www.getmyuni.com UNIT-6 DC Choppers 7.1 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. 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. 7.2 Principle of Step-down Chopper Chopper i0 + V R V0 − • 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. Page 168 www.getmyuni.com v0 V Vdc t tON tOFF i0 V/R Idc t T VAdc = verage value of output or load voltage. IAdc = verage value of output or load current. tON = Time interval for which SCR conducts. tOFF = Time interval for which SCR is OFF. T= tON + t OFF = Period of switching or chopping period. 1 f = = Freq. of chopper switching or chopping freq. T Average Output Voltage t VV= ON dc tON+ t OFF tON Vdc = V = V. d T t but ON = d = duty cycle t Average Output Current V I = dc dc R VVtON Idc = = d RTR RMS value of output voltage tON 1 2 VO= ∫ v o dt T 0 But during t, v= V ON o Therefore RMS output voltage t ON 1 2 VO = ∫ V dt T 0 2 V tON VO= t ON = . V TT VO = d. V Page 169 www.getmyuni.com Output power PVIOOO= V But I = O O R ∴ Output power 2 VO PO = R dV 2 PO = R Effective input resistance of chopper V Ri = Idc R Ri = d The output voltage can be varied by varying the duty cycle. 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. – Pulse Width Modulation • tON is varied keeping chopping frequency ‘f’ & chopping period ‘T’ constant. • Output voltage is varied by varying the ON time tON V0 V tON tOFF t T V0 V t tON tOFF 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 Page 170 www.getmyuni.com v0 V tON tOFF t T v0 V tON tOFF t T 7.2.1 Step-down Chopper with R-L Load Chopper i0 + R V V FWD L 0 E − • 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’. • 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. Page 171 www.getmyuni.com v 0 Output voltage V t t ON OFF t T i0 Output Imax current Continuous Imin current t i0 Output current Discontinuous current t Expressions for Load Current Io for Continuous Current Operation When Chopper is ON (0 ≤ T ≤ Ton) i0 + R V V L 0 E - di V= i R + LO + E O dt Taking Laplace Transform VE− =RIOOO()() S + L S. I S − i () 0 + SS − At t=0, initial current iO ()0 = Imin VE− I IS() = + min O R R LS S + S + L L Page 172 www.getmyuni.com Taking Inverse Laplace Transform RR − t − t VE− LL iO () t=1 − e + Imin e 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() t ON = Imax When Chopper is OFF i0 R L E When Chopper is OFF ()0 ≤t ≤ tOFF diO 0 =RiO + L + E dt Talking Laplace transform − E 0=RIOOO()() S + L SI S − i () 0 + S Redefining time origin we have at t = 0, − initial current iO ()0 = Imax I E ∴IS() = max − O R R S + LS S + L L Taking Inverse Laplace Transform RR −t − t LLE iO () t= Imax e −1 − e R Page 173 www.getmyuni.com 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 i t= I O() OFF min To Find IImax& min From equation RR − t − t VE− LL iO () t=1 − e + Imin e R At t= tON = dT, i O () t = Imax dRT dRT VE− − − LL ∴Imax =1 − e + Imin e R From equation RR −tE − t LL iO () t= Imax e −1 − e R Att= tOFF = T − t ON , i O () t = Imin t= tOFF =()1 − d T ()1−d RT() 1 − d RT − − LLE ∴Imin = I max e −1 − e R Substituting for I in equation min dRT dRT − − VE− LL Imax=1 − e + I min e R we get, dRT − L V1− e E Imax =RT − RR− 1− e L Substituting for Imax in equation ()1−d RT() 1 − d RT −E − LL Imin= I max e −1 − e R we get, dRT V eL −1 E I = − min RRRT e L −1 Page 174 II− is known as the steady state ripple. () max min www.getmyuni.com Therefore peak-to-peak ripple current ∆III =max − min Average output voltage V = d. V dc Average output current II+ I = max min dc() approx 2 Assuming load current varies linearly from IImin to max instantaneous load current is given by ()∆I. t i= I + for 0 ≤ t ≤ t() dT Omin dT ON IImax− min iO = Imin + t dT RMS value of load current 1 dT I= i2 dt O() RMS ∫ 0 dT 0 2 1 dT ()I− I t I = I + max min dt O() RMS dT∫ min dT 0 dT 2 1 2II− 2 2Imin() I max− I min t max min IO() RMS =∫ Imin + t + dt dT0 dT dT 1 2 2 ()IImax− min I= d I2 + + I I − I CH min min() max min 3 ICH = d IO() RMS Effective input resistance is V Ri = IS Page 175 www.getmyuni.com Where IS = Average source current IS= dI dc V ∴Ri = dIdc 7.3 Principle of Step-up Chopper LI D + + − L C O V A VO D Chopper − • 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. • 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 V= V + L i. e ., V > V OOdt • 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. Page 176 www.getmyuni.com (i) 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 LV= Therefore energy stored in inductor = V. I . t ON Where t= ON period of chopper. ON When Chopper is OFF (energy is supplied by inductor to load) Voltage across LVV=O − Energy supplied by inductor L=() VO − V It OFF where tOFF = OFF period of Chopper. Neglecting losses, energy stored in inductor L = energy supplied by inductor L ∴VItON =() V O − V It OFF V[] tON+ t OFF VO = tOFF T VVO = T− tON Where T = Chopping period or period of switching. T= tON + t OFF 1 VV= O t 1− ON T 1 ∴VV = O 1− d t Whered =ON = duty cyle T Page 177 www.getmyuni.com 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. Problem 1. 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. Solution: VV = 460 V, dc = 350 V, f = 2 kHz 1 Chopping period T = f 1 T=−3 = 0.5 msec 2× 10 t ON Output voltage VVdc = T Conduction period of thyristor TV× t = dc ON V −3 0.5× 10 × 350 t = ON 460 tON = 0.38 msec Problem 2.