Comparing CAPE Short Circuit Results with Fault Records J. C. Umaña, ICE , D. A. Zavala, UCR Abstract - Modern protection devices permit storing records of events that have occurred in the network. ICE maintains a database of fault recordings. Those records providing the most information were chosen to be re-created using the Short Circuit module of CAPE. The goal was to determine if the relay models in the database presented an operation close to their real counterpart. The results from the comparison showed satisfactory margin errors both in currents and impedances. Index Terms: Short circuit, fault locator, fault record.
I. NOMENCLATURE CAPE: Computer-Aided Protection Engineering ICE: Instituto Costarricense de Electricidad
II. INTRODUCTION Today’s power system protective devices are set and simulated with the help of computer programs that facilitate and reduce the calculation time of protection studies. However, if the model system does not closely reproduce the real system then the protection system could be set incorrectly and may cause unnecessary switching actions or even power outages. Therefore, it is important to compare the actual operation of real protective devices against their computer model to ensure accurate results or to correct data errors in a timely fashion. III. FAULT LOCATION AND FAULT IMPEDANCE COMPUTATION To reproduce the fault in CAPE, it was necessary to know the type of fault (single phase, three phase, etc.), the location of the fault and the fault impedance. This information can be drawn from the voltage and current signals extracted from fault records at the time of the fault inception. These voltage and current values are then introduced into the protection equations according to the type of fault to compute the fault location and fault impedance. For the studies presented in this paper, the distance of the fault from the location of the fault recorder was computed based on the methodology proposed for SIEMENS protective relays [1]. This methodology establishes fault loops for each type of short circuit fault, as shown in Table I.
TABLE I FAULT TYPES AND FAULT LOOPS Fault type
Phases involved
Fault loops for the distance measurement
L1-L2
L1-L2
Two-phase short circuit without earth
L2-L3
L2-L3
L3-L1
L3-L1
Three-phase short circuit
L1-L2-L3
L1-L2 or L2-L3 or L3-L1
L1-E
L1-E
L2-E
L2-E
L3-E
L3-E
L1-L2-E
L1-E or L2-E or L1-L2
L2-L3-E
L2-E or L3-E or L2-L3
L3-L1-E
L3-E or L1-E or L3-L1
L1-L2-L3-E
L1-L2 or L2-L3 or L3-L1
Single phase earth-fault
Two-phase short circuit with earth Three-phase short circuit with earth
L1-E or L2-E or L3-E
Table I shows that it is possible to calculate the fault distance for the most common faults, solely by using two fault loops, a phase-to-phase loop and a single phase-to-ground loop, for the faulted phases. An equivalent faulted loop circuit with one single terminal source is displayed in Figure 1. In this figure, E is the system equivalent electromotive force and Zs is the system impedance. Zsc is the short circuit impedance, which generally corresponds to the impedance of the line from the relay location plus the fault resistance (RF). In the figure, the subscript "fwd" indicates sourcefault direction, meaning those elements located between the source and the fault; the subscript "ret" indicates a fault-source direction, i.e., the elements on the return path.
Figure 1. Fault Loop Equivalent Circuit, Single Source on One Extreme (Radial System) Table II defines the voltage and currents on the circuit of Figure 1 according to the type of fault. In Table II, Usc is the short circuit voltage and Isc is the short circuit current measured by the relay. The current flowing through the phases at the time of the fault is labeled Iph. A subscript,
for example Iph1, distinguishes fault currents involving more than one phase. Uph-E is the phaseto-ground voltage and Uph-ph is the voltage between faulted phases.
TABLE II Parameters depending on the fault type Fault Single phase ground Phase- phase
Usc
Iscfwd
Iscret
Zscfwd
Zscret
Uph-E Uph-ph
Iph Iph1
IE Iph2
Zsc1 Zsc1
ZE Zsc1
In the case of a system having two terminal sources (Fig. 2), the calculation of the impedance seen by Relay A should take into consideration an additional voltage drop due to current contribution to the fault from terminal B [1].
Figure 2. Fault Loop Equivalent Circuit, Double Source (Meshed System)
(1)
Equation 1 defines the computation of the distance from the relay location to the fault as apparent impedance. In the equation, ZL is the total line impedance, X is the distance to the fault, L the total length of the line, RF is the fault resistance, IA is the current contribution to the fault from the local end and IB is the current contribution to the fault from the remote terminal. From equation 1 is drawn that measured apparent fault impedance increases with a factor of (1+IB/IA) respect measured apparent fault impedance of one source (radial system, where IB = 0) as long as the fault resistance remains fixed [1]. The short circuit impedance generally corresponds to the line impedance from the relay to the fault and this is calculated using the impedance per km as shown equations 2 and 3. ̅ ′ ′ ∗
̅
(2)
̅ ′ ′ ∗
̅
(3)
The quantities R’L1, R’L0, X’L1, X’L0 are the positive- and zero-sequence reactances and resistances in ohms per kilometer [Ω / km], respectively. Moreover ZL1 is the positive-sequence
impedance, ZL0 is the zero sequence impedance and l is the distance from the relay to the fault in km. To determine the distance one must know the impedance per kilometer of the line section and its total length. A. Phase-to-phase fault loop: According to Reference 1, the loop resistance and loop reactance equations for the phase-tophase fault loop are defined as follows:
̅ ̅ !" !"! ! ̅ ̅ ! !"!
(4)
̅ ̅ − !"! !" ! ̅ ̅ ! !"!
(5)
From Figure 2, the loop impedance can be determined as follows: $% ̅ &
(6)
where R’F is the fault resistance in secondary ohms. The fault resistance RF in primary ohms can then be express as: ′
'( ')
(7)
where TP and TC are the ratios of the voltage and current transformers connected to the relay, respectively. The loop reactance is equal to the line reactance to the fault location, meaning: =
(8)
Then, the distance to the fault in km is obtained as follows: =
*+,* /" %*.
(9)
where X’L1 corresponds to the reactance per unit of line length in Ω/Km. For a fault with sources on both extremes of the line, the term R’F in equation 6 should be replaced by R'F(1+IB/IA) as shown in Fig. 2 and equation 1.
B. Phase-to-ground fault loop: Equation 9 is used to determine the phase-to-ground impedance Zph-E.
̅01 2 = 31 2 + 31 2
(10)
RPh-E and XPh-E are the resistance and reactance of the phase-to-phase fault loop: 31 2 =
31 2 !̅ + !" 31 2 !"!̅ !$̅ !̅ + !"!$̅ !"!̅
31 2 =
!" 31 2 !$̅ − 31 2 !"!$̅ !$̅ !̅ + !"!$̅ !"!̅
(11)
(12)
These are obtained by means of the phase-to-ground voltage UPh-E and the currents IR and IX, which depend on the current flowing through the fault loop Iph. ̅ − !$̅ = !01
2 ! ̅ 4 2
̅ − !̅ = !01
2 ! ̅ 4 2
(13)
(14)
Factors RE/RL and XE/XL correspond to the adjusted relay compensation factor: 2 1 = 7 − 18 3
(15)
2 1 = 7 − 18 3
(16)
The distance to the fault is computed by dividing equation 12 by the reactance by unit of line length X’L1: =
31 2 /" ′
(17)
The phase-to-ground fault loop resistance is computed using equations 18 or 19, depending on whether the circuit has one source (radial system) or the circuit has two sources on the extremes of the line (meshed system): 31 2 =
31 2 =
9 ̅ 8;$%& *̅ $* 7 *̅ : : 9 * 9 ̅
*̅ 7 : 8 : 9*
(18)
! ?!̅ − 2 !2̅ @ + ′ ?1 + !A @ !̅
!̅ − ? 2 @ !2̅ CDE
B
(19)
The fault distance computed with equation 17 and the value of RF in primary ohms, as in equation 7, are used in CAPE to reproduce the event. IV. COMPUTATION PROCEDURE The following steps were followed for the comparison: •
Select a real event for which fault records exist. According to the fault type, select the fault loop according to Table I.
•
Choose the time to sample voltage and current fault. The sample was taken a couple of cycles after signals stabilize but before the breaker opens. Current and voltages were filtered at 60Hz so they are comparable with the symmetrical IEEE values computed in CAPE. For example, for the fault of Figure 3, sampling was taken at 36ms.
Figure 3: Deciding Time of Sampling on the Fault Record •
Calculate the impedance using equations 4 and 5 for the phase-to-phase fault loop and equations 11 and 12 for phase-to-ground fault loop. Two worksheets previously prepared with the phase-to-phase and phase-to-ground loop equations of impedance and distance were employed for this computation.
•
Determine the distance of the fault according to equations 9 or 17, as appropriate for the type of fault.
•
Compute the fault resistance in secondary ohms from equations 7 or18, according to the type of fault. Use equation 8 to compute the fault resistance in primary ohms. For the calculation of fault resistance in meshed circuits, there were three different cases to consider with the described procedures: o When there was an increase of of the local current due to the opening of the remote breaker: in order to avoid error sources when the current and voltage in at the remote terminal are unknown, the equation 19 was not used and the circuit was assumed to become radial once the remote breaker was opened; at this point the current and voltages
information was taken, as shown in Figure 4, where the initial meshed circuit becomes radial once the remote breaker opened. In this example, the current and voltage information were taken at the yellow mark, where the RMS current increased after achieving a stable short circuit value.
Figure 4: Example of Increased Short Circuit RMS Current due to the Opening of the Remote Breaker o When the local current remained unchanged upon opening of the remote breaker: Here the fault resistance was assumed constant and equation 19 was employed. o When fault records of the remote terminal were not available: the ratio IB/IA is estimated by applying a short circuit in CAPE at the line location computed with equations 9 or 17, according to the type of fault. The fault can be applied with zero fault resistance since the ratio IB/IA is constant independent of the fault resistance value, as shown in Table III, where the ratio IB/IA was computed for a specific line. TABLE III RATIO IB/IA COMPUTED FOR THE LINE GAB-CAS FOR DIFFERENT FAULT LOCATIONS AND DIFFERENT FAULT RESISTANCES. Fault location
•
•
10% of the line
50% of the line
90% of the line
Fault resistance (Ω)
Local extreme IA(A)
Remote extreme IB(A)
Ratio IB/IA
Local extreme IA(A)
Remote extreme IB(A)
Ratio IB/IA
Local extreme IA(A)
Remote extreme IB(A)
Ratio IB/IA
0
2446
7463
3.05
3914
4450
1.14
6301
2844.1
0.45
5
2220.8
6774.9
3.05
3624
4120
1.14
5790.9
2613.8
0.45
10
1873.3
5714.9
3.05
3162
3596
1.14
4972.7
2244.9
0.45
15
1554
4743
3.05
2704.3
3074
1.14
4188.5
1890.5
0.45
Simulate the fault in CAPE with the computed fault distance and computed fault resistance. The network in CAPE was built as close as possible to the existing topology at the time of the event. For the study, four different generation scenarios were chosen (summer maximum, summer minimum, winter maximum and winter minimum) according to the occurrence of the fault. CAPE was run with the Classical IEEE short circuit method (no load currents). Compute the errors as percentages using the CAPE results and the fault records.
V. RESULTS A sample of 14 fault records and the same number of simulated fault scenarios were used for the study. Tables IV, VI, VIII and X present the percent error of primary currents and Tables V, VII, IX and XI show the percent errors of the estimated primary impedance of the results of short circuit computations of CAPE compared against fault records. The impedance percent error for all fault types are based on the rectangular form of the impedance (R, X). For example, for the line GAB-CAS the percent error is 0.5% for the resistance and 0.1% for the reactance, shown in Table IV as (0.5, 0.1). A margin of 15% percent error is allowed on the estimation of the reactance since this is the maximum recommended safe margin of the zone 1 setting of the distance protection. Great attention was paid to those lines whose estimated reactance increased over the 15% percent error margin since the distance protection at those locations may produce miscoordinations. In general, it is observed that the percent error is higher in resistance than the percent error presented on the estimation of the reactance. The reason for this is that the method for resistance computation is based on the assumption that the fault resistance is fixed which is not always true, mostly for faults with arc. Another factor to consider is that in CAPE the ground resistance was simplified as a symmetric average for all the line length. The value of the percent error in the currents is associated with the fact that no load (pre-fault) currents were used for the computation of the fault currents. The most common faults in the Costa Rican transmission system are single line-to-ground faults. For this reason more studies were performed for this fault type. Coincidentally, the single lineto-ground faults presented the highest percentages of error (Tables III and IV) compared to the other fault types. One reason for this is that the zero-sequence network model is more difficult to model accurately. For example, there is no zero-sequence data for some transformers and it was necessary to estimate its value. Other approximations were assuming average soil resistivity, towers in same section having same dimensions, etc. A. Single line-to-ground faults As an example, Appendix 1 presents the complete computation of a single line-to-ground fault in the line GAB-CAS that occurred on May 30, 2012. Tables IV and V summarize the percent error on the estimated current and estimated impedance on different lines around the single line-to-ground fault on the line GAB-CAS described in Appendix I, respectively. Similar entries in Table IV and V represent separate events occurred in the same line (CAH-CHA and LIN-BAR).
TABLE IV ESTIMATED CURRENT PERCENT ERROR FOR SINGLE LINE-TO-GROUND FAULT Line fault GAB-CAS LIN-TAR CAH-CHA CAH-CHA LIN-BAR LIN-BAR ARE-MIR BAR-GAB CAJ-HER
IPHreg [KA]
IPHcape [KA]
% error I
5.31 3.74 1.34 1.97 3.25 2.46 3.47 2.79 13.06
6 3.44 1.4 1.94 3.18 2.44 3.93 2.53 10.82
13.1 7.9 4.17 1.5 2.12 0.5 13.4 9.36 17.1
TABLE V ESTIMATED IMPEDANCE PERCENT ERROR FOR SINGLE LINE-TO-GROUND FAULT Line fault GAB-CAS LIN-TAR CAH-CHA CAH-CHA LIN-BAR LIN-BAR ARE-MIR BAR-GAB CAJ-HER
ZPHreg [Ω] 1.14 + 3.5i 2.8 + 12.2i 32.05 + 20.42i 3.25 + 6.19i 7.4 + 15.2i 17.9 + 21.1i 9.2 + 10.4i 0.91 + 1.4i 0.31 + 0.71i
ZPHcape [Ω] 1.14 + 3.5i 3.39 + 13.6i 25.87 + 19.49i 3.12 + 6.13i 6.59 + 15.53i 16.18 + 22.2i 11.9 + 10.73i 1.03 + 1.53 0.33 + 0.87i
% error Z (R,X) 0.5, 0.1 21.1, 10.6 19.3, 4.5 4.0, 1.01 11.1, 2.1 10.0, 5.1 28.6, 2.8 1.9, 6.2 6.94, 22.8
The CAJ-HER line presents the greatest difference in both current (17.1%, Table IV), and in reactance (22.8%, Table V). It is observe also that it is the only line that exceeds the minimum 15% margin of error allowed for safely set impedance protection. Additionally, this line has the lowest estimated fault impedance across the table, therefore any variation off the results greatly affect the percent error computation. The other lines present reasonable impedance percent errors. The failure CAH-CHA line fault has two records: the first presented a 19.3% percent error in the resistance and a 4.5% percent error in the reactance. After observing this unfavorable result, a revision of the line parameters was performed. The record of a second fault was used to prepare a comparison with the revised line; here the percent error was reduced both in current and impedance (4% in resistance and 1.01% in reactance). The reduction of 3.49% in the reactance percent error represent a saving of 2 km that the maintenance personnel does not have to walk to find the fault location.
B. Phase-to-phase fault Appendix 2 summarizes the complete computation for a phase-to-phase fault on the line CARSMI that occurred on June 3, 2012. TABLE VI ESTIMATED CURRENT PERCENT ERROR FOR PHASE-TO-PHASE FAULT Line fault SMI-CAR LIB-CAS LIB-PAP
IPHreg [KA] 3.6 2.04 4.7
IPHcape [KA] 3.23 2.25 5.01
% error I 10 10.4 6.62
TABLE VII ESTIMATED IMPEDANCE PERCENT ERROR FOR PHASE-TO-PHASE FAULT Line fault SMI-CAR LIB-CAS LIB-PAP
ZPHreg [Ω] 2.21 + 15.7i 4.62 + 17.5i 1.35 + 1.11i
ZPHcape [Ω] 2.21 + 15.7i 4.7 + 17.5i 1.34 + 1.13i
% error Z (R,X) 0, 0 1.73, 0 0.22, 1.27
C. Double phase-to-ground fault TABLE VIII ESTIMATED CURRENT PERCENT ERROR FOR DOUBLE PHASE-TO-GROUND FAULT Line fault RMA-SIS
IPHreg [KA] 3.03
IPHcape [KA] 3.05
% error I 1.49
TABLE IX ESTIMATED IMPEDANCE PERCENT ERROR FOR DOUBLE PHASE-TO-GROUND FAULT Line fault RMA-SIS
ZPHreg [Ω] ZPHcape [Ω] 5.73 + 18.3i 6.27 + 18.22i
% error Z (R,X) 16.8, 0.8
D. Three phase fault TABLE X ESTIMATED CURRENT PERCENT ERROR FOR THREE PHASE FAULT Line fault CAS-COD
IPHreg [KA] 2.8
IPHcape [KA] 2.72
% error I 3.11
TABLE XI ESTIMATED IMPEDANCE PERCENT ERROR FOR THREE PHASE FAULT Line fault CAS-COD
ZPHreg [Ω] ZPHcape [Ω] 7.07 + 12.3i 7.08 + 12.26i
% error Z (R,X) 0, 1
VI. CONCLUSIONS The CAPE Short Circuit module yielded results close to the ones presented on the fault records. The differences are attributed to the difficulty of developing a network system model whose simulation render fault results 100% similar to the ones recorded. However, the comparison using the CAPE Short Circuit module also makes possible evaluation of the quality of the network system model, since the greater differences point to those places where the transmission line data may be erroneously entered. The sample of 14 compared faults yield the result of one line whose reactance was above the 15% percent error margin allowed. The impedance data of this line is under revision and, if necessary, a request for direct measurement may be issued. The single line-to-ground faults had higher error percentages compared to other fault types. To improve these results, it is necessary to improve in the modeling of the zero-sequence network both for the transmission lines and for the power transformers.
VII. REFERENCES [1]
G. Ziegler, Numerical Distance Protection. Principles and Applications. Berlin: SIEMENS, 2006 (Book).
Julio Cesar Umaña works for the Office of Coordination and setting protections, UEN-TE, Instituto Costarricense de Electricidad (ICE), San José, Costa Rica. (E-mail:
[email protected]). Dennis Alonzo Zavala is an under graduate student at the School of Electrical Engineering, University of Costa Rica (UCR), San José, Costa Rica (e-mail: dennis.zavala @ ucr.ac.cr).
