Reducing first-cycle and contact-parting networks to equivalent reactance and resistance values results in simplified netwrork calculations of fault currents and short-circuit X/R ratios.

In Part 2 of this series of articles (December 1995 issue), we used a simple example to show the data preparation steps used in finding the appropriate per-unit reactances and resistances of power system apparatus for the first-cycle (momentary) and contact-parting (interrupting) networks. In this last installment, we'll explain how to use this data in calculating short- circuit current [TABULAR DATA FOR TABLE 1 OMITTED] [TABULAR DATA FOR TABLE 2 OMITTED] [TABULAR DATA FOR TABLE 3 OMITTED] (symmetrical rms current). Specifically, we'll explain how to construct the networks from a one-line diagram, locate the fault connection on the networks, and use basic AC circuit theory to reduce these networks to equivalent reactance and resistance values. These values, in turn, will then be used to calculate the first-cycle (momentary) and contact-parting (interrupting) symmetrical rms currents and short-circuit X/R ratios. Parts 4 and 5 in future issues will discuss how to use these results in selecting circuit breakers and fuses from manufacturers' tables.

Simplified reactance and resistance networks

Fig. 1, on page 52, is a single-line diagram of a simplified industrial power system, the same used in our reader's quiz in Part 2.

Fig. 2, on page 54, presents the steps used to construct four types of simplified networks from the adjusted per-unit reactances and resistances of Tables 1, 2, and 3: first-cycle (momentary) reactance network, first-cycle (momentary) resistance network, contact-parting (interrupting) reactance network, and contact-parting (interrupting) resistance network.

In Step A of Fig. 2, we begin the construction of the simplified network by drawing upper and lower busses. An unlabeled sinusoidal AC voltage source is connected across the busses. Eventually ([ILLUSTRATION FOR FIGURE 3 OMITTED], on page 58), this voltage source is labeled the prefault phase-to-neutral voltage at the faulted bus.

Step B is the key step in the construction of a simplified network. For every source of short-circuit current (i.e., machines and utility), we connect one terminal of its reactance to the upper bus of the network. We connect the other terminal of the reactance to a new bus whose label is the bus number from the one-line diagram.

Finally in Step C, we interconnect the remaining reactances of passive apparatus (i.e., transformers, feeders, etc.) to match the one-line diagram.

Fault connection on the simplified network

In Fig. 3, we see the three-phase fault location simulated by connecting a jumper from the faulted bus to the lower reference bus. This diagram shows this procedure for three-phase faults at Busses 2 and 4. Since the prefault bus voltage magnitudes throughout the power system are very close to 1.0 per-unit under normal load conditions, we can make a conservative assumption and select the bus voltage of the sinusoidal AC voltage source to be greater than or equal to 1.0 per-unit. Also, we set the phase angle of the source at 0 [degrees]; this will serve as the phase angle reference for the power system.

Reduction of simplified network

An important advantage of the simplified reactance (or resistance) network is the ease with which you can reduce the network to a single equivalent reactance [X.sub.EQ] (or resistance [R.sub.EQ]). All you need to do is apply the equations shown in Table 4, on page 58, to combine series and parallel arrangements of reactances. (These equations are the same for series and parallel arrangements of resistances.) Reactances in series "see" the same current and are combined by addition (e.g., [X.sub.M4] + [X.sub.T2] and [X.sub.U] + [X.sub.T1]). Parallel reactances (indicated by double slashes,; e.g. [X.sub.M2]//[X.sub.M3]) have common bus voltage.

Fig. 4, on page 60, summarizes the procedure used to reduce the simplified reactance network to an equivalent reactance ([X.sub.EQ]) for a three- phase fault at Bus 4. Note that in the top network, the three left-most branches are connected in parallel and are combined into a single reactance in the middle network. The trick is to notice that this single reactance is in series with [X.sub.T3], and that both these reactances are combined by addition in the bottom network. Finally, these two reactances in the bottom network are connected in parallel, and are combined to yield [X.sub.EQ].

In practice, it's easier to use numerical values instead of symbols to reduce the simplified networks. Symbols are used in Figs. 4 and 5 only to show how to use the equations to do the reductions. Furthermore, the reduction procedure is identical for any of the four types of simplified networks.

Table 5, on page 61, lists the numerical results of the equivalent first-cycle (momentary) and contact-parting (interrupting) reactances and resistances for the three-phase faults at the major busses of the Fig. 1 one-line. Note that the equivalent contact-parting (interrupting) reactance and resistance are not calculated at low voltage Bus 3; this is because only the first-cycle (momentary) results are needed in selecting the short-circuit capabilities of low-voltage circuit breakers and fuses. Parts 4 and 5 of this series (in future issues) will provide further information a bout this subject.

Finally the equations used to calculate the first-cycle (momentary) and contact-parting (interrupting) symmetrical rms currents and short-circuit X/R ratios are given in Table 4.

Final cautionary notes

Once again, you're cautioned not to select circuit breakers and fuses from a manufacturer's table solely on the basis of symmetrical rms current. There are circumstances when symmetrical rms current must be adjusted by a multiplying factor to account for asymmetrical limitations. (These limitations will be discussed in Parts 4 and 5 of this series.)

We strongly urge you to check the results noted in Table 5. Important note: Just because you successfully performed these calculations does not certify or qualify you to do these calculations in your practice. To employ or promote yourself on this basis alone is a serious breach of professional ethics.

[TABULAR DATA FOR TABLE 5 OMITTED]