Why Square root of Three enters all Three phase calculations

Have you ever thought why there is always a √3 present in every 3 phase calculations, let it be a delta or star transformer.

Actually this was not derived with heavy thinking or with supercomputers; rather we have to apply the simple basics of transformers which we have studied primarily.

And keep in mind, one main fact is that the differentiation between phase voltage and line voltage. Let me explore that first.

Line voltage is nothing but the output voltage measured at transformer externally i.e. Voltage available between any 2 wires out of 3 wires. We call it as V_L.

But Phase voltage is the output voltage available internally i.e. Voltage available between single phase wire and neutral. We call it as V_ph.

And the same definition holds good for current available which shall be called as I_L & I_ph.

Our basic rule is to measure power available at secondary which is nothing but the product of Phase Voltage x Phase Current and summation of all three phases,

                                              P             =             3 x V_ph x I_ph                                          …. (1)

But as you see it is very difficult to measure the phase voltages from a transformer which may involve complex connections and may be impossible rather it’s easy to measure from the lines present outside.

So here we go with a bit trigonometric work to derive the phase data from available line data.

As we know in a star connected transformer, the line voltage is nothing but the combination of two phase voltages which are out of phase by 120°. But current will be same for both phase and line. And in delta connected transformer, two currents will be out of phase by 120° and voltages will be equal.

Here we take the case of star connected transformer,

Since the line voltage is combination of two phase voltages we cannot just add together to make V_L  = 2 x V_ph which doesn’t make sense since there is a phase shift of 120°.

So,                                        V_L  = 2 x V_ph x sin(120)

                                              V_L  = 2 x V_ph x √3/2

                                              V_L  = √3 x V_ph

                       V_ph  = V_L  /√3                                                      …. (2)

Substituting (2) in (1),

We get                                 P = 3 x V_L  /√3 x I_L               since I_ph  = I_L  

                                              P = √3 .V_L .I_L

This holds good for transformers and for other loads like motors, generators etc another factor called power factor gets introduced in the equation and converted as,

                                    P = √3 .V_L .I_L.cosθ

Open Delta Transformers

Open Delta Connection:

An open-delta connection is a method of providing a three-phase supply, using two single-phase transformers. It is particularly useful if , say, one single-phase transformer, part of a three single-phase transformers forming a three-phase transformer bank, becomes damaged -allowing the two remaining transformers to provide a temporary three-phase supply to the load.
The drawback with this connection is that the capacity of the transformer bank is reduced, and it can only provide a lower load current.

It should be noted that the output power of an open delta connection is only 87% of the rated power of the two transformers. For example, assume two transformers, each having a capacity of 25 kVA, are connected in an open delta connection. The total output power of this connection is 43.5 kVA (50 kVA x 0.87 = 43.5 kVA).

Another figure given for this calculation is 58%. This percentage assumes a closed delta bank containing 3 transformers. If three 25 kVA transformers were connected to form a closed delta connection, the total output would be 75 kVA (3 x 25 = 75 kVA). If one of these transformers were removed and the transformer bank operated as an open delta connection, the output power would be reduced to 58% of its original capacity of 75 kVA. The output capacity of the open delta bank is 43.5 kVA (75 kVA x .58% = 43.5 kVA).

The voltage and current values of an open delta connection are computed in the same manner as a standard delta-delta connection when three transformers are employed. The voltage and current rules for a delta connection must be used when determining line and phase values of voltage current.

Closing a Delta:

When closing a delta system, connections should be checked for proper polarity before making the final connection and applying power. If the phase winding of one transformer is reversed, an extremely high current will flow when power is applied. Proper phasing can be checked with a voltmeter at delta opening. If power is applied to the transformer bank before the delta connection is closed, the voltmeter should indicate 0 volts. If one phase winding has been reversed, however, the voltmeter will indicate double the amount of voltage. It should be noted that a voltmeter is a high impedance device. It is not unusual for a voltmeter to indicate some amount of voltage before the delta is closed, especially if the primary has been connected as a wye and the secondary as a delta. When this is the case, the voltmeter will generally indicate close to the normal output voltage if the connection is correct and double the output voltage if the connection is incorrect

Calculation on how 58% arrived for open delta transformers:

There are two biggest advantages:

1) In an unearthed system like capacitor banks, it is possible to detect ground faults though earth path is not available.

2) In case of bulk power transmission where transformer banks are used, their advantage is that if one leg is out for maintenance/replacement than also approx. 57% power can be transmitted.

Diff between Earthed & Unearthed cable

In 3phase earthed system, phase to earth voltage is 1.732 times less than phase to phase 

voltage. Therefore voltage stress on cable to armor is 1.732 times less than voltage stress

between conductor to conductor. Whereas in unearthed system, (if system  neutral is not

grounded) phase to ground voltage can be equal to phase to phase voltage. In such case the

insulation level of conductor to armor should be equal to insulation level of conductor to 

conductor.

Also can be detailed as:

For cables to be used in solidly earthed systems, the phase-to-armour insulation has to be rated for U/root(3) only which is the phase-to-ground voltage when the system-neutral is  solidly earthed with no intentional resistance in the neutral grounding circuit. But in the case of system-neutral being resistance-earthed, then the phase-to-ground voltage of the two healthy phases rise up when an earth fault occurs on the third phase. When the system-neutral is high-resistance-earthed or left unearthed, the phase-to-ground voltage of healthy phases come close to or attain phase-to-phase values depending on the degree of effectiveness of system-neutral earthing. Therefore the phase-to-armour insulation of cables used in ungrounded systems could be rated for the full phase-to-phase voltage U instead of for U/root(3). The cables to be used in solidly earthed systems can have the phase-to-armour insulation rated for U/root(3). The U/Uo rating of the cable indicates the voltage rating of the core-to-core insulation and the core-to-armour insulation. For example for a 6.6kV ungrounded system, 6.6kV/6.6kV (UE) class cable has to be used while 6.6kV/3.8kV (E) class cables are adequate for solidly earthed systems. The UE-class cable is
naturally costlier than the earthed class of cable.

Testing purpose

Electrical Quiz

Basic Electrical Test! (Testing mode)

---

1. Calculate the value of "i2" from below circuit?

a) 0.5A

b) 1A

c) 1.5A

d) 2A

2. Which of the below is an electrical analysis program?

a) Etap

b) Office 2007

c) Autocad

d) None of the Above

3. In DMS no. of SAP, which abbreviation stands for Cable Schedule?

a) CSH

b) CBD

c) CSD

d) CSC

4. Standard Lux level for Office Buildings?

300-500

150-200

50-150

1000-1250

Corona and its Effects

Corona is a phenomenon that has the capability for degrading insulators, and causing  systems to fail. In this discussion, formulas are provided to calculate the voltage at which corona occurs, and a mention is made of a useful application for corona.

What is Corona?
Corona, also known as partial discharge, is a type of localized emission resulting from transient gaseous ionization in an insulation system when the voltage stress, i.e., voltage gradient, exceeds a critical value.
The ionization is usually localized over only a portion of the distance between the electrodes of the system. Corona can occur within voids in insulators as well as at the conductor/insulator interface.

Corona Inception
Corona inception voltage is the lowest voltage at which continuous corona of specified pulse amplitude occurs as the applied voltage is gradually increased. Corona inception voltage decreases as the frequency of the applied voltage increases. Corona can occur in applications as low as 300V.

Corona Extinction
Corona extinction voltage is the highest voltage at which continuous corona of specified pulse amplitude no longer occurs as the applied voltage is gradually decreased from above the corona inception value. Thus, once corona starts, the voltage must be decreased to get it to stop.

Corona Detection
Corona can be visible in the form of light, typically a purple glow, as corona generally consists of micro arcs. Darkening the environment can help to visualize the corona. We once attached a camera (set to a long exposure time) to a viewing window in a vacuum chamber to confirm that corona was indeed occurring, and thereby confirming our suspicions.
You can often hear corona hissing or cracking. Thus, stethoscopes or ultrasonic detectors (assuming you can place them in a safe location) can be used to find corona. In addition, you can sometimes smell the presence of ozone that was produced by the corona.

The corona discharges in insulation systems result in voltage transients. These pulses are superimposed on the applied voltage and may be detected, which is precisely what corona detection equipment looks for. In its most basic form, the following diagram is a corona (or partial discharge) measuring system:

It is important that the voltage source and the coupling capacitor exhibit low noise so as not to obscure the corona. In its simplest form the pulse detection network is a resistor monitored by an oscilloscope. Don’t dismiss this simple technique as crude, as we once used this method to observe the presence of corona in an improperly terminated high voltage connector, even after a dedicated corona tester failed to find any. Commercially available corona detectors include electronic types (as above) as well as ultrasonic types.

Corona Effects
The presence of corona can reduce the reliability of a system by degrading insulation. While corona is a low energy process, over long periods of time, it can substantially degrade insulators, causing a system to fail due to dielectric breakdown. The effects of corona are cumulative and permanent, and failure can occur without warning. Corona causes:
• Light
• Ultraviolet radiation
• Sound (hissing, or cracking as caused by explosive gas expansions)
• Ozone
• Nitric and various other acids
• Salts, sometimes seen as white powder deposits
• Other chemicals, depending on the insulator material
• Mechanical erosion of surfaces by ion bombardment
• Heat (although generally very little, and primarily in the insulator)
• Carbon deposits, thereby creating a path for severe arcing

Corona Calculations
The following corona calculations are from Dielectric Phenomena in High Voltage Engineering, F.W. Peek, 1929
For Concentric Cylinders in Air:
• Corona will not form when RO / RI < 2.718. (Arcing will occur instead when the voltage is too high.)
For Parallel Wires in Air:
• Corona will not form when X / r < 5.85. (Arcing will occur instead when the voltage is too high.)
For Equal Spheres in Air:
• Corona will not form when X / R < 2.04. (Arcing will occur instead when the voltage is too high.)
• Arcing difficult to avoid when X / R < 8
Where
 RO = Radius of outer concentric sphere
 RI = Radius of inner concentric sphere
 R = Sphere radius
 r = wire radius
 X = Distance between wires or between spheres

Corona Prevention
Corona can be avoided by minimizing the voltage stress and electric field gradient. This is accomplished by using utilizing good high voltage design practices, i.e., maximizing the distance between conductors that have large voltage differentials, using conductors with  large radii, and avoiding parts that have sharp points or sharp edges. Corona inception voltage can sometimes be increased by using a surface treatment, such as a semiconductor layer, high voltage putty or corona dope. Also, use a good, homogeneous insulator. Void free solids, such as properly prepared silicone and epoxy potting materials work well. If you are limited to using air as your insulator, then you are left with geometry as the critical parameter.
Finally, ensure that steps are taken to reduce or eliminate unwanted voltage transients, which can cause corona to start.

Cooling Classes of Transformers

As a point of clarification, the cooling classes of transformers
have changed in recent years and are explained in
the following information. The IEEE transformer cooling
designations were changed to become consistent with the
IEC (IEC 60076-2: 1998). The new classifications are
detailed in IEEE C57.12.00-2000.
The new cooling designations have four-letter descriptions
that indicate specific criteria relative to 1) the type of
oil, 2) how the oil is internally circulated, 3) what is used to
cool the oil, and 4) how the oil is externally cooled.
As an example:

Figure 1 — Cooling Designations

The cooling class is identified by the following
methodology:

First Letter

Internal Cooling Medium in Contact with the Windings
Letter Definition
O Mineral oil or synthetic insulating liquid with fire point ≤ 300°C
K Insulating liquid with fire point > 300°C
L Insulating liquid with no measurable fire point

Second Letter

Circulation Mechanism for Internal Cooling Medium
Letter Definition
N Natural convection flow through cooling equipment
and in windings
F Forced circulation through cooling equipment (i.e.,
coolant pumps) and natural convection flow in
windings (also called nondirected flow)
D Forced circulation through cooling equipment, directed
from the cooling equipment into at least the
main windings

Third Letter

External Cooling Medium
Letter Definition
A Air
W Water

Fourth Letter

Circulation Mechanism for External Cooling Medium
Letter Definition
N Natural convection
F Forced circulation [fans (air cooling) or pumps
(water cooling)]

Comparison of past transformer cooling designations
versus present-day transformer cooling designations is
detailed in the following table:

Glossary of Electrical Terms

An alphabetical list of technical terms in Electrical field of knowledge.
Along with the Abbreviations & Conversion Charts.

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