlo Method
To obtain the distribution function of the expected values
of voltage sags (SARFIx), is used the Monte Carlo simulation,
which generates values of stochastic variables associated
with the study, as is summarized in Figure 4 [11,12,24].
5.2 Area of vulnerability
The elements of the AOV are identified by means of
power system analysis software that takes into account fault
analysis. Faults are simulated at each node of the network,
taking into account the worst scenery, thus:



Figure 4. General structure of Monte Carlo method applied to evaluation of
voltage sags.
Three-phase fault solidly-grounded (Rf=0)
Minimum generation dispatch
Time of maximum demand
Faults are simulated sequentially by voltage level,
recording for each fault the residual voltage in the node under
study and the electrical distance between node and fault
point. Thus, for each voltage level is obtained the maximum
distance for which the residual voltage is lower than 0,9 p.u.
(critical distance).
The steps of the algorithm to implement the Monte Carlo
method are [9,11,12]:
1. Select the observation node
2. Select the years of simulation
3. For elements in the AOV, generate a random number
and convert it in fault time according to the probability
distribution of failure rate of the element. Compute the
accumulated time.
4. Generate a random number and convert it in a position
over the transmission line according to the probability
distribution of this parameter.
5. For each fault, generate a random number and convert
it in one fault type (SLG, LL, LLG, LLL) according
to the probability distribution function of fault type.
6. Compute the residual voltage as a result of the fault in
the observation node, according to analytical
calculations.
5.3 Simulation time
According to records of meters installed in the node of
interest, the number of voltage sags per year are between 250
and 340. Thus, considering 360 voltage sags per year and the
expected error lower than 2% for a confidence of 95%, the
minimum number of years to be considered in the simulation
is 25.
5.4 Stochastic factors
There are five stochastic factor considered in this work.
a. Resistance at the fault point
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b.
c.
d.
e.
Fault type
Fault position (lines)
Time period of the faults
Generation dispatch (number of plants in AOV)
under study (El Rio substation). Table 2 shows probabilities
of different fault types at each voltage level of the network
under study.
Table 1.
Probability of faults for each voltage level
Voltage
Probability by fault type (%)
(kV)
1
2
3
13.8
31.5
46.2
22.3
34.5
25.3
49.0
25.7
110
79.0
15.6
5.4
Total
42.0
39.0
19.0
These five factors are considered in the simulations in
order to evaluate their impact in the voltage sags into the
network.
5.4 Resistance
The resistance is modeled stochastically as a normal
random variable with standard deviation equal to 1 [26]. The
mean value of resistance is obtained from records of phaseground faults recorded by distance protection relays located
in zone 2 close to neighbor substation. A statistical validation
was conducted with at least 20 records obtained from the
distance relays in the AOV.
The mean value of the resistance at the fault point was
calculated by means of this procedure: it was employed
historical data (at least 20 events) of phase-ground faults that
involves distance relay in zone 2 located near to substation B
(see Figure 5). The voltage and current waveform from
records stored in the relay are considered for the calculation.
Based on these waveforms and neglecting the impedance in
zone 2 after substation B in transmission line B-C (Zl2), is
calculated the fault impedance.
𝐼𝑓 =
𝑉𝑓
𝑉𝑓
𝑉𝑓
=
≈
𝑍𝑠𝑝 𝑍𝑙 + 𝑍𝑙2 + 𝑍𝑓 𝑍𝑙 + 𝑍𝑓
For each voltage level (bus bars), the total voltage sags is
counted (1 phase, 2 phases and 3 phases). The probability of
each one is calculated as a percentage from the total events
for each voltage level.
5.6 Fault position in transmission lines
Many methods in the literature consider a constant
number of segments for dividing the transmission line;
therefore each segment has a fixed failure rate. In this work
the transmission line is not divided into segments but the fault
position is computed by means of a random number
generated from the probability distribution. This random
number is multiplied for the length of the overhead line and
the fault position is obtained.
(4)
5.7 Time period of the faults
Therefore, Zf can be obtained from the above equation, as
expressed in (5)
𝑍𝑓 =
where:
Vf =
If =
Zsp =
Zl =
𝑉𝑓 − 𝐼𝑓 ∗ 𝑍𝑙
𝐼𝑓
The time of occurrence of a fault is obtained by means of
a random number generated between 0 and 23. 0 means the
time from 00:00 to 01:00, 1 means the time from 01:00 to
02:00 and so on; 23 means the time from 23:00 to 24:00.
From the time of occurrence generated randomly and the load
profile at each bus bar is computed the demand of each node
in the network and the pre-fault voltage by means of a power
flow.
(5)
Fault voltage
Fault current
Impedance from source up to fault point
Impedance of transmission line A – B
5.8 Generation dispatch
The mean value of fault impedance is the average value
of the fault impedances estimated by means of equation (4)
based on the records of faults of the power system.
As the previous parameters, the generation dispatch is
also generated randomly from the probability distribution. In
this work, the generation dispatch has two options: 1) all
generation plants dispatched and, 2) operation without
generation plants connected to 110 kV bus bars. The voltage
sags analysis was developed in a real power system
considering four generation scenarios:
a. Baseline scenario: 30% of time are all generators
dispatched. This is a typical behavior during the dry
season in Colombia (4 months).
b. Scenario 2: 40% of time are all generators dispatched.
This occurs when the dry season is a little bit longer
(5 months).
c. Scenario 3: 60% of time are all generators dispatched.
Dry season is even longer (7 months).
Figure 5. Transmission line representation
5.5 Type of fault
The type of fault was obtained randomly from the
probability distribution of faults at each voltage level. The
probability of each fault is computed from voltage sags data
in bus bars at 13.8 kV, 34.5 kV and 110 kV of the substation
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d. Scenario 4: 70% of time are all generators dispatched.
This scenario is present during “El Niño”
phenomenon, thus the dry season is even longer (8
months)
The Atlantic Coast area of the National Interconnected
Power System of Colombia was used to test the proposed
method. General information about this power system is
presented in Table 3.
5.9 Definition of dynamic variables
Table 3.
Number of elements of the power system.
Voltage
Bus bar
Line
(kV)
13.8
228
620
34.5
120
121
66
33
20
110
102
51
220
17
34
500
10
10
Total
510
856
The load profile at each bus bar of the network is
simulated as dynamic variable. Additionally, the failure rate
of transmission lines and substations of the AOV are
considered dynamics.
For the failure rate, it is assumed that the time between
bus bar and substation faults and the power system
substations follow an exponential distribution. Failure rate of
elements in the AOV is calculated from the real statistics of
the power quality obtained from the actual power system.
5.10
Figure 6 shows the single-line diagram of the Atlantic
Coast area of the National Interconnected Power System of
Colombia, which is used for power quality studies.
Model validation
The main purpose of this section was to compare the
actual measures of three years with the expected average of
voltage sags found with simulations during a long period (25
years) [25].
The first step of the statistical procedure is to determine
the confidence intervals from the results of the simulation in
the points of interest. The confidence intervals provide the
estimated range of values which may include the true
population parameter. If some independent samples of the
population are measured repeatedly and the confidence
interval is calculated, then a percentage (confidence level) of
the obtained intervals will include the population parameter
[11,12].
To estimate the confidence intervals, the method of
percentiles is used, regardless of the probability distribution
[25]. Then, with a significance level of α% [a confidence
level of (1-α)%], the upper and lower limit of the confidence
interval is calculated using the percentile α/2, denoted by Pα/2,
and a percentile of 100-α/2, denoted by P
respectively. The adopted confidence level is usually 95%
(α=5%) and confidence interval limits are P
[25].
5.11
Figure 6. Single-line diagram of the power system test case.
The aim of the simulation was to characterize the
behavior of the power system using the number of voltage
sags as a function of the magnitude and the duration in a
point. The selected point was the bus bar 13.8 kV of the El
Río substation with coupled and uncoupled bus bars, B1 and
B2, as shown in Figure 6.
Voltage sags duration
6.2 Bus bars of interest
Theoretically, the best way to calculate the duration of
each voltage sag is to know the clearance time of the fault.
Therefore, a knowledge of the fault currents, protection
relays settings and breakers time is needed. Obtaining all the
information from distribution networks is sometime a
difficult assignment, due to the amount of data required to
update continuously the databases. Based on [27], in this
research a random generation of voltage sags duration was
implemented in simulation, considering the distribution
probability of voltage sags durations, registered by meters at
the bus bars.
6
Length
(km)
29779
3100
290
1401
1870
1870
38310
This study analyzed stochastically the behavior of the
voltage sags at a bus bar with a number of users connected to
the point. Table 4 shows the information of the number of
users connected to the bus bar. The simulation considered
8687 users connected to the bus bar B1, 3672 users connected
to the bus bar B2, and 12359 users connected to the coupled
bus bars.
Table 4.
Number of users in the El Rio substation.
Type of users
Bus bar
Bus bar
B1
B2
Commercial
1619
1209
Industrial
95
134
Government
38
31
Residential
6935
2298
Power system test case
6
Bus bars B1 and
B2
2828
229
69
9233
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Total
8687
3672
12359
7 Results and analysis
7.1 Area of vulnerability
Figure 7 shows a diagram of the reduced power system to
conduct the different studies. The AOV for the selected bus
bars were calculated using three-phase faults at each bus bar
to evaluate the voltage magnitudes.
(a)
Figure 7. Single-line diagram of El Río substation.
A fault at each bus bar was applied with zero impedance
and a minimum number of maximum demand generation
plants. Table 5 presents a summary of the critical distances
for different voltage levels defining the AOV.
Table 5.
Results of the AOV.
Voltage
Critical
(kV)
Distance
(km)
13.8
20
34.5
15
110
20
220
280
500
700
(b)
Figure 8. SARFI90% per year for the scenario 1, (a) bus bar B1 (b) bus bar
B2.
Substations
7.3 Distribution of voltage sags
Barranquilla
Barranquilla
Barranquilla
Atlantico, Bolivar and Magdalena
Costa Atlántica, San Carlos, Primavera
and Ocaña
Figure 9 and Figure 10 show the frequency distribution of
SARFI90% for the bus bars B1 and B2, respectively.
7.2 Power quality indices
Figure 8 shows the behavior of Monte Carlo simulation for
bus bars B1 and B2, respectively. Figures 8a and 8b show the
SARFI90% for each year of simulation and the behavior of the
voltage sags in the bus bar B1 and B2 of El Rio substation.
The index SARFI90% changes for the first years, but after the
8th year becomes stable.
Figure 9. Frequency distribution of SARFI90% for the bus bar B1.
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Comparing the results of the Monte Carlo simulation for
both scenarios, coupled and uncoupled bus bars and
considering the same failure rate of the elements in the AOV,
the results show that the coupled bus bars generate a high
number of voltage sags than the uncoupled bus bars. If the
number of generation plants increase, the problem becomes
less detectable.
With the exception of the bus bar, B2, for the year 2010,
the values obtained through monitoring the bus bars, B1 and
B2, are contained in the corresponding confidence intervals
of the expected number of voltage sags considering at least
two scenarios.
7.5 Voltage sags duration
The probability distribution function used in this research
to generate the duration of the voltage sags is shown in Figure
12 for 13.8 kV, in Figure 13 for 34.5 kV and in Figure 14 for
110 kV. These results were obtained combining the
magnitude and duration of the voltage sags.
Figure 10. Frequency distribution of SARFI90% for the bus bar B2.
In this figure, the differences between the distribution of
the bus bars, B1 and B2, for the scenarios simulated are
presented. Most of the annual voltage sags for bus bar B2 are
lower that bus bar B1, which helps identify best
configurations from the electrical network.
Figure 11 shows the expected number of sags per year and
the SARFIx for ranges between 0% and 90% for the bus bars,
B1 and B2, of El Rio substation.
Figure 12. Accumulative distribution function of voltage sags duration in
13.8 kV
Figure 11. Number of sags vs magnitude ranges and SARFIx.
7.4 Results of the model
Table 6 shows the number of actual voltage sags versus
the number of voltage sags simulated for the bus bars, B1 and
B2. The measurements of the actual voltage sags were carried
out for the years 2010, 2011 and 2012. The results of the
Monte Carlo simulation were obtained according to the fourgeneration dispatch scenarios defined in the methodology.
In the long term, the expected number of voltage sags
with magnitude  90% (SARFI90%) is lower for the bus bar
B2 than the bus bar B1, due the expected value for the
SARFI90% in bus bar B2 is less than the corresponding
percentile P2.5% for all scenarios.
Figure 13. Accumulative distribution function of voltage sags duration in
34.5 kV.
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Figure 14. Accumulative distribution function of voltage sags duration in
110 kV.
Table 7 shows the accumulated voltage sags for the
coupled and uncoupled bus bars, B1 and B2. The voltage sags
magnitudes with the coupled bus bars, B1 and B2, are similar
to the voltage sags magnitudes obtained with the uncoupled
bus bars, B1 and B2. The number of voltage sags is greater
with the coupled bus bars.
Table 6.
Actual vs simulated voltage sags for bus bars B1 and B2.
Monitoring
Scenario 1 (Gmax 30%)
Bus
bar
2010
2011
2012
P2.5%
P97.5%
VE
Confidential interval of 95%
Scenario 2 (Gmax 40%)
Scenario 3 (Gmax 60%)
Scenario 4 (Gmax 70%)
P2.5%
P97.5%
VE
P2.5%
P97.5%
VE
P2.5%
P97.5%
VE
B1
326
313
293
321.6
353.2
336.0
306.2
342.4
323.5
282.2
314.0
298.0
272.0
302.4
286.8
B2
341
315
315
300.2
330.4
314.6
284.6
317.6
301.9
265.6
291.0
277.7
253.6
282.0
266.9
B1
B2
-
-
-
366.2
397.4
379.6
342.0
373.2
356.5
296.6
334.0
314.5
276.6
314.0
295.1
Table 7.
Voltage sags density according to the magnitude and the duration.
Magn.
Bus
(pu)
bar
0
50
100
150
B1
336.04
305.92
231.96
65.12
0.9
B2
314.56
287.80
216.48
61.36
B1B2
379.56
339.44
254.80
69.80
B1
196.72
185.04
140.60
39.04
0.8
B2
184.12
175.00
131.80
36.76
B1B2
209.80
195.80
145.40
39.88
B1
130.80
124.68
94.28
26.72
0.7
B2
121.88
117.64
87.32
23.56
B1B2
143.00
135.92
100.36
26.72
B1
73.52
70.00
53.80
15.16
0.6
B2
67.52
65.04
47.60
13.12
B1B2
88.68
84.28
62.36
17.20
B1
37.84
35.88
26.84
7.36
0.5
B2
32.60
31.40
22.12
6.48
B1B2
43.64
40.96
31.48
8.32
B1
24.40
23.32
17.24
4.76
0.4
B2
22.04
21.24
14.80
4.28
B1B2
25.56
23.84
18.00
4.64
B1
15.92
15.28
11.08
3.20
0.3
B2
14.44
13.84
9.92
2.72
B1B2
19.48
18.36
13.76
3.28
B1
10.96
10.44
7.40
2.32
0.2
B2
9.60
9.20
6.64
1.84
B1B2
13.00
12.20
9.44
2.36
B1
4.16
3.84
2.52
0.96
0.1
B2
3.88
3.56
2.60
0.96
B1B2
5.84
5.40
4.28
0.92
200
40.16
38.44
44.08
23.76
22.36
24.56
16.44
14.32
16.72
9.08
7.84
10.92
4.00
3.76
5.00
2.68
2.44
2.68
1.80
1.72
1.80
1.28
1.16
1.28
0.60
0.56
0.60
Duration in miliseconds
250
300
350
28.64
20.64
12.36
27.04
19.88
11.24
30.56
21.72
12.80
16.16
11.44
6.36
15.00
11.08
5.16
16.60
11.60
5.88
11.44
8.20
4.60
9.36
6.88
2.96
10.84
7.56
3.52
6.36
4.28
2.44
5.08
3.84
1.76
7.20
5.04
2.04
2.96
2.28
1.32
2.44
1.76
1.04
3.44
2.24
1.08
2.04
1.64
1.08
1.72
1.28
0.76
1.96
1.28
0.60
1.24
1.00
0.64
1.28
0.96
0.60
1.32
0.92
0.40
0.92
0.72
0.44
0.80
0.64
0.40
1.04
0.84
0.36
0.44
0.32
0.16
0.48
0.48
0.36
0.52
0.44
0.16
9
400
6.36
6.28
7.32
2.24
2.20
2.72
1.44
0.92
1.28
0.68
0.52
0.76
0.44
0.40
0.44
0.36
0.36
0.24
0.28
0.36
0.20
0.24
0.32
0.20
0.12
0.28
0.08
500
4.44
4.52
5.40
1.48
1.44
2.00
1.04
0.60
0.92
0.48
0.36
0.52
0.32
0.28
0.36
0.24
0.28
0.20
0.20
0.28
0.16
0.20
0.24
0.16
0.12
0.24
0.08
600
2.72
3.12
3.28
0.88
0.92
1.48
0.64
0.40
0.68
0.32
0.24
0.36
0.24
0.20
0.24
0.20
0.20
0.12
0.16
0.20
0.08
0.16
0.16
0.08
0.08
0.16
0.04
700
1.68
1.76
1.80
0.48
0.40
0.84
0.28
0.20
0.48
0.12
0.04
0.24
0.12
0.04
0.16
0.08
0.04
0.08
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
800
0.80
0.80
1.00
0.20
0.28
0.48
0.12
0.08
0.28
0.04
0.04
0.16
0.04
0.04
0.08
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
900
0.40
0.36
0.48
0.08
0.12
0.36
0.04
0.04
0.24
0.04
0.04
0.16
0.04
0.04
0.08
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
DYNA
http://dyna.medellin.unal.edu.co/
Table 8 shows the accumulated voltage sags for different
percentages of SARFI. The information is presented for the
coupled and uncoupled bus bars, B1 and B2.
Table 8.
Voltage sags evaluated for bus bars B1 and B2 with different SARFIx.
SARFI
Bus
Scenarios
bars
1
2
3
4
B1
336.04
323.52
298.00
286.76
90%
B2
314.56
301.92
277.68
266.92
B1-B2
379.56
356.48
314.48
295.08
B1
196.72
190.80
179.20
173.48
80%
B2
184.12
178.72
166.96
162.60
B1-B2
209.80
200.24
182.60
174.68
B1
130.80
124.96
112.84
107.12
70%
B2
121.88
116.52
104.76
100.64
B1-B2
143.00
133.84
115.72
108.48
B1
73.52
69.60
60.64
56.32
60%
B2
67.52
64.32
55.52
52.48
B1-B2
88.68
82.00
67.52
60.36
B1
37.84
36.00
32.24
30.76
50%
B2
32.60
31.12
29.24
28.04
B1-B2
43.64
41.24
34.60
31.24
For all the SARFI studied, the number of accumulated
voltage sags is greater for the bus bar B1 than the bus bar B2.
Furthermore, the coupled bus bars present a greater number
of voltage sags for all scenarios studied.
8 Conclusion
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In this research the extended fault positions and the
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transmission lines, variation of generation dispatch, and
variation of load were considered for the simulation. As the
results show a high impact of the voltage sags into the power
system operation, the parameters and the method consider in
this research should be included in future power quality
analysis.
Statistical tests were conducted with the results that the
greater number of generation plants dispatched in the AOV,
the lower the magnitude of the voltage sags and the index
SARFI. The proposed method allowed to evaluate the
reconfiguration of bus bars to reduce the number of voltage
sags, obtaining that the coupled bars brings a greater impact
in voltage sags, compared to the results obtained with
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This research was supported in part by the energy strategic
area of the Universidad del Norte, Barranquilla, Colombia.
The authors thank to the company ELECTRICARIBE for the
valuable information provided for this research.
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Jorge W. Sagre received his Bs. degree in Electrical Engineering in 1978
from the Universidad Nacional de Colombia (Bogotá) and a M.Sc. in
Electrical Engineering from Universidad del Norte, Barranquilla, Colombia.
His employment experiences include: the Corporación Eléctrica de la Costa
Atlántica, CORELCA TRANSELCA S.A. E.S.P. and ELECTRICARIBE
S.A. E.S.P. His research interests include: planning, operation and control of
power systems, power quality and regulation.
John Edwin Candelo Becerra received his Bs. degree in Electrical
Engineering in 2002 and his PhD in Engineering with emphasis in Electrical
Engineering in 2009 from Universidad del Valle, Cali, Colombia. His
employment experiences include the Empresa de Energía del Pacífico EPSA,
Universidad del Norte, and Universidad Nacional de Colombia. He is now
an Assistant Professor of the Universidad Nacional de Colombia, Medellín,
Colombia. His research interests include: planning, operation and control of
power systems, and smart grids.
Johny Montaña is full time professor of the Department of Electrical
Engineering at Universidad Federico Santa María in Valparaiso, Chile. He
received his Electrical Engineer degree in 1999, M.Sc. in High Voltage in
2002 and Ph.D. in Electrical Engineering in 2006 from Universidad Nacional
de Colombia. His employment experiences include Universidad Nacional de
Colombia as Research Assistant (2000-2005), Siemens SA as Design
Engineer Jr. (2006-2009) and full time professor at Universidad del Norte Colombia (2010-2013). His research and teaching interests include lightning
protection systems, lightning location systems and grounding systems.
11