#### What is in this article?:

- Short Circuit Current Duties of Circuit Breakers and Fuses โ Part 1
- Medium-Voltage Circuit Breakers
- Medium-Voltage Power Fuses

Understanding the methodologies behind the math

This is the first of a two-part series on the processes used to find the short circuit current duties of circuit breakers and fuses. In Part 1, we’ll use a simplified power system to illustrate the methodologies for medium-voltage circuit breakers and fuses. In Part 2, we’ll do the same for low-voltage circuit breakers and fuses.

It’s important to note that this discussion is intended only to illustrate (by way of example) the ANSI methodologies to find the short circuit current duties to select the short circuit withstand and interrupting capabilities of ANSI-rated circuit breakers and fuses. Other ratings and application considerations beyond the scope of these two articles must be considered for the proper selection of circuit breakers and fuses. The reader is directed to the latest editions of the applicable ANSI/IEEE C37 standards, cited in the references of Chapter 10 of the IEEE Violet Book (IEEE Std 551-2006), for complete coverage.

# Background

A short circuit fault is an unintentional phase-to-phase or phase-to-ground connection in an electrical system that is caused by insulation breakdown, equipment malfunction, or human error. Oftentimes, the short circuit fault causes an extremely high level of current to flow; and (1) electrical equipment must be capable of withstanding the extreme mechanical and thermal stresses associated with the short circuit current, and (2) interrupting devices must be capable of quickly and safely interrupting the short circuit current. Inadequate short circuit withstand or interrupting capability can lead to catastrophic failure of equipment, posing a threat to facility operations (i.e., electrical outage, infrastructure damage, or fire) and personnel (i.e., electric shock, burns, physical trauma, or death).

Fig. 1. Components of asymmetrical short circuit current waveform.

**Figure 1 **(above) illustrates a typical short circuit current waveform for one phase of a 3-phase synchronous generator, previously unloaded, which has been subjected to a bolted 3-phase short circuit across its accessible terminals. The asymmetrical short circuit current waveform can be broken down into two components: 1) a unidirectional (DC) component; and 2) a symmetrical alternating (AC) component. The DC component exponentially decays to zero, while the envelope of the symmetrical AC component eventually decays to a constant amplitude sine wave in the steady-state. The rate of exponential decay (or time constant) of the DC component is related to the short circuit X/R ratio, where X and R are the equivalent reactance and resistance at the fault location, respectively. To simplify analysis, steady-state AC circuit theory is exploited to calculate a worst-case (initial) root-mean-square (rms) magnitude of the symmetrical AC component to characterize a particular time interval of the fault-on time period. To simplify verbiage, the expression “worst-case (initial) root-mean-square (rms) magnitude of the symmetrical AC component” is hereafter shortened to “symmetrical rms current.”

Three types of networks are used to represent the power system over three time intervals of the fault-on time period. The first-cycle (momentary) network characterizes the first few cycles (at 60 Hz) of the fault-on time period. For this network, the AC motors and generators are modeled by first-cycle or subtransient reactances, and steady-state AC circuit analysis is used to calculate the first-cycle (momentary) symmetrical rms current. To account for the DC component of the short circuit current waveform, the first-cycle (momentary) symmetrical rms current is multiplied by an appropriate multiplying factor (MF) to yield the first-cycle (momentary) short circuit current duty; and first-cycle (momentary) short circuit duties must not exceed: (i) closing and latching (momentary) capabilities of medium-voltage circuit breakers, (ii) interrupting capabilities of medium-voltage fuses, (iii) interrupting capabilities of low-voltage circuit breakers, and (iv) interrupting capabilities of low-voltage fuses. The contact-parting (interrupting) network is used to calculate the contact-parting (interrupting) symmetrical rms current for medium-voltage circuit breaker minimum contact-parting times of 1.5 to 4 cycles after the inception of the short circuit fault. For this network, the AC motors and generators are represented by different (same or larger) constant reactances than those for the first-cycle (momentary) network. To account for the DC component of the short circuit current waveform, the contact-parting (interrupting) symmetrical rms current is multiplied by an appropriate MF to yield the contact-parting (interrupting) short circuit current duty; and contact-parting (interrupting) short circuit current duties must not exceed the interrupting capabilities of medium-voltage circuit breakers. Finally, the approximately 30 cycle network is a minimum source representation that characterizes the faulted power system in the steady-state (beyond 30 cycles), and it is used to investigate whether minimum short circuit currents are sufficient to operate current-actuated relays.

Fig. 2. One-line diagram of simplified industrial power system. |

**Figure 2 **(above) is a one-line diagram of a simplified industrial power system we’ll use to illustrate the ANSI methodologies to find the short circuit current duties of ANSI- rated medium-voltage circuit breakers and fuses. The **Table **below summarizes the results of the short circuit study by listing the first-cycle (momentary) and contact-parting (interrupting) symmetrical rms currents and short circuit X/R ratios for a bolted 3-phase fault at each bus. [In general, it is important that the study be performed on the system configuration involving maximum fault current contributions. The reader is directed to Chapter 9 of the IEEE Violet Book (IEEE Std 551-2006) and the references cited therein for the procedure to perform these calculations.] Note in the Table that the contact-parting (interrupting) symmetrical rms current and short circuit X/R ratio are not listed for low-voltage Bus 3, since the interrupting capabilities of low-voltage circuit breakers and fuses are selected based on first-cycle (momentary) short circuit current duty. As mentioned earlier, we’ll discuss the methodologies to find the short circuit current duties of low-voltage circuit breakers and fuses in Part 2.

Short circuit study results of simplified industrial power system.

Finally, it should be mentioned that the bolted 3-phase fault represents the worst-case condition at every bus of this example, insofar as contact-parting (interrupting) short circuit current duty is concerned. Generally speaking, the bolted single line-to-ground fault could represent the worst-case condition, and the methodologies to calculate contact-parting (interrupting) duty will differ from those described below. [For an example of this case, the reader is directed to Sec. 5.3 of ANSI/IEEE C37.010-1979 for the older constant MVA rated medium-voltage circuit breakers and Sec. 6.3 of IEEE Std C37.010-1999 (R2005) for the newer constant kA rated medium-voltage circuit breakers.]** **