Transformer Flashcards
Why do we use transformers?
- Transmission: Step-up, Step-down
- Isolation
- Metering and relaying (protection) Transformers or Instrumentation Transformers
- System Matching
- HV DC
Equation for Apparent Power (S)
S = V x I
Equation for Power Loss (Ploss)
Ploss = I^2 X R
What is this law?
In all cases of electromagnetic induction, an induced voltage will cause a current to flow in a closed
circuit in such a direction that the magnetic field which is caused by that current will oppose the change
that produced the current
Lenz Law
Current Primary (Ipri) is equal to what?
Ipri = Iex + I1
To reduce the exciting current during design:
o Increase μ, → higher quality core steel
o Reduce the air gaps.
Better quality of construction → (reduce size of air gaps)
Interleaving → reduces the effective air gap.
o Insulation on the lamination reduces eddy current in core.
o Flux density, lower β → lower IEX.
If we look at system losses, there are losses in the:
Generator
Transmission line losses from the generator to the transformer
Transformer losses
Line losses from the transformer to the load
Losses in the load (depends on load- electrical (I2 R, I2 X), magnetic, frictional)
what is it when another lead is brought out at a different number of turns?
Tap
Is the apparent power of primary and secondary the same?
Yes —> S1 = S2
V1/V2 = I2 /I1 —-> V1I1 = V2I2
What is the equation for the loading factor?
%Loading Factor = ( IActual / IRated ) * 100
What is the equation for Voltage Ratio Tolerance? (Percent Error)
%Error = (V2Act – V2Rated) / V2Rated * 100
True/False: Always use lowest voltage winding as turns reference and use turns ratio to find HV turns
True
What is the transformer equation?
V = 4.44 * N * f * A Net * β
How do you find Anet?
Anet = Stacking factor x Agross
How do you find Agross?
Agross = Lamwidth x Stack
What are parts of a transformer?
Core, Coils, Support Structures, Mounting Feet Terminals
What are the things that the coil consists of?
Primary and Secondary
True or false: HV winding is the closest to the core?
False
Low voltage winding – it is closest
winding to the core, or the inner
winding
What insulates the LV winding from HV winding?
A main gap insulation
What are the support structures of a transformer?
Structural Steel Frames, Core rods, Tie straps, and Yoke pads
What are the connection points for the customers in a transformer?
Terminals
The core of a transformer is made out of a special material. What is it?
Laminated Silicon Steel
What is this used for? 1 phase 3 leg
Small transformers < 5000 VA
What is this used for? 1 phase 2 leg 1 coil
Typically for higher voltage ratings (13800-600V)
What is this used for? 1 phase 2 leg 2 coil
Typically for lower voltage ratings (600 - 120/240V)
Typically Series parallel connections
What is this used for? 3 phase 3 leg
Most common - 120 degree phase shift
What is this used for? 3 phase 5 leg
Typically for wye wye - zero sequence currents ; currents with same magnitude and same phase angle
True or false:
When using the transformer equation, the calculation is based on the steel area not the core area.
True
What does interleaving do?
Reduces the effective gap, which reduces the IEX and core losses.
How to find volume of the core?
Volume = { (core height * core width) – (# windows * window height * window width) } * stack (Or width of transformer) * SF
What makes up total loss in a transformer?
Total Loss = No load loss (core loss) + Load loss (winding loss)
P Loss Total = P NLL + PLL
Are these statements true?
* No Load losses are present all the time (dependent on the supply voltage)
* Load losses are present only when the load is present (dependent on the load current).
True
What are no load losses (core losses)?
Core loss = Hysteresis loss + eddy loss
What is the equation for hysteresis loss?
P H = k1 * f * βm^n
Where:
P H – Hysteresis Loss (Watts)
k1 – constant dependent on the material, proportional to the hysteresis loop shape/area
f – frequency of β, which is I, which is V, the system frequency (Hz)
βm - maximum flux density in the magnetic material (T)
n – Steinmetz constant, usually 1.6
How can the designer lower the Hysteresis losses?
- A lower f would result in lower losses
- A better grade of steel would lower the losses (lowers k1 ).
- Design for a lower βMax results in lower losses by a factor of power of 1.6.
o Reduces the size (area) of the hysteresis curve.
o V = 4.44 * N * f * A Net * β
What is the equation for eddy loss?
P E = k2 t^2 f^2βm^2
Where:
P E - Eddy Loss (W)
k 2 – constant dependent on the material
t – thickness of material (m)
f – frequency of β, which is I, which is V, the system frequency (Hz)
βm - maximum flux density in the magnetic material (T), this is dependent on the material and on
performance limitations such as sound, IEX and losses.
How to reduce eddy currents?
Use better steel material.
o Type of material affects the eddies. For pure iron the resistivity is around 10μΩcm.
o By using 1% silicon steel resistivity is around 25μΩcm.
o This would reduce the eddy currents in the steel by over half
What happens to the eddy losses if you increase the frequency
P E = k2 t^2 f^2βm^2
Based on this equation, it will increase.
True or false:
A designer can choose to design at higher magnetic flux to lower the losses.
False:
A designer can choose to design at a lower βm to lower the losses.
Design to operate at the knee point.
True or false:
Does thinner steel reduce eddy current?
Yes:
The thickness is tied to the grade of steel that is chosen; thinner steel will reduce the eddy losses.
o Divided the core up into laminations.
o If the thickness is divided in half, and have two laminations, which reduces the losses to a
quarter
Overall, how would a designer reduce eddy losses?
- A better grade of steel would lower the losses (lowers k2 ), increase the resistance which reduces the
eddy currents. - A lower f would result in lower losses, but we can’t control that (it is the system frequency)
o A source of high frequencies is harmonics. - A lower β results in lower losses by a factor of the exponent of 2.
o Reduces the flux which reduces V= dφ / dt.
o Design at lower flux density by increasing the number of turns or increasing the core cross-
sectional area (higher cost). - A lower t results in lower losses by a factor of the exponent of 2.
o Reduces the flux (which reduces V= dφ / dt) in each lamination plus increases the resistance
which reduces the eddy current in each lamination.
Where do the two noises come from in a transformer?
o One comes from the core at no load.
o The other comes from the core and coil at full load
What is Magnetostriction?
- The core sound is a result of magnetostriction.
- This is where a piece of steel is magnetized, it will extend and when the magnetism is removed it
will contract.
True or false:
The more flux, the more magnetism, the less noise.
False
The more flux, the more magnetism, the MORE noise.
How can a designer reduce the sound level of the core?
o Can reduce flux density to reduce noise level but at an increase cost and gain is not linear.
* Lower β ⇒ lower magnetization⇒lower extension⇒lower noise level.
* To reduce β, either increase A or N, or combination of both.
o Core construction style
* Reduce the amount of cross grain flux flow → go to a mitre cut core.
o Dampen the vibrations → Impregnate core with varnish.
* Adequate varnishing system (not too solid a varnish)
o Higher grade steel
o Ensure the insulation on the lamination is present.
o Reduce the air gap.
* Interleaving reduces the effective air gap.
* Higher core construction quality to reduce gap size, more care in stacking
What are the four core types?
EI, Strip, Toroid, and Wound
True or false:
The windings are concentrically wound
True
Are EI cores usually small or large?
Usually on a small, single phase transformers up to 5000VA
Is cross grain flux good or bad?
Bad
leads to higher losses and higher Iex
EI dimentions:
- EI cores are usually specified by the center lamination width, call x.
- ⇒ outer lam width = ½ * x (due to ½ * φ)
- ⇒ top & bottom yoke lam width = ½ * x (due to ½ * φ)
- ⇒ window width = top yoke lam width = ½ * x (I is punched to make the window)
- ⇒ core width = 3 * x
- ⇒ window height = ½ * core width (I is punched to make the window of two E’s)
= 3/2 * x - ⇒ core height = window height + 2 * yoke lam width = window height + center lam width.
= 5/2 * x - Stack is independent of x
True or false:
* For an EI core you must design the coil to fit the core.
* For a strip (butt & lap or mitre core), the core is designed to fit the coil.
True
What are highlights of 3 phase Butt and Lap
Construction
- Flux must cross the grain at the
corners. - 7 gaps.
- Highest core losses, excitation VA
(IEX) and noise level. - Cutting equipment required is fairly
simple, since all cuts are 90°. - No scrap.
- Easy to stack, stacking is more
forgiving. - No sharp points
What are the steps to assemble a transformer?
- Remove Top Yoke.
- Install Insulation between LV and Core.
- Install Bottom Yoke Pads.
- Install Coils.
- Both coils are installed.
- Move leads out of way.
- Ready to install Top Yoke.
- Insulation (barriers) installed between
coils (Coil to Coil insulation. - Top Yoke installed.
- Top Yoke Pads installed
What are highlights of 3 Phase Partial Mitre
Construction
- Minimal cross grain flux.
- 8 gaps.
- Medium level core losses,
excitation VA (IEX ) and noise level. - Cutting equipment is more complex
since some cuts are 45° are 90°. - No scrap but losses higher than full
mitre but lower than a butt and lap. - More difficult to stack, requires
better accuracy. - Very sharp points.
What are Highlights of 3 Phase Full Mitre Construction
- No cross grain flux.
- 6 gaps
- Lowest core losses, excitation VA (IEX) and noise level.
- Cutting equipment is very complex, since there are two 45° cuts at the same time.
- Full mitre – the notches and corner pieces of center leg are scrapped.
- More difficult to stack, require better accuracy.
- Very sharp points
What is a toroid core used for?
Used for CT’s (Current Transformers)
o Very low core losses.
o Very low IEX
What type of winding is this?
* is more space efficient.
* has worse short circuit capabilities.
* more difficult to accurately calculate impedance, because it is not really symmetrical.
Rectangular winding
What type of winding is this?
* takes up more space, therefore core ends up being bigger.
* has better short circuit capabilities.
* impedance calculations are fairly accurate.
* easier to wind, everything is symmetrical.
* better cooling.
Circular winding
True of false:
* The cross-sectional shape of the core could be rectangular for a rectangular winding
* Square for a circular winding
* Stepped for a circular winding, this more effectively uses the space inside the coil
True
How to find dimensions of a coil?
X = ( Coil width – Lam width ) /2 = ( Coil OD – Lam width ) / 2
How to find dimensions of 2 leg 1 coil?
Window Width
To calculate the window width, it would be:
WDO = X + Clearance
Window Height
To calculate the window height, it would be:
WDO H = Coil Height + 2 * yoke pad (height)
Overall Core Dimension
The overall core dimensions would be
Core H = Wdo H + 2 * Lam width
Core W = Wdo W + 2 * Lam width
How to find window dimensions of 2 leg 2 coil?
Window Width
To calculate the window width, it would be:
WDO = 2 * X + Clearance
Window Height
To calculate the window height, it would be:
WDO H = Coil Height + 2 * yoke pad height
Overall Core Dimension
The overall core dimensions would be
Core H = Wdo H + 2 * Lam width
Core W = Wdo W + 2 * Lam width
Turn dimensions: Axial is _____ and Radial is ________
Thichness (Height) is the radial direction, Width is the axial direction. Width has larger dimension than thickness.
Axial is width and radial is height
Example: 6 parallel - 6 axial —-> “ “ “ “ “ “ (1 turn)
6 parralel - 3 axial, 2 radial —–> “ “ “
“ “ “
How to find turn size of conductors?
- Look at table find width and height (make sure its the right table)
*Determine what the question is asking; parallel axially? etc
*Use the largest number for height
*Add the widths
for turn size: largest height x added widths
How to find area of turn
*Look at table find width and height
*Find area by width x height of each conductors
*Add them to get total area
What are the four winding types?
Scatter, Layer, Foil, Disc
What is the most common winding type?
Layer wound
What are the axial dimensions?
- Turns per Layer = N / (# Layers)
- Electrical Length = (Turns per Layer) * (Turn Width)
- Helix Turn = Turn Width
- Mechanical Length = (Turns per Layer) * (Turn Width) + Helix Turn
= (Turns per Layer + 1) * (Turn Width) - End Margin
- Coil Length = Mechanical Length + 2 * (End Margin)
- End Fill
What are the radial dimensions?
- Layers
- Cooling Ducts
- Interlayer Insulation
Radial Build = total layer build + total duct build + total interlayer insulation build
Radial Build = (# layers) * (Turn Height) + (# of ducts) * (duct size) + (# layers – 1) * (interlayer
insulation thickness)
