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Voltage sag index calculation: Comparison between time-domain simulation and short-circuit calculation
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Electric Power Systems Research 78 (2008) 676–682
Voltage sag index calculation: Comparison between time-domain simulation and short-circuit calculation Jose Maria Carvalho Filho a , Roberto Chouhy Leborgne b,∗ , Paulo M´arcio da Silveira a , Math H.J. Bollen c b
a Universidade Federal de Itajub´ a, Brazil Chalmers University of Technology, Sweden c STRI AB, Sweden
Received 11 May 2006; received in revised form 21 November 2006; accepted 17 May 2007 Available online 24 July 2007
Abstract This paper describes a case study where voltage sags indices are estimated using Monte Carlo approach combined with ATP (Alternative Transient Program) and short-circuit calculation program. Voltage sag magnitude and frequency are used to evaluate the correlation between both programs. The results indicate that time-domain simulation and short-circuit calculation gives similar voltage sag indices. Considering the high correlation between the results, short-circuit calculation programs are preferable over the time-domain simulation tools as the modelling for time-domain simulation is more complex, time consuming, and rarely covers the whole network. © 2007 Elsevier B.V. All rights reserved. Keywords: Simulation; Power quality; Voltage sag (dip)
1. Introduction A voltage sag is a power quality disturbance defined as a reduction of the voltage to a value below a given threshold followed by a recovery of the voltage within a short interval of time. Faults in the transmission and distribution systems are often the origin of the severe sags [1]. Transformer energizing, motor starting, and heavy-load switching are responsible for more shallow sags [2]. Voltage sags are evaluated in terms of voltage magnitude, sag duration, and frequency of occurrence [3]. All these parameters can be obtained through long-term measurements or simulations. The main limitation of a network-monitoring program is the long time needed to obtain accurate results. For example, for an expected number of 150 sags per year, to obtain an accurate (error less than 10%) frequency, the minimum monitoring period is around 3 years [2]. Another limitation is the high cost
∗
Corresponding author. Tel.: +46 31 772 1632; fax: +46 31 772 1633. E-mail addresses: [email protected] (J.M.C. Filho), [email protected] (R.C. Leborgne), [email protected] (P.M. da Silveira), [email protected] (M.H.J. Bollen). 0378-7796/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2007.05.017
of buying and installing power quality monitors in the whole network. Furthermore, the changes in the network topology and the installation of new generation plants change the expected voltage sags statistics, so that past surveys may no longer be reliable to describe future sag indices. Considering that most of the severe voltage sags are caused by faults in the networks, fault simulation has been used for voltage sags estimation [4]. Fault simulation can be performed using time-domain tools and short-circuit calculation programs. Electromagnetic transient programs, one of the most common time-domain simulation tools, and short-circuit calculation programs have been applied for voltage sag simulation in the last years. However, the correspondence of the results obtained by the simulations has not been investigated enough. A previous work [5] compared dynamic and static analysis procedures to estimate the fault currents. The paper concluded that short-circuit duties calculated by the static method lead to a conservative result, i.e., fault currents obtained by a static program are higher than faults currents obtained by the dynamic tool. Nevertheless, the bus voltages were not assessed, so there is no conclusion about the voltage sag indices resulting from the application of electromagnetic transient programs and short-circuit calculation programs.
J.M.C. Filho et al. / Electric Power Systems Research 78 (2008) 676–682
Therefore, this paper provides an extensive work to analyse the correlation between an electromagnetic transient program (ATP) and a short-circuit calculation program for the estimation of sag indices. 2. Voltage sag simulation Simulation methods are an inexpensive choice to obtain voltage sags characteristics, thus avoiding long and expensive periods of measurements. The tools used to calculate voltage sags can be classified in three types: waveform simulation, fault calculation, and complex voltage estimation as a function of time (time-dependent phasors) [6]. During waveform simulation voltage sags are considered as transients and the waveform distortion in time domain is calculated. This methodology can provide complete information on the characteristic of the disturbance; but it requires a long time for the computing process due to the complexity of system and component modelling [7,8]. Built-in capabilities are available in most electromagnetic transient programs. They can be used to reproduce very accurately most transients in power systems. However, the detailed representation of some components is not straightforward. For example, the transformer model requires the representation of its non-linear and frequency-dependent behaviour. The detailed model of power electronic devices like the DVR or the VSCHVDC requires a very small time step size in time-domain simulation [9,10]. Therefore, the user is forced to choose between a very accurate model and a feasible one [11]. The components included in voltage sag simulation are: conventional and distributed generators, power components, protective devices, mitigation devices, and loads. The model of the large generators includes the effect of the voltage regulation; whereas the small generators are modelled by a voltage source behind the machines’ sub-synchronous reactance. The long transmission lines are modelled by distributed parameters considering the series resistance and reactance and the shunt capacitance per kilometer. The short lines are modelled using lumped parameters, considering the resistance and the reactance. The model of the transformers considers the short-circuit impedance, the saturation, and the phase shift between the primary and the secondary voltages. Shunt reactors and capacitors are modelled by their reactance and susceptance. The circuit breakers, reclosers and any type of disconnectors are represented as an ideal switch. The load model has influence on the during fault voltage at low and medium voltage buses [12]. Usually the loads are modelled as constant impedances. However, in order to analyse the performance of a sensitive equipment connected in a grid with a high penetration of induction machines a more detailed load modelling is needed. For stochastic assessment of voltage sags the load model should incorporate both daily and random variations. The short-circuit tool is more popular for voltage sag assessment due to their easy application and simple network modelling. The voltage magnitude is obtained in a straightforward manner from the bus impedance matrix, the sag duration
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can be estimated using the fault-clearing time, and the sag frequency is associated to the fault rate of the nearby network (region of vulnerability) [13,14]. The short-circuit programs use the sequence representation of the network and sparse matrix properties to estimate the state of the network for a given event. Events are characterised by the fault location, fault type, and fault impedance. The generators are modelled as an ideal voltage source behind the synchronous or sub-synchronous reactance of the machines. In general the generator voltage is set to 1 per unit. The model adopted for the transmission lines considers the resistance and the reactance, neglecting the shunt capacitance. The transformer model includes the short-circuit impedance and the phase shift due to the winding configuration. The line and bus reactors and capacitors are modelled by a constant reactance and capacitance. Usually, the loads are neglected when performing this static simulation, with the exception of large motor loads. There is a third simulation method based on the estimation of the complex voltages as a function of time. This approach is also known as “time-dependent phasors”. The fault current calculation obtained from the short circuit analysis is repeated every time step. The generator and load are represented through a complex voltage and impedance, which are updated every time step. To obtain the sag duration the protective devices are included into the model either with a pre-defined fault-clearing time or by modelling the fault detection and clearing process in more detail. The calculation of the sag magnitude and duration requires some additional steps. It is reasonably to consider the magnitude and the angle of the complex voltage to be equal to the rms voltage and the phase angle [11]. 3. Voltage sag indices Voltage sags indices are the set of values used to describe the performance of a given site or system regarding voltage sags. In order to obtain the system performance a five step method is recommended [3,15]: • • • •
Obtain instantaneous voltages. Calculate event characteristics as a function of time. Calculate single event characteristics. Calculate site indices from the single event-characteristics of all registered voltage sags. • Calculate system indices from the site indices. Instantaneous voltages can be obtained from either measurement devices or time-domain simulation. Short-circuit calculation provides an approximation of single eventcharacteristics. Once the single event-characteristics are estimated, a statistical approach can be used to estimate the site and system indices. The magnitude, duration, and sag frequency are the most used voltage sag indices. Voltage sag magnitude is defined as the minimum rms voltage. For example, the three-phase voltage sag shown in Fig. 1 is characterised by a magnitude of 0.29 per unit and a duration of 50 ms. The expressions “retained voltage”, “remaining voltage”, and “residual voltage” are considered syn-
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4. Case study 4.1. System modelling
Fig. 1. Voltage sag characterisation by magnitude and duration.
onyms with magnitude and they all refer to the minimum rms voltage [3]. The voltage sag frequency is quantified using the SARFI index. SARFI is the anachronism for System Average RMS Variation Frequency Index. It can refer for a single site, a group of substations, or the whole system. There are two types of SARFI indices: SARFI-X and SARFI-Curve. The SARFI-X refers to a certain voltage threshold (X = 90%, 70%, 50%, etc.). The SARFI-Curve indicates the number of events below a certain reference curve of sensitivity (CBEMA, ITIC, SEMI). Basically, this index gives the number of times per year that the magnitude of a voltage sag is below a specified threshold [3].
A scheme of the system used in the case study is shown in Fig. 2. The network contains 67 transmission lines (138 and 230 kV) with a total length of 6619 km. There are 93 substations with a transformer-installed capacity of 2076 MVA. The generation capacity is 1643 MVA and the present demand is 690 MW with a high load factor. The excess of generated power is exported to the Brazilian southeast region through the substation called RND. The long distances between the power generators and the loads characterise a system with long and sub-compensated transmission lines. A total of 12 buses (230, 138, 34.5, and 13.8 kV) located at 5 substations are selected for voltage sag assessment. The monitored buses (P1, . . ., P12) are indicated in Fig. 2. The criteria for the bus choice included: network topology, load concentration, sensitive-loads location, main generation plants, and transformer connections. The short-circuit calculation program applied in this work is a program used by most of the utilities in Brazil [17]. Table 1 summarizes the system modelling used for the ATP simulation and the short-circuit calculation. 4.2. Simulations In order to assess voltage sags the first step is the characterisation of the single event. The unbalanced three-phase sags are
Fig. 2. The analysed network. The 12 monitor locations are indicated (P1, . . ., P12).
J.M.C. Filho et al. / Electric Power Systems Research 78 (2008) 676–682 Table 1 System modelling
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Table 4 Voltage sag matrix
Equipment
ATP [16]
Short-circuit [17]
ATP
P1
P2
P3
...
P12
Generators Short lines Long lines Transformers Reactors/capacitors Loads
Dynamic/ideal source Lumped parameters Distributed parameters R, X, and saturation Reactance Constant impedance
Ideal source Lumped parameters Lumped parameters R, X and phase shift Reactance Neglected
Event 1 Event 2 .. . Event 136
0.86 0.93 .. . 0.93
0.87 0.93 .. . 0.93
0.89 0.94 .. . 0.95
... ... .. . ...
0.94 0.97 .. . 0.98
Table 5 Average voltage sags indices corresponding to 136 simulated faults
Table 2 Utility faults statistics Voltage level (kV)
ATP
Fault type LG (%)
138 230
62 80
LL (%)
LLG (%)
LLL (%)
10 7
14 3
14 10
SARFI—90% (# sags) Average sag magnitude (per unit)
523 0.73
Short-circuit 442 0.75
that pre-fault voltages are equal to 1.0 per unit for all buses. This is a common assumption in short-circuit calculations. On the other hand, the ATP pre-fault voltages are a consequence of the steady-state load flow. Thus, in order to minimize the effects of the different pre-fault voltages on the sag estimation, the loads modelled in the ATP were adjusted until the pre-fault voltages were close to 1.0 per unit. This manipulation is done making small changes on the load values according to the utility load information. Table 3 shows the pre-fault voltages obtained at the 12 simulated buses.
characterised by the critical phase: the phase that presents the deepest sag. Another approach is to consider three independent sags, one for each phase. Here, we chose to aggregate the phases taking the most severe sag to characterise the three-phase event. Two MatLab routines are created to treat the output of the ATP and the short-circuit program. The ATP delivers the instantaneous voltages, and then the MatLab routine computes the rms voltages and selects the smallest value of the three phases. The short-circuit program supplies the sag magnitude for each phase and the MatLab routine chooses the smallest voltage. The simulated faults are generated using the Monte Carlo approach. The main idea of the Monte Carlo simulation is the creation of simulated data taking into account as much uncertainty as possible by using random numbers. In others words, we intend to create several cases and the corresponding sag monitoring results so that the variability of several factors are considered. The main stochastic variables that affect the sag indices are the fault position, the fault type, the fault impedance, the fault rate, and the pre-fault voltage. In order to have a statistical reliability of 95% and a statistical error below 10% more than 100 cases are considered. Hence, 136 cases are generated through a Monte Carlo approach: 121 faults in lines (138 and 230 kV) and 15 faults in distribution buses (13.8 and 34.5 kV). The utility fault statistics, shown in Table 2, are used for the generation of the cases. At this stage two fault impedances are considered for LG and LLG faults: 15 and 40 with the same probability (50%).
4.4. Results obtained The simulated results are organized in a matrix, known as voltage sag matrix. The matrix has 12 columns, one for each monitored bus (P1, . . ., P12) and 136 lines, one for each simulated case, as shown in Table 4. Each matrix cell contains the sag magnitude Vkf that means the sag magnitude at bus k for a certain event f. An event f is fully characterised by: the fault location, the fault type, the fault impedance, and the network topology. Two sag matrices are built, one for the ATP results and another for the short-circuit results. As a result of the 136 events simulated a total of 1632 voltage values are obtained for each program. It is important to observe that most of the obtained voltages are above the selected sag threshold (0.9 per unit). As shown in Table 5, the ATP estimates 523 voltage sags whereas the short-circuit program estimates 442 voltage sags. The average sag magnitude estimated using ATP is 0.73 per unit whereas the short-circuit estimates an average sag magnitude of 0.75 per unit. Therefore, at the system index level, the ATP simulation is more conservative than the short-circuit calculation, giving a higher number of sags and a lower average sag magnitude.
4.3. Influence of pre-fault voltages An important parameter to take into account is the pre-fault bus voltage. For the short-circuit calculations we have assumed Table 3 Pre-fault voltages at the 12 analysed buses Pre-fault voltages (per unit)
P1
P2
P3
P4
P5
P6
P7
P8
P9
P10
P11
P12
ATP Short-circuit program
0.99 1.0
0.99 1.0
1.01 1.0
0.98 1.0
0.98 1.0
1.00 1.0
1.00 1.0
0.98 1.0
0.98 1.0
0.99 1.0
0.98 1.0
1.00 1.0
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Fig. 3. Voltage sag cumulative distribution.
4.5. Voltage sag frequency The total number of sags with magnitude below a certain threshold (SARFI-X) for the 12 monitored buses is plotted in Fig. 3. The number of sags obtained from the ATP simulation is higher for all thresholds. It means that for any given load sensitivity, the number of expected outages is higher when the study is performed using the ATP program than when using a short-circuit calculation program. The results are analysed for each bus individually. Fig. 4 shows the SARFI-90% calculated using ATP and short-circuit program for the 12 buses. It is clear that the ATP provides a more pessimistic scenario for the 12 monitored buses. The difference is higher at the buses P4 and P5. One of the explanations for this large difference at buses P4 and P5 are the pre-fault voltages at the analysed buses. When the pre-fault voltage is set below 1.0 per unit the number of sags tends to be higher because the reference voltage used to estimate the sag in per unit is the bus rated voltage and not the pre-fault voltage. So, a voltage drop of 0.09 per unit is not computed as a voltage sag when the pre-sag voltage is 1.0 per unit but it is computed as a sag when the pre-sag voltage is 0.98 per unit. On the other hand, the pre-fault voltage at the generation buses plays an opposite role. A high voltage at a generation bus will produce larger fault currents flowing in the system. Consequently, the high currents will produce larger voltage drops and deeper sags.
Fig. 5. Average sag magnitude estimated at the monitored buses.
small. In most of the buses (9 of 12) the short-circuit program estimates larger average sag magnitudes (less severe sags). Another way to analyse the difference on the magnitude estimated using ATP and short-circuit programs is through a divergence index. The divergence is computed using (1) for each event where the retained voltage is below 0.9 per unit for at least one of the programs. DIV = VATP − VSC
(1)
The average sag magnitude estimated for each analysed bus is presented in Fig. 5. It can be seen that the differences are rather
being VATP and VSC the sag magnitude in per unit obtained by the ATP and by the short-circuit program, respectively. Fig. 6 shows the distribution of the divergences. It can be seen that only 3% of the estimated divergences are positive. This means that in 3% of simulated cases the ATP estimates higher sag magnitudes (more shallow sags). On the other hand, in most of the cases the ATP estimated deeper sags. However, the divergence is rather small and only 2% of the cases presents a divergence larger than 10%. It is clear that both programs give similar results for the sag magnitude. A closer look in the events that present divergence above 10% shows that they happen in the buses P9, P10 and P11, as shown in Table 6. All these buses belong to the substation RND. This substation presents a particular behaviour because the excess of generation on the network (400 MW) flows through this substation to the Brazilian southeast network. The dynamic program models this special characteristic, whereas the static program neglects the load current, obtaining larger sag magnitudes (VSC > VATP ). Consequently, the divergence is larger and negative in these cases.
Fig. 4. SARFI-90 for the 12 monitored buses.
Fig. 6. Distribution of divergences.
4.6. Voltage sag magnitude
J.M.C. Filho et al. / Electric Power Systems Research 78 (2008) 676–682 Table 6 Events with divergence over 10% Divergence (%)
Event 1 Event 46 Event 48 Event 91 Event 118 Event 121
P9
P10
P11
−12 −11
−10 −12 −10
−12
−10
−11
−10 −10
−10
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larger number of sags and lower average magnitude. However, the results show that the divergence of the estimated sag indices is not significant. A second series of simulation intended to analyse the influence of the fault type and the fault impedance on the comparison between the two simulation approaches was performed. The results are in agreement with the previous findings: for any type of fault and fault impedances considered, the ATP provides a more pessimistic scenario. Finally, considering the rather low divergence of the sag magnitude and the sag frequency obtained from the ATP and the short-circuit calculation tool, it can be concluded that both of them are suitable to estimate voltage sag indices. Considering the simplification of the system modelling for short-circuit calculation compared with the rather complex models required for the ATP simulation and the time spent to run a large number of simulations, it is recommended to use short-circuit programs to estimate voltage sag indices at site and system levels. Acknowledgement Roberto Chouhy Leborgne acknowledges CAPES—Ministry of Education of Brazil for the financial support. References
Fig. 7. Magnitude divergence distribution for 6 types of faults.
4.7. Influence of fault type and fault impedance The influence of the fault type and the fault impedance on the estimated sag magnitude is analysed. This study is performed over a new set of simulated cases. A total of 67 fault locations are randomly chosen, one location at each line. Then 6 types of fault are simulated at each position: LG 0 fault impedance, LG 25 fault impedance, LLG 0 , LLG 25 , LL, and LLL. The divergence index is estimated for the simulated sags. The distribution of divergences is presented in Fig. 7. It is observed that the divergences are concentrated between 0 and −5%. Consequently, the difference in the estimated average magnitude is concentrated at values below 5%. Therefore, the results obtained by using ATP or short-circuit program follows the same tendency for any type of fault. The same conclusion applies for the fault impedance; the choice of 25 or 0 will not affect the divergence index. In other words, the result of the comparison of the two approaches is not sensitive to uncertainties such as the fault type and the fault impedance. 5. Conclusions Voltage sag indices have been calculated using two simulation approaches: ATP and a short-circuit program. The ATP simulation considers the load and the pre-fault system condition, whereas the short-circuit program neglects the load and simplifies all pre-fault voltages to 1.0 per unit. As a result, the voltage sag assessment using the ATP is more conservative than the one using the short-circuit program; the ATP simulation leads to a
[1] L. Conrad, K. Little, C. Grigg, Predicting and preventing problems associated with remote fault-clearing voltage dips, IEEE Trans. Ind. Appl. 27 (1) (1991) 167–172. [2] M.H.J. Bollen, Understanding Power Quality Problems—Voltage Sags and Interruptions, IEEE Press, New York, 1999. [3] IEEE Working Group P1564, Voltage Sags Indices, Draft 6, January 2004. [4] M.R. Qader, M.H.J. Bollen, R.N. Allan, Stochastic prediction of voltage sags in large transmission system, IEEE Trans. Ind. Appl. 35 (1) (1999) 152–162. [5] O.E. Roennspiess, A.E. Efthymiadis, A comparison of static and dynamic short circuit analysis procedures, IEEE Trans. Ind. Appl. 26 (3) (1990) 463–475. [6] W. Xu, Component modeling issues for power quality assessment, IEEE Power Eng. Rev. 21 (11) (2001) 12–17. [7] M.H.J. Bollen, G. Yalcinkaya, G. Hazza, The use of electromagnetic transient programs for voltage sags analysis, in: Proceedings of Eighth IEEE International Conference on Harmonics and Quality of Power, Athens, Greece, October 1998. [8] J.A. Martinez, J. Martin-Arnedo, Voltage sag stochastic prediction using an electromagnetic transients program, IEEE Trans. Power Deliv. 19 (4) (2004) 1975–1982. [9] C. Du, M.H.J. Bollen, Power-frequency control of VSC-HVDC during island operation, in: Proceedings of Eighth IEE International Conference on AC and DC Power Transmission, London, March 2006. [10] M. Bongiorno, A. Sannino, L. Dusonchet, Cost-effective power quality improvement for industrial plants, in: Proceedings of IEEE Bologna PowerTech, Italy, June 2003. [11] Cigre Task Force C4.1.02, Voltage Dip Evaluation and Prediction Tools, draft, November 2005. [12] M.H.J. Bollen, M. Hager, C. Roxenius, Voltage dips in distribution systems: load effects, measurements and theory, in: Proceeding of Congr`es International des R´eseaux Electriques de Distribution CIRED 2003, Barcelona, 2003. [13] G. Olguin, Voltage dip (sag) estimation in power system based on stochastic assessment and optimal monitoring, Ph.D. Thesis 2276, Division of Electric Power Engineering, Chalmers University of Technology, Gothenburg, 2005.
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[14] J.M. Carvalho Filho, J.P.G. Abreu, J.C. Caminha Noronha, H. Arango, Analysis of power system performance under voltage sags, Electric Power Syst. Res. 55 (3) (2000) 211–218. [15] G. Beaulieu, M.H.J. Bollen, S. Malgarotti, R. Ball, Power quality indices and objectives. Ongoing activities in CIGRE WG 36-07, in: Proceedings of IEEE Power Engineering Society Summer Meeting, Chicago, July 2002. [16] CAUE—Comite Argentino de Usuarios de EMTP-ATP, ATP-Rule Book, Buenos Aires, December 2001. [17] Cepel—Centro de Pesquisas de Energia El´etrica, Programa de an´alise de faltas simultˆaneas–ANAFAS, vers˜ao 3.0, Manual do Usu´ario, Rio de Janeiro, Brasil, December 1998 (in Portuguese). Jose Maria Carvalho Filho received his M.Sc. and D.Sc. degree in electrical engineering from the Itajub´a Federal University, Brazil, in 1996 and 2000, respectively. At present he is associate professor at Itajub´a Federal University and a Power Quality Study Group member. His fields of interest include voltage sags (dips), electrical system protection and other power quality issues. He is also a specialized consultant in industrial planning. Roberto Chouhy Leborgne received his E.E. degree and MSc. in E.E. from Itajub´a Federal University, Brazil, in 1998 and 2003, respectively. He received his Licentiate degree from Chalmers University of Technology in 2005. His employment experience includes ABB-Daimler Benz Transportation Brazil and Teyma Abengoa Uruguay. He is currently a Ph.D. candidate at Chalmers University
of Technology, Sweden. His fields of interest are voltage sags and other power quality issues. Paulo M´arcio da Silveira was born in Itajub´a, Brazil, in 1960. He received his BSEE and M.Sc. degrees from the Itajub´a Federal University, Brazil, and his D.Sc. degree from the Federal University of Santa Catarina, Brazil, in 2001. He is associate professor at Itajub´a Federal University, where he is also the Power Quality Group sub-coordinator. His research interests include power system protection and power quality issues. Math H.J. Bollen received his M.Sc. and Ph.D. degrees from Eindhoven University of Technology, Eindhoven, The Netherlands, in 1985 and 1989, respectively. He is manager of EMC and power quality at STRI AB, Ludvika, Sweden and guest professor at EMC-on-site, Lule˚a University of Technology, Skellefte˚a, Sweden. Before joining STRI in 2003 he was a research associate at Eindhoven University of Technology from 1989 to 1993; lecturer at the University of Manchester, Institute of Science and Technology between 1993 and 1996; and professor in electric power systems at Chalmers University of Technology between 1997 and 2003, Gothenburg, Sweden. His research interests cover a wide range of power-system issues, with special emphasis on power quality and reliability. He has published a number of fundamental papers on voltage dip analysis and a textbook on power quality. Math Bollen is active in several IEEE, CIGRE and IEC working groups on power quality.
Electric Power Systems Research 78 (2008) 676–682
Voltage sag index calculation: Comparison between time-domain simulation and short-circuit calculation Jose Maria Carvalho Filho a , Roberto Chouhy Leborgne b,∗ , Paulo M´arcio da Silveira a , Math H.J. Bollen c b
a Universidade Federal de Itajub´ a, Brazil Chalmers University of Technology, Sweden c STRI AB, Sweden
Received 11 May 2006; received in revised form 21 November 2006; accepted 17 May 2007 Available online 24 July 2007
Abstract This paper describes a case study where voltage sags indices are estimated using Monte Carlo approach combined with ATP (Alternative Transient Program) and short-circuit calculation program. Voltage sag magnitude and frequency are used to evaluate the correlation between both programs. The results indicate that time-domain simulation and short-circuit calculation gives similar voltage sag indices. Considering the high correlation between the results, short-circuit calculation programs are preferable over the time-domain simulation tools as the modelling for time-domain simulation is more complex, time consuming, and rarely covers the whole network. © 2007 Elsevier B.V. All rights reserved. Keywords: Simulation; Power quality; Voltage sag (dip)
1. Introduction A voltage sag is a power quality disturbance defined as a reduction of the voltage to a value below a given threshold followed by a recovery of the voltage within a short interval of time. Faults in the transmission and distribution systems are often the origin of the severe sags [1]. Transformer energizing, motor starting, and heavy-load switching are responsible for more shallow sags [2]. Voltage sags are evaluated in terms of voltage magnitude, sag duration, and frequency of occurrence [3]. All these parameters can be obtained through long-term measurements or simulations. The main limitation of a network-monitoring program is the long time needed to obtain accurate results. For example, for an expected number of 150 sags per year, to obtain an accurate (error less than 10%) frequency, the minimum monitoring period is around 3 years [2]. Another limitation is the high cost
∗
Corresponding author. Tel.: +46 31 772 1632; fax: +46 31 772 1633. E-mail addresses: [email protected] (J.M.C. Filho), [email protected] (R.C. Leborgne), [email protected] (P.M. da Silveira), [email protected] (M.H.J. Bollen). 0378-7796/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2007.05.017
of buying and installing power quality monitors in the whole network. Furthermore, the changes in the network topology and the installation of new generation plants change the expected voltage sags statistics, so that past surveys may no longer be reliable to describe future sag indices. Considering that most of the severe voltage sags are caused by faults in the networks, fault simulation has been used for voltage sags estimation [4]. Fault simulation can be performed using time-domain tools and short-circuit calculation programs. Electromagnetic transient programs, one of the most common time-domain simulation tools, and short-circuit calculation programs have been applied for voltage sag simulation in the last years. However, the correspondence of the results obtained by the simulations has not been investigated enough. A previous work [5] compared dynamic and static analysis procedures to estimate the fault currents. The paper concluded that short-circuit duties calculated by the static method lead to a conservative result, i.e., fault currents obtained by a static program are higher than faults currents obtained by the dynamic tool. Nevertheless, the bus voltages were not assessed, so there is no conclusion about the voltage sag indices resulting from the application of electromagnetic transient programs and short-circuit calculation programs.
J.M.C. Filho et al. / Electric Power Systems Research 78 (2008) 676–682
Therefore, this paper provides an extensive work to analyse the correlation between an electromagnetic transient program (ATP) and a short-circuit calculation program for the estimation of sag indices. 2. Voltage sag simulation Simulation methods are an inexpensive choice to obtain voltage sags characteristics, thus avoiding long and expensive periods of measurements. The tools used to calculate voltage sags can be classified in three types: waveform simulation, fault calculation, and complex voltage estimation as a function of time (time-dependent phasors) [6]. During waveform simulation voltage sags are considered as transients and the waveform distortion in time domain is calculated. This methodology can provide complete information on the characteristic of the disturbance; but it requires a long time for the computing process due to the complexity of system and component modelling [7,8]. Built-in capabilities are available in most electromagnetic transient programs. They can be used to reproduce very accurately most transients in power systems. However, the detailed representation of some components is not straightforward. For example, the transformer model requires the representation of its non-linear and frequency-dependent behaviour. The detailed model of power electronic devices like the DVR or the VSCHVDC requires a very small time step size in time-domain simulation [9,10]. Therefore, the user is forced to choose between a very accurate model and a feasible one [11]. The components included in voltage sag simulation are: conventional and distributed generators, power components, protective devices, mitigation devices, and loads. The model of the large generators includes the effect of the voltage regulation; whereas the small generators are modelled by a voltage source behind the machines’ sub-synchronous reactance. The long transmission lines are modelled by distributed parameters considering the series resistance and reactance and the shunt capacitance per kilometer. The short lines are modelled using lumped parameters, considering the resistance and the reactance. The model of the transformers considers the short-circuit impedance, the saturation, and the phase shift between the primary and the secondary voltages. Shunt reactors and capacitors are modelled by their reactance and susceptance. The circuit breakers, reclosers and any type of disconnectors are represented as an ideal switch. The load model has influence on the during fault voltage at low and medium voltage buses [12]. Usually the loads are modelled as constant impedances. However, in order to analyse the performance of a sensitive equipment connected in a grid with a high penetration of induction machines a more detailed load modelling is needed. For stochastic assessment of voltage sags the load model should incorporate both daily and random variations. The short-circuit tool is more popular for voltage sag assessment due to their easy application and simple network modelling. The voltage magnitude is obtained in a straightforward manner from the bus impedance matrix, the sag duration
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can be estimated using the fault-clearing time, and the sag frequency is associated to the fault rate of the nearby network (region of vulnerability) [13,14]. The short-circuit programs use the sequence representation of the network and sparse matrix properties to estimate the state of the network for a given event. Events are characterised by the fault location, fault type, and fault impedance. The generators are modelled as an ideal voltage source behind the synchronous or sub-synchronous reactance of the machines. In general the generator voltage is set to 1 per unit. The model adopted for the transmission lines considers the resistance and the reactance, neglecting the shunt capacitance. The transformer model includes the short-circuit impedance and the phase shift due to the winding configuration. The line and bus reactors and capacitors are modelled by a constant reactance and capacitance. Usually, the loads are neglected when performing this static simulation, with the exception of large motor loads. There is a third simulation method based on the estimation of the complex voltages as a function of time. This approach is also known as “time-dependent phasors”. The fault current calculation obtained from the short circuit analysis is repeated every time step. The generator and load are represented through a complex voltage and impedance, which are updated every time step. To obtain the sag duration the protective devices are included into the model either with a pre-defined fault-clearing time or by modelling the fault detection and clearing process in more detail. The calculation of the sag magnitude and duration requires some additional steps. It is reasonably to consider the magnitude and the angle of the complex voltage to be equal to the rms voltage and the phase angle [11]. 3. Voltage sag indices Voltage sags indices are the set of values used to describe the performance of a given site or system regarding voltage sags. In order to obtain the system performance a five step method is recommended [3,15]: • • • •
Obtain instantaneous voltages. Calculate event characteristics as a function of time. Calculate single event characteristics. Calculate site indices from the single event-characteristics of all registered voltage sags. • Calculate system indices from the site indices. Instantaneous voltages can be obtained from either measurement devices or time-domain simulation. Short-circuit calculation provides an approximation of single eventcharacteristics. Once the single event-characteristics are estimated, a statistical approach can be used to estimate the site and system indices. The magnitude, duration, and sag frequency are the most used voltage sag indices. Voltage sag magnitude is defined as the minimum rms voltage. For example, the three-phase voltage sag shown in Fig. 1 is characterised by a magnitude of 0.29 per unit and a duration of 50 ms. The expressions “retained voltage”, “remaining voltage”, and “residual voltage” are considered syn-
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4. Case study 4.1. System modelling
Fig. 1. Voltage sag characterisation by magnitude and duration.
onyms with magnitude and they all refer to the minimum rms voltage [3]. The voltage sag frequency is quantified using the SARFI index. SARFI is the anachronism for System Average RMS Variation Frequency Index. It can refer for a single site, a group of substations, or the whole system. There are two types of SARFI indices: SARFI-X and SARFI-Curve. The SARFI-X refers to a certain voltage threshold (X = 90%, 70%, 50%, etc.). The SARFI-Curve indicates the number of events below a certain reference curve of sensitivity (CBEMA, ITIC, SEMI). Basically, this index gives the number of times per year that the magnitude of a voltage sag is below a specified threshold [3].
A scheme of the system used in the case study is shown in Fig. 2. The network contains 67 transmission lines (138 and 230 kV) with a total length of 6619 km. There are 93 substations with a transformer-installed capacity of 2076 MVA. The generation capacity is 1643 MVA and the present demand is 690 MW with a high load factor. The excess of generated power is exported to the Brazilian southeast region through the substation called RND. The long distances between the power generators and the loads characterise a system with long and sub-compensated transmission lines. A total of 12 buses (230, 138, 34.5, and 13.8 kV) located at 5 substations are selected for voltage sag assessment. The monitored buses (P1, . . ., P12) are indicated in Fig. 2. The criteria for the bus choice included: network topology, load concentration, sensitive-loads location, main generation plants, and transformer connections. The short-circuit calculation program applied in this work is a program used by most of the utilities in Brazil [17]. Table 1 summarizes the system modelling used for the ATP simulation and the short-circuit calculation. 4.2. Simulations In order to assess voltage sags the first step is the characterisation of the single event. The unbalanced three-phase sags are
Fig. 2. The analysed network. The 12 monitor locations are indicated (P1, . . ., P12).
J.M.C. Filho et al. / Electric Power Systems Research 78 (2008) 676–682 Table 1 System modelling
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Table 4 Voltage sag matrix
Equipment
ATP [16]
Short-circuit [17]
ATP
P1
P2
P3
...
P12
Generators Short lines Long lines Transformers Reactors/capacitors Loads
Dynamic/ideal source Lumped parameters Distributed parameters R, X, and saturation Reactance Constant impedance
Ideal source Lumped parameters Lumped parameters R, X and phase shift Reactance Neglected
Event 1 Event 2 .. . Event 136
0.86 0.93 .. . 0.93
0.87 0.93 .. . 0.93
0.89 0.94 .. . 0.95
... ... .. . ...
0.94 0.97 .. . 0.98
Table 5 Average voltage sags indices corresponding to 136 simulated faults
Table 2 Utility faults statistics Voltage level (kV)
ATP
Fault type LG (%)
138 230
62 80
LL (%)
LLG (%)
LLL (%)
10 7
14 3
14 10
SARFI—90% (# sags) Average sag magnitude (per unit)
523 0.73
Short-circuit 442 0.75
that pre-fault voltages are equal to 1.0 per unit for all buses. This is a common assumption in short-circuit calculations. On the other hand, the ATP pre-fault voltages are a consequence of the steady-state load flow. Thus, in order to minimize the effects of the different pre-fault voltages on the sag estimation, the loads modelled in the ATP were adjusted until the pre-fault voltages were close to 1.0 per unit. This manipulation is done making small changes on the load values according to the utility load information. Table 3 shows the pre-fault voltages obtained at the 12 simulated buses.
characterised by the critical phase: the phase that presents the deepest sag. Another approach is to consider three independent sags, one for each phase. Here, we chose to aggregate the phases taking the most severe sag to characterise the three-phase event. Two MatLab routines are created to treat the output of the ATP and the short-circuit program. The ATP delivers the instantaneous voltages, and then the MatLab routine computes the rms voltages and selects the smallest value of the three phases. The short-circuit program supplies the sag magnitude for each phase and the MatLab routine chooses the smallest voltage. The simulated faults are generated using the Monte Carlo approach. The main idea of the Monte Carlo simulation is the creation of simulated data taking into account as much uncertainty as possible by using random numbers. In others words, we intend to create several cases and the corresponding sag monitoring results so that the variability of several factors are considered. The main stochastic variables that affect the sag indices are the fault position, the fault type, the fault impedance, the fault rate, and the pre-fault voltage. In order to have a statistical reliability of 95% and a statistical error below 10% more than 100 cases are considered. Hence, 136 cases are generated through a Monte Carlo approach: 121 faults in lines (138 and 230 kV) and 15 faults in distribution buses (13.8 and 34.5 kV). The utility fault statistics, shown in Table 2, are used for the generation of the cases. At this stage two fault impedances are considered for LG and LLG faults: 15 and 40 with the same probability (50%).
4.4. Results obtained The simulated results are organized in a matrix, known as voltage sag matrix. The matrix has 12 columns, one for each monitored bus (P1, . . ., P12) and 136 lines, one for each simulated case, as shown in Table 4. Each matrix cell contains the sag magnitude Vkf that means the sag magnitude at bus k for a certain event f. An event f is fully characterised by: the fault location, the fault type, the fault impedance, and the network topology. Two sag matrices are built, one for the ATP results and another for the short-circuit results. As a result of the 136 events simulated a total of 1632 voltage values are obtained for each program. It is important to observe that most of the obtained voltages are above the selected sag threshold (0.9 per unit). As shown in Table 5, the ATP estimates 523 voltage sags whereas the short-circuit program estimates 442 voltage sags. The average sag magnitude estimated using ATP is 0.73 per unit whereas the short-circuit estimates an average sag magnitude of 0.75 per unit. Therefore, at the system index level, the ATP simulation is more conservative than the short-circuit calculation, giving a higher number of sags and a lower average sag magnitude.
4.3. Influence of pre-fault voltages An important parameter to take into account is the pre-fault bus voltage. For the short-circuit calculations we have assumed Table 3 Pre-fault voltages at the 12 analysed buses Pre-fault voltages (per unit)
P1
P2
P3
P4
P5
P6
P7
P8
P9
P10
P11
P12
ATP Short-circuit program
0.99 1.0
0.99 1.0
1.01 1.0
0.98 1.0
0.98 1.0
1.00 1.0
1.00 1.0
0.98 1.0
0.98 1.0
0.99 1.0
0.98 1.0
1.00 1.0
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Fig. 3. Voltage sag cumulative distribution.
4.5. Voltage sag frequency The total number of sags with magnitude below a certain threshold (SARFI-X) for the 12 monitored buses is plotted in Fig. 3. The number of sags obtained from the ATP simulation is higher for all thresholds. It means that for any given load sensitivity, the number of expected outages is higher when the study is performed using the ATP program than when using a short-circuit calculation program. The results are analysed for each bus individually. Fig. 4 shows the SARFI-90% calculated using ATP and short-circuit program for the 12 buses. It is clear that the ATP provides a more pessimistic scenario for the 12 monitored buses. The difference is higher at the buses P4 and P5. One of the explanations for this large difference at buses P4 and P5 are the pre-fault voltages at the analysed buses. When the pre-fault voltage is set below 1.0 per unit the number of sags tends to be higher because the reference voltage used to estimate the sag in per unit is the bus rated voltage and not the pre-fault voltage. So, a voltage drop of 0.09 per unit is not computed as a voltage sag when the pre-sag voltage is 1.0 per unit but it is computed as a sag when the pre-sag voltage is 0.98 per unit. On the other hand, the pre-fault voltage at the generation buses plays an opposite role. A high voltage at a generation bus will produce larger fault currents flowing in the system. Consequently, the high currents will produce larger voltage drops and deeper sags.
Fig. 5. Average sag magnitude estimated at the monitored buses.
small. In most of the buses (9 of 12) the short-circuit program estimates larger average sag magnitudes (less severe sags). Another way to analyse the difference on the magnitude estimated using ATP and short-circuit programs is through a divergence index. The divergence is computed using (1) for each event where the retained voltage is below 0.9 per unit for at least one of the programs. DIV = VATP − VSC
(1)
The average sag magnitude estimated for each analysed bus is presented in Fig. 5. It can be seen that the differences are rather
being VATP and VSC the sag magnitude in per unit obtained by the ATP and by the short-circuit program, respectively. Fig. 6 shows the distribution of the divergences. It can be seen that only 3% of the estimated divergences are positive. This means that in 3% of simulated cases the ATP estimates higher sag magnitudes (more shallow sags). On the other hand, in most of the cases the ATP estimated deeper sags. However, the divergence is rather small and only 2% of the cases presents a divergence larger than 10%. It is clear that both programs give similar results for the sag magnitude. A closer look in the events that present divergence above 10% shows that they happen in the buses P9, P10 and P11, as shown in Table 6. All these buses belong to the substation RND. This substation presents a particular behaviour because the excess of generation on the network (400 MW) flows through this substation to the Brazilian southeast network. The dynamic program models this special characteristic, whereas the static program neglects the load current, obtaining larger sag magnitudes (VSC > VATP ). Consequently, the divergence is larger and negative in these cases.
Fig. 4. SARFI-90 for the 12 monitored buses.
Fig. 6. Distribution of divergences.
4.6. Voltage sag magnitude
J.M.C. Filho et al. / Electric Power Systems Research 78 (2008) 676–682 Table 6 Events with divergence over 10% Divergence (%)
Event 1 Event 46 Event 48 Event 91 Event 118 Event 121
P9
P10
P11
−12 −11
−10 −12 −10
−12
−10
−11
−10 −10
−10
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larger number of sags and lower average magnitude. However, the results show that the divergence of the estimated sag indices is not significant. A second series of simulation intended to analyse the influence of the fault type and the fault impedance on the comparison between the two simulation approaches was performed. The results are in agreement with the previous findings: for any type of fault and fault impedances considered, the ATP provides a more pessimistic scenario. Finally, considering the rather low divergence of the sag magnitude and the sag frequency obtained from the ATP and the short-circuit calculation tool, it can be concluded that both of them are suitable to estimate voltage sag indices. Considering the simplification of the system modelling for short-circuit calculation compared with the rather complex models required for the ATP simulation and the time spent to run a large number of simulations, it is recommended to use short-circuit programs to estimate voltage sag indices at site and system levels. Acknowledgement Roberto Chouhy Leborgne acknowledges CAPES—Ministry of Education of Brazil for the financial support. References
Fig. 7. Magnitude divergence distribution for 6 types of faults.
4.7. Influence of fault type and fault impedance The influence of the fault type and the fault impedance on the estimated sag magnitude is analysed. This study is performed over a new set of simulated cases. A total of 67 fault locations are randomly chosen, one location at each line. Then 6 types of fault are simulated at each position: LG 0 fault impedance, LG 25 fault impedance, LLG 0 , LLG 25 , LL, and LLL. The divergence index is estimated for the simulated sags. The distribution of divergences is presented in Fig. 7. It is observed that the divergences are concentrated between 0 and −5%. Consequently, the difference in the estimated average magnitude is concentrated at values below 5%. Therefore, the results obtained by using ATP or short-circuit program follows the same tendency for any type of fault. The same conclusion applies for the fault impedance; the choice of 25 or 0 will not affect the divergence index. In other words, the result of the comparison of the two approaches is not sensitive to uncertainties such as the fault type and the fault impedance. 5. Conclusions Voltage sag indices have been calculated using two simulation approaches: ATP and a short-circuit program. The ATP simulation considers the load and the pre-fault system condition, whereas the short-circuit program neglects the load and simplifies all pre-fault voltages to 1.0 per unit. As a result, the voltage sag assessment using the ATP is more conservative than the one using the short-circuit program; the ATP simulation leads to a
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[14] J.M. Carvalho Filho, J.P.G. Abreu, J.C. Caminha Noronha, H. Arango, Analysis of power system performance under voltage sags, Electric Power Syst. Res. 55 (3) (2000) 211–218. [15] G. Beaulieu, M.H.J. Bollen, S. Malgarotti, R. Ball, Power quality indices and objectives. Ongoing activities in CIGRE WG 36-07, in: Proceedings of IEEE Power Engineering Society Summer Meeting, Chicago, July 2002. [16] CAUE—Comite Argentino de Usuarios de EMTP-ATP, ATP-Rule Book, Buenos Aires, December 2001. [17] Cepel—Centro de Pesquisas de Energia El´etrica, Programa de an´alise de faltas simultˆaneas–ANAFAS, vers˜ao 3.0, Manual do Usu´ario, Rio de Janeiro, Brasil, December 1998 (in Portuguese). Jose Maria Carvalho Filho received his M.Sc. and D.Sc. degree in electrical engineering from the Itajub´a Federal University, Brazil, in 1996 and 2000, respectively. At present he is associate professor at Itajub´a Federal University and a Power Quality Study Group member. His fields of interest include voltage sags (dips), electrical system protection and other power quality issues. He is also a specialized consultant in industrial planning. Roberto Chouhy Leborgne received his E.E. degree and MSc. in E.E. from Itajub´a Federal University, Brazil, in 1998 and 2003, respectively. He received his Licentiate degree from Chalmers University of Technology in 2005. His employment experience includes ABB-Daimler Benz Transportation Brazil and Teyma Abengoa Uruguay. He is currently a Ph.D. candidate at Chalmers University
of Technology, Sweden. His fields of interest are voltage sags and other power quality issues. Paulo M´arcio da Silveira was born in Itajub´a, Brazil, in 1960. He received his BSEE and M.Sc. degrees from the Itajub´a Federal University, Brazil, and his D.Sc. degree from the Federal University of Santa Catarina, Brazil, in 2001. He is associate professor at Itajub´a Federal University, where he is also the Power Quality Group sub-coordinator. His research interests include power system protection and power quality issues. Math H.J. Bollen received his M.Sc. and Ph.D. degrees from Eindhoven University of Technology, Eindhoven, The Netherlands, in 1985 and 1989, respectively. He is manager of EMC and power quality at STRI AB, Ludvika, Sweden and guest professor at EMC-on-site, Lule˚a University of Technology, Skellefte˚a, Sweden. Before joining STRI in 2003 he was a research associate at Eindhoven University of Technology from 1989 to 1993; lecturer at the University of Manchester, Institute of Science and Technology between 1993 and 1996; and professor in electric power systems at Chalmers University of Technology between 1997 and 2003, Gothenburg, Sweden. His research interests cover a wide range of power-system issues, with special emphasis on power quality and reliability. He has published a number of fundamental papers on voltage dip analysis and a textbook on power quality. Math Bollen is active in several IEEE, CIGRE and IEC working groups on power quality.