According to the ANSI/IEEE 946
Contents
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.
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 (R_{eq}, L_{eq} are used for the time constant) and the system voltage is being used for the fault current calculation:
[math]{{I}_{shc}}=\frac{{{U}_{n}}}{{{R}_{eq}}}[/math]
[math]\tau =\frac{{{L}_{eq}}}{{{R}_{eq}}}[/math]
- 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:
[math]{{R}_{B}}=\frac{{{E}_{B}}}{100{{I}_{8hrs}}}[/math]
Where E_{B} is the battery rated voltage and I_{8hrs} is the 8-hour battery capacity.
The maximum (or peak) short-circuit current is:
[math]{{i}_{pB}}=\frac{{{E}_{B}}}{{{R}_{BBr}}}[/math]
R_{BBr} is the sum of the battery internal resistance R_{B} and the line resistance R_{Br} up to the fault location.
The initial maximum rate of rise of the current at t=0 s is as follows:
[math]RR=\frac{di}{dt}=\frac{{{E}_{B}}}{{{L}_{BBr}}}[/math]
The time constant is calculated as:
[math]\tau =\frac{{{L}_{BBr}}}{{{R}_{BBr}}}[/math]
The sustained short-circuit current is calculated using:
[math]{{I}_{kB}}={{i}_{pB}}\left( 1-{{e}^{-\frac{1}{\tau }}} \right)[/math]
And the fault current from the battery for the time t:
[math]{{i}_{B}}(t)={{i}_{pB}}\left( 1-{{e}^{-\frac{t}{\tau }}} \right)[/math]
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, r_{d} 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 r_{d} 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 of the cables between the motor and the fault. A complete expression for the short-circuit current is:
[math]{{i}_{a}}(t)=\frac{{{e}_{0}}}{{{r}_{d}}}-\frac{{{e}_{0}}}{r_{d}^{'}}{{e}^{-{{\sigma }_{a}}t}}+{{e}_{0}}\frac{{{r}_{d}}-r_{d}^{'}}{{{r}_{d}}r_{d}^{'}}{{e}^{-{{\sigma }_{f}}t}}[/math]
Where: i_{a} per-unit current, e_{0} is the internal emf prior short-circuit (p.u.), r_{d} 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 e_{0}=0,97 p.u., and for generators e_{0}=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:
[math]L_{a}^{'}=\frac{19.1{{C}_{x}}{{U}_{M}}}{P{{n}_{n}}{{I}_{M}}}[/math]
Where P is the pole number, n_{n} nominal speed, U_{M} nominal voltage and I_{M} nominal current. C_{x} depends on the machine type: C_{x}=0,4 is for motors without pole face windings, C_{x}=0,1 is for motors with pole face windings, C_{x}=0,6 is for generators without pole face windings, and C_{x}=0,2 is for generators with pole face windings.
The base resistance of the machine is derived from:
[math]{{R}_{M}}=\frac{{{U}_{M}}}{{{I}_{M}}}[/math]
Then the transient resistance in Ohms is derived from:
[math]R_{d}^{'}=r_{d}^{'}{{R}_{M}}[/math]
The peak short-circuit current in Amps:
[math]{{i}_{pM}}=\frac{{{I}_{M}}}{r_{d}^{'}}[/math]
Or in p.u.:
[math]i_{pM}^{'}=\frac{{{e}_{0}}}{r_{d}^{'}}[/math]
The initial rate of rise of the current is:
[math]RR=\frac{di}{dt}=\frac{{{U}_{M}}{{e}_{0}}}{L_{a}^{'}}[/math]
The first 2/3-time constant of rise is:
[math]{{\tau }_{1a}}=\frac{2L_{a}^{'}}{3r_{d}^{'}}[/math]
And the second 1/3-time constant of rise is:
[math]{{\tau }_{2a}}=\frac{L_{a}^{'}}{3R_{d}^{'}}[/math]
The total time constant is:
[math]{{\tau }_{a}}={{\tau }_{1a}}+{{\tau }_{2a}}=\frac{L_{a}^{'}}{R_{d}^{'}}[/math]
The armature circuit decrement factor is:
[math]{{\sigma }_{a}}=\frac{r_{d}^{'}2\pi f}{{{C}_{x}}}=377\frac{r_{d}^{'}}{{{C}_{x}}}[/math]
The field circuit decrement factor is:
[math]{{\sigma }_{f}}=\frac{{{R}_{f}}}{{{L}_{f}}}[/math]
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:
[math]{{I}_{da}}=\frac{{{K}_{2}}}{{{z}_{c}}}{{I}_{D}}[/math]
The factor K_{2} is taken from the diagram of sustained fault current factor versus rectifier terminal voltage, z_{C} is the commutating impedance per unit and I_{R} is the rated rectifier current. The commutating impedance includes AC side impedance with transformer (R_{C} and X_{C}).If the commutating impedance is in per-unit value then it should be converted.
Conversion of z_{C} (p.u.) to Z_{C} (Ohms):
- Case of double-way rectifier, equation is:
[math]{{Z}_{c}}={{z}_{C}}\cdot 0,6\cdot \frac{{{E}_{D}}}{{{I}_{D}}}[/math]
- Case of double-wye rectifier:
[math]{{Z}_{c}}={{z}_{C}}\cdot 2,3\cdot \frac{{{E}_{D}}}{{{I}_{D}}}[/math]
The current I_{da} is used to determine equivalent rectifier resistance and inductance on the DC side, which are then given by:
[math]{{R}_{R}}=\frac{\left( {{E}_{D}}-{{E}_{da}} \right)}{{{I}_{da}}}[/math]
Where E_{da} is the assumed voltage at the rectifier terminals during the fault and equals e_{0} (p.u.) x System Voltage (Volts).
If the fault current is calculated using the superposition method, then the following relations are used:
When: [math]{{I}_{dc}}\gt\frac{0,75\cdot {{I}_{D}}}{{{z}_{C}}}[/math] Then: [math]{{R}_{R}}=\frac{1,7\cdot {{z}_{C}}\cdot {{E}_{D}}}{1,02\cdot {{I}_{D}}}[/math]
When: [math]{{I}_{dc}}\lt\frac{0,75\cdot {{I}_{D}}}{{{z}_{C}}}[/math] Then: [math]{{R}_{R}}=\frac{1,08\cdot {{z}_{C}}\cdot {{E}_{D}}}{1,27\cdot {{I}_{D}}}[/math]
[math]{{L}_{R}}=\frac{{{z}_{C}}{{E}_{R}}}{367,2{{I}_{D}}}[/math]
The sustained value of the fault current is:
[math]{{I}_{dc}}=\frac{{{E}_{D}}}{{{R}_{R}}+{{R}_{Br}}}[/math]
The rectifier terminal voltage is:
[math]E_{dc} = E_{D} - I_{dc} R_{R}[/math]
The rate of rise fault current is:
[math]RR=\frac{di}{dt}=\frac{{{E}_{D}}}{{{L}_{R}}+{{L}_{Br}}}[/math]
The peak current is given as:
[math]i_{pR} = K_{1} I_{dc}[/math]
Where the factor K_{1} is taken from the diagram and is in function of K_{3} and K_{4}, which are calculated as follows, for the full-wave bridge connected rectifier:
[math]{{K}_{3}}=\frac{{{X}_{RBr}}}{2{{X}_{C}}}[/math]
[math]{{K}_{4}}=\frac{{{R}_{c}}+\frac{1}{2}{{R}_{RBr}}}{{{X}_{C}}}[/math]
Note: The value E_{da} = e_{da}E_{D} should be within 10% of the calculated value E_{dc}, the rectifier terminal voltage under sustained short-circuit current. The iterative process is repeated until the desired tolerance is achieved.
- K_{1} - peak fault current factor
- K_{2} - sustained fault current factor
- K_{3} - reactance constant (used to determine K_{1})
- K_{4} - resistance constant (used to determine K_{1})
- 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 For more informations please refer to the standard itself IEEE 946-1992.
2. Industrial power systems data book, General Electric, 1956 At the Iowa Digital Library General Electric Industrial Power Systems Data Book.
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