derive the output equation of single

phase transformer Shell-type and core-type transformers are

two common designs used in power and
Certainly! The output equation of a
distribution transformers. Let's compare
single-phase transformer relates the some design aspects between these two Heat dissipation in electrical
output voltage, output current, and input types: machines, such as motors and
voltage, turns ratio, and transformer transformers, is essential to maintain
losses. The ideal transformer equation is their operating temperature within safe
used as the basis for the derivation. 1. Construction: limits. Various modes of heat dissipation
 Shell-Type Transformers: help remove excess heat generated
during the operation of these machines.
For an ideal transformer, neglecting  In a shell-type transformer, the Some of the primary modes of heat
losses: windings surround the core, dissipation in electrical machines
forming a cylindrical shape.
include:
Let:
 The windings are arranged in 1. Conduction:
multiple layers, one on top of
 1V1 = Input voltage (primary side) another.  Conduction is the transfer of
heat through a solid material
 2V2 = Output voltage (secondary side)  The core is divided into several
without the movement of the
sections, and each section is built
 1I1 = Input current (primary side) of strips or laminations. material itself.

 2I2 = Output current (secondary side)  Core-Type Transformers:

 In electrical machines, heat
generated in the conductors,
 1N1 = Number of turns in the primary  In a core-type transformer, the core, and other components
coil core surrounds the windings. is conducted to the
 2N2 = Number of turns in the secondary  The windings are wound around surrounding materials, such
the core limbs or legs. as the housing or frame of
coil
the machine.
 ϕ = Magnetic flux  The core consists of a single
continuous path or several  Heat is transferred through
stacked laminations. materials with higher thermal
conductivity to dissipate it
The ideal transformer equation states:
away from the machine's
2. Winding Arrangement: critical components.
 Shell-Type Transformers: 2. Convection:

 The windings in shell-type  Convection is the transfer of

transformers have shorter turns, heat through the movement
which results in lower leakage flux of fluids (liquid or gas)
and reduced leakage reactance. caused by temperature
This equation signifies that the voltage
ratio across the primary and secondary  The winding arrangement leads to differences.
coils is equal to the turns ratio, and the a more compact design.  Cooling fans or blowers are
current ratio is also equivalent to the
turns ratio in an ideal transformer
 Core-Type Transformers: often employed in electrical
machines to facilitate
without considering losses.  In core-type transformers, the convection by circulating air
longer winding turns lead to around the machine's
higher leakage flux and increased
components.
Now, consider an actual transformer that leakage reactance.
accounts for losses. The output equation  The longer winding length results
 The heated air near the
can be expressed as: in a larger physical size compared machine's surfaces rises and
to shell-type transformers. is replaced by cooler air,
establishing a continuous
flow that carries away heat.
3. Cooling and Heat Dissipation: 3. Heat Sinks:
 Shell-Type Transformers:  Heat sinks, often made of
 Shell-type transformers offer materials with high thermal
better cooling characteristics due conductivity (such as
Where: to the windings' arrangement aluminum or copper), are
used to absorb and dissipate
 2V2 = Output voltage (secondary side)
around the core.
 The cylindrical shape allows for
heat from specific
 1V1 = Input voltage (primary side) effective circulation of cooling oil
components.
 2N2 = Number of turns in the secondary around the windings, facilitating  They provide an increased
heat dissipation.
coil surface area for better heat
 1N1 = Number of turns in the primary
 Core-Type Transformers: dissipation and are
commonly used in power
coil  Core-type transformers may have electronic devices and
 2I2 = Output current (secondary side)
relatively less effective cooling
due to the winding arrangement
certain motor types.
4. Forced Air Cooling:
 R = Resistance of the secondary and longer winding turns.
winding  Cooling is generally achieved by  In forced air cooling, external
means such as fans or
 X = Reactance of the secondary winding
natural convection or with the
help of cooling fans. blowers are used to force air
circulation around the
machine's components.
The equation considers the voltage drop 4. Mechanical Strength:
due to resistance and reactance in the  This method enhances
secondary winding. This drop reduces  Shell-Type Transformers: convection by increasing the
the actual output voltage from the  Shell-type transformers tend to airflow rate, thereby
theoretical ideal voltage calculated using have better mechanical strength improving heat transfer
the turns ratio. and are less prone to mechanical efficiency.
deformation or damage. 5. Oil or Liquid Cooling:

Please note that this equation neglects

 The winding arrangement  Some larger electrical
provides better support and machines, especially
certain factors such as leakage stability to the windings.
reactance, core losses, and other transformers and certain
losses, which can affect the actual  Core-Type Transformers: types of motors, utilize oil or
liquid-based cooling
output voltage in practical transformers.  Core-type transformers may be
systems.
The derivation provided here is a basic more susceptible to mechanical
representation of the output equation in stress, particularly if the windings  The machine components
an ideal transformer and doesn't account are not adequately supported. are immersed or surrounded
for all losses and complexities present in by a cooling fluid (such as
real-world transformers. oil) that absorbs heat and
 transfers it away from the desired output voltage and power under requirements. Designers use these rules as
machine. various operating conditions. guidelines to select suitable slot numbers
that enhance the motor's efficiency and
 The heated fluid can then be performance while avoiding undesirable
circulated to a cooling characteristics like harmonic content and
filed winding for a salient pole 3 phase torque pulsations.
alternator is designed
explain the various rules for selection of
Designing field windings for a salient pole A Brushless DC (BLDC) motor is a type of
rotor slots in 3 phase induction motor
3-phase alternator involves careful synchronous electric motor that operates
The selection of rotor slots in a 3-phase
consideration of various factors such as the using direct current (DC) electrical power. It
induction motor is crucial for achieving
machine's operating characteristics, is known for its high efficiency, reliability,
optimal performance, reducing losses, and
magnetic circuit design, desired voltage and controllability. Unlike traditional
ensuring efficient operation. Various rules
output, and efficiency. Here's an overview brushed DC motors, BLDC motors use
and guidelines are considered during the
of the process: electronic commutation instead of
design process. Here are some rules
1. Determining Operating Requirements: mechanical brushes for switching the
commonly used for selecting rotor slots:
 Define the generator's specifications current in the motor windings. Here's a
detailed explanation of the construction and
including rated voltage, frequency, power
1. Rule of Even Distribution: operation of a BLDC motor:
output, and intended applications.
 Determine the required magnetic field  The number of rotor slots (S) is usually
strength and excitation current necessary chosen to ensure an even distribution of Construction of a BLDC Motor:
for producing the desired voltage output. slots across the periphery of the rotor to 1. Stator: The stator of a BLDC motor
2. Magnetic Circuit Design: reduce harmonics and improve the motor's consists of a stack of laminated steel sheets
performance. with multiple windings or coils wound
 Salient pole alternators have projecting pole
pieces or salient poles. The shape, size,  Commonly used slot numbers are a around the teeth of the stator poles. These
windings are usually arranged in a star (Y)
and material of these poles are crucial for multiple of 2 or 3 to achieve an even
or delta (Δ) configuration and are stationary.
efficient magnetic flux generation and distribution, such as 24, 36, 48, etc.
2. Rotor: The rotor of a BLDC motor
distribution. comprises permanent magnets (usually
 The design involves calculating the 2. Avoidance of Low Harmonic Content:
made of neodymium or ferrite) embedded
dimensions of the pole shoes, pole arc, within the rotor core. The rotor can have
pole pitch, and pole core based on the  The number of rotor slots should be either surface-mounted magnets or interior
required magnetic flux density. selected to avoid the occurrence of low- permanent magnets (IPM), influencing the
3. Field Winding Configuration: order harmonics (especially 5th and 7th motor's design and performance.
harmonics) in the magnetic field, which can 3. Hall Effect Sensors (Optional): Some
 Choose the appropriate type of field cause torque pulsations and noise. BLDC motors incorporate Hall effect
winding, such as a concentrated winding or sensors mounted in the stator to detect the
distributed winding.  To minimize low-order harmonics, the rotor position. These sensors provide
number of slots should not be divisible by 5
 Determine the number of turns, wire size, or 7.
feedback to the motor controller, aiding in
the precise timing of current commutation.
and winding arrangement based on the 4. Motor Controller: A BLDC motor requires
excitation voltage, current carrying capacity an electronic motor controller or drive unit to
of the winding, and the required ampere- 3. Rule of Even and Prime Numbers: control the energization of the stator
turns for generating the magnetic field.
 Some designers prefer using rotor slot windings. The motor controller determines
 For distributed windings, the windings are numbers that are both even and prime to
the sequence and timing of current flow to
distributed along the pole faces to achieve the windings based on rotor position
achieve better distribution of flux and
a more uniform field distribution, reducing feedback or sensorless control methods.
reduce harmonic content.
harmonics and enhancing performance.
4. Winding Arrangement:  Examples of such slot numbers are 18, 30,
42, etc., which are even and prime. Operation of a BLDC Motor:
 The field winding arrangement can vary 1. Synchronous Operation: BLDC motors
based on the pole configuration and the operate based on synchronous principles,
intended operating characteristics. 4. Avoidance of Fractional Slot where the rotor's magnetic field follows the
 For salient pole machines, field windings Windings: rotating magnetic field generated by the
are often wound around the pole faces  Fractional slot windings, where the number
stator windings. This synchronous operation
contributes to the motor's efficiency.
using insulated copper or aluminum of slots per pole per phase is not an integer,
conductors. 2. Electronic Commutation: Instead of using
are avoided in induction motors as they can brushes and a commutator, the motor
 The windings may be connected in series lead to increased complexity and controller electronically switches the current
or parallel to achieve the desired voltage harmonics. in the stator windings in a specific sequence
and current ratings.  Whole number slot per pole per phase based on the rotor's position. This
5. Insulation and Protection: combinations (such as 1, 2, 3, etc.) are controlled commutation creates a rotating
magnetic field that interacts with the
 Ensure proper insulation of the field preferred for simplicity.
permanent magnets on the rotor, causing it
windings to prevent short circuits and to rotate.
breakdown due to high voltage and current. 3. Rotor Position Sensing: In sensor-based
5. Rule of Minimum Tooth Ripple:
 Use appropriate insulating materials and
 The selection of rotor slot numbers should
BLDC motors, Hall effect sensors or other
insulation techniques to withstand the position sensors detect the rotor's position
operating temperature and mechanical aim to minimize tooth ripple, which refers to and polarity. This information is used by the
stresses. the variation in the air gap reluctance due to motor controller to apply the correct
6. Testing and Validation: variations in the magnetic path. sequence of currents to the stator windings,

 Perform tests on prototype windings to

 Avoiding slot numbers that result in
ensuring smooth and efficient motor
operation.
significant tooth ripple helps in reducing
validate the design and characteristics, 4. Trapezoidal or Sinusoidal Commutation:
losses and improving motor efficiency.
including insulation resistance, withstand The switching sequence in a BLDC motor
voltage tests, and performance evaluation can follow a trapezoidal or sinusoidal
under load conditions. pattern. Trapezoidal commutation is simpler
6. Consideration of Starting Torque and and commonly used in low-cost BLDC
7. Manufacturing and Installation:
Squirrel Cage Design: systems, while sinusoidal commutation
 Fabricate the field windings according to
 The design of the rotor slots also considers provides smoother operation and reduced
the design specifications and install them torque ripple, suitable for higher
the starting torque requirements and the
onto the rotor assembly. performance applications.
structure of the squirrel cage for optimal
 Ensure precise assembly and alignment of performance during starting and running 5. Variable Speed and Torque Control: By
the windings to achieve optimal conditions. controlling the amplitude and frequency of
the current supplied to the stator windings,
performance and minimize losses.
The design of field windings for salient pole
 The slot shape, depth, width, and skewing the motor controller regulates the motor's
are factors considered in optimizing torque speed and torque. This variable speed
alternators requires a combination of
characteristics. control capability is a significant advantage
electromagnetic principles, material
science, and electrical engineering of BLDC motors.
considerations. Careful design and
The selection of the optimal number of rotor
implementation are necessary to ensure the
slots in a 3-phase induction motor involves BLDC motors find applications in various
efficient generation of a magnetic field,
a balance between achieving even industries such as automotive (electric
enabling the alternator to produce the
distribution, minimizing harmonics, reducing vehicles), appliances, aerospace, robotics,
losses, and meeting specific performance and industrial automation due to their
efficiency, reliability, and controllability.
Their construction and operation offer
advantages in terms of reduced
maintenance, improved efficiency, and
precise speed control compared to brushed
DC motors