Transformer Theory
Transformer Theory
Introduction
What is a transformer? According to Google AI:
“A transformer is a passive electrical device that transfers electrical energy between two or more circuits through electromagnetic induction, usually to change (step up or step down) voltage levels without altering frequency. Operating exclusively on Alternating Current (AC), they consist of primary and secondary wire coils wrapped around a magnetic core.”, Google Artificial Intelligence.
What are shell type transformers? According to Google AI:
“Shell type transformers are electrical transformers where the iron core surrounds the windings, providing high mechanical strength and efficient magnetic shielding. They feature a central limb—housing both HV and LV sandwich-type coils—and two side limbs, making them ideal for high-voltage, high-capacity, or short-circuit-prone applications.”, Google Artificial Intelligence.
What are core type transformers? According to Google AI:
“Core-type transformers (or core-form) are electrical devices where the windings surround a laminated, high-permeability steel core, which acts as a continuous magnetic path. They are commonly used in power transmission and distribution because they are easy to repair, offer high mechanical stability, and are efficient for high-voltage, low-current applications.”, Google Artificial Intelligence.
The differences between shell type transformers and core type transformers are well illustrated and explained in this link:
https://grant-transformers.com.au/difference-between-core-type-and-shell-type-transformer/
The primary transformer winding creates a magnetic field that induces current in the secondary winding. The induction between the two windings is mutual.
What is transformer magnetising current? According to Google AI:
“Transformer magnetising current (or exciting current) is the small, typically 2–5% of rated current, drawn by a transformer’s primary winding to establish magnetic flux in the core. It is essential for transformer operation, creating the alternating magnetic field that induces voltage in the secondary, regardless of load.”, Google Artificial Intelligence.
What is transformer iron loss? According to Google AI:
“Transformer iron loss (also known as core loss or no-load loss) is the energy wasted as heat in a transformer's magnetic core due to alternating magnetic flux, occurring regardless of the load. It consists of hysteresis loss (molecular friction) and eddy current loss (circulating currents). It is a constant loss found using open-circuit tests.”, Google Artificial Intelligence.
Transformer Equations
The relationship between the voltage and number of turns is defined by:
For lossless transformer:
According to Faraday’s law:
Therefore volts per turn is equal to:
For sinusoidal inputs K = 4.44. Therefore:
The power output of a three phase transformer is equal to:
Leakage Reactance
What is transformer leakage reactance? According to Google AI:
“Transformer leakage reactance is the self-reactance produced by magnetic flux that leaks through the windings rather than linking both primary and secondary coils. Caused by imperfect magnetic coupling, it forms part of the transformer's internal impedance, resulting in voltage drops and poor regulation under load. It is crucial for limiting fault currents and can be controlled through winding geometry.”, Google Artificial Intelligence.
Transformer ratio of voltage drop over the full load voltage is equal to:
On-Load Tap Changers (OLTC)
The load impedance constantly changes during the day. Because of transformer output impedance the load voltage would change with the load impedance, dropping below or increasing above required values. This is why different transformer tap positions (providing different voltage outputs) are needed.
What are On-Load Tap Changers (OLTC)? According to Google AI:
“An On-Load Tap Changer (OLTC) adjusts a transformer's voltage ratio by changing tap positions while the transformer remains energised and under load, avoiding supply interruptions. Typically used on high-voltage windings, they provide stepped voltage regulation (usually $\pm$10% in steps) via motor-driven, oil-immersed mechanical switches.”, Google Artificial Intelligence.
Three Phase Transformer
A three phase transformer design can have delta (D) input and star (Y) output.
Figure 1: Delta Input Star Output Three Transformer Physical Connections.
Figure 2: Delta Input Star Output Three Transformer Vectorial Representations.
The phase displacement for different transformer types is the output phase shift with reference to the input:
Table 1: Phase Displacement for Different Transformer Groups.
The winding connection designations are shown in the following table:
Table 2: Winding Connection Designations.
Additive and Subtractive Transformer Polarity
What is the difference between additive and subtractive transformer polarity? According to Google AI:
“Additive Polarity: If a jumper is connected between adjacent high- and low-voltage terminals (e.g., (H2) to (X1)) and voltage is applied, the voltage measured across the other two terminals ((H1) to (X2)) is the sum of the two winding voltages (Vprimary + Vsecondary)).Subtractive Polarity: Using the same jumper method, the voltage measured across the remaining terminals is the difference (Vprimary - Vsecondary)).”, Google Artificial Intelligence.
Parallel Connected Transformers
Why are transformers sometimes connected in parallel? According to Google AI:
“Transformers are connected in parallel to increase power capacity beyond a single unit, improve system reliability, and maximize efficiency by only running necessary units. This setup allows for flexible load management, such as adding transformers as demand increases or maintenance without interrupting service.”, Google Artificial Intelligence.
Parallel connected transformers must have the same:
Phase shift.
Voltage ratio.
Percentage impedance.
Polarity.
Phase sequence.
What is phase sequence? According to Google AI:
“Transformer phase sequence refers to the specific chronological order in which the three phases (usually labeled R-Y-B, L1-L2-L3, or A-B-C) of a three-phase AC system reach their maximum positive voltage peaks.“, Google Artificial Intelligence.
Transformer Construction
Those are different types of transformers that can be constructed:
ONAN - Oil Natural Air Natural. According to Google AI:
“An ONAN transformer (Oil Natural Air Natural) is a type of oil-immersed transformer that uses passive, natural convection to cool its core and windings. It is widely used for distribution, small-to-medium power, and industrial applications because it is reliable, low-maintenance, and requires no external fans or pumps to operate.”, Google Artificial Intelligence.
ONAF - Oil Natural Air Forced. According to Google AI:
“ONAF (Oil Natural Air Forced) transformers are oil-immersed units that use natural convection for internal oil circulation but employ electric fans to force air over external radiators, significantly increasing heat dissipation. This method allows transformers to handle higher, often variable loads (typically 25-33% more capacity) compared to natural cooling (ONAN) alone.”, Google Artificial Intelligence.
OFAF - Oil Forced Air Forced. According to Google AI:
“OFAF (Oil Forced Air Forced) transformers use specialized pumps to circulate oil and fans to blow air across radiators, providing highly efficient cooling for large power transformers (typically above 30 MVA). This active system allows for a compact design and higher load capacity, making it ideal for large power stations and substations.”, Google Artificial Intelligence.
Oil filled transformers are usually installed outside because those transformers have higher chances of catching fire than other types. Appropriate ventilation and physical isolation is required if oil filled transformers are installed inside. Firewalls are sometimes built around the transformer.
Spillage of dielectric can cause a fire. Therefore, transformers that are installed in buildings should be made with dry-type resin-encapsulated units instead of liquid filled units. The following must be considered when selecting the dielectric for those transformers:
Dielectric has to be non-toxic and biodegradable,
The fire point need to be above 300 degrees Celsius,
The material must not be flammable and combustion output must not be toxic,
Must not generate fumes that are toxic or corrosive under normal transformer operation.
Noise absorbing barriers are constructed around transformers because transformers generate annoying low frequency sound under normal operation that can be heard by humans. Transformers are sometimes placed in natural or human made pits to block the noise.
Transformer Protection
Transformer characteristics that should be considered in transformer protection are explained in this section of the article.
9.1 Transformer Magnetising Properties
This is what Google AI states about transformer magnetisation characteristics:
“Transformer magnetization characteristics define the relationship between the magnetic flux and the magnetizing current in the transformer's core. Because magnetic cores exhibit non-linear permeability and hysteresis, this characteristic is crucial for analyzing inrush currents, harmonic distortion, and protection relaying.”, Google Artificial Intelligence.
9.2 Transformer Inrush Current
Inrush current is the current spike when the transformer is first turned ON. This is what Google AI states about transformer inrush current:
“Transformer inrush current is a high, transient surge of current that occurs when a transformer is first energized, often reaching 8 to 14 times (sometimes up to 20x) the nominal full-load current for a few cycles. It happens because of temporary magnetic core saturation as flux builds up, resulting in potential nuisance tripping of overcurrent protection.”, Google Artificial Intelligence.
9.3 Mismatch In Current Transformers
This is what Google AI states about current transformer mismatch:
“A mismatch in current transformers (CTs) occurs when the secondary output current does not properly align with the connected measuring or protection device. This most frequently happens due to mismatched ratios (e.g., a 1 A meter connected to a 5 A CT), differing saturation characteristics during faults, or incorrect polarity alignment.”, Google Artificial Intelligence.
9.4 Transformer Earth Faults
This is what Google AI states about transformer earth faults:
“An earth fault in a transformer is an unintended electrical connection between a live conductor and the earth (or grounded tank/frame). This breakdown of winding insulation—usually caused by oil degradation, moisture, or lightning surges—creates dangerous currents and triggers protective devices to isolate the unit.”, Google Artificial Intelligence.
9.5 Transformer Inter-Turn Faults
This is when insulation between turns faults and connection between turns occurs. This is what Google AI states about transformer inter-turn faults:
“Transformer inter-turn faults are highly dangerous internal short circuits that occur when insulation breaks down between adjacent turns in a winding. They generate localized heat and heavy current within the shorted loop, potentially causing winding deformation and catastrophic failure.”, Google Artificial Intelligence.
9.6 Transformer Core Faults
Transformer core faults occur when fault currents cause the core layers to move that result in eddy current and thus overheating. Fault currents increase magnetisation current that can cause physical damage to the transformer. Those types of faults cannot be detected by electrical protection devices. However, those faults can be detected via image recognition devices.
More information on transformer core faults is provided by Google AI:
“Transformer core faults are localized anomalies—such as core grounds, interlaminar insulation breakdowns, or core saturation—that disrupt the magnetic path and cause local overheating, arcing, or efficiency loss. These issues can severely degrade insulation and shorten the unit's lifespan.”, Google Artificial Intelligence.
9.7 Transformer Tank Faults
This is what Google AI states about transformer tank faults:
“Transformer tank faults involve mechanical damage, structural degradation, or leaks that compromise the insulation and cooling of the transformer. Common causes include corrosion, high internal pressure, and physical impact, which lead to oil leakage and eventual equipment failure.”, Google Artificial Intelligence.
Faults Protection Relays
10.1 IDMTL Relays
This is what Google AI states about IDMTL relays:
“IDMTL stands for Inverse Definite Minimum Time Lag. It is a protective relay characteristic where the operating (tripping) time is inversely proportional to the magnitude of the fault current. Higher currents result in faster trips, while lower currents result in slower trips.”, Google Artificial Intelligence.
10.2 Differential Transformer Protection
The following diagram shows differential transformer protection:
Figure 3: Differential Transformer Protection.
The current transformers output voltages are equal and are connected in reverse polarity. The current transformer 2 cancels the voltage of current transformer 1 if there is no fault. However, if the fault occurs then there is a difference between the current transformer voltages and the relay turns ON.
References
1. Practical Power Distribution for Industry, Jan de Kock, Cobus Strauss, Elsevier, Copyright 2004.
2. Google Artificial Intelligence.
3. Wikipedia.
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