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University of Bahrain, Department of Electrical and Electronics Engineering P.O. Box 32038, Kingdom of Bahrain [email protected] Copyright © JASE 2012 on-line: jase.esrgroups.org J. Automation & Systems Engineering 6-1 (2012): 30-35 Brief paper An Accurate Formula For The Firing Angle Of The Phase Angle Control In Terms Of The Duty Cycle Of The Integral Cycle Control S.Ali AL-MawsawiN. AllaithH. QassimS. Dhiya JASE Journal of Automation & Systems Engineering AbstractThispaperpresentsdevelopmentofasimpleandaccurateformulaforevaluationofthe firing angle () of the phase angle control in terms of the duty cycle (K) of the integral cycle control when the same average output power transfer is required. The accuracy of the formula developed is verified by comparing the values obtain from the exact iterative solution. It has been shown that, the maximumerroroverthewholerangeoftheentirefiringangle()computedforanyvalueofthe exactvalueisfoundtobelessthan2degree.Theformulapresentsaverysimplewayforthe evaluationofthecomparisonoftheharmonicspropertiesofthephaseanglecontrolandintegral cyclecontrolforthesameaveragepowertransfer.Inaddition,thedevelopedformulareducesthe computational time and also reduces time for manual classroom calculation. Keywords: Phase angle control, Integral cycle control, Duty cycle, firing angle. 1. INTRODUCTION It is well established that for a signal phase A.C. voltage regulator with resistor load shown in figure(1), there are two methods used normally for controlling the power transfer which are (1-12) : 1-ON-OFF control (Integral Cycle Control). 2-Phase-Angle Control. Figure 1: Single phase ac voltage regulator Inintegralcyclecontrol,thyristorswitches(Triacs)connecttheloadtotheacsourcefor few cycles of input voltage and then disconnect it for another few cycles as shown in figure 6 2.While,inphaseanglecontrol,thyristorswitches(Triacs)connecttheloadtotheac source for a portion of each cycle of (/download/link/articleinput voltage as shown in figure 3. J. Automation & Systems Engineering 6-1 (2012): 30-35 31 0 0.5 1 1.5 2 2.5 All materials on our website are shared by users. If you have any questions about copyright issues, please firing-delay-angle) 3 3.5 4 4.5 x 10 4 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure 2: Output voltage waveform in case of integral report (/document/report/article-firing-delay-angle) us to resolve them. We are always happy to assist you. cycle control. 0 1000 2000 3000 4000 5000 6000 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure 3: Output Report (/document/report/article-firing-delay-angle) voltage waveform in case of phase angle control. Inmanypowerelectronicsbooksevaluationofeachmethodperformancehasbeenwell published individually without comparing the power transfer of each method. Therefore, it (https://www.facebook.com/sharer.php? (https://twitter.com/home? (https://plus.google.com/share? (https://pinterest.com/pin/create/bookmarklet/? (https://www.linkedin.com/shareArticle? hasbeentheobjectiveofthispapertodevelopasimpleandaccurateformulaforthe DESCRIPTION s=100&p[url]=https://documents.mx/documents/articlestatus=Article url=https://documents.mx/documents/articlemedia=https://documents.mx/public/others/images/default.png&url=https://documents.mx/documents/articlemini=true&url=https://documents.mx/documents/articlecomputationofthefiringangle()intermsofthedutycycle(K)incaseofsamepower transfer. 2. DEVELOPMENT OF THE FORMULA In case of the integral cycle control, the output voltage waveform is shown in figure (2). If the input A published article regarding the precise formula for firing delay angle. firing- Firing firing- firing- firingvoltage [Vs=√2sinwt] is connected to load for N cycles and is disconnected for M cycles, then the rms output voltage can be found from: dt wt V M N N V s o ò + = 2 0 2 2 sin 2 ) ( 2 (1) M N N V V s o + = (2) K V V s o = TEXT delayDelay delay- delay- delay(3) Where K=N/(N+M) and it is called the duty cycle. Hence the output power (average power) can be found from: R V K R V P s o o 2 2 = = (4) S.Ali AL-Mawsawi et al.: An Accurate Formula for the Firing Angle of the University of Bahrain, Department of Electrical and Electronics Engineering P.O. Box 32038, Kingdom of Bahrain [email protected] angle.html&p[title]=Article Angle angle.html) angle.html&is_video=false&description=Article angle.html&title=Article Copyright © JASE 2012 on-line: jase.esrgroups.org J. Automation & Systems Engineering 6-1 (2012): 30-35 Brief paper An Accurate Phase Angle Control In Terms … 32 On the other hand, in case of phase angle control (the output voltage Formula For The Firing Angle Of The Phase Angle Control In Terms Of The Duty Cycle Of The Integral Cycle Control S.Ali AL-MawsawiN. waveform is shown infigure3),ifthedelayangle(firingangle)is(0º Firing Firing Firing AllaithH. QassimS. Dhiya JASE Journal of Automation & Systems Engineering Abstract-

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Thispaperpresentsdevelopmentofasimpleandaccurateformulaforevaluationofthe firing angle () of the phase angle control in terms of the duty Please download to view Delay Documents+https://documents.mx/documents/articleDelay Delay cycle (K) of the integral cycle control when the same average output power transfer is required. The accuracy of the formula developed is verified by comparing the values obtain from the exact iterative solution. It has been shown that, the Angle firingAngle Angle maximumerroroverthewholerangeoftheentirefiringangle()computedforanyvalueofthe exactvalueisfoundtobelessthan2degree.Theformulapresentsaverysimplewayforthe evaluationofthecomparisonoftheharmonicspropertiesofthephaseanglecontrolandintegral delaycyclecontrolforthesameaveragepowertransfer.Inaddition,thedevelopedformulareducesthe computational time and also reduces time for manual classroom calculation. Keywords: Phase angle control, Integral cycle control, Duty cycle, firing angle. 1. INTRODUCTION It is well Documents&p[summary]=A angle.html) Documents) Documents&source=https://documents.mx/documents/articleestablished that for a signal phase A.C. voltage regulator with resistor load shown in figure(1), there are two methods used normally for controlling the power transfer which are (1-12) : 1-ON-OFF control (Integral Cycle Control). 2-Phase-Angle Control. Figure 1: Single phase ac published firingvoltage regulator Inintegralcyclecontrol,thyristorswitches(Triacs)connecttheloadtotheacsourcefor few cycles of input voltage and then disconnect it for another few cycles as shown in figure 2.While,inphaseanglecontrol,thyristorswitches(Triacs)connecttheloadtotheac source article delayfor a portion of each cycle of input voltage as shown in figure 3. J. Automation & Systems Engineering 6-1 (2012): 30-35 31 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 x 10 4 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure 2: Output voltage waveform in case of integral cycle control. 0 1000 2000 regarding angle.html) 3000 4000 5000 6000 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure 3: Output voltage waveform in case of phase angle control. Inmanypowerelectronicsbooksevaluationofeachmethodperformancehasbeenwell published individually without comparing the power transfer the of each method. Therefore, it hasbeentheobjectiveofthispapertodevelopasimpleandaccurateformulaforthe computationofthefiringangle()intermsofthedutycycle(K)incaseofsamepower transfer. 2. DEVELOPMENT OF THE FORMULA In case of the precise integral cycle control, the output voltage waveform is shown in figure (2). If the input voltage [Vs=√2sinwt] is connected to load for N cycles COMMENTS and is disconnected for M cycles, then the rms output voltage can be found from: dt wt V M N N V s o ò + = 2 0 2 2 sin 2 ) ( 2 (1) M N N V formula V s o + = (2) K V V s o = (3) Where K=N/(N+M) and it is called the duty cycle. Hence the output power (average power) can be found from: 0 Comments Sort by Newest R V K R V P s o o 2 2 = = (4) S.Ali AL-Mawsawi et al.: An Accurate Formula for the Firing Angle of the Phase Angle Control In Terms … 32 for On the other hand, in case of phase angle control (the output voltage waveform is shown infigure3),ifthedelayangle(firingangle)is(0º

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