Emirates Aviation University Module 3 Electrical Fundamentals II AC Theory PDF

Module 3 Electrical Fundamentals II Topic 3.13: AC Theory  INTRODUCTION On completion of this topic you should be able to: 3.13.1 Identify a sinusoidal waveform and describe the following associated terms: Phase...

Module 3 Electrical Fundamentals II Topic 3.13: AC Theory  INTRODUCTION On completion of this topic you should be able to: 3.13.1 Identify a sinusoidal waveform and describe the following associated terms: Phase Period Frequency Cycle Continued... 30-03-2024 Slide No. 2  INTRODUCTION On completion of this topic you should be able to: 3.13.2 In relation to voltage, current and power, describe the following terms and perform calculations for these: Instantaneous Average Root Mean Square Peak Peak to Peak 3.13.3 Identify triangular and square waveforms. 3.13.4 Describe principles of single phase, and three phase AC power. 30-03-2024 Slide No. 3  SINE WAVE A sine wave is a symmetrical waveform that varies equally around a fixed level and can be either a representation of voltage or current. The sine wave is an alternating (swings both positive and negative) waveform and is most commonly identified as the alternating current (AC) waveform. It bears a direct relationship to circular rotation. 30-03-2024 Slide No. 4  ALTERNATING CURRENT With AC, electrons flow first in one Vertical axis direction, then in the other. represents the magnitude and Both current and voltage vary direction of current or voltage. continuously. Horizontal axis Graphic representation for AC is a represents time, or angle of rotation sine wave, which can represent in degrees. current or voltage. Waveform above ‘time axis There are two axes used to depict a sine wave – Vertical and positive – waveform below ‘time Horizontal. axis’ – negative. A complete cycle occurs in 360º, half of which is positive and half negative. 30-03-2024 Slide No. 5  SINE WAVE 1 cycle of a sine wave, like a circle, is equal to 360 degrees. Complete set of +ve and -ve values. 30-03-2024 Slide No. 6  SIMPLE AC GENERATOR As armature rotates through magnetic field – induced voltage varies. At initial position (0º). Conductors moving parallel to magnetic field Not cutting through any magnetic lines of flux – NO voltage is induced As armature rotates from 0º to 90º. Conductors cut through more & more lines of flux Induced voltage builds to a maximum in positive direction 30-03-2024 Slide No. 7  SIMPLE AC GENERATOR As generator continues to rotate from 90º to 180º. Armature cuts less and less lines of flux Induced voltage decreases from a maximum positive value to zero As armature continues to rotate from 180º to 270º. Conductors cut more and more lines of flux, but in opposite direction Voltage is induced in negative direction building up to a maximum at 270º 30-03-2024 Slide No. 8  SIMPLE AC GENERATOR Full sine wave production as armature rotated through 360º. 30-03-2024 Slide No. 9  SIMPLE AC GENERATOR SINUSOIDAL WAVEFORM Note polarity change during 360 degree rotation. 30-03-2024 Slide No. 10  SINUSOIDAL SINE WAVE 0º 90º 270º 180º Single coil rotating 360° through Induced EMF – proportional to rate at uniform magnetic field at a constant which lines of flux are cut. speed. Coil moving perpendicular to lines of Visual representation of changing flux – faster cut rate – higher EMF amplitude and polarity of induced induced. EMF. Coil moving parallel to lines of flux – NO lines of flux cut – NO EMF induced. 30-03-2024 Slide No. 11  CYCLE AND ALTERNATION Cycle – 1 complete sequence of Alternation – ½ of an AC cycle in voltage or current change from which the voltage or current rises or zero, through a positive peak, back falls from zero to a peak and back to to zero, through a negative peak, zero again. and back to zero again. 30-03-2024 Slide No. 12  FREQUENCY Frequency of AC – number of cycles completed in one second. Frequency is expressed in Hertz (Hz.) One hertz (1 Hz) is equal to one cycle per second. Two cycles per second = 2 Hz – 4 cycles per second = 4 Hz. Household power cycles 50 times / second – 50Hz. Aircraft power cycles 400 times / second – 400Hz. 30-03-2024 Slide No. 13  PERIOD Period – time required to complete one cycle of a waveform. A period is expressed in time. Household power at 50Hz – period equals? Period is 1/50th of a second or 0.02 seconds (20 mSecs) Aircraft power at 400Hz – period equals? Period is 1/400th of a second or 0.0025 seconds (2.5 msecs) 30-03-2024 Slide No. 14  FREQUENCY and PERIOD What is the frequency of the illustrated waveform as displayed on a CRO? First thing to do is to determine the period. Period is 100s (T). 1 𝐹𝑟𝑒𝑞 = 𝑃𝑒𝑟𝑖𝑜𝑑 Frequency = 10000 Hz (10kHz). With only two poles – frequency is same as number of rotations per second. 30-03-2024 Slide No. 15  FREQUENCY Increase in number of poles causes corresponding increase in number of cycles completed in a revolution: A two-pole generator completes one cycle per revolution A four-pole generator completes two cycles per revolution 𝑁𝑜 𝑜𝑓 𝑃𝑜𝑙𝑒𝑠 𝑥 𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝑅𝑜𝑡𝑎𝑡𝑖𝑜𝑛 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 = 120 30-03-2024 Slide No. 16  ALTERNATING CURRENT VALUES Alternating current and voltage is often expresses in following values: Instantaneous Average RMS (Root Mean Square) Peak Peak to Peak 30-03-2024 Slide No. 17  PEAK VOLTAGE OR CURRENT Peak value of a sine wave occurs twice each cycle. Once at the positive maximum value and once at the negative maximum value. + Peak Value 0 Time Peak Value - 30-03-2024 Slide No. 18  PEAK-TO-PEAK VOLTAGE OR CURRENT Magnitude of voltage or current between peak positive and peak negative values. + 0 Time Peak to Peak Value - 30-03-2024 Slide No. 19  INSTANTANEOUS VOLTAGE OR CURRENT Instantaneous value of voltage or current at anytime on the sine wave. Can be anywhere from zero to peak value. + 900 = 100V 1500 = 50V 0 2400 = -86.6V - 30-03-2024 Slide No. 20  INSTANTANEOUS VOLTAGE OR CURRENT Instantaneous value of voltage or current at anytime on the sine wave. Can be anywhere from zero to + 900 = 100V peak value. Instantaneous value is found by 1500 = 50V following formula: Vinst = Vpk x Sin Ø 0 Ø is the angle of rotation of the cycle 2400 = - 86.6V - 30-03-2024 Slide No. 21  INSTANTANEOUS VOLTAGE OR CURRENT Can be calculated if ‘peak value’ and ‘degrees of electrical rotation’ are known. Calculate sine of the angle of electrical rotation and then multiply by the peak value. Example: 2 pole generator (360º = 360 electrical degrees) Peak value = 100 volts Sin 150º x 100 volts = + 50 volts Sin 240º x 100 volts = − 86.6 volts If plotted onto graph for every degree of rotation, a perfect sine wave would develop. This is why a ‘sine wave’ is so named. What is the instantaneous voltage at 45º of rotation? Sin 45º x 100 volts = +70.7 volts 30-03-2024 Slide No. 22  SINUSOIDAL SINE WAVE 30-03-2024 Slide No. 23  RMS VOLTAGE OR CURRENT Method of translating varying values For example, If the voltage is said to be of AC into an equivalent constant 120 volts, this is the RMS value. value. For a sine wave – RMS value is 0.707 Known as RMS (root-mean-square) times the peak value. value. Voltmeters indicate AC as RMS. Common method of expressing the value of AC. 30-03-2024 Slide No. 24  AVERAGE VALUE The average value of a full cycle of AC signal perfectly half-wave rectified – a sine wave is the value of it’s average value equals peak value ÷ π. horizontal axis. Average value is the value that would be If sine wave is half-wave rectified, indicated by a DC voltmeter. only one alternation remains. Average value of above ½ wave rectified Average value is now determined signal = 12   = 3.82V by calculating area under curve over full cycle. 30-03-2024 Slide No. 25  AVERAGE VALUE Average value of a full-wave rectified output of a sine wave equals: 2 x peak value ÷ π or 63.7% of peak Average value is the value that would be indicated by a DC voltmeter. Average value – 63.7% of peak value over one alternation. Average value of shown full-wave rectified signal = 2 x 12   = 7.64V or 0.637 x 12 = 7.64V 30-03-2024 Slide No. 26  PHASE Phase is a frequently-used term with AC. Comes from Greek word ‘fasis’ meaning ‘appearance’. Originally referred to regular changing appearance of moon through each month. Later applied to periodic changes of some quantity, such as voltage in AC circuit. Electrical phase is measured in degrees – 360° corresponding to a complete cycle. When sine waves cross the zero line at same time, they are said to be ‘in phase’. 30-03-2024 Slide No. 27  PHASE Is green signal leading blue or blue leading green? Use a vertical reference. Green is leading blue. Figures up to 180° are used to quantify lead or lag of a signal. 30-03-2024 Slide No. 28  SINE WAVES IN PHASE Voltage sine wave applied to pure resistance, resulting current is also sine wave. Follows Ohm's law which states current is directly proportional to applied voltage. Voltage and current sine waves are superimposed on same time axis. As voltage increases in a positive direction, current increases along with it. As voltage reverses direction, current also reverses direction. In Phase – Two sine waves must go through their maximum and minimum points at the same time and in the same direction. 30-03-2024 Slide No. 29  SINE WAVES OUT OF PHASE Sine waves do not go through their maximum and minimum points at same instant. Frequency is identical – phase angle/shift only expressed with same frequency. PHASE DIFFERENCE exists between the two waves. Two waves are said to be OUT OF PHASE. For two waves in figure – phase difference is 90° – typical 3 Ø - 120º apart. 30-03-2024 Slide No. 30  SINGLE AND THREE PHASE POWER Single phase (1Ø) generator – One conductor/winding rotating in a magnetic field. Produces a single phase (one sine wave) of AC power. Three phase (3Ø) generator – Three conductors – Three phases of AC power (120º apart). 30-03-2024 Slide No. 31  VARIOUS AC SIGNAL TYPES Voltage levels change with time and A distinguishing feature of alternating alternate between positive values waves is that equal areas are (above the X-axis) and negative values enclosed above and below the X-axis. (below the X-axis). Signals with repeated shapes include sine waves, square waves, triangular waves and sawtooth waves. 30-03-2024 Slide No. 32  CONCLUSION Now that you have completed this topic, you should be able to: 3.13.1 Identify a sinusoidal waveform and describe the following associated terms: Phase Period Frequency Cycle Continued... 30-03-2024 Slide No. 33  CONCLUSION Now that you have completed this topic, you should be able to: 3.13.2 In relation to voltage, current and power, describe the following terms & perform calculations for these: Instantaneous Average Root Mean Square Peak Peak to Peak 3.13.3 Identify triangular and square waveforms. 3.13.4 Describe principles of single phase, and three phase AC power. 30-03-2024 Slide No. 34  This concludes: Module 3 Electrical Fundamentals II Topic 3.13: AC Theory