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Frequency in electrical eng
1. FREQUENCY in ELECTRICAL ENG.
A Presentation on
“ Frequency in Electrical Engineering”
By RAJNEESH BUDANIA
(B.Tech Electrical Engineering,
a 4th year student in jaipur
national university, jaipur)
2. Definition and Unit
In cyclical processes, frequency is
defined as a number of cycles per unit time. Cyclical
processes are rotation, oscillations, waves etc.
Frequency is usually denoted by a latin letter ‘f’.
In SI units, the unit of frequency is
‘hertz(Hz)’. 1 Hz means that an event repeats once per
second.
4. Generation of Power
Electric power is generated by synchronous
alternator and frequency of output is decided by speed
of rotor:
Here number of poles ‘P’ is constant.
5. How is Frequency related to load ?
As load increases, frequency decreases. For an
alternator, as load (current drawn) increases,
opposing(lenz’s law) electromagnetic induced
emf(faraday’s law) in alternator winding increases and
hence it opposes the movement of prime mover. Thus
the speed of rotor decreases which results decrease in
frequency.
6. As electric load on grid increases,
generators tend to operate at lower speed. This is
compensated for by turbine governors which feed
more steam to turbines. If one of turbine generator
cannot increase speed due to steam capacity
limitations, another generator on grid will compensate
for this. When all generators reach their input capacity
limitation , grid start operating at a lower frequency
than 50 Hz.
7. Coal fired thermal power plants are slow to
respond to load changes because of thermal inertia,
whereas hydropower plants or gas power plants
respond much faster. A good grid must have a proper
mix of all types of power plants so that it can quickly
control the load. Allowable variation of grid frequency
is in a small range of ±0.5 Hz or less.
8. Effect of Frequency on
Transformers
Transformer EMF equation is given as:
Hence EMF of a transformer at a given flux
density increases with increase in ‘f’. By operating at
high frequencies, transformers can be physically more
compact because a given core is more able to transfer
more power and fewer turns are needed to achieve
same impedance. It results to reduce core and winding
weight. Conclusion is that frequency decides the cost
of transformer.
9. Aircrafts and military equipments employ
400 Hz power supplies which reduce core and winding
weight and so reduce the cost of equipment.
Frequencies used for some railway
electrification system are much lower (e.g. 16.7 Hz or
25 Hz) than utility frequency. For such system,
transformers used for step down purpose are much
heavier due to low frequency. It increases the cost of
transformers.
10. Effect of Frequency on
Transmission System
Reactive drop in a transmission line is directly
proportional to frequency because reactive drop =
2πfL*I
If frequency increases from utility frequency,
reactive drop increases which results in reduce to
receiving end voltage ‘Vr’. Therefore (Vs-Vr) increases
where ‘Vs’ is sending end voltage.
11. As we know,
Voltage Regulation =
Conclusion is that on increasing frequency
directly affects our voltage regulation and voltage
regulation would be high at higher frequency which is
undesirable.
12. Concept of Complex Frequency
A frequency that characterize simple harmonic
motion is called as ordinary frequency and indicated
by ‘f’.
A frequency that characterize exponential and
damped sinusoidal motion is called as complex
frequency and denoted by ‘s’.
s=σ+jω
As ‘s’ is a complex quantity, so its name is
complex frequency.
13. Sigma(σ) is real part of ‘s’ and is called “neper
frequency”. It controls the magnitude of signal.
When σ < 0 , signal will be exponentially
decreasing.
When σ = 0 , signal has steady state value.
When σ > 0 , signal will be exponentially
increasing.
14. Omega(ω) is imaginary part of complex
frequency and is known as radian frequency. It
controls the rotation of signal.
‘σ’ is measured in neper/sec and ‘ω’ is measured
in radian/sec.
15. Resonant Frequency
Resonance is the tendency of a system to
oscillate at a greater amplitude at some frequency than
others. This is known as resonant frequency of that
system.
In electrical engineering, there are two types of
resonance exist:
(1) Series resonance
(2) Parallel resonance
16. Series Resonance
Series resonance occurs in series circuits
containing R, L, C elements when input impedance is
minimum.
resonant frequency is given as
ƒr =
18. Parallel Resonance
Parallel resonance is associated with simple
parallel network containing R, L, C elements. It occurs
when input impedance is maximum at a certain
frequency and this frequency is called resonant
frequency.
20. Application of Resonance
Resonant circuits are very important
because they have sharp maximum or minimum at
certain frequency(resonant freq.). Hence these circuits
are very important in the operation of radio, television
receivers and transmitters.
