FREQUENCY in ELECTRICAL ENG.A Presentation on

“ Frequency in Electrical Engineering”

By RAJNEESH BUDANIA

(B.Tech Electrical Engineering,(B.Tech Electrical Engineering,

a 4th year student in jaipur

national university, jaipur)

Definition and UnitIn 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 ’.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.

Current Waveforms

Generation of PowerElectric power is generated by synchronous

alternator and frequency of output is decided by speed of rotor:

Here number of poles ‘P’ is constant.

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 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.

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 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.

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 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.

Effect of Frequency on

TransformersTransformer EMF equation is given as:

Hence EMF of a transformer at a given flux 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.

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 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.

Effect of Frequency on

Transmission SystemReactive drop in a transmission line is directly

proportional to frequency because reactive drop = 2πfL*I

If frequency increases from utility frequency, 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.

As we know,

Voltage Regulation =

Conclusion is that on increasing frequency Conclusion is that on increasing frequency directly affects our voltage regulation and voltage regulation would be high at higher frequency which is undesirable.

Concept of Complex FrequencyA frequency that characterize simple harmonic

motion is called as ordinary frequency and indicated by ‘f ’.

A frequency that characterize exponential and A frequency that characterize exponential and damped sinusoidal motion is called as complex frequency and denoted by ‘s’.

s = σ + j ω

As ‘s’ is a complex quantity, so its name is complex frequency.

Sigma(σ) is real part of ‘s’ and is called “neperfrequency”. It controls the magnitude of signal.

When σ < 0 , signal will be exponentially decreasing.decreasing.

When σ = 0 , signal has steady state value.

When σ > 0 , signal will be exponentially increasing.

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 ‘σ’ is measured in neper/sec and ‘ω’ is measured in radian/sec.

Resonant FrequencyResonance 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.system.

In electrical engineering, there are two types of resonance exist:

(1) Series resonance

(2) Parallel resonance

Series ResonanceSeries resonance occurs in series circuits

containing R, L, C elements when input impedance is minimum.

resonant frequency is given as

ƒr =

Series Resonance

Parallel ResonanceParallel 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 and this frequency is called resonant frequency.

Parallel Resonance

Application of ResonanceResonant 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 are very important in the operation of radio, television receivers and transmitters.

Thank You