according to the ansi_ieee 946 - open electrical
DESCRIPTION
How to calculate short circuit current In DC SystemTRANSCRIPT
Figure 1. 125 VDC system key diagram
According to the ANSI/IEEE 946
Contents [hide]
1 Introduction
2 Voltage Considerations
3 Available Short-Circuit Current
4 Calculation Approach
5 Partial Fault Currents
5.1 Short-Circuit Current from Batteries
5.2 Short-Circuit Current from DC Motors/Generators
5.3 Short-Circuit Currents from Chargers
6 References
Introduction
Scope of the IEEE 946-1992: This recommended practice provides guidance for the design of the DC
auxiliary power systems for nuclear and non-nuclear power generating stations. The components of the
DC auxiliary power system addressed by this recommended practice include lead-acid storage batteries,
static battery chargers and distribution equipment. Guidance for selecting the quantity and types of
equipment, the equipment ratings, interconnections, instrumentation, control and protection is also
provided.
This recommended practice is intended for nuclear and
large fossil-fueled generating stations. Each
recommendation may or may not be appropriate for
other generating facilities; e.g., combustion turbines,
hydro, wind turbines, etc. The AC power supply (to the
chargers), the loads served by the DC systems, except
as they influence the DC system design, and engine
starting (cranking) battery systems are beyond the
scope of this recommended practice.
For more informations please refer to the standard
itself IEEE 946-1992 .
Voltage Considerations
The nominal voltages of 250, 125, 48, and 24 are
generally utilized in station DC auxiliary power systems.
The type, rating, cost, availability, and location of the
connected equipment should be used to determine
which nominal system voltage is appropriate for a
specific application. 250 VDC systems are typically used
to power motors for emergency pumps, large valve operators, and large inverters. 125 VDC systems are
typically used for control power for nest relay logic circuits andthe closing and tripping of switchgear
circuit breakers. 48 VDC or 24 VDC systems are typically used for specialized instrumentation.
Figure 2. Recommended voltage range of 125 V and 250 V DC (nominal) rated components (for designs in which the
battery is equalized while connected to the load)
Available Short-Circuit Current
For the purpose of determining the maximum available short-circuit current (e.g., the required interrupting
capacity for feeder breakers/fuses and withstand capability of the distribution buses and disconnecting
devices), the total short-circuit current is the sum of that delivered by the battery, charger, and motors
(as applicable). When a more accurate value of maximum available short-circuit current is required, the
analysis should account for interconnecting cable resistance.
Calculation Approach
As defined in "Industrial power systems data book" [2], there are two calculation ways to acquire the
fault current:
1. Approximation Method: All the network is converted into the equivalent impedance (Req, Leqare
used for the time constant) and the system voltage is being used for the fault current calculation:
2. Superposition Method: The fault current is calculated for each source individually, while other,
not observed sources, are being shorted out (with their internal resistances). The voltage for each
partial current is the rated voltage of the source. The total current is the sum of the partial currents.
This approach shall be described in following articles.
Partial Fault Currents
Short-Circuit Current from Batteries
The current that a battery will deliver on short-circuit depends on the total resistance of the short-
circuit path. A conservative approach in determining the short-circuit current that the battery will deliver
at 25°C is to assume that the maximum available short-circuit current is 10 times the 1 minute ampere
rating (to 1.75 V per cell). For more than 25°C the short-circuit current for the specific application should
be calculated or actual test data should be obtained from the battery manufacturer. The battery nominal
voltage should be used when calculating the maximum short-circuit current. Tests have shown that an
increase in electrolyte temperature (above 25°C) or elevated battery terminal voltage (above nominal
voltage) will have no appreciable effect on the magnitude of short-circuit current delivered by a battery.
The internal battery resistance is calculated using:
Where EB is the battery rated voltage and I8hrs is the 8-hour battery capacity.
The maximum (or peak) short-circuit current is:
RBBr is the sum of the battery internal resistance RBand the line resistance RBr up to the fault location.
The initial maximum rate of rise of the current at t=0 s is as follows:
The time constant is calculated as:
The sustained short-circuit current is calculated using:
And the fault current from the battery for the time t:
Short-Circuit Current from DC Motors/Generators
DC motors, if operating, will contribute to the total fault current. The maximum current that a DC motor
will deliver to a short-circuit at its terminals is limited by the effective transient armature resistance (r'd)
of the motor. For DC motors of the type, speed, voltage, and size typically used in generating stations,
rd is in the range of 0.1 to 0.15 per unit. Thus, the maximum fault current for a short-circuit at the motor
terminals will typically range from 7 to 10 times the motor’s rated armature current. Therefore, it is
conservative to estimate the maximum current that a motor will contribute to a fault as 10 times the
motor’s rated full load current. When a more accurate value is required, the short-circuit contribution
should be calculated, using specific rd data for the specific motor, or actual test data should be obtained
from the motor manufacturer. For additional accuracy, the calculation should account for the resistance
Figure 3. Typical short-circuit characteristic of DC motor/generator
of the cables between the
motor and the fault. A
complete expression for
the short-circuit current
is:
Where: ia per-unit current, e0 is the internal emf prior short-circuit (p.u.), rd steady-state effective
resistance of machine (p.u.), r'd transient effective resistance of machine (p.u.). The frequency is 60 Hz.
Typically, for motors e0=0,97 p.u., and for generators e0=1,03 p.u.
The machine electrical parameter are to be calculated in case when no additional data is known for
observed machine. Normally, it is more practical to use the real machine data given by the manufacturer.
The machine inductance is derived from the following equation:
Where P is the pole number, nn nominal speed, UMnominal voltage and IM nominal current. Cx depends on
the machine type: Cx=0,4 is for motors without pole face windings, Cx=0,1 is for motors with pole face
windings, Cx=0,6 is for generators without pole face windings, and Cx=0,2 is for generators with pole
face windings.
The base resistance of the machine is derived from:
Then the transient resistance in Ohms is derived from:
The peak short-circuit current in Amps:
Or in p.u.:
The initial rate of rise of the current is:
The first 2/3-time constant of rise is:
And the second 1/3-time constant of rise is:
The total time constant is:
The armature circuit decrement factor is:
The field circuit decrement factor is:
Short-Circuit Currents from Chargers
The maximum current that a charger will deliver into a short-circuit, coincident with the maximum battery
short-circuit current, is determined by the charger current-limit circuit. The current-limit setting is
adjustable in most chargers and may vary from manufacturer to manufacturer. Thus, the maximum
current that a charger will deliver on short circuit will not typically exceed 150% of the charger ampere
rating.
The initial sustained short-circuit current (or quasi steady-state current) is given by:
The factor K2 is taken from the diagram of sustained fault current factor versus rectifier terminal voltage,
zC is the commutating impedance per unit and IR is the rated rectifier current. The commutating
impedance includes AC side impedance with transformer (RC and XC).If the commutating impedance is in
per-unit value then it should be converted.
Figure 4. Peak fault current factor as a function of system
constants
Figure 5. Sustained fault current vs rectifier terminal voltage
Conversion of zC (p.u.) to ZC (Ohms):
Case of double-way rectifier, equation
is:
Case of double-wye rectifier:
The current Ida is used to determine
equivalent rectifier resistance and
inductance on the DC side, which are
then given by:
Where Eda is the assumed voltage at the
rectifier terminals during the fault and
equals e0 (p.u.) x System Voltage
(Volts).
If the fault current is calculated using
the superposition method, then the
following relations are used:
When: Then:
When: Then:
The sustained value of the fault current is:
The rectifier terminal voltage is:
The rate of rise fault current is:
The peak current is given as:
Where the factor K1 is taken from the diagram and is in function of K3 and K4, which are calculated as
follows, for the full-wave bridge connected rectifier:
Note: The value Eda = edaED should be within 10% of the calculated value Edc, the rectifier terminal
voltage under sustained short-circuit current. The iterative process is repeated until the desired
tolerance is achieved.
K1 - peak fault current factor
K2 - sustained fault current factor
K3 - reactance constant (used to determine K1)
K4 - resistance constant (used to determine K1)
Index "RBr" refers to the combined resistance of the rectifier and the branch up to the fault location
References
1. IEEE 946-1992: IEEE Recommended Practice for the Design of DC Auxiliary Power Systems for
Generating Stations
2. Industrial power systems data book, General Electric, 1956