Circuit Breaker Short-Circuit Duty Calculation | IEC60909
- Sample Network
- Calculation of Short-Circuit Impedance
- Calculation of Initial Symmetrical Short-Circuit Currents
- Calculation of the Peak Short-circuit Current
- Calculation of Symmetrical Short-circuit Breaking Current
- Calculation of Asymmetrical Short-circuit Breaking Current
- Calculation of Steady-State Short-Circuit Current
- References
Circuit breaker short-circuit duty calculation is a very important step in our discussion on IEC 60909. We had just completed our discussion on the basic concepts of IEC 60909. We started with the introduction of IEC 60909 by defining the common terms used in the standard and how they compare to the terms in the ANSI-approved standards.
Next, we introduced the concept of ‘meshed’ and ‘non-meshed’ networks, how to identify them, and how important they are in the calculation of short-circuit currents. Then we introduced another important concept in IEC 60909 which is the ‘far from’ and ‘near’ generator short-circuits where we dived deeper into the calculation of short-circuits by introducing multiplying factors, how and when to use them.
Lastly, we took a step back and presented a discussion on how IEC 60909 determines the short-circuit impedances for common network components.
In this article, we will reinforce the concepts presented though a simple application example. Circuit breaker short-circuit duty calculation will be presented in a step-by-step approach. For comparison, we will use the same sample network from our application example for the ANSI-approved standard.
Sample Network
Figure 1 shows a network with two sources, one is network feeder through a transmission line and the other is a synchronous generator. Our faulted point is the bus where the synchronous generator is directly connected.
Calculation of Short-Circuit Impedance
We will start by creating an impedance diagram using the concepts that we learned from our previous discussions.
Network Feeder
Network feeders are usually represented by the initial symmetrical short circuit MVA, SkQ, or the initial symmetrical short circuit current, IkQ”. With the nominal voltage UnQ, the impedance can be calculated as follows.
In this example, we will be calculating the maximum short-circuit duty. Given this, we will set the voltage correction factor cmax = 1.1. Refer to this link for the list of voltage correction factors used in IEC 60909.
Next, we calculate the reactance based on our computed ZQ and the given X/R ratio.
From there, it is easy to calculate RQ.
Transmission Line
The method in calculation of transmission lines impedance was omitted in our previous discussion since its determination is the same throughout different standards and is available in different power system analysis books. It is important to note, however, that since we are dealing with the calculation of the maximum short-circuit currents, it is necessary to adjust the transmission line resistance to a temperature of 20°C as prescribed in IEC 60909.
With the reactance equal to
The impedance of the transmission line can be easily calculated using
The total impedance from the network feeder to the fault point can be calculated from the sum of the feeder and transmission line resistance and reactance, therefore,
and the R/X ratio
Synchronous Generator
The easiest way to determine the generator impedance is to start with the calculation of its reactance using,
Next is to determine the generator resistance. Since the generator in this example has a rated apparent power of 5.952MVA, we can approximate its resistance using,
The generator impedance is calculated using,
To account for the generator substransient behavior, IEC 60909 has recommended impedance correction factors. For generators this is,
The corrected impedance is calculated using,
The impedance diagram is shown in figure 2.
Calculation of Initial Symmetrical Short-Circuit Currents
Network Feeder
The calculation of initial symmetrical short-circuit current contribution from the network feeder through the transmission can be calculated using,
Synchronous Generator
The same process is done to calculate the initial symmetrical short-circuit current contribution from the generator.
Total Initial Symmetrical Short-Circuit Current
The total initial symmetrical short-circuit current is calculated as follows,
Calculation of the Peak Short-circuit Current
Network Feeder
The calculation of the peak short-circuit current contribution from the network feeder through the transmission can be calculated from
The crest factor is determined using
The peak short-circuit current contribution from the network feeder is
Synchronous Generator
The same process is done to calculate the peak short-circuit current contribution from the generator.
Total peak short-circuit current
The total peak short-circuit current is calculated as shown
Calculation of Symmetrical Short-circuit Breaking Current
Network Feeder
Since network feeders’ short-circuit contribution are considered ‘far-from’ generator short-circuit, the symmetrical short-circuit breaking current is equal to the initial symmetrical short-circuit current.
Synchronous Generator
For a synchronous generator, it is necessary to determine first whether the short-circuit is ‘far-from’ or ‘near’ generator. We can check the ratio of its initial symmetrical short-circuit current contribution to its rated current if its greater than 2.
Since I”kG/IrG is greater than 2, the synchronous generator in this example is a ‘near’ generator.
To calculate the symmetrical short-circuit breaking current contribution of the generator, a factor µ is introduced.
IEC 60909 has provided the equations to calculate µ based on a particular minimum time delay. For this example, let us assume a minimum time delay of 0.05s.
Calculating for the generator symmetrical short-circuit breaking current contribution we get,
Total Symmetrical Short-Circuit Breaking Current
The total symmetrical short-circuit breaking current is calculated as shown
Calculation of Asymmetrical Short-circuit Breaking Current
If the calculation of the asymmetrical short-circuit breaking current is of interest, the following procedures apply.
Determine the aperiodic DC component of the initial symmetrical short-circuit current using the following equation,
Network Feeder
Synchronous Generator
For synchronous generators, the calculation of the aperiodic DC component requires an X/R ratio provided by the manufacturer. Unfortunately, the approximation of RG to get the X/R ratio cannot be used. For this example, based on the manufacturer’s data, the X/R ratio for the given generator is 19.
Calculate the total aperiodic DC component using,
Total Asymmetrical Short-Circuit Breaking Current
Calculate the total asymmetrical short-circuit breaking current using,
Calculation of Steady-State Short-Circuit Current
Network Feeder
Since network feeders’ short-circuit contributions are considered ‘far-from’ generator short-circuit, the steady-state short-circuit current is equal to the initial symmetrical short-circuit current.
Synchronous Generator
Steady-state short-circuit current for ‘near’ generator short-circuits is normally lower in magnitude than the symmetrical short-circuit breaking current. The calculation of the steady-state short-circuit current is rather straightforward in that it depends only on the generator rated current and the excitation voltage.
Since the circuit breaker short-circuit duty is of interest here, the maximum steady-state short-circuit current is calculated using,
The multiplying factor λmax depends on whether the generator is a turbo or salient-pole generator and the ratio of the maximum excitation voltage to the excitation voltage under normal load conditions (series 1 or 2).
The generator in this example is a turbogenerator with a maximum excitation voltage of 1.3 times its rated. Therefore, we will be using the series 1 curve for turbo generators. From the manufacturer’s data, the saturated value of synchronous reactance is 1.55.
Based on the given curve, the multiplying factor λmax is determined as shown
The steady-state short-circuit current contribution from the generator is calculated as shown
Total Steady-State Short-Circuit Current
The total steady-state short-circuit current is calculated as shown
And that’s about it.
Circuit breaker short-circuit duty calculation based on IEC 60909 is quite lengthy and would take a lot of time when done manually. A good computer software will surely help in the analysis!
In our next article, we’ll present the IEC 60909 analysis procedure using ETAP software.
References
BS EN 60909-0:2001: Short-circuit currents in three-phase a.c. systems Part 0: Calculation of currents (2002).
Kaskci, I. (2002). Short Circuit in Power Systems: A Practical Guide to IEC 60909. Weinheim, Germany: Wiley-VCH Verlag-GmbH.
ETAP Enterprise Solution for Electrical Power Systems Online Help
Great article. However, I have question regarding the summation of short-circuit currents from short-circuit sources.
Are the short-circuit currents added vectorially (phasor form) or just adding the magnitudes of the short-circuit current?
Thank you
Hi Elvin,
Thank you for your interest in this topic.
As stated in the standard, for non-meshed sources, the total short-circuit current is calculated as the arithmetic sum of the individual source contribution. We hope this answers your question.
Kind Regards,
PAC Basics Team