POWER TRANSFORMER DESIGN VARIABLES BASICS

Our basic design variables are:

(1) B Core flux density in Tesla

(2) Js OA current density in the secondary or LV winding in kAmps/ in2

(3)Re Core radius in inches

(4)g HV-LV gap in inches

(5)Rs Mean radius of the secondary or LV winding in inches

(6)Rp Mean radius of the primary or HV winding in inches

(7)hs Height of the secondary winding in inches

(8)ts Thickness (radial build) of the secondary winding in inches

(9)tp Thickness (radial build) of the primary winding in inches

(10)Mc Weight of the core steel in kilo-pounds

(11)Mt Weight of the tank in kilo-pounds

Note that the last two weights can be expressed in terms of the othe design variables. However, since some of the material and labor costs and losses are easily expressed in terms of them, we find it convenient to include them in the set of basic design variables.

Their dependence on the other variables will be expressed in terms of equality constraints. The units chosen for the above variables are such that their magnitudes are all in the range of about 1 to 100.

These units are used internally in the computer optimization program. As far as input and output is concerned, i.e. what the user deals with, the units are a matter of familiarity and can differ from the above.

We have not considered the height of the primary winding a design variable since, in our designs, it is usually taken to be an inch shorter then the secondary winding.

We express this as hp=αhs, where hp is the height of the primary winding and α is a fraction ≈0.95. gc and go are gaps which are fixed and inputted by the user, gc depends on whether a tertiary or tap winding is present under the LV winding and go depends on the phase to phase voltages.

H is the window height and T the window width. X is the maximum stack width ≈2Rc. These are expressible in terms of the other variables.

CURRENT TRANSFORMER (CT GROUNDING) BASIC INFORMATION

IEEE standard C57.13.3 serves as the ANSI guide to standardize instrument transformer grounding practices. The grounding of CTs is important to both safety and the correct operation of protective relays.

To assure safe and reliable operation, the neutral of the CT secondary should have a single ground location for each circuit. The single ground is irrespective of the number of CTs or the chosen grounding location.

Utilizing a single ground eliminates the risk of redundant ground loops and associated problems.

During normal operation more than one ground on a CT circuit is not an obvious problem, other than the difficulties it may cause during testing. However, during a fault condition, multiple grounds allow a different ground potential rise for each CT.

The result is a significant current flow through the CT circuit that is not representative of the primary current. This ground loop typically creates a potential across the operating coil of the differential relay, causing the relay to pick up as though a fault exists in the relay’s protective zone.

Tripping a differential relay due to a fault external to the zone of protection is one of the more frequent nuisance trips. These nuisance trips may not only shut down the load but may require a maintenance crew to spend days testing to determine that no real problem exists in the differential zone.

Further, the actual problem may go undiscovered until the system is re-energized into the original fault.

To demonstrate what happens with a second ground on the CT circuit, refer to Figure 1. Figure 1 shows a typical differential relay with two CTs per phase. The recommended method of grounding is to install a single ground point at the first point of application (switchboard or relay panel) of the CT secondary circuit.

In the case of a fault internal to the protective zone, the voltage developed by the CTs is of the same polarity. The magnitude of voltage drop across the operating coil is sufficient to operate the relay.

A second ground is on a CT mounted near where a ground fault occurs. If the fault creates a ground potential rise of 100 volts, the protective relay will experience sufficient voltage across the operating coil to cause the relay to nuisance trip even though the fault was outside the fault zone

.

Just as with any other event, there is an exception to this standard. Many of the new multifunction relays (ABB, Schweitzer, GE/Multilin, and Basler) are designed to connect all CTs coming into the relay in a wye connection. Each wye has to be grounded.

The most desirable way to do this is to bus the wye points together at the relay panel and have a single conductor to ground to make certain the relay has but one ground potential.