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- 1. Power Electronics Dr. Imtiaz Hussain Assistant Professor email: imtiaz.hussain@faculty.muet.edu.pk URL :http://imtiazhussainkalwar.weebly.com/ Lecture-2 Definitions and Terminologies 1
- 2. Measuring a Sine Wave 2 Peak value • The PEAK value of the wave is the highest value the wave reaches above a reference value. • In a voltage waveform the peak value may be labelled VPK or VMAX (IPK or IMAX in a current waveform). c c c c c
- 3. Measuring a Sine Wave 3 Peak to Peak value • The PEAK TO PEAK value is the vertical distance between the top and bottom of the wave. • It is measured in volts on a voltage waveform, and may be labelled VPP or VPK−PK. • In a current waveform it would be labelled IPP or IPK−PK as I is used to represent current.
- 4. Measuring a Sine Wave 4 Amplitude • The AMPLITUDE of a sine wave is the maximum vertical distance reached, in either direction from the centre line of the wave. • As a sine wave is symmetrical about its centre line, the amplitude of the wave is half the peak to peak value.
- 5. Measuring a Sine Wave 5 Periodic Time & Frequency • The PERIODIC TIME is the time, in seconds taken for one complete cycle of the wave. • Thus if the periodic time of a wave is 20ms then there must be 50 complete cycles of the wave in one second (50Hz). c
- 6. Measuring a Sine Wave 6 Average Value • The average voltage (or current) of a periodic waveform whether it is a sine wave, square wave or triangular waveform is defined as: “the quotient of the area under the waveform with respect to time”. • In other words, the averaging of all the instantaneous values along time axis with time being one full period, (T). 𝑉 𝑎𝑣 = 𝑉1 + 𝑉2 + 𝑉3 + ⋯ + 𝑉11 + 𝑉12 12
- 7. Measuring a Sine Wave 7 Average Value • In a pure sine wave if the average value is calculated over the full cycle, the average value would be equal to zero as the positive and negative halves will cancel each other out. • Then the average value is obtained by adding the instantaneous values of voltage over one half cycle only. 𝑉 𝑎𝑣 = 1 𝜋 0 𝜋 𝑉 𝑝 sin 𝜃 𝑑𝜃 𝑉 𝑎𝑣 = 𝑉 𝑝 𝜋 −cos 𝜃 0 𝜋 𝑉 𝑎𝑣 = 2𝑉 𝑝 𝜋 = 0.637𝑉 𝑝
- 8. Measuring a Sine Wave 8 RMS Value Effective DC Value: RMS value gives the same heating effect as an equivalent DC power. 𝑉𝑅𝑀𝑆 = 𝑉1 2 + 𝑉2 2 + 𝑉3 2 + ⋯ + 𝑉11 2 + 𝑉12 2 12
- 9. Measuring a Sine Wave 9 𝑉𝑅𝑀𝑆 = 1 𝑇 0 𝑇 𝑉𝑃 2 cos2(𝜔𝑡) 𝑑𝑡 𝑉𝑅𝑀𝑆 = 𝑉𝑃 2 2𝑇 𝑡 + 1 2𝜔 sin(2𝜔𝑡) 0 𝑇 𝑉𝑅𝑀𝑆 = 𝑉 𝑝 2 = 0.707𝑉 𝑝
- 10. Measuring a Sine Wave 10 INSTANTANEOUS VALUE • The INSTANTANEOUS value of an alternating voltage or current is the value of voltage or current at one particular instant. • The value may be zero if the particular instant is the time in the cycle at which the polarity of the voltage is changing. • It may also be the same as the peak value, if the selected instant is the time in the cycle at which the voltage or current stops increasing and starts decreasing. • There are actually an infinite number of instantaneous values between zero and the peak value.
- 11. Measuring a Sine Wave 11 Form Factor • The form factor of an alternating current waveform is the ratio of the RMS value to the average value . • For a pure sinusoidal waveform the Form Factor will always be equal to 1.11. 𝑉𝐹𝐹 = 𝑉𝑅𝑀𝑆 𝑉 𝑎𝑣 𝑉𝐹𝐹 = 0.707𝑉𝑝𝑘 0.637𝑉𝑝𝑘 = 1.11
- 13. Measuring a Sine Wave 13 𝑉𝐶𝐹 = 𝑉𝑝𝑘 𝑉𝑅𝑀𝑆 Crest Factor • Crest Factor is the ratio between the R.M.S. value and the Peak value of the waveform. • For a pure sinusoidal waveform the Crest Factor will always be equal to 1.414. • Crest factor indicates how extreme the peaks are in a waveform. • Both Form Factor and Crest Factor can be used to give information about the actual shape of the AC waveform.
- 15. Measuring a Sine Wave 15 Power Factor • In an AC circuit, power is used most efficiently when the current is aligned with the voltage. • However, most equipment tend to draw current with a delay, misaligning it with the voltage. • What this means is more current is being drawn to deliver the necessary amount of power to run the equipment. And the more an equipment draws current with a delay, the less efficient the equipment is.
- 16. Measuring a Sine Wave 16 Power Factor • The power factor is the ratio of the real power that is used to do work and the apparent power that is supplied to the circuit. • The power factor can get values in the range from 0 to 1. • When all the power is reactive power with no real power (usually inductive load) - the power factor is 0. • When all the power is real power with no reactive power (resistive load) - the power factor is 1. • The power factor is equal to the real or true power P in watts (W) divided by the apparent power |S| in volt-ampere (VA): 𝑃𝐹 = 𝑃𝑤𝑎𝑡𝑡 𝑆𝑉𝐴
- 17. Importance of Power Factor 17 • A power factor of one or "unity power factor" is the goal of any electric utility company since if the power factor is less than one, they have to supply more current to the user for a given amount of power use. • Industrial facilities tend to have a "lagging power factor", where the current lags the voltage (like an inductor). • This is primarily the result of having a lot of electric induction motors • Capacitors have the opposite effect and can compensate for the inductive motor windings. • Some industrial sites will have large banks of capacitors strictly for the purpose of correcting the power factor back toward one to save on utility company charges.
- 19. Formulae 19 Peak value of 𝑉 (𝑽𝒑) : As the name suggests 𝑉 𝑝 = 𝑉 𝑚𝑎𝑥 over all time. Average (DC) value of 𝑽 (𝑽𝒂𝒗): Assuming 𝑉 to be periodic over the time period 𝑇 then 𝑉 𝑎𝑣 can be calculated as 𝑉 𝑎𝑣 = 1 𝑇 0 𝑇 𝑉 𝑑𝑡 RMS (effective) value of 𝑽 (𝑽𝒓𝒎𝒔) : For 𝑉 , periodic over the time period 𝑇, 𝑉 𝑟𝑚𝑠 = 1 𝑇 0 𝑇 𝑉2 𝑑𝑡 Form factor of 𝑽 (𝑽𝑭𝑭) : Form factor of ‘𝑉 ‘ is defined as 𝑉𝐹𝐹 = 𝑉 𝑟𝑚𝑠 𝑉 𝑎𝑣 Power Factor (PF): As for any other equipment, the definition of the power factor of a rectifier is 𝑃𝐹 = 𝐴𝑐𝑡𝑢𝑎𝑙 𝑃𝑜𝑤𝑒𝑟 𝐼𝑛𝑝𝑢𝑡 𝑡ℎ𝑒 𝑅𝑒𝑐𝑡𝑖𝑓𝑖𝑒𝑟 𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑃𝑜𝑤𝑒𝑟 𝐼𝑛𝑝𝑢𝑡 𝑡𝑜 𝑡ℎ𝑒 𝑅𝑒𝑐𝑡𝑖𝑓𝑖𝑒𝑟
- 20. Sinusoidal Waveform Conversion Table 20 Convert From Multipy By Or By To Get Value Peak 2 (√2)2 Peak-to-Peak Peak-to-Peak 0.5 1/2 Peak Peak 0.7071 1/(√2) RMS Peak 0.637 2/π Average Average 1.570 π/2 Peak Average 1.111 π/(2√2) RMS RMS 1.414 √2 Peak RMS 0.901 (2√2)/π Average
- 21. END OF LECTURE-2 To download this lecture visit http://imtiazhussainkalwar.weebly.com/ 21