- Email: [email protected]
Analysis of overtravel in induction disc overcurrent relays
Electric Power Systems Research 136 (2016) 8–11
Contents lists available at ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Analysis of overtravel in induction disc overcurrent relays Elmer Sorrentino ∗ Universidad Simón Bolívar, Dpto. de Conversión y Transporte de Energía, Apdo. Postal 89.000, Caracas 1080, Venezuela
a r t i c l e
i n f o
Article history: Received 12 December 2015 Received in revised form 26 January 2016 Accepted 1 February 2016 Keywords: Induction disc overcurrent relay Overtravel Distribution system protection Electromechanical modeling
a b s t r a c t This article analyzes the overtravel in induction disc overcurrent relays. Based on experimental results, obtained from tests on three relays from different manufacturers, it is verified that the equivalent overtravel time can be considered constant for a wide range of settings in the device. Dynamic equations of the device are analyzed, in order to find the root of this behavior. This analysis was performed in two ways: by assuming a first-order differential equation, and by assuming a second-order differential equation. Both methods allow to demonstrate the fact of a constant value for the equivalent overtravel time. The method based on a first-order differential equation is very simple, and this fact is attractive from a pedagogical perspective; however, it is based on assumptions which are not rigorously valid. Thus, the method based on a second-order differential equation should be preferred for the sake of accuracy. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Induction Disc Overcurrent Relays (named IDOR here, to abbreviate) are electromechanical devices which have been widely applied for the protection of electric power distribution systems around the world. Nowadays, the predominant technology of protective relays is based on microprocessors, but there are IDOR still operating in diverse electrical systems. The “overtravel” of IDOR is a term related to the fact of an additional disc displacement, due to its inertia, after the overcurrent has been properly interrupted by a downstream protective device. An undesired trip of IDOR could occur due to the overtravel. Therefore, overtravel of the IDOR has been usually considered by the inclusion of a time interval (0.1 s) between time-current curves, in order to obtain selectivity [1–4]. Here, this time interval is called “equivalent time due to the overtravel” (t). Usually, t is considered constant (i.e., independent of relay settings and overcurrent values), and some documents mention that this assumption could be an unjustified approximation [3,4]. Certainly, it is not evident that t could be considered constant when the values of overcurrent (and, consequently, the initial values of disc speed for the overtravel condition) can be considerably different. Actually, this research project was begun by guessing that the afore-mentioned “usual approximation” would be in some sense unaccurate; however, the experimental results definitively indicated that the afore-mentioned usual approximation was excellent. Due to this reason, a deep review
∗ Tel.: +58 212 906 3720. E-mail address: [email protected] http://dx.doi.org/10.1016/j.epsr.2016.02.003 0378-7796/© 2016 Elsevier B.V. All rights reserved.
of the motion equation was necessary, for the purpose of this article. Consequently, the structure of this article begins with a conceptual overview about different time intervals related to the overtravel, followed by the presentation of the experimental results, and the article finishes with two different ways to justify (based on the equation motion of the IDOR) that the equivalent time due to the overtravel can be considered as a constant. A contribution of this article is the theoretical justification for the fact of having a constant value for t in IDOR. On the other hand, the theoretical analysis also emphasizes the difference between t and other time intervals related to the overtravel, in order to avoid confusions about this subject. Additionally, the experimental results of this article show that t can be considered constant for a wide range of overcurrent values and relay settings (an experimental verification about this point was not available in the literature; this experimental verification is important because some documents [3,4] mention reasonable doubts about this point). Thus, this article shows a clear justification to keep the use of a constant additional time interval for considering the overtravel of the IDOR, in the coordination of an upstream IDOR with downstream devices, and this coordination is still necessary in diverse existing installations. 2. Equivalent time due to the overtravel The time-current curves of IDOR show the tripping time (tT ) for a given constant overcurrent. If that overcurrent is injected for a time lower than tT , the relay could operate due to the overtravel. The injection of that current can be stopped at the moment when the disc overtravel would be just enough to reach the trip position with speed equal to zero. The required injection time in order to
8.00
8.00
6.00
6.00
Δt (cycles)
Δt (cycles)
E. Sorrentino / Electric Power Systems Research 136 (2016) 8–11
4.00 2.00
Relay Relay A TAP=4 TAP=4AA
0.00 8
16
24
32
4.00 2.00
Relay B RelayB TAP=0.5 A TAP=0.5A
0.00 1
40
2
20%
3
4
5
Current (A)
Current (A) DIAL :
9
50%
2
DIAL :
100%
4
10
8.00
Δt (cycles)
6.00 4.00 2.00
Relay C TAP=0.5A
0.00 1
2
3
4
5
6
Current (A) 2
DIAL :
7
8
9
10
4
Fig. 1. Experimental measurement of the equivalent times due to the overtravel (t).
obtain this condition is simply called “limit-time” (tL ) here. tT and tL (tL < tT ) depend on the magnitude of the current and the IDOR settings. Actually, tL also depends on the current during the overtravel but this current is assumed to be null in this article. Therefore, the equivalent time due to the overtravel (t) is t = tT − tL
(1)
On the other hand, the overtravel time is the required time to reach the speed (ω) equal to zero (without trip). A different definition (t0 ) is the overtravel time to reach the trip condition just with ω = 0. Thus, t0 really is the overtravel time for the condition for the measurement of tL , but the equivalent time due to the overtravel (t) is not the overtravel time of the disc. 3. Experimental results The procedure for the measurement of t is: (a) first, the operation time (tT ) is measured for a given overcurrent; (b) later, the same overcurrent is injected during a time lower than tT , in order to find the limit condition (tL ) between trip and no-trip. t was measured for 3 relays (relay A:BBC, model ICM21; relay B:General Electric, model IAC78; relay C:Westinghouse, model CO11). Results are shown in Fig. 1. Time resolution is 0.5 cycles for tL , and 0.01 cycles for tT (cycles at 60 Hz).
(b) The restraint torques due to the permanent magnet and due to friction are assumed to be proportional to disc speed. Thus, both effects can be grouped in a variable, TP . (c) The restraint torque due to the spring (TR ) is assumed to be proportional to the disc position. (d) For the last part of the disc travel with overcurrent, the disc speed is assumed to be constant. If the overcurrent were not finished, it is assumed that the disc would move during the last part of its travel with the same instantaneous speed that the disc has at the end of the overcurrent (ω0 ). ω0 is different for each value of overcurrent, and ω0 is the initial speed for the overtravel condition. Therefore, it is assumed that for the limit condition of the trip with overtravel, the angular displacement () which is required for the trip condition is related to the speed ω0 and with t by the rule of an uniform movement: t =
ω0
(2)
Assumption of uniform movement (with current) is not exact, but it is a good approximation due to the braking effect of magnet. Thus, Eq. (2) implies that is proportional to ω0 . Initial conditions are at the instant when the overcurrent finishes (t = 0, = 0, ω = ω0 ). Only restraint torques are present (TP , TR ), and the condition of interest is the limit for the relay operation with overtravel (t = t0 , = , ω = 0).
4. Analysis of relay equations 4.1. General overview The following simplifications are assumed in this article: (a) The restraint torque due to the permanent magnet is assumed to be only dependent on disc speed.
4.2. Analysis based on a first-order differential equation Disc motion is described by a first-order differential equation by assuming that torque due to the spring is constant: J
dω dt
+ TP + TR = 0
(3)
10
E. Sorrentino / Electric Power Systems Research 136 (2016) 8–11
Dividing this expression by the inertia constant (J):
For these conditions, the motion equation when the overcurrent disappears is:
dω + kω = (−FR ) dt
(4)
TR FR = J
(5)
TP kω = J
(6)
ω = [ω0 + A] e
(−kt)
−A
(7)
FR k
(8)
The instant for ω = 0 corresponds to t = t0 ; thus:
ln 1 + ω0 /A
t0 =
can be obtained by integration of between 0 and t0 :
x=
ω 0
k
1−
= A1 e(−p1t) + A2 e(−p2t) + C p2, p1 = C=
(ln(1 + x)) x
(10)
ω0 A
(11)
= ω0
1 k
1−
(ln(1 + x)) x
(12)
here t depends on ω0 through x. A is the steady state speed for the disc return, and A is usually much lower than ω0 ; therefore, x is usually much greater than 1. It is useful to analyze the following function:
(ln(1 + x)) y = k(t) = 1 − x
(13)
(19)
A2 =
(C p1 + ω0 ) (p2 − p1)
(20)
The instant for reaching the speed equal to zero corresponds to t = t0 ; therefore:
−(A p2) 1/(p1−p2) 2
et0 =
By substitution of this expression in the definition of the angular displacement (), and by the inclusion of the other required substitutions, the expression for is obtained: =
ω0 (p2 − p1)
B1 = − 1 +
≈
(14)
where kR is the spring constant divided by the inertia constant; F0 is the value of FR for the initial condition (t = 0, = 0).
(21)
(A1 p1)
4.3. Analysis based on a second-order differential equation
TR = kR + F0 J
(17)
(−C p2 − ω0 ) (p2 − p1)
B2 = 1 +
FR =
)
(18)
y tends to 1 when x is much greater than 1. Therefore, t tends to 1/k (which is the time constant related to the disc), by assuming a constant TR and by assuming A ω0 . ω0 is approximately the adjusted Dial divided by tT , and A is approximately this Dial divided by the total reset time (tR ) of the disc. Thus, x ≈ tR /tT . For the cases of the experimental results, Table 1 shows that x is approximately between 1.02 and 190.06. These results indicate that the analysis from first-order differential equation is based on a false assumption (x is not always much greater than 1).
By considering that the restraint torque due to the spring is proportional to the disc position, then:
1/2
A1 =
Thus, the equivalent time due to the overtravel is t =
(−k ± (k2 − 4kR ) 2
(16)
−F0 kR
(9)
k
=
(15)
The solution of the differential equation is:
FR and k are constants. The solution of the equation is
A=
dω + kω + kR = (−F0 ) dt
C p2 ω0
C p1 ω0
[B1 + B2 ]
(22)
(1 + B3 )p1/(p1−p2) − 1
(23)
(1 + B3 )p2/(p1−p2) − 1
(24)
(p2−p1) B3 =
p1 C p2 ω0
1+
(25)
Fortunately, p2 p1 . Thus, [p2/(p1 − p2)] tends to be null, and consequently B2 tends to be null. On the other hand, [p1/(p1 − p2)] tends to be equal to 1, and consequently B1 tends to be equal to 1. Furthermore, [p2 − p1] tends to be [−p1]; thus:
ω 0
(26)
−p1
The equivalent time due to the overtravel is: t =
≈− ω0
1
(27)
p1
p1 is negative, and its absolute value is similar to k (p1 ≈ −k). This result is coherent with the result obtained by using the first-order
Table 1 Extreme values of x, from the measured values of tT and tR (in cycles, at 60Hz). Relay
A
Dial
20%
50%
100%
2
4
10
2
4
tT (MIN) tT (MAX) tR x (MIN) x (MAX)
38.31 125.23 132 1.05 3.45
90.19 300.27 306 1.02 3.39
176.86 583.78 609 1.04 3.44
7.61 154.44 795 5.15 104.47
13.36 304.35 1665 5.47 124.63
37.77 948.49 4290 4.52 113.58
6.76 215.74 978 4.53 144.67
10.57 97.59 2010 20.60 190.16
B
C
E. Sorrentino / Electric Power Systems Research 136 (2016) 8–11
differential equation, but here the afore-mentioned assumption about the value of x is not necessary. 5. Conclusion The equivalent time due to the overtravel is approximately constant for wide ranges of relay settings. This fact was verified by experimental measurements on three relays, from different manufacturers. Dynamic equations of the device were analyzed in order to find the root of this behavior. This analysis was performed in two ways. First method is very simple, because it uses a first-order differential equation, but this method is based on an assumption which is not rigorously valid. Second method uses a second-order differential equation and it should be preferred.
11
Acknowledgement ˜ Author is grateful to Alex Molina, Orlando Leánez and Jorge Melián, for their valuable help during the experimental measurements. References [1] IEEE 242 Std., IEEE Recommended Practice for Protection and Coordination of Industrial and Commercial Power Systems, 2001. [2] C. St Pierre, T. Wolny, Standarization of benchmarks for protective device time–current curves, IEEE Trans. Ind. Appl. 22 (4) (1986) 623–633. [3] GE Power Management, Distribution System Feeder Overcurrent Protection, Application note GET-6450, without date. [4] R. Mason, The Art and Science of Protective Relaying, John Wiley & Sons Inc., New York, 1956.
Contents lists available at ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Analysis of overtravel in induction disc overcurrent relays Elmer Sorrentino ∗ Universidad Simón Bolívar, Dpto. de Conversión y Transporte de Energía, Apdo. Postal 89.000, Caracas 1080, Venezuela
a r t i c l e
i n f o
Article history: Received 12 December 2015 Received in revised form 26 January 2016 Accepted 1 February 2016 Keywords: Induction disc overcurrent relay Overtravel Distribution system protection Electromechanical modeling
a b s t r a c t This article analyzes the overtravel in induction disc overcurrent relays. Based on experimental results, obtained from tests on three relays from different manufacturers, it is verified that the equivalent overtravel time can be considered constant for a wide range of settings in the device. Dynamic equations of the device are analyzed, in order to find the root of this behavior. This analysis was performed in two ways: by assuming a first-order differential equation, and by assuming a second-order differential equation. Both methods allow to demonstrate the fact of a constant value for the equivalent overtravel time. The method based on a first-order differential equation is very simple, and this fact is attractive from a pedagogical perspective; however, it is based on assumptions which are not rigorously valid. Thus, the method based on a second-order differential equation should be preferred for the sake of accuracy. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Induction Disc Overcurrent Relays (named IDOR here, to abbreviate) are electromechanical devices which have been widely applied for the protection of electric power distribution systems around the world. Nowadays, the predominant technology of protective relays is based on microprocessors, but there are IDOR still operating in diverse electrical systems. The “overtravel” of IDOR is a term related to the fact of an additional disc displacement, due to its inertia, after the overcurrent has been properly interrupted by a downstream protective device. An undesired trip of IDOR could occur due to the overtravel. Therefore, overtravel of the IDOR has been usually considered by the inclusion of a time interval (0.1 s) between time-current curves, in order to obtain selectivity [1–4]. Here, this time interval is called “equivalent time due to the overtravel” (t). Usually, t is considered constant (i.e., independent of relay settings and overcurrent values), and some documents mention that this assumption could be an unjustified approximation [3,4]. Certainly, it is not evident that t could be considered constant when the values of overcurrent (and, consequently, the initial values of disc speed for the overtravel condition) can be considerably different. Actually, this research project was begun by guessing that the afore-mentioned “usual approximation” would be in some sense unaccurate; however, the experimental results definitively indicated that the afore-mentioned usual approximation was excellent. Due to this reason, a deep review
∗ Tel.: +58 212 906 3720. E-mail address: [email protected] http://dx.doi.org/10.1016/j.epsr.2016.02.003 0378-7796/© 2016 Elsevier B.V. All rights reserved.
of the motion equation was necessary, for the purpose of this article. Consequently, the structure of this article begins with a conceptual overview about different time intervals related to the overtravel, followed by the presentation of the experimental results, and the article finishes with two different ways to justify (based on the equation motion of the IDOR) that the equivalent time due to the overtravel can be considered as a constant. A contribution of this article is the theoretical justification for the fact of having a constant value for t in IDOR. On the other hand, the theoretical analysis also emphasizes the difference between t and other time intervals related to the overtravel, in order to avoid confusions about this subject. Additionally, the experimental results of this article show that t can be considered constant for a wide range of overcurrent values and relay settings (an experimental verification about this point was not available in the literature; this experimental verification is important because some documents [3,4] mention reasonable doubts about this point). Thus, this article shows a clear justification to keep the use of a constant additional time interval for considering the overtravel of the IDOR, in the coordination of an upstream IDOR with downstream devices, and this coordination is still necessary in diverse existing installations. 2. Equivalent time due to the overtravel The time-current curves of IDOR show the tripping time (tT ) for a given constant overcurrent. If that overcurrent is injected for a time lower than tT , the relay could operate due to the overtravel. The injection of that current can be stopped at the moment when the disc overtravel would be just enough to reach the trip position with speed equal to zero. The required injection time in order to
8.00
8.00
6.00
6.00
Δt (cycles)
Δt (cycles)
E. Sorrentino / Electric Power Systems Research 136 (2016) 8–11
4.00 2.00
Relay Relay A TAP=4 TAP=4AA
0.00 8
16
24
32
4.00 2.00
Relay B RelayB TAP=0.5 A TAP=0.5A
0.00 1
40
2
20%
3
4
5
Current (A)
Current (A) DIAL :
9
50%
2
DIAL :
100%
4
10
8.00
Δt (cycles)
6.00 4.00 2.00
Relay C TAP=0.5A
0.00 1
2
3
4
5
6
Current (A) 2
DIAL :
7
8
9
10
4
Fig. 1. Experimental measurement of the equivalent times due to the overtravel (t).
obtain this condition is simply called “limit-time” (tL ) here. tT and tL (tL < tT ) depend on the magnitude of the current and the IDOR settings. Actually, tL also depends on the current during the overtravel but this current is assumed to be null in this article. Therefore, the equivalent time due to the overtravel (t) is t = tT − tL
(1)
On the other hand, the overtravel time is the required time to reach the speed (ω) equal to zero (without trip). A different definition (t0 ) is the overtravel time to reach the trip condition just with ω = 0. Thus, t0 really is the overtravel time for the condition for the measurement of tL , but the equivalent time due to the overtravel (t) is not the overtravel time of the disc. 3. Experimental results The procedure for the measurement of t is: (a) first, the operation time (tT ) is measured for a given overcurrent; (b) later, the same overcurrent is injected during a time lower than tT , in order to find the limit condition (tL ) between trip and no-trip. t was measured for 3 relays (relay A:BBC, model ICM21; relay B:General Electric, model IAC78; relay C:Westinghouse, model CO11). Results are shown in Fig. 1. Time resolution is 0.5 cycles for tL , and 0.01 cycles for tT (cycles at 60 Hz).
(b) The restraint torques due to the permanent magnet and due to friction are assumed to be proportional to disc speed. Thus, both effects can be grouped in a variable, TP . (c) The restraint torque due to the spring (TR ) is assumed to be proportional to the disc position. (d) For the last part of the disc travel with overcurrent, the disc speed is assumed to be constant. If the overcurrent were not finished, it is assumed that the disc would move during the last part of its travel with the same instantaneous speed that the disc has at the end of the overcurrent (ω0 ). ω0 is different for each value of overcurrent, and ω0 is the initial speed for the overtravel condition. Therefore, it is assumed that for the limit condition of the trip with overtravel, the angular displacement () which is required for the trip condition is related to the speed ω0 and with t by the rule of an uniform movement: t =
ω0
(2)
Assumption of uniform movement (with current) is not exact, but it is a good approximation due to the braking effect of magnet. Thus, Eq. (2) implies that is proportional to ω0 . Initial conditions are at the instant when the overcurrent finishes (t = 0, = 0, ω = ω0 ). Only restraint torques are present (TP , TR ), and the condition of interest is the limit for the relay operation with overtravel (t = t0 , = , ω = 0).
4. Analysis of relay equations 4.1. General overview The following simplifications are assumed in this article: (a) The restraint torque due to the permanent magnet is assumed to be only dependent on disc speed.
4.2. Analysis based on a first-order differential equation Disc motion is described by a first-order differential equation by assuming that torque due to the spring is constant: J
dω dt
+ TP + TR = 0
(3)
10
E. Sorrentino / Electric Power Systems Research 136 (2016) 8–11
Dividing this expression by the inertia constant (J):
For these conditions, the motion equation when the overcurrent disappears is:
dω + kω = (−FR ) dt
(4)
TR FR = J
(5)
TP kω = J
(6)
ω = [ω0 + A] e
(−kt)
−A
(7)
FR k
(8)
The instant for ω = 0 corresponds to t = t0 ; thus:
ln 1 + ω0 /A
t0 =
can be obtained by integration of between 0 and t0 :
x=
ω 0
k
1−
= A1 e(−p1t) + A2 e(−p2t) + C p2, p1 = C=
(ln(1 + x)) x
(10)
ω0 A
(11)
= ω0
1 k
1−
(ln(1 + x)) x
(12)
here t depends on ω0 through x. A is the steady state speed for the disc return, and A is usually much lower than ω0 ; therefore, x is usually much greater than 1. It is useful to analyze the following function:
(ln(1 + x)) y = k(t) = 1 − x
(13)
(19)
A2 =
(C p1 + ω0 ) (p2 − p1)
(20)
The instant for reaching the speed equal to zero corresponds to t = t0 ; therefore:
−(A p2) 1/(p1−p2) 2
et0 =
By substitution of this expression in the definition of the angular displacement (), and by the inclusion of the other required substitutions, the expression for is obtained: =
ω0 (p2 − p1)
B1 = − 1 +
≈
(14)
where kR is the spring constant divided by the inertia constant; F0 is the value of FR for the initial condition (t = 0, = 0).
(21)
(A1 p1)
4.3. Analysis based on a second-order differential equation
TR = kR + F0 J
(17)
(−C p2 − ω0 ) (p2 − p1)
B2 = 1 +
FR =
)
(18)
y tends to 1 when x is much greater than 1. Therefore, t tends to 1/k (which is the time constant related to the disc), by assuming a constant TR and by assuming A ω0 . ω0 is approximately the adjusted Dial divided by tT , and A is approximately this Dial divided by the total reset time (tR ) of the disc. Thus, x ≈ tR /tT . For the cases of the experimental results, Table 1 shows that x is approximately between 1.02 and 190.06. These results indicate that the analysis from first-order differential equation is based on a false assumption (x is not always much greater than 1).
By considering that the restraint torque due to the spring is proportional to the disc position, then:
1/2
A1 =
Thus, the equivalent time due to the overtravel is t =
(−k ± (k2 − 4kR ) 2
(16)
−F0 kR
(9)
k
=
(15)
The solution of the differential equation is:
FR and k are constants. The solution of the equation is
A=
dω + kω + kR = (−F0 ) dt
C p2 ω0
C p1 ω0
[B1 + B2 ]
(22)
(1 + B3 )p1/(p1−p2) − 1
(23)
(1 + B3 )p2/(p1−p2) − 1
(24)
(p2−p1) B3 =
p1 C p2 ω0
1+
(25)
Fortunately, p2 p1 . Thus, [p2/(p1 − p2)] tends to be null, and consequently B2 tends to be null. On the other hand, [p1/(p1 − p2)] tends to be equal to 1, and consequently B1 tends to be equal to 1. Furthermore, [p2 − p1] tends to be [−p1]; thus:
ω 0
(26)
−p1
The equivalent time due to the overtravel is: t =
≈− ω0
1
(27)
p1
p1 is negative, and its absolute value is similar to k (p1 ≈ −k). This result is coherent with the result obtained by using the first-order
Table 1 Extreme values of x, from the measured values of tT and tR (in cycles, at 60Hz). Relay
A
Dial
20%
50%
100%
2
4
10
2
4
tT (MIN) tT (MAX) tR x (MIN) x (MAX)
38.31 125.23 132 1.05 3.45
90.19 300.27 306 1.02 3.39
176.86 583.78 609 1.04 3.44
7.61 154.44 795 5.15 104.47
13.36 304.35 1665 5.47 124.63
37.77 948.49 4290 4.52 113.58
6.76 215.74 978 4.53 144.67
10.57 97.59 2010 20.60 190.16
B
C
E. Sorrentino / Electric Power Systems Research 136 (2016) 8–11
differential equation, but here the afore-mentioned assumption about the value of x is not necessary. 5. Conclusion The equivalent time due to the overtravel is approximately constant for wide ranges of relay settings. This fact was verified by experimental measurements on three relays, from different manufacturers. Dynamic equations of the device were analyzed in order to find the root of this behavior. This analysis was performed in two ways. First method is very simple, because it uses a first-order differential equation, but this method is based on an assumption which is not rigorously valid. Second method uses a second-order differential equation and it should be preferred.
11
Acknowledgement ˜ Author is grateful to Alex Molina, Orlando Leánez and Jorge Melián, for their valuable help during the experimental measurements. References [1] IEEE 242 Std., IEEE Recommended Practice for Protection and Coordination of Industrial and Commercial Power Systems, 2001. [2] C. St Pierre, T. Wolny, Standarization of benchmarks for protective device time–current curves, IEEE Trans. Ind. Appl. 22 (4) (1986) 623–633. [3] GE Power Management, Distribution System Feeder Overcurrent Protection, Application note GET-6450, without date. [4] R. Mason, The Art and Science of Protective Relaying, John Wiley & Sons Inc., New York, 1956.