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)
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.
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.
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.
As electric load on grid increases,generators tend to operate at lower speed. This iscompensated for by turbine governors which feedmore steam to turbines. If one of turbine generatorcannot increase speed due to steam capacitylimitations, another generator on grid will compensatefor this. When all generators reach their input capacitylimitation , grid start operating at a lower frequencythan 50 Hz.
Coal fired thermal power plants are slow torespond to load changes because of thermal inertia,whereas hydropower plants or gas power plantsrespond much faster. A good grid must have a propermix of all types of power plants so that it can quicklycontrol the load. Allowable variation of grid frequencyis in a small range of ±0.5 Hz or less.
Effect of Frequency onTransformers 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.
Aircrafts and military equipments employ400 Hz power supplies which reduce core and windingweight and so reduce the cost of equipment. Frequencies used for some railwayelectrification system are much lower (e.g. 16.7 Hz or25 Hz) than utility frequency. For such system,transformers used for step down purpose are muchheavier due to low frequency. It increases the cost oftransformers.
Effect of Frequency onTransmission 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.
As we know, Voltage Regulation = Conclusion is that on increasing frequencydirectly affects our voltage regulation and voltageregulation would be high at higher frequency which isundesirable.
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.
Sigma(σ) is real part of ‘s’ and is called “neperfrequency”. It controls the magnitude of signal. When σ < 0 , signal will be exponentiallydecreasing. When σ = 0 , signal has steady state value. When σ > 0 , signal will be exponentiallyincreasing.
Omega(ω) is imaginary part of complexfrequency and is known as radian frequency. Itcontrols the rotation of signal. ‘σ’ is measured in neper/sec and ‘ω’ is measuredin radian/sec.
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
Series Resonance Series resonance occurs in series circuits containing R, L, C elements when input impedance is minimum. resonant frequency is given as ƒr =
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.
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.