CALCULATIONS OF GENERATOR SOURCE SHORT- CIRCUIT CURRENT ACCORDING TO ANSI/IEEE AND IEC STANDARDS, WITH EMTP VERIFICATIONS. J.C. Das, FIEE, FIEE, FIE, PE AMEC, INC. Atlanta, Georgia
Abstract: For the interruption of a large generator source-short-circuit current, a current zero may not be obtained at the contact parting time of the circuit breaker. Large generators which have high X/R ratio, and depending upon the relative impedances and time constants the dc component can be higher than the ac decaying component delaying the occurrence of current zero well beyond contact parting time of the circuit breaker. The subject is well addressed in the current literature, though not the calculations of it. This paper presents calculations of a large practical generator using ANSI/IEEE and IEC standards with verifications of results using EMTP. It demonstrates large differences which impact the selection of generator circuit breaker interrupting duties.
UAT, (3) from the generator itself. However, the generator breaker sees only the component (3) contributed by the generator. Similarly for fault at F1, the generator breaker sees the sum of the utility source and auxiliary distribution system short-circuits current contributions, but not the contribution from the generator itself. While selecting a generator breaker, higher of these two fault currents at F1 and F2 should be considered. considered. Generally, the generator contribution for fault at F2 gives rise to higher asymmetry than the fault at F1,because large generators have a higher X/R ratio compared to the short-circuit X/R ratios in the utility systems.
I. INTRODUCTION INTRODUCTION
Fig. 2 shows a bus connected generator in an industrial distribution system running in synchronism with utility. Again the faults at F1 and F2 can be considered and the generator breaker sees only the generator contribution for a fault at F1.
Consider system configurations shown in Fig. 1 and Fig.2. Fig.1 shows a generating station, the generation voltage is stepped up to 500 kV, the ratings of generators and transformers are not shown for generality of the discussions. Generators 2 and 3 have a generator breaker, while generators 1 and 4 do not. Provision of a generator breaker makes it possible to use the generator step up transformer as step down transformer during start-up. (The relative merits of providing a generator breaker are not discussed. In-line generators breakers rated at 50 kA continuous current and short-circuit interrupting current up to 250 kA are available.) Consider fault locations F1 and F2 in Fig.1. The generator breaker short-circuit duties are of interest. For a fault at F2, there are three contributions of the short-circuit currents; which are: (1) from the utility source, (2) from the auxiliary distribution system rotating loads through
ANSI/IEEE Std. C37.010 [1] cautions that the longer dc time constants could cause a problem with SF6 type puffer circuit breakers. The interrupting window, which is the time difference between the minimum and maximum arcing times, may be exceeded because of delayed current zero, and arc energy and interruption window are of concern. The calculation methods described in this standard are qualified that the E/Z method of calculation with adjustments of ac and dc decrements can be used provided the X/R does not exceed 45 at 60 Hz, i.e., the dc time constant is not more than 120 ms. Yet, the commercial software available in the USA is based upon the empirical calculations of the short-circuit currents according to ANSI/IEEE standard [1], and unfortunately unfortunately the industry ignores the qualifying statement of dc time constant with respect to short-circuit calculations.
Key terms: generator source asymmetrical short-circuit current, degree of asymmetry, lack of current zero at contact separation.
IEEE std. C37.013 [2] for generator circuit breakers, states that any combination of ac symmetrical and dc components of short-circuit currents are permissible provided the following conditions are met at the primary contact parting time:
from generator source short-circuit current may exceed 110% in the large generators being manufactured today. Ref. [2] recognizes this asymmetry and states that at the time of current interruption, the arc fault resistance will add to the generator armature resistance. This reduces the time constant of the dc component and forces it to decay faster:
1. The symmetrical component does not exceed required generator source symmetrical capability.
T a
2. The degree of asymmetry from generator source does not exceed 110%.
X d "
=
2π f ( Ra + Radd )
Where T a is the armature time constant, Ra is the armature resistance, Radd is the added arc resistance and X”d is the subtransient reactance and f is the system frequency.
3. The total source current does not exceed the required generator-source asymmetrical capability. It is the second condition that is discussed in this paper, which shows that asymmetry
52
52
52
52
52
52
500 kV double bus
52
52
52
GSU1
52
52
52
GSU3
GSU2
GSU4
F2 52 G
G1
52 G
UAT2
UAT1
F1
G2
52
52
G3
G4
Interlocks and auto switching 4.16 kV Bus 1
4.16 kV Bus 2 52
Aux Transf. 1
52
52
52
Generation Medium-voltage auxiliary loads
Aux. Transf. 2
Third standby source of power Interlocks and auto switching 0.48 kV Bus 1
(1)
0.48 kV Bus 2
Generation Low-voltage auxiliary loads
Fig.1. A diagram of connections, large utility generating station.
Fig.2.
A bus connected industrial generator
IEC standard [3], does not discuss the asymmetry at the contact parting time of the breaker. Short-circuit current profiles for “far from” and “near to” the generator are shown in Figs. 1 and 2 of this standard , respectively. There is no discussion of not obtaining a current zero at the contact parting time of the breaker. The IEC standard showing the examples of short-circuit calculations, part- 4 is yet to be published. Note that some examples of calculations were included in earlier 1988 issue of this standard, which have been withdrawn. IEC may adopt IEEE standard [2] for the generator breakers. II. AC CURRENT INTERRUPTION
A short-circuit current with maximum asymmetry in one phase may not have zero crossing in many periods, while the asymmetry in the other two phases will be minimum and these phases will interrupt first.
Fig.3. A current zero obtained at the contact parting time with added arc fault resistance.
Fig. 3 shows this effect on decay of the dc component and the current zero obtained at the contact parting time. However, the performance with arc fault resistance is difficult to simulate and demonstrate even in a test station. When no current zero is obtained, the current interruption in this mode will be equivalent to that of interrupting a dc current without current zero crossing. The high voltage circuit breakers have limited interrupting capability in this mode of operation, unless specifically designed to introduce resistance in the arc fault path at current zero. Generator circuit breakers capable of interrupting with 130% asymmetry at the contact parting time are commercially available. Current technologies in some SF6 breaker designs use arc rotation techniques to force a current zero. The vacuum interruption technology may also achieve the same results. The available continuous current rating and the interrupting symmetrical rating of generator breakers at the upper end is 50 kA and 250 kA, respectively.
A short-circuit in the phase having zero asymmetry (depending upon the instant of fault on the voltage wave), will be interrupted first, the short-circuit changes to a two-phase fault, the current is reduced by a factor of 0.866, which will further prevent short-circuit current envelope from crossing the zero-axis. When a two-phase fault escalates to a three-phase fault, zero crossing may not occur after several periods of contact opening time. With no current zero, the current interruption is equivalent to interrupting a dc current. The high voltage circuit breakers have limited current interrupting capability in this mode. Some modern technologies in ac circuit breakers intended for generator applications , say SF6 designs, use arc rotation techniques to force a current zero, and the vacuum technology may also achieve the same results. But caution has to be exercised that all ANSI/IEEE rated breakers may not be suitable for high asymmetrical current interruption. It is prudent to consult the manufacturer for this application.
III. GENERATOR SOURCE SHORTCIRCUIT CALCULATIONS
The generator source fault current, for a practical machine, is calculated by three methods: (1) IEEE standard, (2) IEC standard and, (3) EMTP simulation. A comparative analysis of the results of these calculations is made for further discussions and analysis .. A generator of 234 MVA, 2-pole, 18 kV, 0.85 power factor, (198.9 MW), 7505 rated current, 60 Hz. 350 field volts, wye connected 0.56 SCR (short-circuit ratio), high resistance grounded and connected directly to a step up transformer is considered. Table 1, shows the manufacturer’s data, which is limited to the modeling and the calculations in this paper. All data is in per unit on generator MVA base of 234 MVA. All time constants are in seconds . Table shows saturated reactance’s, which are used in the short-circuit calculations 1V. ANSI CALCULATIONS
Generator source short circuit current, in the phase with maximum asymmetry and the generator unloaded is calculated using the following equation, from [2]:
⎡⎛ 1 1 ⎞ −t / T ⎤ ⎜ ⎟ − e ⎢⎜ " ⎥ ' ⎟ P 2 ⎢⎝ X d X d ⎠ ⎥ cos2ω t I asym = ⎢ ⎥ V 3 ⎛ 1 ⎢+ ⎜ − 1 ⎞⎟e−t / T + 1 ⎥ ⎢⎣ ⎜⎝ X d ' X d ⎠⎟ X d ⎥⎦ ⎡⎛ 1 1 ⎞ −t / T ⎤ ⎢⎜⎜ " + " ⎟⎟e ⎥ X X ⎥ q ⎠ P 2 ⎢⎝ d + ⎢ ⎥ V 3 ⎢ 1 ⎛ 1 ⎞ ⎥ 1 ⎢− 2 ⎜⎜ X '' − X " ⎟⎟ cos2ω t ⎥ q ⎠ ⎣ ⎝ d ⎦ " d
' d
a
(2) Where I asym is the generator source asymmetrical current, P = rated power, V =rated maximum voltage, ω is the angular frequency, and t is the time in seconds. All other symbols are defined in Table 1. The second harmonic term in this equation is neglected. Note that there is no commercially available software computerizing the short-circuit calculations
Table 1. Generator Manufacturer’s Data
Description
Symbol
Data
Per unit reactance data, direct axis
Synchronous
X d
2.120
Transient
X’ d
0.230
Subtransient
X’’ d
0.150
Saturated negative sequence
X2v
0.150
Leakage reactance, overexcited
XLM,OXE
0.135
Leakage reactance, under excited
XLM,UEX
0.150
Per unit reactance data, quadrature axis
Synchronous
X q
1.858
Transient
X’ q
0.434
Subtransient
X’’ q
0.140
Generator effective X/R
X/R
125
Field time constant data, direct axis
Open circuit
T’do
5.615
Three-phase shortcircuit transient
T’d
0.597
Short-circuit subtransient
T’’ d
0.015
Open circuit subtransient
T’’do
0.022
Field time constant data quadrature axis
Open circuit
T’qo
0.451
Open circuit subtransient
T”q0
0.046
Armature dc component time constant data
Three-phase shortcircuit
Ta
0.330
The calculations in this paper follow a sample example in [2]. If the generator is operating underexcited at leading power factor a higher asymmetry can be expected at the contact parting time [2].
The equation (2) considers that the generator is operating at no-load. ANSI/IEEE Short-circuit calculations ignore the prior loading of generators and motors and the calculations are, generally, made at the rated voltage. This is rather an oversimplification of a complex transient phenomenon. In practice the generator will be connected to an interconnected system, and its terminal voltage, rotor angle and frequency will all change. For a terminal fault, as discussed here, the terminal voltage will be zero, and power supplied to the load reduces to zero, while the prime mover output cannot change abruptly. Thus, the generator will accelerate. In multi-machine system speeds of all machines will change, so that these generate their share of synchronizing power in the overall impact, as these strive to reach a mean retardation through oscillations [6]. The paper confines to the basis laid out in the standard. Using the data from Table 2 and considering a 5 cycle breaker, with contact parting time of 3-cycles, consisting of ½ cycle tripping delay and 2.5 cycles opening time, the calculated short-circuit currents are:
•
Close and latch: 112.2 kA peak.
•
Generator source ac symmetrical interrupting current: 30.9 kA rms.
•
Dc component = 59.22 kA.
•
Total rms asymmetrical interrupting current at contact parting=66.80 kA.
•
Asymmetry factor = 135.5% and the current zero is not obtained.
The step-by step details of the calculations are not shown. The asymmetry factor α is given by: α =
dc component 2 symmetrical int errupting current
(3)
And the total asymmetrical interrupting current is given by:
I total , asym
= (ac sym ) 2 + (dc) 2
(4)
An important parameter of calculation is the X/R ratio. The effective resistance of the generator used in the short-circuit calculations is calculated from the following expression, from [1].
RG
=
X 2v 2π f T a
(5)
Where RG is the generator effective resistance, and all the symbols have been described in Table 2. Using appropriate values from Table 2, this gives an X/R of 125, which correlates with the data supplied by the manufacturer in Table 2. Ref. [2], however, specifies a dc component decay time constant of 133 ms. Required asymmetrical interrupting capability for three phase faults is 110% of the peak value of the symmetrical generator source current. It implies that a current zero will always be obtained at the contact parting time due to added arc resistance at the current interruption. V. IEC CALCULATIONS
There are analytical and conceptual differences between the ANSI/IEEE methods of short circuit calculations and IEC [7, 8, 9, and 10]. It is not the intention to go into the details of the IEC calculations, except to present the calculated results. For near to generator faults, IEC distinguishes between the generators directly connected to systems and generators and unit transformers of power station units, i.e., the generator and transformer is considered a single unit. IEC requires calculation of initial symmetrical shortcircuit current in each contributing source, which forms basis of further calculations. Tracking each contributing source current throughout the system is necessary, and each of these component currents is a function of X/R ratio, type of network, (meshed or radial), type of excitation system for synchronous generators, preloading, minimum time delay and the determination whether the contribution is from near to (local) or far from (remote) short-circuit sources. For the calculations of peak short-circuit current with sufficient accuracy, [3] recommends a fictitious resistance, which considers ac and dc decay: RGf = 0.05 times the subtransient reactance for machines of U rG > 1 kV and S rG ≥ 100 MVA. (6)
Where U rG is the generator rated voltage, RGf is the fictitious generator resistance and S rG is its rating in MVA. Using the values from Table 2, this gives an X/R ratio of 20, which is much lower than the X/R ratio of 125 calculated using (5). IEC [3], however, cautions that the actual generator resistance can be much lower and the value arrived from (5) can not be used for calculating the aperiodic dc component of short-circuit current. The partial initial short-circuit current of the "
generator, I kG , is given by: " I kG
cU rG
=
3 K G ,SO Z G
(7)
Where c is the IEC voltage factor =1.10 for maximum short-circuit current calculations for medium and high voltages (>1-230 kV), U rG is the generator rated voltage, Z G is generator impedance and K G,SO is a defined factor for generators and unit transformers of the power stations. It is given by the following expression:
K G ,SO
=
1
c
1 + pG 1 + X sin φ rG " d
(8)
Where φ rG is the load power factor angle prior to the generator fault and factor pG considers generator voltage regulation. For the purpose of this calculation, it is ignored as ANSI/IEEE methods and EMTP simulations are made with rated generator voltage. Also the generator is considered at no-load, i.e., φ rG =0. Substituting all the values, K G,SO=1.10 Z G is the generator impedance, given by:
Z G
= RGf + jX d "
(9) "
Then, from (7), I kG
= 49.97 kA .
Generator
peak current is given by:
i pG
= χ
" 2 I kG
(10)
Where i pG is the peak short-circuit current (equivalent ANSI /IEEE close and latch current). The factor χ can be ascertained from the X/R curves in [3] or from analytical expression in [3]. This gives i pG = 131.6 peak .
The generator breaking (ANSI interrupting) current for minimum time delay of 0.05 s (ANSI contact parting time) is:
ibsym
" = μ I kG
(11)
Where ibsym is the symmetrical component of the generator source fault current and μ is the multiplying factor, calculated from the expressions in [3]. This calculation gives, ibsym = 38.5 kA. Compare this calculation with IEEE calculation of generator source symmetrical fault current calculated as 30.90 kA. There is considerable difference in the calculated results using the same data. The aperiodic dc component at minimum time delay is calculated from equation (64) of [3]:
I dc
" = 2 I kG e −2π ftR / X
(12)
Here X/R =20 cannot be used . Using X/R=125, as calculated before, I dc=60.73 kA. Thus, the asymmetry factor is 112% versus 135% with ANSI calculations. The calculations described above omit many steps and explanations, Ref. [3, 7, 9 and 10] provide further reading. VI. EMTP SIMULATION
Short-circuit calculations are conducted using EMTP program, with detail modeling and Park’s transformations. EMTP uses Park’s transformation, which is a powerful analytical transformation for the study of synchronous machine behavior. Conceptually this transformation is shown in Fig. 4. The inductance matrix of a synchronous machine reactance in the stator frame of reference is not constant and varies with the position of the rotor with respect to the stator coils. Consider that the field winding is co phasial with the direct axis and also that the direct axis carries a damper winding. The q-axis also has a damper winding. The field flux is directed along d-axis; therefore, the machine generated voltage is at right angles to it, along q-axis. Consider phase ‘a’ inductance, which is a combination of its own self inductance, and its mutual inductance with respect to phases b an c. All these inductances vary with the position of the rotor with respect to the stator.
Park’s transformation describes a new set of variables, such as currents, voltages and flux linkages in 0dq axes. The stator parameters are transferred to the rotor parameters. Using matrix notation:
i0 dq
= P iabc
v0 dq
= P v abc
λ 0 dq
= P λ abc
(13)
Here the matrix and vectors are denoted by a top bar, subscript 0dq refers to transformed axes and subscript abc refers to stator frame of reference. i , v , λ are currents, voltages and flux linkage vector and P the transformation matrix. The abc constants in the stator windings produce a synchronously rotating field, stationary with respect to the rotor. This rotating field is produced by constant currents in the fictitious rotating coils in d-q axes, Fig.4 (b). It is not the intention to go into the details of the synchronous machine modeling theory or the calculation routines in EMTP. Manufacturer’s data is always supplied in the stator frame of reference, Table 2. The input of this data into EMTP modeling converts it to 0dq axes. For example the decoupled flux matrix in d-axis can be written as:
λ d
Ld
λ f
= KM fd
λ kd
KM dkd
KM fd KM dkd id L f M fkd
Fig.4. To illustrate Park’s transformation and inverse Park’s transformation
M fkd i f Lkd
ikd
(16) Where Ld = self inductance of the armature L f = self inductance of the field winding Lkd =self inductance of the damper winding M fd =mutual inductance between the field and armature windings M dkd = mutual inductance between armature and damper windings
M fkd = mutual inductance between field and damper windings id , i f , ikd =Currents in the direct axis, field and damper windings. K = 3/2 These all pertain to transformed d-axis. Similar transformation applies to q-axis. EMTP routine calculates the transformed parameters based upon the input manufacturer’s data. It can also accept the transformed parameters in 0dq axes directly, which can be first externally calculated from the manufacturer’s data in a-b-c frame of reference. These calculations are not shown. Refs [11-15] provide further reading. Also the system inertia constant and mechanical damping has been modeled. These details are not presented. Ref. [16] may be seen for the EMTP model.
The three-phase short-circuit current profile is shown in Fig. 7 for phases a, b and c. It is seen that in phase c, current zero is not obtained for a number of cycles. The calculated values at the contact parting time are:
•
Generator symmetrical interrupting /breaking short circuit current = 33.59 kA rms
•
Dc component = 62.5 kA
•
Asymmetry factor = 131%.
This simulation is, however, to show the impact of low load and very low power factor. Practically, while absorbing power from the power system, a generator will not be operated at such a low power factor.
The results are read from the computer outputs; Ref.[17] describes a geometric construction for the calculation of ac symmetrical and dc components from offset asymmetrical wave. Table 3 shows the comparative results obtained with the three methods of calculations. VII. THE EFFECT OF POWER FACTOR
The load power factor (lagging) in IEC calculations (7)).Similarly
will a
increase leading
" I kG (equation
power
factor
will
" kG
decrease I . This is correct; as a lagging power factor increases the internal voltage behind the machine transient reactance, and conversely a leading power factor decreases it. However from (11) and (12) it does not change the asymmetry at "
the contact parting time, because I kG is common to these equations. But , the asymmetry does change with the power factor and prior load. This is clearly shown in the EMTP simulation in Fig. 8. Fig. 8(a) shows the generator operating at no-load; it is the same plot as shown in Fig. 7 for phase c, except that the simulation is carried for 500 ms. The comparative results are shown in Table 2, which shows considerable differences in the asymmetry factor, calculated by the three methods. Fig. 8(b) shows the simulation with prior load on the generator as follows: MW=28, Mvar= 92.4 Mvar, 0.29 PF, 93.3 MVA. The first cycle peak current is reduced from 132 kA at no-load to 129 kA and the asymmetry at contact parting time is increased from 131% at no load to 142%, and the current zero is further delayed compared to Fig. 8 (a).
Fig.7. EMTP simulations of the generator shortcircuit currents, see text
Table 2 Comparison of Calculations using IEEE/IEC Standards and EMTP Simulations Calculated Parameter
IEEE
IEC
EMTP
Close and Latch , kA peak ( IEC peak short-circuit current) Generator source Interrupting kA sym. RMS (IEC symmetrical breaking current i bsym. Dc component, kA Total asymmetrical, kA RMS (IEC i basym)
112.2
131.60
132.05
Asymmetry factor
30.90
38.50
33.59
59.22 66.80
60.73 71.90
62.50 70.90
135%
112%
131%
ms, (b) short-circuit current in phase C, with generator loaded, 28 MW, 0.29 leading power factor VIII. CALCULATIONS FOR BUS CONNECTED GENERATOR
Fig. 2 shows a generator of 81.82 MVA, 12.47 kV, 0.85 power factor directly connected to a 12.47 kV bus, also powered by a 30/40/50 MVA, 115-12.47 kV utility transformer. The two sources are run in synchronism, and the plant running load is 45 MVA; the excess generated power is supplied into the utility system. The size of a generator that can be bus connected in an industrial distribution is approximately limited to 100 MVA, as an acceptable level of short-circuit should be maintained at the medium voltage switchgear and the downstream distributions. Such large units in the industrial distribution pose the same problem of higher asymmetry at the contact parting time as the directly connected utility generators through step up transformers. Following are the specific parameters of the 81.82 MVA generator shown in Fig. 10.
X d '' X q'' T d '
= 16.2, X d ' = 22.3, X d = 201.8, = 15.9, T d '' = 0.015 s,
= 0.638 s, T a = 0.476 s
Considering a 5-cycle symmetrical rated breaker, the asymmetry at the contact parting time from (2) and (3) = 132%. The calculations are not carried out using IEC standards and EMTP simulation. IX. CONCLUSIONS
Fig. 8, (a) EMTP simulation of the generator short circuit current, generator unloaded, same as in Fig. 7, phase C, except the simulation carried for 500
A power system engineer must be cautious when applying calculation methods according to accepted standards. There can be differences in the calculations using the same data. When using IEC calculations, actual X/R specified by the manufacturers should be used for calculation of aperiodic dc current at the contact parting time. The example of calculation in this paper clearly demonstrates that asymmetry at contact parting time can be even 130% or more. The delayed current zeros can also occur on short-
circuits in large industrial systems, with cogeneration facilities. In general, a generator breaker capable of interrupting 130% asymmetrical current seems to be an appropriate application in most cases. Developments in generator circuit breakers have produced designs, which can handle 130% asymmetry, [18, 19 and 20]. The manufacturers can supply test certificates showing successful interruption at this asymmetry. All generator breakers in the market may not meet these criteria. The possibility of catastrophic failure exist when this phenomena is ignored and short-circuit currents are not properly calculated. The manufacturer should be consulted for applicability of their breakers to interrupt the high asymmetry currents as demonstrated by testing. One solution to the problem can be purposely delaying the opening of the breaker; though this will increase the fault energy let-through and will have profound impact on stability of the power system.
[6] Jacobs Dunki JR, Lam P, Stafford P, A Comparison of ANSI-based andDynamically Rigorous Short-Circuit Current Calculation Procedures, Trans. IEEE, Industry Applications Society,1988, Vol. 24, pp 11801194. [7] Das JC, Short-Circuit Calculations— ANSI/IEEE & IEC Methods, Similarities and Differences, Proceedings of 8 th International Symposium on Short-Circuit Currents in Power Systems, 1988, Brussels. [8] Das, JC, Power System Analysis, Chapter 8, Short-Circuit Calculations According to IEC Standards,2002, Marcel Dekker, New York [9] Knight Gene, Sieling Harry, Comparison of ANSI and IEC 909 Short-Circuit Current Calculation Procedures,” IEEE Trans. Industry Applications, May/June 1993, Vol.29, No.3, pp 625-630.
X. REFERENCES
[1] ANSI/IEEE Std. C37.010, Guide for AC High Voltage Circuit Breakers Rated on Symmetrical Current Basis, 1999. [2] IEEE Std. C37.013, 1997. IEEE Standard for Generator Circuit Breakers Rated on Symmetrical Current Basis, 1997 and IEEE Std. C37.013a, Amendment 1: supplement for use with Generators rated 10-100 MVA, 2007. [3] IEC 60909.-0, Short-Circuit Currents in Three Phase AC Systems, 0- Calculation of Currents , 2001-07, Also IEC 60909-1;, Factors for Calculation of Short-Circuit Currents in Three Phase AC Systems According to IEC 60909-0, 1991. [4] Ragaller K. Current Interruption in High Voltage Networks, 1978, New York, Plenum Press. [5] Braun A., Edinger, A., Rouss, E., Interruption of Short-Circuit Currents in High Voltage AC Networks, BBC Review, April 1979, Vol. 66, Baden.
[10] Berizzi A, Massucco S, Silvestri A, and Zanin D, Short-Circuit Current Calculations: A comparison between Methods of IEC and ANSI Standards Using Dynamic Simulation as Reference, IEEE Trans. Industry Applications, July/August, 1994, Vol.30, No.4, pp. 1099-1106,. [11] Adkins B, The General Theory of Electrical Machines, 1964, Chapman and Hall, London. [12] Anderson PM, Analysis of Faulted Power Systems, 1973, Ames, 1A: Iowa State University Press. [13] Hancock NN, Matrix Analysis of Electrical Machinery, 1964, Pergamon Press. [14] Anderson PM, Fouad A, Power SystemControl and Stability , 1991, IEEE Press, New york. [15] Boldea Ion, Synchronous Generators, 2005, CRC Press, Boca Raton, FL. [16] Canadian/American EMTP User Group, ATP Rule Book , 1992, Portland Oregon.
[17] ANSI/IEEE Std. C37.09, IEEE StandardTest Procedure for AC HighVoltage Circuit Breakers rated on a Symmetrical Current Basis, 1999. [18] Canay IM, Warren L. Interrupting Sudden Asymmetrical Short-Circuit Currents without Zero Transition, BBC Review 56, 1969, pp. 484-493. [19] Canay IM, Comparison of Generator Circuit Breaker Stresses in Test Laboratory and Real Service Condition, IEEE Trans. Power Delivery, 2001, Vol. 16, pp 415-421. [20] Dufournet D, Willieme JM, and Montillet GF, Design and Implementation of a SF6 Interrupting Chamber Applied to Low Range Generator Breakers Suitable for Interrupting Currents Having a Non-zero Passage, IEEE Trans. Power Delivery, Oct. 2002, Vol 17, pp 963-969.
