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Back to Back Capacitor Switching Formulas from IEEE C37.99-1990

There are two formulas shown in this section both have the same fundamental beginning.

On the capacitor inrush current calculations sheet (20) stated

IMAX = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

When Switching a Capacitor Step with Other Steps Already Energized, the Banks, at this Instant are in Series Therefore, We Have the Following

 CEQ = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia or, for two steps gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(29)

Formula (20) Will Now Become

 IMAX =gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(30)

From (21) C = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia , Substituting this into (30) We Get

Let (2A F)= T

 gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(31)

Factoring Under the Radicand We Get

 gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

Let V2 = V2L-L = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(32)

Factoring this (32) We Get the Following

 gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(33)

This Will Reduce to

 IMAX = 1330 gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(34)

For 60 Hz and 50 Hz

 IMAX = 1456.7 gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(35)

The Second Formula from IEEE C37.99-1990 Development is as Follows

 Let KVAR = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(36)

Example:

A bank of 600 KVAR @ 12.47KV with 1-200KVAR per phase

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = 27.7 Amps

 gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(37)

Looking Back at (34) We Had

IMAX = 1330 gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

Replacing KVAR with (36) gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

 IMAX = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia 1330 gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

 gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia To allow VL-L
(38)

Factoring We Get

 IMAX =gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(39)

 IMAX = 1747 gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(40)
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