Circuit breaker sizing calculation for medium- and high-voltage circuit breakers basically involves two symmetrical current calculations, one for the first cycle duty and another for the interrupting duty. This guide presents a step-by-step approach. A sample calculation is provided in each step to reinforce learning.
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1. Using the ½ cycle network impedances, construct the impedance diagram of the system. Refer to the impedance table presented here.
*Note: The values presented in this example are overly simplified. Highlight is given to the calculation process instead.
2. Calculate the Thevenin’s equivalent impedance.
Alternatively, you may use the equivalent impedance calculated using the separate X and R networks. This approach is generally conservative.
3. Calculate the symmetrical RMS current using the following formula.
where Vpre-fault is the line-to-line fault point voltage and is equal to the operating voltage under actual service conditions.
*Note: The solution for the symmetrical RMS current is calculated from the actual voltage and ohmic value of the impedances. For more systems with two (2) or more voltage levels, use per unit approach.
4. Calculate the fault point X/R ratio using the separate X and R reduction process.
5. Calculate the first cycle asymmetrical peak current multiplying factor using the following formula.
6. Calculate the first cycle asymmetrical peak current by applying MFpeak to the previously calculated symmetrical RMS current.
7. Calculate the first cycle asymmetrical RMS current multiplying factor using the following formula.
8. Calculate the first cycle asymmetrical rms current by applying MFrms to the previously calculated symmetrical RMS current.
1. Calculate the interrupting duty multiplying factor using the following formula.
2. Calculate the No AC Decay (NACD) using the ratio of the remote generators (if available) fault current contribution to the total available fault.
In our example, the remote contribution to the fault comes from the utility source. Using common circuit analysis technique such as current division and/or superposition theorem, the remote contribution can be easily calculated to be
From this, we can calculate the NACD ratio.
3. Calculate the remote multiplying factor using the X/R ratio at the fault point and a CPT of 2 cycles.
Adjust MF for symmetrically rated circuit breaker.
Verify circuit breaker rating structure. For totally rated circuit breakers use S = 1. For symmetrically rated circuit breakers use the S-factor indicated on the nameplate. If not available, use the S-factor provided in C37.010-1979. You can access this table here.
In our example, we assume a symmetrically rated circuit breaker. With a CPT of 2 cycles, the S factor is equal to 1.2.
4. The local multiplying factor can be derived from the local curves provided in IEEE Std C37.5 for totally rated circuit breakers and IEEE Std C37.010 for symmetrically rated circuit breakers.
In our example, the fault point X/R ratio was calculated to be 13.29. Selecting the multiplying factor for a CB interrupting time of 3 cycles (CPT = 2cycles), we get
Again, adjust MF for symmetrically rated circuit breaker.
5. Calculate the AMF.
6. Calculate the circuit breaker interrupting duty using the following formula.
Since reactances for ½ cycle and 1.5 – 4 cycle network are the same for both utility and generator,
*Note: In calculating for the interrupting RMS symmetrical current, use reactances on the 1.5 – 4 cycle network.
That’s it for circuit breaker sizing calculation. Share your insights by leaving a comment below.
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You may want read these articles:
Short Circuit Study: An Introduction to Circuit Breaker Sizing
Circuit Breaker Interrupting Rating Calculations
kAIC Rating of Circuit Breakers: Calculation in Low Voltage System
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View Comments
Great article!
There are two points I wish to know though.
What is the use of the first duty cycle rating and is the breaker intended to interrupt during the first cycle? And is it really a symmetrical current calculation?
Would appreciate if you add this in the article.
Thanks!
Hi there!
Thanks for commenting.
> First cycle duty is used to verify if the circuit breaker can withstand the short-circuit current magnitude at the instant of the fault. Low voltage circuit breakers interrupt during this time but for medium- and high-voltage circuit breakers, the interruption happens after at least 1.5 cycles from initiation of the fault. You can refer to this link for more info. https://pacbasics.org/short-circuit-study-an-introduction-to-circuit-breaker-sizing/
> Symmetrical current calculation is done because it's simpler. You can use V/Z approach to that. To account for the dc quantity which makes the fault asymmetrical, we apply multiplying factors. Simple, right?
What a nice and detailed article on breaker sizing calculation! Great job, Cian!
Good job cian! Thank you for sharing.