Calculation and Theory
ANSI Standard Short Circuit Calculations
EasyPower provides a full implementation of ANSI Standards C37.010-19791, C37.5-19792, and C37.13-19813. A separate "R" (resistance) equivalent circuit is formed for the analysis of the high voltage interrupting impedance circuit. The X/R ratio used for the calculation of the interrupting duty multipliers is then found from the relationship Z/R. NACD (No AC Decrement) ratios are calculated with consideration of generator Local and Remote contributions as outlined in ANSI Std. C37.010-1979 and Reference4. High voltage interrupting duty multipliers are also derived from Reference5.
Reference:
1 AC High Voltage Circuit Breakers Rated on a Symmetrical Current Basis, ANSI/IEEE Std. C37.010-1979.
2 Calculation of Fault Current for Application of AC High Voltage Circuit Breakers Rated on a Total Current Basis, ANSI/IEEE St. C37.5-1979.
3 Low Voltage Power Circuit Breakers Used in Enclosures, ANSI/IEEE Std. C37.13-1981.
4 Interpretation of New American National Standards For Power Circuit Breaker Applications, Walter C. Huening Jr., IEEE/IAS Sept/Oct 1969.
5 AC High Voltage Circuit Breakers Rated on a Symmetrical Current Basis, ANSI/IEEE Std. C37.010-1979.
Methodology
EasyPower calculates three-phase and unbalanced fault duties using a nodal admittance network and sparse vector solutions. The system is modeled in the form given below.
[ I ] = [ V ] [ Y ]
V = voltage matrix
I = current matrix
Y = Nodal Admittance vector (G +j B)
All values are expressed as complex vectors.
From the nodal admittance matrix, the Thevenin equivalent fault point admittance is calculated. Fault currents are found from the relationship I=V*Y for all branches in the system. A system fault point voltage of 1.0 per unit is assumed unless you state otherwise in the Control tab of the Short Circuit Options dialog box. Pre-fault load current is ignored.
For momentary duty (1/2 cycle) faults, the positive sequence impedance is assumed equal to the negative sequence impedance. X/R ratios are derived from the complex network.
Interrupting duty faults are modeled using multipliers to modify rotating machine subtransient impedances (positive sequence) as outlined in ANSI Standards C37.010-1979, and C37.5-1979. Negative sequence impedances are modeled using the rotating machine subtransient impedances with no multipliers. A separate "R" (resistance) network is formed for calculation of the fault point X/R ratio. The X/R ratio used for the calculation of the interrupting duty multipliers is then found from the relationship Z/R. This method fully complies with the ANSI Standard and has the advantage of accurate currents and voltages, increased speed, and increased accuracy over the Separate X Separate R solution technique.
For 30 cycle faults, all motor contributions have decayed to zero, and a modified generator impedance of 1.5 X"dv is used. This provides conservative results which are typically higher than most dynamic studies indicate.
Proper Application of ANSI Standards
We would like to clarify a common misconception about the calculation of short circuit currents in electrical power systems. Many programs on the market calculate short circuit currents which are theoretically correct for infinite source supplies. Unfortunately, these programs do not properly consider the AC and DC decrement characteristics of motors and generators as outlined in ANSI Standards C37.010-1979, C37.5-1979, and C37.13-1981.
To properly consider this decrement and its associated multipliers, separate X and R or Z and R reductions of the equivalent high voltage interrupting impedance circuit must be performed. This is necessary to obtain the proper X/R ratio that will correctly account for the actual AC and DC current decay rates for a system with multiple exponentially decaying terms.
It is important to understand that what is theoretically a correct model for an infinite source system, may vary greatly from what the system does under actual short circuit conditions. There is no completely accurate way to combine parallel circuits with different values of X/R into one circuit with a single value of X/R. The currents from the different circuits will be the sum of several exponentially decaying terms, while the theoretical model of the circuit will contain only one term.
Investigations have shown that by calculating the X/R ratio using separate reductions, a better correlation to the actual X/R ratio of the system is obtained than from any other reasonably simple procedure (including phasor representation). The error resulting from this procedure is on the conservative side.
Since the interrupting duty multipliers are calculated from the X/R ratio, it is imperative that the correct and conservative ratio be used. Errors ranging from 10-20 percent of the actual interrupting duty current are possible when the phasor representation (without a separate R reduction) is used to calculate the X/R ratio.
Solution techniques which calculate only a momentary current and use a transient decay rate for an asymmetrical solution completely disregard ANSI Standards. Therefore, they should not be used to apply high voltage interrupting duties to ANSI Standard breakers. The legal (liability) ramifications of this should be considered.
What this means in practical terms is that it is very difficult to compare ANSI Standard breakers using calculations from other methods. It is apparent that results from other methods will vary widely from ANSI Standard results depending on the type of system.
