In voltage, when the excitation of a winding is at a positive max with respect to the dot, the second winding's voltage is at a positive max with respect to the dot.

In current flow, the transformer obeys the conservation of power law. Current flowing into the dot of a winding cause a current to flow out of the dot on the other winding given the transformer transmits a power flow.

Transformers of 3+ windings have the same dot convention applies to the voltage. For current, the windings are often made for arithmetic loading meaning the load rating on the primary winding equals to the sum of the loads on the secondary and tertiary windings.

Functions

Windings

[20]

Primary winding/side (P)/power input winding collects power and is the input side where AC power supply connect, the powered winding, indicating the transformer is powered by an AC source. It creates a varying magnetic field in the transformer's core. The primary's number turns is NP.
Secondary winding (S)/load output winding gives power and is the output side where the transformed voltage and current are sent (connect) to the load.

Power-distribution transformers' sides may be referred by voltage levels:

High-voltage (HV) side: side of higher voltage winding
Low-voltage (LV) side: side of lower voltage winding

This winding diagram shows the coils's internal connections for both windings, with the leads' markings for high and low voltage terminals (H1, H2, and H3 for the high voltage; X1, X2, X3, and X0 for the low voltage).

Fig. 1

The winding with the most turns has the higher voltage--labelled “H or high voltage terminals”. Lower voltage terminals are labelled “X” (Fig. 1).

Windings configuration Although a (step-down) transformer's primary is often on the left and higher turn and the secondary on the right and lower turn (especially in schematics), it's not always the case.

Methods to tell which is the primary, which is the secondary:

Voltage ratings: Primary connects to input power source (e.g., mains voltage, generator). Secondary sends the output voltage to the load.

Look for labels like:

HV (High voltage): Often the primary in step-down transformers.
LV (Low voltage): Often the secondary in step-down transformers.

Step-up transformers are the opposite.

Resistance measure (if no power applies): The primary (for higher voltage) often has thinner wire with more turns, giving higher resistance.

The secondary winding (for higher current) often has thicker wire with fewer turns, giving lower resistance.

Use a multimeter in resistance (Ω) mode to check which side has higher/lower resistance.

Physical wire thickness:

Thinner wire is likely the primary (higher voltage, lower current).
Thicker wire is likely the secondary (lower voltage, higher current).

Look for manufacturer labels/datasheets: Many transformers are labeled:

"P/Pri" = primary
"S/Sec" = secondary

If available, check the its datasheet/part number online.

transformer core

Core and coils

A transformer has high voltage bushings connected to it inside.

A transformer's hearts are its coils and cores.

Current goes from the power source into the main coils, with currents making strong magnetic field, inducing coil into the second coil set, a process called induction.

ratio of loops or turns in coil to the secondary coil determines the voltage a transformer converts the power to.

In this case, the ratio of the main voltage = 12k V and secondary voltage = 480: 12000/480 = 25 is a ratio of 25/1, so a turn is in each 25 turns of a main coil.

Coils are looped around a special steel core, picking up main core's magnetic field, enforced for better induction.

Load break switches

A load break switch is a load brake switch that work even if the transformer energizes and in underload.

A special rotary switch manually disconnect a transformer from the power source.,

Fuses being replaced.

Fuse

A fuses protects a system if an overcurrent occurs. In high heat/current, fuses' thin wire, an element, melts and opens (disconnects) the circuit from the power source.

As the issue causing the fuse to blow is done, fuses are replaced.

Bayonet fuses are labeled “BAY” and the isolation links are labeled “ISO”. Special current limiting fuses may be labeled “CLF”.

Loop and radial feed

The wiring diagram also shows if the transformer is a loop feed or radial feed transformer. A loop feed transformer has a bushing configuration specifically designed for a loop distribution system, although it can also be used in other systems. A loop feed transformer will be labeled like this with six different primary bushings (H1A, H1B, H2A, H2B, H3A, and H3B):

Voltage adjugement tap

Voltage adjugement taps keeps the correct secondary voltage, if the main voltage is higher/lower than usual.

The transformer's tap setting is adjusted by rotating the tap changer. As it rotates, main coils' small parts are disengaged, altering the ratio of main to secondary turn, lowering the main voltage rating.

Oil cooling

As transformer heat up when working, its cooling system cools its temperature for proper function, done with its tank filled with special fluid as coolant and electrical insulator as well.

A nitrogen blanket is in the tank, stopping comtaminants (e.g. oxygens and moisture) from entering.

Coils have spacers between each layer of winding creating duct channels, with fluid flowing through, pulling heat away. Fluid rises in temperature to the tank and enters the radiators, where ambient temperature cools it off. Fluid cools and drops to the bottom of the radiators reenters, a process called natural convection.

Some transformers have fans blowing air through radiator fins, speeding cooling.

Gauge

Gauges monitor operating states.

Liquid level watches the fluid level in the tank.

Thermometer measures the fluid's temperature.

Pressure vaccum gaige does the pressure amount in it.

Low-voltage bushing

Low-voltage bushings connect the load to the transformer.

This case uses a liquid-filled padmount transformer. They have the same purpose despite varying in shapes/styles/sizes.

Types

[14.2], [20],

Ideal transformer

Ideal transformer: an imaginary transformer model assuming perfect energy transfer without losses, has 100% efficiency (input power equals output power, and no voltage regulation), unlike real transformers that experience losses due to factors (copper resistance/core losses/leakage flux).

Their voltages are the same in both windings, but some powers are actually lost due to inefficiencies (e.g. heat and resistance) irl.

No winding resistance: The ideal transformer has no ohmic power loss and resistive voltage drop.
No magnetic leakage has no leakage flux and all the flux set up is confined to the core and links both the windings.
No iron loss: hysteresis and eddy current losses in a transformer core are zero.
Tiny magnetizing current: Tiny magnetizing current is needed to establish needed flux amount in a core

Power distribution transformer

[9] A power distribution transformer or distribution transformer gives a final voltage in a electric power distribution system, reducing the voltage for distribution lines to a level for customers: homes/businesses/industries

Distribution transformers often have their ratings in kVA on the front.

[1.5]

Current transformer

[1.5] Current transformer (CT) measures AC current by making a proportional current in its secondary, based on the current flowing in its primary. It's like a device "reducing" high current to lower measurable current.

CT formula: Is = Ip/N

N = turns ratio

Formulas:

Autotransformer

An autotransformers uses 1 winding for both the winding--no electrical isolation inbetween, being smaller, lighter, and more efficient than usual transformers.

Advantages:

Smaller--at least part of a winding is shared.

more compact
For small voltage changes (E.g. 208-240 V).

Disadvantages:

Unsuitable for big voltage changes--the shared winding is less significant.
If it common winding opens, primary voltage connects to secondary.

They have a common winding between the primary and secondary windings.

This primary winding is in pink.

The secondary winding is in blue.

The red winding is common to the primary and secondary windings.

This transformer has a ratio of 1.

a step-up autotransformer:

a step-down autotransformer:

Calculations

This voltage supply is 24 V.

What voltage does the load see?

ES = NS → ES = NS x EP = [(25 + 25 + 25 + 50)/(25 + 25 + 50)]x24 = 30 V

Voltage ratio formula:

26-266 (2); CEC Pg ) Auto-transformers musn't connect to interior wiring systems, other than a wiring system or circuit used wholly for motor purposes, unless:

(a) the system supplied has an identified grounded conductor solidly connected to a similar grounded conductor of the system supplying the autotransformer;

(b) the autotransformer is used to start/control an induction motor; or

A usual autotransformer:

E.g. 1# A building has 120/208 W but we have a small piece of equipment neeeding single phase 240 V power. What must the autotransformer ratio be?

a = EP/ES = 208/240 = 0.87

E.g. 1.2# A autotransformer’s primary has 150 turns. How many turns does the secondary need?

a small variable AC voltage supply:

120 VAC on the primary

0 to 140 V on the secondary

Autotransformers at high power This is an autotransformer of oil immersed and floor-standing/high-power--max 1 200 MVA with a system interconnection and a voltage regulation.

A normal transformer can be used as a autotransformer by connecting both coils to the input current. Suppose to boost an AC voltage by 10%, get a 120V to 12V step down transformer and connect the secondary winding in series to the primary, ensure both winding are in phase. Connect the primary to the 120V supply.

Connect the load to the series combination and we get 132V. The advantage is that the transformer is much smaller. It can be rated at just 10% the total VA at the output, as long as we don’t need the isolation since the transformer is only supplying 10% more of the output voltage.

Mega volt-ampere transformer

[1.11] A mega volt-ampere (MVA) transformer

Transformer configurations

A transformer configuration is the way (primary and secondary) windings connect, influencing how a it acts in a 1Φ or 3Φ system. Common configurations are delta-delta, wye-wye, delta-wye, and wye-delta, each with upsides and downsides.

The 2 main transformer configuration types are 1Φ and 3Φ transformer configurations.

- Single-phase transformer

A single/one-phase (1Φ) transformer converts energy between a single phase system.

Isolation transformer

Secondary winding is physically and electrically isolated from the primary winding
Some have a 1:1 ratio
- Same input and output voltage
- For isolation only
- Safety

Current transformer

Measure or monitor current in a line while isolating metering and relay equipment
Conductor through a toroid becomes primary. Single turn primary
Rated secondary current is often 5A

A usual single phase distribution transformer X2 is grounded and becomes the load neutral

H1 and H2 are the high voltage connections (here being 7620 V).

Another variation To form Single phase DT, X2 and X3 will be joined then grounded and become the load neutral OR

X1 and X3 are joined

X2 and X4 are joined

provide power at 120 V only but via more power

- Three-phase transformer

A three-phase (3Φ) transformer converts energy between 3-phase systems, made of 3 single-phase transformers as 1 unit, connected in a "Wye" or "Delta" configuration.

Single vs three-phase transformer comparisons

Single phase transformer bank

Small size
Can supply single phase only
easier to move
If one fails, we still have the others
Less power/Bank

Less cost

Used for power distribution purposes (home and lighter load)

Three phase transformer

Bigger size but more compact, less weight, size, more power
Can supply both.
Simpler installation/ maintenance in larger sizes
More costly and repairing inconveniences
Used for power transmission purposes such as industrial and commercial applications

Notations

- Z reflected = reflected resistance seen by the primary
- N: # turns
  - Np = # of turns of primary winding
  - Ns = # of turns in secondary winding
- Ep or Vp: voltage in primary winding
- Vs: voltage in secondary winding
- Ip: current in primary winding
- Is: current in secondary winding
- Rl = load resistance connected to secondary

Values

Voltage

Transformer voltage ratings at times need interpretation.

If you are unsure, research &/or ask the manufacturer.

Voltages are often listed from highest to lowest.

8KV/240/120V is This is a common rating.

The high voltage winding is rated 8000 V.
The low voltage winding is center tapped.

Voltage root mean square

Voltage root mean square (Vrms/RMS) in math, is a measure of effective voltage of an AC waveform, for the equivalent DC voltage dissipating the same power in a load. It's calculated as the square root of the average of the squared instantaneous voltage values over a complete cycle.

vrms

AC circuits' voltages vary polarities and magnitudes--it isn't constant like DC voltage.

To know how much power is sent to a load (e.g. resistor/motor), relate the AC voltage to a constant value (e.g. DC voltage) that sends the same amount of power.

RMS value is crucial to treat AC voltages as a constant DC voltage making the same power.

Math An AC waveform's RMS voltage is calculated as square root of a square's average of the instantaneous voltage values over a full cycle.

Math sinusoidal waveform is:

T = period ofAC waveform
v(t) = instantaneous voltage at any time

The formula is simplified as:

Current

Ratio of primary to secondary current inverse of the turns ratio.
Ratio of primary to secondary current inverse of the voltage ratio.
A transformer reducing the voltage increases the current.

E.g. A common distribution transformer can supply 208 A at 240 V. The primary connects to 7.4 kV. Find the rated primary current?

Vp/Vs = Is/Ip: 7400/240 = 208/Ip

Ip = 208/(7400/240) = 6.75 A

high voltage with low current
low voltage with high current

Efficiency

Efficiency is the

Big transformers are 99% efficient.

Under 1% input energy is lost as heat.

Apparent power

Apparent power (S) is, measured in volt ampere (VA/kVA/MVA)

Apparent power formula: S = F*I

As heat losses are small, treat power in as equal to power out.

Transformers have a single power rating.

The calculation model of many calculations:

a 25 kVA distribution transformer

E.g. 1# A transformer is rated 25 kVA, 8kV /120/240 V

What's the rated primary current in a step-down application?

S = E*I = 25k/8k = 3.1A

What's the rated secondary current in a step-down application?

S = EI = 25k/240 = 104.17 A--Such transformer is often used in residential areas in 25, 37, 50 and 75 kVA ratings.

E.g. 2# This transformer's rating is slow voltage side at 24 V, 40 VA. Its high voltage side rates 120 V.

Can it supply a load at 3 A at 24 V?

S = EI = 40/24 = 1.7 A

No, the transformer will overheat and fail.

Primary and secondary coil

Transformers send power from a primary coil to secondary coil.

Power transferred from primary to secondary = power on ideal transformer

"Ideal" means no power losses are across the coils. We use this example to explain the way transformers work.

There's always efficiency losses. If primary coil is the same number of turns as secondary--E.g. 80 turns, ratio is 1:1, so both windings' voltage and current are the same.

A transformer cross-section shows primary and secondary windings is a few inches tall (~10 cm).

E.g. This is a step-down transformer (its primary winding's turn is higher than secondary's).

As a step-down unit, it converts:

high-voltage into low-voltage
low-current power into high-current power

The larger-gauge wire used in the secondary winding is needed due to the current increase.

The primary winding (doesn’t have to conduct as much current) may be made of smaller-gauge wire.

This is a 2:1 = 80:40 step-down transformer.

Secondary voltage is half, but current changes inversely or by 2. Same for power.

inversely: opposite manner

This is a 1:2 = 80:160 step-up transformer. Voltage doubles on secondary and current changes inversely--decreases by 2.

Power again stays the same.

Ampere-turns of a coil

[1.10] Ampere-turn is the measurement of

E.g. Find a coil's amp-turn via 1500 turns and 4 mA current, N = 1500, I = 4x10⁻³ A -> NI = 1500x4x10⁻³ = 7 A-t

Transformer ratio

Vp and Vs relationship: Ep/Es = Np/Ns
Ip and Is relationship: Ip/Is = Ns/Np
Current and voltage relationship: Ip/Is = Es/Ep
- Note: Ip must be in phase with Vp: resistive load
N = number of turns
E or V = Voltage
I = Current

- Examples

1# A transformer has a primary winding with 20 turns and 240 V and its secondary is 60 turns.

Find the secondary voltage.

Reveal answer

2# A transformer's primary winding is X turns and 120 V.

The secondary winding has 40 turns.

Find x (# of turns) needed for a 20 V secondary.

Reveal answer

3# With a 1:2 ratio, this is a step-up transformer. There's twice voltage on secondary than primary.

Find all voltages, currents, and powers here.

Known values:

Np = 80
Ep = 100 V
Is = 1 A
Pp = 300 W

Answers:

Ns = 160
Es = 100x2 = 200 V
Ip = 100/200 = 1/Ip = 1/0.5 = 2 A
Pp = IE = 2x100 = 200 W
Ps = IE = 200x1 = 200 W

4# With a ratio of 1:3, this is a step-up transformer. There will be three

times the voltage on the secondary compared to the primary.

Find all voltages, currents, and powers.

Vs = 100x3 = 300 V

Ip = 100/300 = 1/Ip = 3 A

Pp = 100 * 3 = 300 W

Ps = 300 * 1 = 300 W

Find voltage on secondary.

Es = 12 V

Find voltage on secondary.

Es = 30 V

Find voltage on secondary.

Es = 20 V

5# Find voltages, currents, and powers here.

With a ratio of 5:1, this is a step-down transformer.

Es = 60/5 = 12 V
Is = 12/24 = 500 mA
Ip = 60/12 = 0.5/Ip
- = (12x0.5)/60 = 100 mA
Pp = 60x100 m = 6 W
Ps = 12x0.5 = 6 W

Find all voltages, currents, and powers.

With a ratio of 5:1, this is a step-down transformer.

Vs = 600/5 = 120 V
Is = 120/20 = 5 A
Ip = 600/120 = 5/Ip
- Ip = (5x120)/ 600 = 1 A
Ps = 600x1 = 600 W
Ps = 120x5 = 600 W

Flux

[1.6] In electricity, flux (Φ) is the electric field amout passing through an area, crucial to measure how much an electric field "flows" through a surface. See, it as the number of magnetic lines going through an area.

Flux density formula: B = Φ/A or web/m²

B = magnetic flux per unit area of a section perpendicular to the flux's direction, measured in Tesla (T) or the Gauss unit at times.
A = area

E.g. What's the flux density in Tesla if the there's 600 wb of flux through an area of 0.003 m².

B = Φ/A = (6x10⁻⁴)web/(3x10⁻⁴) m² = 2 Tesla (T)

Centre tapped transformers

Have an extra wire on the secondary.

Splits the secondary voltage in half. Centre tapped transformers are often used in power supplies, to give a positive and negative value with the centre serving as the COM.

Find all voltages, currents, and powers.

Es = 120 V, so its center tap has 60 V.

½ Is: 60 / 30 = 2 A
second ½ Is: 60 / 50 = 1.2 A
Ip = 600/60 = 3.2/Ip
- = 3.2x60 / 600 = 320 mA
Pp = 600x320m = 192 W
Ps 1/2 = 60x2 = 120 W
- = 1/2 = 60x1.2 = 72 W
PTs = 192

Current on the neutral

The current on the Neutral (common):

IN = IR1 – IR2

= 2 – 1.2 = 800 mA

Impedance

Impedance (Z) is the total opposition to AC current, measured in ohms, combining resistance and reactance (X).

Its formula is written in rectagular form: Impedance formula: Z = R + jX

In DC systems, impedance = resistance are the same, defined as voltage across an element divided by current (R = V/I).

Reflected impedance

Reflected impedance or resistance (R/R'p/Z_reflected) is the

resistance "seen" by the primary, caused by the secondary's complex load--As if the primary feels the secondary's effect, based on the transformer' s turns ratio.

Reflected impedance formula: Z_reflected = (Np/Ns)² x Rl

E.g. If the secondary has a heavy load, it makes the primary side "feel" it, but adjusted by the turns ratio.

Complex load

A complex load is an electrical load with both resistive (real) and reactive (imaginary) components. Unlike simple resistors (only opposing current and dissipates power as heat), complex load interact via AC signals in a way involving energy storage (in inductors/capacitors) or phase shifts between voltage and current.

Reflected resistance and reflected impedance are used interchangeably, mainly pecially for purely resistive loads. Both refer to a load's effect on the secondary being "reflected" back to the primary side, adjusted by the transformer’s turns ratio.

But, for a complex load (e.g. inductive, capacitive), "reflected impedance" is more accurate as it includes both resistance and reactance (impedance components ).

1# E.g. Find the reflected impedance on primary.

Is = 500 mA

Ip = 100 mA

Powers:

Pp = 60 * 100 m = 6 W

Ps = 12 * 0.5 = 6 W

The reflected impedance back to primary is:

R’P= (Np/Ns)2 * 24 = (5/1) 2 * 24 = 25 * 24 = 600 Ω

R’P= 60/0.1 = 600 Ω

2# E.g. Find the reflected impedance (on primary).

RTs = 3.2 A

Ip 600/60 = 3.2/Ip = 0.32 A

R’ = 600/0.32 = 1875 Ω or with reflected impedance formula: 80x(5/1)² = 2000 Ω

[6] Basic concepts:

(1) Transformer turns ratios (2) Power conservation (power out = power in) (3) Ohm's law

If a 10:1 turns reduction transformer and primary has 100V, output voltage = 1/10 of 100 = 10 V.

Connecting a 10 ohm load to secondary makes the secondary have 1 amp.

If the transformer is 100% efficient, power out = power in, so primary current is 1/10th the secondary current (0.1 A).

So primary has 100V and 0.1 A.

If the transformer is 1 equivalent load, (Ohm's law) this is 100V / 0.1A = 1000 ohms, which is reflected impedance of 10 ohm load of secondary.

Percentage impedance

Percentage impedance is the percentage of primary voltage needed to force a rated max current to flow in a short circuited secondary.

Impedance affects transformer performance, voltage regulation, and short-circuit currents. High impedance limits fault currents.

Low impedance improves voltage stability.

A test often done in the field, an ammeter makes a short circuit on the low voltage winding.

A variable AC source connects to the high voltage winding.

In power distribution, Z% helps in maintaining stable voltage levels in power grid. It also helps in analyzing and limiting short circuit currents ( fuse & breakers rating calculations).

Variable AC supply voltage slowly rise 0 V til the ammeter reads rated current.

Percent impedance formula:

Period of the input voltage

Find the time it takes for a full cycle of a voltage waveform, done by measuring the time interval between 2 same points on consecutive cycles.

Taps

Markings like this often show a choice of transformer “taps”.

We only use one of H1, H2 and H3

E.g. The transformer maybe wound such that:

625 V: H1 to H4 gives 120 V to X1 and X2
600V: H2 to H4 gives 120 V to X1 and X2
575 V: H3 to H4 gives 120 V to X1 and X2

High voltage tap

A high voltage taps (HV tap) is a transformer's connection points on its primary/HV side for adjustments to its output voltage, often often given on its HV winding as it has a greater # turns, letting finer voltage control and avoiding high currents in tapping process.

Rating

Power calculated in VA (volt-Amps) or kVA

A transformer's percent efficiency:

%eff = PSEC / PPRI

H1 & H2 – high voltage winding

X1 & X2 – low voltage winding

Power used by a transformer is called power loss

1. Hysteresis loss

Residual Magnetism

2. Eddy Current loss

Current circulating in the core

3. Copper loss (I2R)

Power dissipated in windings

Nameplate and markings

[14.1], [15.1], [15.2], [16], [17] A transformer's nameplate a metal/plastic placard of essential info for electricians/users to use the transformer.

Location A namplate maybe inside its cabinet door. Substations and dry types have the nameplate outside or enclosure.

substation: a high-voltage electric system facility

[16]

[17]

[15.1]

[15.2]

(sual) infos

"kVA" is a transformer's power capacity in kilovolt-amperes (kVA)--its rated kVA, how much load it handles safely.
"HV" (primary or high voltage) and "LV" (secondary or low voltage) are next to each other.
- "HV taps" (high voltage taps) (Fig. 2) may also be included.
"LV amps" Secondary amps ("low voltage") is the LV's ampere.
- "Temperature rise" is a winding's average tempareture above ambient temperature if the transformer is at full load (max kVA), e.g., 65C in this case
"% IZ" (Impedance) relates to the to the current's flow.
- "HL/LV mat" (high voltage/secondary voltage material) is the materials used for HV and LV windings. e.g., "AL" for aluminium in both winding, here.
Frequency shows the frequency transformer is built for (often 50-60 Hz).
"Fluid" is a transformer's insulating oil, for cooling and as a dielectric insulator.
"Class" is the
Transformer phasing (Fig. 3) maybe on a plate's top right/left, e.g., "3-phase transformer"
Rated voltage: Voltage levels for the primary (input) and secondary (output) windings.
- E.g. 11kV/415V
Rated current: Amount of current a transformer handles at rated voltage and power, on both primary and secondary.

Max current for windings:

IP = kVA/EP
IS = kVA/ES

Wiring diagram

A wiring like this shows the markings for the LV and HV's leads, with often its fusings labeled on it: E.g., Bayonet fusing will be written as "Bay", isolation as "ISO."

A special limiting fuses maybe labelled "CLF/PR"(Fig. 4).

Load break switches

[17]

Fig. 2

Fig. 3

Terminal markings

By ANSI/IEEE Standard [1.12], transformers are marked as:

On primary winding (High voltage; HV)

H1: Start of the primary (polarity reference).
H2, H3: Other primary terminals (for multi-tap transformers).
Neutral (if present): May be labeled H0.

On secondary winding (Low voltage; LV)

Labeled X1, X2, X3, etc.

X1: Start of secondary winding (matches H1 polarity).
X2, X3: Other secondary terminals (for multiple outputs).
Neutral (if present): Often labeled X0.

Dot convention

A dot (•) near H1 and X1 tells same-phase polarity.

If H1 is positive, so is X1.

Phase Shift:

In 1Φ transformers, H1 and X1 are in-phase.

In 3Φ transformers, windings may introduce a 30° shift (e.g., Delta-Wye).

Current standards of transformers

Transformers are governed by international and regional standards for safety, efficiency, and interoperability. Below are the key standards for power transformers, including IEEE, IEC, ANSI, and NEMA guidelines.

computer systems/softwares' abilities to exchange and use info.

International Standards (IEC)

IEC 60076 – Power Transformers (Most widely used globally)

IEC 60076-1: General requirements
IEC 60076-2: Temperature rise & cooling
IEC 60076-3: Insulation levels & dielectric tests
IEC 60076-5: Ability to withstand short circuits
IEC 60076-7: Loading guide for oil-immersed transformers
IEC 60076-11: Dry-type transformers

Key features:

Defines kVA ratings, impedance, losses, and efficiency classes.

Uses IEC 60076-8 for application guides.

U.S. Standards (ANSI/IEEE & NEMA)

ANSI/IEEE C57 Series – Power Transformers

IEEE C57.12.00: General requirements (liquid-immersed)
IEEE C57.12.01: Dry-type distribution transformers
IEEE C57.12.90: Test procedures
IEEE C57.91: Loading guide for mineral-oil transformers
IEEE C57.154: Standard for pad-mounted transformers

Key features:

Defines voltage classes (e.g., 600V, 15kV, 35kV).
Specifies BIL (Basic Insulation Level) for surge protection.
Efficiency tiers (e.g., DOE 2016, NEMA TP-1 for dry-types).

NEMA Standards

NEMA ST-20: Dry-type transformers (600V and below)

NEMA TP-1: Energy efficiency for distribution transformers

European Standards (EN)

EN 50588: Dry-type transformers

EN 50464: Oil-immersed distribution transformers

EN 60076 (aligned with IEC 60076)

Key Features:

Follows EU Efficiency Directive (Tier 1, Tier 2, Tier 3).

Requires CE marking for compliance.

Indian Standards (IS)

IS 2026: Power transformers (similar to IEC 60076)
IS 1180: Distribution transformers
IS 11171: Dry-type transformers

Key features:

Mandates BIS certification.
Follows energy efficiency levels (e.g., Star ratings).

Faraday's law of electromagnetic induction

[11] Now Faraday adds a second coil – not connected to the first one.

What happens when the switch is closed now?

A: Deflection in Galvanometer

A conductor placed in a varying magnetic field induces the electromotive force.

If the conductor circuit close, it induces the current, called induced current.

If we add a second coil. not connected to the first one. If the switch is closed now a deflection is in the Galvanometer. A magnetic field is made. As the field expands, it cuts across the second winding and induces current.

If a conductor is placed in a varying magnetic field, an electromotive force is induced. If the conductor circuit is closed, a current is induced, which is called induced current.

A magnetic field is created.

As the field expands, it cuts across the second winding and a current is induced.

.but there is only a current when the field strength is changing

As the button releases, the field collapses.

As the field contracts, it cuts across the second winding and a current is induced with the opposite polarity!a

What would happen if the input voltage was always changing – if it was AC? The output is be AC too.

Can change voltage and current not power rating.

Why is this important (step up transformer used in substation)

This used can be used in fault current calculations of any short circuit faults, impedance matching Z Source = Z load for max power transfer to a connected load.

Works at high efficiencies--99% for big power transformers works at high frequencies.

Formulae

1. Voltage, current, and turn ratio formula:

2. Power conservation formula: VpIp = VsIs

3. Reflected impedance formula: Zp = a² Zs = (Np/Ns)²*Rl

Zp = impedance "seen" by the primary
Zs = Rl = load impedance connected to the secondary (maybe resistive/inductive/capacitive).
a = (Np/Ns)² = turns ratio (primary:secondary)

Transformer phasor equations (AC Analysis):

4. Primary voltage formula: Vp = Ip(Rp+ jXp) + Ep

Ep = back-EMF due to mutual flux).

5. Secondary voltage formula: Vp = Es - Is(Rs+ jXs)

Ep = back-EMF due to mutual flux).

6. Magnetizing current (Im): Im = Vp/jXm (shunted in equivalent circuit)

7. THD (Total Harmonic Distortion):

8. Temperature rise and thermal modeling

9. Load sharing formula (For parallel-connected transformers):

S = kVA rating
Z = impedance

10. Peak inrush current during energization formula (transient behavior):

Base impedance formula:

Per-unit impedance formula:

Turns per volt:

f = frequency
Bmax = max flux density
Ac = core area

All-day efficiency formula:

Voltage ratio formula:

Voltage ratio formula (for CTs): Is = Ip/N

Polarity

Battery polarity Batteries polarities is correct and they add. The light comes on. What occurs if we reverse the connection to 1 battery?

Additive and subtractive polarity

In transformer polarity, additive polarity means 2 windings are connected, the resulting voltage is the sum of individual winding voltages.

Subtractive polarity is the resulting voltage, the difference between 2 winding voltages, found by coils' direction are wound and how the terminals are brought out.

Additive polarity

Substractive polarity

[1.2], [13], [14]

Testings

[12]

Contuinity:

Must be done at power off.
Best via disconnected transformer.
Check the high voltage winding for continuity.
What are the possibilities?
The winding has a low DC resistance
A good winding looks like a short circuit (beeping in continuity test)
An open winding will be in the mega-ohm range – an open “OL”
The same applies to the low voltage winding

Ground faults:

A good winding must have a high resistance to ground--in the mega-ohm range.

Check both windings

Do this test:

before powering up a new transformer
when a transformer trips an overcurrent

Megohmmeter:

In power transformers, this test may be done with a megohmmeter or “Megger”.

This may use 600 VDC or 1000 VDC to test the insulation.

Use caution when working with this tool.

Isolation:

An isolation transformer must have no electrical connection between the high voltage and low voltage windings--the Ohmmeter read “OL or isolated transformer.“

Radio test: To test or find the transformer ratio:

supply a low voltage to one winding (A – B)
Measure the voltages V1 and V2
the transformer ratio is the ratio of V1 to V2

E.g.

V1 measured 15.0 V

V2 measured 74.9 V

VP/VS = 15.0/74.9 = 0.20

As connected, this is a step-up.

What would the ratio be connected step down?

0.20⁻¹ = 5

Percent impedance (not often done): An ammeter creates a short circuit on the low voltage winding. A variable AC source connects to the high voltage winding.

The variable AC supply voltage is slowly raised from 0 V til the ammeter reads rated current.

Percent impedance :

%Z = Evariable supply input x 100% E rated

The % of primary voltage (variable AC input voltage applied on primary side)that is required to produce the rated transformer secondary current is what is known as %impedance or per-unit impedance of transformer.

The % of primary voltage (variable AC input voltage on primary side) needed to make the rated transformer secondary current is called % impedance or per-unit impedance of transformer.

E.g. E.g. A transformer is rated 120/600 V and the low voltage side is rated for 150 A. When the variable AC supply on the high voltage side is at 31 volts, there is 150 amps on the low voltage side. = %Z = Evariable supply x 100% = 31 x 100% = 5.2 % E rated 600 Typical values of %Z are at 3–9 % range.

Consequence: What occurs if this transformer is short circuited at rated voltage?

Ishort = Irated = 150 = 2,900 A

%Z 0.052

Any equipment piece at low voltage side must withstand fault current til an overcurrent protection opens.

The Hysteresis Loop

Transformer bank

[4.1], [11.2] A transformer bank is a system of 2-3 single-phase transformers connected to be a 3Φ transformer, a configuration often for a dedicated 3Φ transformer is unavailable/unpractical.

What's an input in a transformer bank

Approches

Input = primary

Output = secondary

Connnections

Transformer bank photos

Transformer bank diagrams

This transformer's current standard is the use of a steel bracket and a single pole.

The photo shows its winding configuration is 3 x 37.5 kVA and

a grounded wye secondary.

"37.5 kVA" is the power rating: 37.5 kilovolt-amperes.

"T 0146P" maybe a serial/model number.

These are liquid filled transformers installed indoors, which need a special room, often called a “vault.”

Note the transformer tank grounding.

[R1] Faraday's law of induction
[R2] Flux
[R3]
[R4]

References

[1] Wikipedia
- [1.1] Polarity (mutual inductance)
- [1.2] Root mean square
- [1.3] Hysteresis
- [1.4] Autotransformer
- [1.5] Current transformer
- [1.6] Flux
- [1.7] Weber (unit)
- [1.8] Magnetic flux
- [1.9] Magnetic field
- [1.10] Ampere-turn
- [1.11] Volt-ampere
- [1.12] ANSI device numbers
- [1.13]
- [1.14]
- [1.15]
[2] Step-up and Step-down Transformers - All About Circuits
[3] The Difference Between Step-up Transformer and Step-down Transformer - Yuebian
[4] Transformers Physics Problems | Voltage, Current & Power Calculations | Electromagnetic Induction - YT
- [4.1] Transformer Banks: Overview
- [4.2] The Reflected Load in a Transformer
- [4.3] How does a Transformer work ?
- [4.4] What Is Inside An Electrical Transformer ?
- [4.5]
- [4.6]
[6] Reflecting impedance in a transformer - ElectricalEngineering | Stack Exchange
[7] What are the different Parts of a Transformers and their Function? - Star Delta
[9] Distribution transformer
[10] pressbooks.bccampus.ca/singlephasetransformers/chapter/additive-and-subtractive-polarity/#:~:text=If%20the%20voltage%20is%20the,then%20the%20transformer%20is%20subtractive.
[11] ELE8923-010: Transformers I - (Algonquin College) Canva
- [11.1] ELE8923-010: Transformers II
- [11.2] WK4 CT TRANSFORMER STBS PART1 2024
[12] Understanding Transformer Polarity - Electrical Engineering Portal
[13] https://mytech-manoj.blogpost.com/2014/11/transformer-dot-conventions.html
[14] Maddox
- [14.1] How to read a transformer nameplate
  - [14.1.1] How to read a transformer nameplate | Maddox Transformer - YT
- [14.2] Types of transformers
[15] Transformer Nameplate Data | Explain the Rating and Features - ElectricalTechnology
[16] Transformer Nameplate Details and Sound Levels - EEPower
[17] Fuses.pdf
[18] Stanley Transformer | 1886 - NationalMaglab
[19] Understanding Three-Phase Transformer Connections in Electrical Power Systems - Allelco
[20] Electrical Transformers Explained - Tameson

Quizzes

Transformer ratio formula:

a = transformer's ratio

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