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DC Choppers Power Electronics by Prof. M. Madhusudhan Rao 1 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Introduction • Chopper is a static device. • A variable dc voltage is obtained from a constant dc voltage source. • Also known as dc-to-dc converter. • Widely used for motor control. • Also used in regenerative braking. • Thyristor converter offers greater efficiency, faster response, lower maintenance, smaller size and smooth control. Power Electronics by Prof. M. Madhusudhan Rao 2 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Choppers are of Two Types Step-down choppers. Step-up choppers. In step down chopper output voltage is less than input voltage. In step up chopper output voltage is more than input voltage. Power Electronics by Prof. M. Madhusudhan Rao 3 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Principle Of Step-down Chopper Chopper i0 + V R V0 Power Electronics by Prof. M. Madhusudhan Rao 4 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • A step-down chopper with resistive load. • The thyristor in the circuit acts as a switch. • When thyristor is ON, supply voltage appears across the load • When thyristor is OFF, the voltage across the load will be zero. Power Electronics by Prof. M. Madhusudhan Rao 5 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT v0 V Vdc t tON tOFF i0 V/R Idc t T Power Electronics by Prof. M. Madhusudhan Rao 6 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Vdc Average value of output or load voltage. I dc Average value of output or load current. tON Time interval for which SCR conducts. tOFF Time interval for which SCR is OFF. T tON tOFF Period of switching or chopping period. 1 f Freq. of chopper switching or chopping freq. T Power Electronics by Prof. M. Madhusudhan Rao 7 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Average Output Voltage tON Vdc V tON tOFF tON Vdc V V .d T tON but d duty cycle t Power Electronics by Prof. M. Madhusudhan Rao 8 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Average Output Current Vdc I dc R V tON V I dc d R T R RMS value of output voltage tON 1 VO v dt 2 o T 0 Power Electronics by Prof. M. Madhusudhan Rao 9 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT But during tON , vo V Therefore RMS output voltage tON 1 VO 2 V dt T 0 2 V tON VO tON .V T T VO d .V Power Electronics by Prof. M. Madhusudhan Rao 10 10 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Output power PO VO I O VO But IO R Output power 2 V PO O R 2 dV PO R Power Electronics by Prof. M. Madhusudhan Rao 11 11 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Effective input resistance of chopper V Ri I dc R Ri d The output voltage can be varied by varying the duty cycle. Power Electronics by Prof. M. Madhusudhan Rao 12 12 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Methods Of Control • The output dc voltage can be varied by the following methods. – Pulse width modulation control or constant frequency operation. – Variable frequency control. Power Electronics by Prof. M. Madhusudhan Rao 13 13 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Pulse Width Modulation • tON is varied keeping chopping frequency ‘f’ & chopping period ‘T’ constant. • Output voltage is varied by varying the ON time tON Power Electronics by Prof. M. Madhusudhan Rao 14 14 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT V0 V tON tOFF t T V0 V t tON tOFF Power Electronics by Prof. M. Madhusudhan Rao 15 15 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Variable Frequency Control • Chopping frequency ‘f’ is varied keeping either tON or tOFF constant. • To obtain full output voltage range, frequency has to be varied over a wide range. • This method produces harmonics in the output and for large tOFF load current may become discontinuous Power Electronics by Prof. M. Madhusudhan Rao 16 16 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT v0 V tON tOFF t T v0 V tON tOFF t T Power Electronics by Prof. M. Madhusudhan Rao 17 17 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Step-down Chopper With R-L Load Chopper i0 + R V V0 FWD L E Power Electronics by Prof. M. Madhusudhan Rao 18 18 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • When chopper is ON, supply is connected across load. • Current flows from supply to load. • When chopper is OFF, load current continues to flow in the same direction through FWD due to energy stored in inductor ‘L’. Power Electronics by Prof. M. Madhusudhan Rao 19 19 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • Load current can be continuous or discontinuous depending on the values of ‘L’ and duty cycle ‘d’ • For a continuous current operation, load current varies between two limits Imax and Imin • When current becomes equal to Imax the chopper is turned-off and it is turned-on when current reduces to Imin. Power Electronics by Prof. M. Madhusudhan Rao 20 20 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT v0 Output voltage V tON tOFF t T i0 Output Imax current Continuous Imin current t i0 Output current Discontinuous current t Power Electronics by Prof. M. Madhusudhan Rao 21 21 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Expressions For Load Current iO For Continuous Current Operation When Chopper Is ON (0 t tON) Power Electronics by Prof. M. Madhusudhan Rao 22 22 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT i0 + R V V0 L E - Power Electronics by Prof. M. Madhusudhan Rao 23 23 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT diO V iO R L E dt Taking Laplace Transform RI O S L S .I O S iO 0 V E S S At t 0, initial current iO 0 I min V E I min IO S R R LS S S L L Power Electronics by Prof. M. Madhusudhan Rao 24 24 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Taking Inverse Laplace Transform V E t R R t iO t 1 e L I min e L R This expression is valid for 0 t tON , i.e., during the period chopper is ON. At the instant the chopper is turned off, load current is iO tON I max Power Electronics by Prof. M. Madhusudhan Rao 25 25 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT When Chopper is OFF i0 R L E Power Electronics by Prof. M. Madhusudhan Rao 26 26 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT When Chopper is OFF 0 t tOFF diO 0 RiO L E dt Talking Laplace transform 0 RI O S L SI O S iO 0 E S Redefining time origin we have at t 0, initial current iO 0 I max Power Electronics by Prof. M. Madhusudhan Rao 27 27 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT I max E IO S S R R LS S L L Taking Inverse Laplace Transform R t E R t iO t I max e L 1 e L R Power Electronics by Prof. M. Madhusudhan Rao 28 28 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT The expression is valid for 0 t tOFF , i.e., during the period chopper is OFF At the instant the chopper is turned ON or at the end of the off period, the load current is iO tOFF I min Power Electronics by Prof. M. Madhusudhan Rao 29 29 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT To Find I max & I min From equation V E t R R t iO t 1 e L I min e L R At t tON dT , iO t I max V E dRT dRT I max 1 e L I min e L R Power Electronics by Prof. M. Madhusudhan Rao 30 30 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT From equation R t E R t iO t I max e L 1 e L R At t tOFF T tON , iO t I min t tOFF 1 d T Power Electronics by Prof. M. Madhusudhan Rao 31 31 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT 1 d RT 1 d RT E I min I max e L 1 e L R Substituting for I min in equation V E dRT dRT I max 1 e L I min e L R we get, dRT V 1 e L E I max R RT R 1 e L Power Electronics by Prof. M. Madhusudhan Rao 32 32 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Substituting for I max in equation 1 d RT 1 d RT E I min I max e L 1 e L R we get, dRT V e 1 E L I min R L RT R e 1 I max I min is known as the steady state ripple. Power Electronics by Prof. M. Madhusudhan Rao 33 33 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Therefore peak-to-peak ripple current I I max I min Average output voltage Vdc d .V Average output current I max I min I dc approx 2 Power Electronics by Prof. M. Madhusudhan Rao 34 34 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Assuming load current varies linearly from I min to I max instantaneous load current is given by iO I min I .t for 0 t tON dT dT I max I min iO I min t dT Power Electronics by Prof. M. Madhusudhan Rao 35 35 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT RMS value of load current dT 1 2 I O RMS i0 dt dT 0 I max I min t dt 2 1 dT I O RMS dT 0 I min dT 2 I max I min 2 2 I min I max I min t dT 2 1 I O RMS dT I min dT t dT dt 0 Power Electronics by Prof. M. Madhusudhan Rao 36 36 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT RMS value of output current 1 2 I max I min I I I 2 2 I O RMS I min min max min 3 RMS chopper current dT 1 i dt 2 I CH 0 T 0 2 I max I min dT 1 I CH T I min dT 0 t dt Power Electronics by Prof. M. Madhusudhan Rao 37 37 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT 1 2 I max I min I I I 2 2 I CH d I min min max min 3 I CH d I O RMS Effective input resistance is V Ri IS Power Electronics by Prof. M. Madhusudhan Rao 38 38 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Where I S Average source current I S dI dc V Ri dI dc Power Electronics by Prof. M. Madhusudhan Rao 39 39 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Principle Of Step-up Chopper I L D + + L C O VO V A D Chopper Power Electronics by Prof. M. Madhusudhan Rao 40 40 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • Step-up chopper is used to obtain a load voltage higher than the input voltage V. • The values of L and C are chosen depending upon the requirement of output voltage and current. • When the chopper is ON, the inductor L is connected across the supply. • The inductor current ‘I’ rises and the inductor stores energy during the ON time of the chopper, tON. Power Electronics by Prof. M. Madhusudhan Rao 41 41 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • When the chopper is off, the inductor current I is forced to flow through the diode D and load for a period, tOFF. • The current tends to decrease resulting in reversing the polarity of induced EMF in L. • Therefore voltage across load is given by dI VO V L i.e., VO V dt Power Electronics by Prof. M. Madhusudhan Rao 42 42 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • A large capacitor ‘C’ connected across the load, will provide a continuous output voltage . • Diode D prevents any current flow from capacitor to the source. • Step up choppers are used for regenerative braking of dc motors. Power Electronics by Prof. M. Madhusudhan Rao 43 43 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Expression For Output Voltage Assume the average inductor current to be I during ON and OFF time of Chopper. When Chopper is ON Voltage across inductor L V Therefore energy stored in inductor = V .I .tON Where tON ON period of chopper. Power Electronics by Prof. M. Madhusudhan Rao 44 44 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT When Chopper is OFF (energy is supplied by inductor to load) Voltage across L VO V Energy supplied by inductor L VO V ItOFF where tOFF OFF period of Chopper. Neglecting losses, energy stored in inductor L = energy supplied by inductor L Power Electronics by Prof. M. Madhusudhan Rao 45 45 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT VItON VO V ItOFF V tON tOFF VO tOFF T VO V T tON Where T = Chopping period or period of switching. Power Electronics by Prof. M. Madhusudhan Rao 46 46 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT T tON tOFF 1 VO V tON 1 T 1 VO V 1 d tON Where d duty cyle T Power Electronics by Prof. M. Madhusudhan Rao 47 47 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT For variation of duty cycle ' d ' in the range of 0 d 1 the output voltage VO will vary in the range V VO Power Electronics by Prof. M. Madhusudhan Rao 48 48 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Performance Parameters • The thyristor requires a certain minimum time to turn ON and turn OFF. • Duty cycle d can be varied only between a min. & max. value, limiting the min. and max. value of the output voltage. • Ripple in the load current depends inversely on the chopping frequency, f. • To reduce the load ripple current, frequency should be as high as possible. Power Electronics by Prof. M. Madhusudhan Rao 49 49 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Problem • A Chopper circuit is operating on TRC at a frequency of 2 kHz on a 460 V supply. If the load voltage is 350 volts, calculate the conduction period of the thyristor in each cycle. Power Electronics by Prof. M. Madhusudhan Rao 50 50 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT V 460 V, Vdc = 350 V, f = 2 kHz 1 Chopping period T f 1 T 3 0.5 m sec 2 10 tON Output voltage Vdc V T Power Electronics by Prof. M. Madhusudhan Rao 51 51 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Conduction period of thyristor T Vdc tON V 3 0.5 10 350 tON 460 tON 0.38 msec Power Electronics by Prof. M. Madhusudhan Rao 52 52 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Problem • Input to the step up chopper is 200 V. The output required is 600 V. If the conducting time of thyristor is 200 sec. Compute – Chopping frequency, – If the pulse width is halved for constant frequency of operation, find the new output voltage. Power Electronics by Prof. M. Madhusudhan Rao 53 53 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT V 200 V , tON 200 s, Vdc 600V T Vdc V T tON T 600 200 6 T 200 10 Solving for T T 300 s Power Electronics by Prof. M. Madhusudhan Rao 54 54 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Chopping frequency 1 f T 1 f 6 3.33KHz 300 10 Pulse width is halved 6 200 10 tON 100 s 2 Power Electronics by Prof. M. Madhusudhan Rao 55 55 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Frequency is constant f 3.33KHz 1 T 300 s f T Output voltage = V T tON 300 106 200 6 300 100 10 300 Volts Power Electronics by Prof. M. Madhusudhan Rao 56 56 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Problem • A dc chopper has a resistive load of 20 and input voltage VS = 220V. When chopper is ON, its voltage drop is 1.5 volts and chopping frequency is 10 kHz. If the duty cycle is 80%, determine the average output voltage and the chopper on time. Power Electronics by Prof. M. Madhusudhan Rao 57 57 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT VS 220V , R 20, f 10 kHz tON d 0.80 T Vch = Voltage drop across chopper = 1.5 volts Average output voltage tON Vdc VS Vch T Vdc 0.80 220 1.5 174.8 Volts Power Electronics by Prof. M. Madhusudhan Rao 58 58 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Chopper ON time, tON dT 1 Chopping period, T f 1 3 T 0.110 secs 100 μsecs 10 10 3 Chopper ON time, tON dT 3 tON 0.80 0.110 tON 0.08 103 80 μsecs Power Electronics by Prof. M. Madhusudhan Rao 59 59 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Problem • In a dc chopper, the average load current is 30 Amps, chopping frequency is 250 Hz, supply voltage is 110 volts. Calculate the ON and OFF periods of the chopper if the load resistance is 2 ohms. Power Electronics by Prof. M. Madhusudhan Rao 60 60 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT I dc 30 Amps, f 250 Hz , V 110 V , R 2 1 1 Chopping period, T 4 10 3 4 msecs f 250 Vdc I dc & Vdc dV R dV I dc R I dc R 30 2 d 0.545 V 110 Power Electronics by Prof. M. Madhusudhan Rao 61 61 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Chopper ON period, 3 tON dT 0.545 4 10 2.18 msecs Chopper OFF period, tOFF T tON 3 3 tOFF 4 10 2.18 10 3 tOFF 1.82 10 1.82 msec Power Electronics by Prof. M. Madhusudhan Rao 62 62 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • A dc chopper in figure has a resistive load of R = 10 and input voltage of V = 200 V. When chopper is ON, its voltage drop is 2 V and the chopping frequency is 1 kHz. If the duty cycle is 60%, determine – Average output voltage – RMS value of output voltage – Effective input resistance of chopper – Chopper efficiency. Power Electronics by Prof. M. Madhusudhan Rao 63 63 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Chopper i0 + V R v0 V 200 V , R 10, Chopper voltage drop Vch 2V d 0.60, f 1 kHz. Power Electronics by Prof. M. Madhusudhan Rao 64 64 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Average output voltage Vdc d V Vch Vdc 0.60 200 2 118.8 Volts RMS value of output voltage VO d V Vch VO 0.6 200 2 153.37 Volts Power Electronics by Prof. M. Madhusudhan Rao 65 65 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Effective input resistance of chopper is V V Ri I S I dc Vdc 118.8 I dc 11.88 Amps R 10 V V 200 Ri 16.83 I S I dc 11.88 Output power is V Vch dT 2 dT 2 1 v 1 PO dt 0 dt T 0 R Rao T 0 R 66 Power Electronics by Prof. M. Madhusudhan 66 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT d V Vch 2 PO R 0.6 200 2 2 PO 2352.24 watts 10 Input power, dT 1 Pi T Vi dt 0 O 1 dT V V Vch PO T R dt 0 Power Electronics by Prof. M. Madhusudhan Rao 67 67 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT dV V Vch PO R 0.6 200 200 2 PO 2376 watts 10 Chopper efficiency, PO 100 Pi 2352.24 100 99% 2376 Power Electronics by Prof. M. Madhusudhan Rao 68 68 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Problem • A chopper is supplying an inductive load with a free-wheeling diode. The load inductance is 5 H and resistance is 10.. The input voltage to the chopper is 200 volts and the chopper is operating at a frequency of 1000 Hz. If the ON/OFF time ratio is 2:3. Calculate – Maximum and minimum values of load current in one cycle of chopper operation. – Average load current Power Electronics by Prof. M. Madhusudhan Rao 69 69 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT L 5 H , R 10, f 1000 Hz, V 200 V , tON : tOFF 2 : 3 Chopping period, 1 1 T 1 msecs f 1000 tON 2 tOFF 3 2 tON tOFF 3 Power Electronics by Prof. M. Madhusudhan Rao 70 70 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT T tON tOFF 2 T tOFF tOFF 3 5 T tOFF 3 3 tOFF T 5 3 3 T 110 0.6 msec 5 Power Electronics by Prof. M. Madhusudhan Rao 71 71 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT tON T tOFF tON 1 0.6 103 0.4 msec Duty cycle, 3 tON 0.4 10 d 3 0.4 T 110 Maximum value of load current is given by dRT V 1 e L E I max R RT R 1 e L Power Electronics by Prof. M. Madhusudhan Rao 72 72 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Since there is no voltage source in the load circuit, E = 0 dRT V 1 e L I max R RT 1 e L 0.4101103 200 1 e 5 I max 101103 10 1 e 5 Power Electronics by Prof. M. Madhusudhan Rao 73 73 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT 1 e 0.8103 I max 20 2103 1 e I max 8.0047A Minimum value of load current with E = 0 is given by dRT V e L 1 I min R RT e L 1 Power Electronics by Prof. M. Madhusudhan Rao 74 74 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT 0.4101103 200 e 1 5 I min 7.995 A 10 10110 3 e 5 1 Average load current I max I min I dc 2 8.0047 7.995 I dc 8 A 2 Power Electronics by Prof. M. Madhusudhan Rao 75 75 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Problem • A chopper feeding on RL load is shown in figure, with V = 200 V, R = 5, L = 5 mH, f = 1 kHz, d = 0.5 and E = 0 V. Calculate – Maximum and minimum values of load current. – Average value of load current. – RMS load current. – Effective input resistance as seen by source. – RMS chopper current. Power Electronics by Prof. M. Madhusudhan Rao 76 76 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT V = 200 V, R = 5 , L = 5 mH, f = 1kHz, d = 0.5, E = 0 Chopping period is 1 1 3 T 110 secs f 110 3 Chopper i0 + R v0 FWD L E Power Electronics by Prof. M. Madhusudhan Rao 77 77 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Maximum value of load current is given by dRT V 1 e L E I max R RT R 1 e L 0.551103 200 1 e 5103 I max 51103 0 5 1 e 5103 1 e0.5 I max 40 1 24.9 A 1 e Power Electronics by Prof. M. Madhusudhan Rao 78 78 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Minimum value of load current is given by dRT V e 1 E L I min R L RT R e 1 0.551103 1 3 200 e 510 I min 51103 0 5 e 5103 1 e0.5 1 I min 40 1 15.1 A e 1 Power Electronics by Prof. M. Madhusudhan Rao 79 79 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Average value of load current is I1 I 2 I dc 2 for linear variation of currents 24.9 15.1 I dc 20 A 2 RMS load current is given by 1 2 I max I min I I I 2 2 I O RMS I min min max min Prof. M. Madhusudhan Rao 3 80 Power Electronics by 80 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT 1 24.9 15.1 15.1 24.9 15.1 2 2 I O RMS 15.1 2 3 1 96.04 2 I O RMS 228.01 147.98 20.2 A 3 RMS chopper current is given by I ch d I O RMS 0.5 20.2 14.28 A Power Electronics by Prof. M. Madhusudhan Rao 81 81 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Effective input resistance is V Ri IS I S = Average source current I S dI dc I S 0.5 20 10 A Therefore effective input resistance is V 200 Ri 20 IS 10 Power Electronics by Prof. M. Madhusudhan Rao 82 82 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Classification Of Choppers • Choppers are classified as – Class A Chopper – Class B Chopper – Class C Chopper – Class D Chopper – Class E Chopper Power Electronics by Prof. M. Madhusudhan Rao 83 83 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Class A Chopper i0 v0 + Chopper L O v0 V V A FWD D i0 Power Electronics by Prof. M. Madhusudhan Rao 84 84 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • When chopper is ON, supply voltage V is connected across the load. • When chopper is OFF, vO = 0 and the load current continues to flow in the same direction through the FWD. • The average values of output voltage and current are always positive. • Class A Chopper is a first quadrant chopper . Power Electronics by Prof. M. Madhusudhan Rao 85 85 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • Class A Chopper is a step-down chopper in which power always flows form source to load. • It is used to control the speed of dc motor. • The output current equations obtained in step down chopper with R-L load can be used to study the performance of Class A Chopper. Power Electronics by Prof. M. Madhusudhan Rao 86 86 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT ig Thyristor gate pulse t i0 Output current CH ON t v0 FWD Conducts Output voltage t tON T Power Electronics by Prof. M. Madhusudhan Rao 87 87 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Class B Chopper D i0 v0 + R V L v0 Chopper E i0 Power Electronics by Prof. M. Madhusudhan Rao 88 88 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • When chopper is ON, E drives a current through L and R in a direction opposite to that shown in figure. • During the ON period of the chopper, the inductance L stores energy. • When Chopper is OFF, diode D conducts, and part of the energy stored in inductor L is returned to the supply. Power Electronics by Prof. M. Madhusudhan Rao 89 89 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • Average output voltage is positive. • Average output current is negative. • Therefore Class B Chopper operates in second quadrant. • In this chopper, power flows from load to source. • Class B Chopper is used for regenerative braking of dc motor. • Class B Chopper is a step-up chopper. Power Electronics by Prof. M. Madhusudhan Rao 90 90 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT ig Thyristor gate pulse t i0 tOFF tON T t Output current Imax Imin D conducts Chopper conducts v0 Output voltage t Power Electronics by Prof. M. Madhusudhan Rao 91 91 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Expression for Output Current Power Electronics by Prof. M. Madhusudhan Rao 92 92 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT During the interval diode 'D' conducts voltage equation is given by LdiO V RiO E dt For the initial condition i.e., iO t I min at t 0 The solution of the above equation is obtained along similar lines as in step-down chopper with R-L load Power Electronics by Prof. M. Madhusudhan Rao 93 93 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT V E R t R t iO t 1 e L I min e L 0 t tOFF R At t tOFF iO t I max V E R tOFF R tOFF I max 1 e I min e L L R During the interval chopper is ON voltage equation is given by LdiO 0 RiO E dt M. Madhusudhan Rao 94 Power Electronics by Prof. 94 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Redefining the time origin, at t 0 iO t I max The solution for the stated initial condition is R t E R t iO t I max e L 1 e L 0 t tON R At t tON iO t I min R tON E R tON I min I max e L 1 e L R Power Electronics by Prof. M. Madhusudhan Rao 95 95 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Class C Chopper CH1 D1 i0 v0 + V R CH2 D2 L v0 Chopper i0 E Power Electronics by Prof. M. Madhusudhan Rao 96 96 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • Class C Chopper is a combination of Class A and Class B Choppers. • For first quadrant operation, CH1 is ON or D2 conducts. • For second quadrant operation, CH2 is ON or D1 conducts. • When CH1 is ON, the load current is positive. • The output voltage is equal to ‘V’ & the load receives power from the source. • When CH1 is turned OFF, energy stored in inductance L forces current to flow through the diode D2 and the output voltage is zero. Power Electronics by Prof. M. Madhusudhan Rao 97 97 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • Current continues to flow in positive direction. • When CH2 is triggered, the voltage E forces current to flow in opposite direction through L and CH2 . • The output voltage is zero. • On turning OFF CH2 , the energy stored in the inductance drives current through diode D1 and the supply • Output voltage is V, the input current becomes negative and power flows from load to source. Power Electronics by Prof. M. Madhusudhan Rao 98 98 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • Average output voltage is positive • Average output current can take both positive and negative values. • Choppers CH1 & CH2 should not be turned ON simultaneously as it would result in short circuiting the supply. • Class C Chopper can be used both for dc motor control and regenerative braking of dc motor. • Class C Chopper can be used as a step-up or step-down chopper. Power Electronics by Prof. M. Madhusudhan Rao 99 99 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT ig1 Gate pulse of CH1 t ig2 Gate pulse of CH2 t i0 Output current t D1 CH1 D2 CH2 D1 CH1 D2 CH2 ON ON ON ON V0 Output voltage t Power Electronics by Prof. M. Madhusudhan Rao 100 100 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Class D Chopper v0 CH1 D2 R i0 L E V + v0 i0 D1 CH2 Power Electronics by Prof. M. Madhusudhan Rao 101 101 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • Class D is a two quadrant chopper. • When both CH1 and CH2 are triggered simultaneously, the output voltage vO = V and output current flows through the load. • When CH1 and CH2 are turned OFF, the load current continues to flow in the same direction through load, D1 and D2 , due to the energy stored in the inductor L. • Output voltage vO = - V . Power Electronics by Prof. M. Madhusudhan Rao 102 102 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • Average load voltage is positive if chopper ON time is more than the OFF time • Average output voltage becomes negative if tON < tOFF . • Hence the direction of load current is always positive but load voltage can be positive or negative. Power Electronics by Prof. M. Madhusudhan Rao 103 103 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT ig1 Gate pulse of CH1 t ig2 Gate pulse of CH2 t i0 Output current t CH1,CH2 D1,D2 Conducting ON v0 Output voltage V Average v0 t Power Electronics by Prof. M. Madhusudhan Rao 104 104 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT ig1 Gate pulse of CH1 t ig2 Gate pulse of CH2 t i0 Output current CH1 CH2 t D1, D2 v0 Output voltage V t Average v0 Power Electronics by Prof. M. Madhusudhan Rao 105 105 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Class E Chopper CH1 D1 CH3 D3 i0 R L E V + v0 CH2 D2 CH4 D4 Power Electronics by Prof. M. Madhusudhan Rao 106 106 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Four Quadrant Operation v0 CH2 - D4 Conducts CH1 - CH4 ON D1 - D4 Conducts CH4 - D2 Conducts i0 CH3 - CH2 ON D2 - D3 Conducts CH2 - D4 Conducts CH4 - D2 Conducts Power Electronics by Prof. M. Madhusudhan Rao 107 107 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • Class E is a four quadrant chopper • When CH1 and CH4 are triggered, output current iO flows in positive direction through CH1 and CH4, and with output voltage vO = V. • This gives the first quadrant operation. • When both CH1 and CH4 are OFF, the energy stored in the inductor L drives iO through D2 and D3 in the same direction, but output voltage vO = -V. Power Electronics by Prof. M. Madhusudhan Rao 108 108 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • Therefore the chopper operates in the fourth quadrant. • When CH2 and CH3 are triggered, the load current iO flows in opposite direction & output voltage vO = -V. • Since both iO and vO are negative, the chopper operates in third quadrant. Power Electronics by Prof. M. Madhusudhan Rao 109 109 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • When both CH2 and CH3 are OFF, the load current iO continues to flow in the same direction D1 and D4 and the output voltage vO = V. • Therefore the chopper operates in second quadrant as vO is positive but iO is negative. Power Electronics by Prof. M. Madhusudhan Rao 110 110 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Effect Of Source & Load Inductance • The source inductance should be as small as possible to limit the transient voltage. • Also source inductance may cause commutation problem for the chopper. • Usually an input filter is used to overcome the problem of source inductance. Power Electronics by Prof. M. Madhusudhan Rao 111 111 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • The load ripple current is inversely proportional to load inductance and chopping frequency. • Peak load current depends on load inductance. • To limit the load ripple current, a smoothing inductor is connected in series with the load. Power Electronics by Prof. M. Madhusudhan Rao 112 112 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Problem • For the first quadrant chopper shown in figure, express the following variables as functions of V, R and duty cycle ‘d’ in case load is resistive. – Average output voltage and current – Output current at the instant of commutation – Average and RMS free wheeling diode current. – RMS value of output voltage – RMS and average thyristor currents. Power Electronics by Prof. M. Madhusudhan Rao 113 113 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT i0 + Chopper L O v0 V FWD A D Power Electronics by Prof. M. Madhusudhan Rao 114 114 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT tON Average output voltage, Vdc V dV T Vdc dV Average output current, I dc R R The thyristor is commutated at the instant t tON V output current at the instant of commutation is R since V is the output voltage at that instant. Power Electronics by Prof. M. Madhusudhan Rao 115 115 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Free wheeling diode (FWD) will never conduct in a resistive load. Average & RMS free wheeling diode currents are zero. tON 1 v dt 2 VO RMS 0 T 0 But vO V during tON Power Electronics by Prof. M. Madhusudhan Rao 116 116 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT tON 1 2 VO RMS V dt T 0 tON VO RMS V 2 T VO RMS dV tON Where duty cycle, d T Power Electronics by Prof. M. Madhusudhan Rao 117 117 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT RMS value of thyristor current = RMS value of load current VO RMS R dV R Average value of thyristor current = Average value of load current dV R Power Electronics by Prof. M. Madhusudhan Rao 118 118 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Impulse Commutated Chopper • Impulse commutated choppers are widely used in high power circuits where load fluctuation is not large. • This chopper is also known as – Parallel capacitor turn-off chopper – Voltage commutated chopper – Classical chopper. Power Electronics by Prof. M. Madhusudhan Rao 119 119 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT LS T1 iT1 + a + IL + b _C T2 iC FWD L O VS A vO D L D1 _ _ Power Electronics by Prof. M. Madhusudhan Rao 120 120 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • To start the circuit, capacitor ‘C’ is initially charged with polarity (with plate ‘a’ positive) by triggering the thyristor T2. • Capacitor ‘C’ gets charged through VS, C, T2 and load. • As the charging current decays to zero thyristor T2 will be turned-off. • With capacitor charged with plate ‘a’ positive the circuit is ready for operation. • Assume that the load current remains constant during the commutation process. Power Electronics by Prof. M. Madhusudhan Rao 121 121 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • For convenience the chopper operation is divided into five modes. – Mode-1 – Mode-2 – Mode-3 – Mode-4 – Mode-5 Power Electronics by Prof. M. Madhusudhan Rao 122 122 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Mode-1 Operation LS T1 + + IL VC _C iC L VS O A D L D1 _ Power Electronics by Prof. M. Madhusudhan Rao 123 123 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • Thyristor T1 is fired at t = 0. • The supply voltage comes across the load. • Load current IL flows through T1 and load. • At the same time capacitor discharges through T1, D1, L1, & ‘C’ and the capacitor reverses its voltage. • This reverse voltage on capacitor is held constant by diode D1. Power Electronics by Prof. M. Madhusudhan Rao 124 124 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Capacitor Discharge Current C iC t V sin t L 1 Where LC & Capacitor Voltage VC t V cos t Power Electronics by Prof. M. Madhusudhan Rao 125 125 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Mode-2 Operation IL + LS _ IL VC C L VS + T2 O A D _ Power Electronics by Prof. M. Madhusudhan Rao 126 126 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • Thyristor T2 is now fired to commutate thyristor T1. • When T2 is ON capacitor voltage reverse biases T1 and turns if off. • The capacitor discharges through the load from –V to 0. • Discharge time is known as circuit turn-off time. Power Electronics by Prof. M. Madhusudhan Rao 127 127 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Circuit turn-off time is given by VC C tC IL Where I L is load current. t C depends on load current, it must be designed for the worst case condition which occur at the maximum value of load current and minimum value of capacitor voltage. Power Electronics by Prof. M. Madhusudhan Rao 128 128 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • Capacitor recharges back to the supply voltage (with plate ‘a’ positive). • This time is called the recharging time and is given by VS C td IL • The total time required for the capacitor to discharge and recharge is called the commutation time and it is given by tr tC td Power Electronics by Prof. M. Madhusudhan Rao 129 129 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • At the end of Mode-2 capacitor has recharged to VS and the free wheeling diode starts conducting. Power Electronics by Prof. M. Madhusudhan Rao 130 130 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Mode-3 Operation IL + LS + IL VS _C T2 L VS O A FWD D _ Power Electronics by Prof. M. Madhusudhan Rao 131 131 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • FWD starts conducting and the load current decays. • The energy stored in source inductance LS is transferred to capacitor. • Hence capacitor charges to a voltage higher than supply voltage, T2 naturally turns off. Power Electronics by Prof. M. Madhusudhan Rao 132 132 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT The instantaneous capacitor voltage is LS VC t VS I L sin S t C Where 1 S LS C Power Electronics by Prof. M. Madhusudhan Rao 133 133 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Mode-4 Operation LS + + IL VC _C L D1 O VS A L D _ FWD Power Electronics by Prof. M. Madhusudhan Rao 134 134 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • Capacitor has been overcharged i.e. its voltage is above supply voltage. • Capacitor starts discharging in reverse direction. • Hence capacitor current becomes negative. • The capacitor discharges through LS, VS, FWD, D1 and L. • When this current reduces to zero D1 will stop conducting and the capacitor voltage will be same as the supply voltage Power Electronics by Prof. M. Madhusudhan Rao 135 135 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Mode-5 Operation IL L • Both thyristors are off FWD O A and the load current D flows through the FWD. • This mode will end once thyristor T1 is fired. Power Electronics by Prof. M. Madhusudhan Rao 136 136 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT ic Capacitor Current IL 0 t Ip iT1 Ip IL Current through T1 t 0 Power Electronics by Prof. M. Madhusudhan Rao 137 137 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT vT1 Vc Voltage across T1 t 0 vo Vs+Vc Vs Output Voltage t vc Vc t Capacitor Voltage -Vc tc td Power Electronics by Prof. M. Madhusudhan Rao 138 138 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT Disadvantages • A starting circuit is required and the starting circuit should be such that it triggers thyristor T2 first. • Load voltage jumps to almost twice the supply voltage when the commutation is initiated. • The discharging and charging time of commutation capacitor are dependent on the load current and this limits high frequency operation, especially at low load current. Power Electronics by Prof. M. Madhusudhan Rao 139 139 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT • Chopper cannot be tested without connecting load. • Thyristor T1 has to carry load current as well as resonant current resulting in increasing its peak current rating. Power Electronics by Prof. M. Madhusudhan Rao 140 140 Prof. T.K. Anantha Kumar, E&E Dept., MSRIT