noc19-ee65-lec23

[Music] [Music] hello and welcome to this lecture on fundamentals of electric drives in the last lecture we were discussing about the DC dynamic braking of induction motor so today we'll take up another type of dynamic braking which is called self-excited dynamic braking of induction motor now in this case what we do we excite the induction motor by using capacitor bank let us see how we achieve the self-excited dynamic braking of induction motor so what we have here is that an induction motor is normally running from the three-phase supply now when we want to break it using self-excited braking we disconnect the three-phase supply and then what we do we apply a capacitor bank to the stator of the induction motor so what we have here is we have three phase line and the motor is a induction motor which is supplied from the three-phase line so we connect the capacitors here also another capacitor between the two so we have three capacitors here and then this is a switch which is disconnected which disconnect the motor from the means so here the motor is running but instead of three-phase AC supply we have connected a bank of capacitors now what happens the capacitor provide the necessary excitation to the motor so motor will have some excited voltage and that is called self excitation and the excitation is something very similar to that of the excitation of a sound generator let's see how it is excited so we have the characteristic here and this is a monetization characteristic and always we have some residual magnetism here so this is the saturation characteristic because the core is a such terrible core and this is e e is the phase voltage and this we call as I M same as or IC the capacitor current RMS value now when we connect the capacitors the capacitor has a load line which is a straight line now this is a slope we can draw a continuous straight line here and there is intersection of this capacitor load line this is a capacitor load line and the slope is what is the slope slope is 1 by Omega C is the capacitance value here and let us say what I am doing here is is root 3 times of e this is the line voltage we are plotting the voltage so this is 1 by Omega C so C is a value of the capacitance so each capacitance has a value C and the frequency is Omega here so the reactance of each capacitance is 1 by Omega C so the capacitive reactance is 1 by Omega C so when the capacitors are connected in Delta across the terminal they see the line voltage so the capacitive current is equal to the line voltage which is root 3 into the phase voltage by XC XC is 1 by Omega C so that is equal to root 3 e into Omega C so this is the capacitance current so the capacitance current will will flow here if we drop a perpendicular here this this current will be the capacitance current now this current will be flowing in the motor so this current is a leading current so the motor is supplying a leading current supplying a leading current is equivalent to taking a lagging current so we can say that this is equal to the magnetizing current line-to-line managing a current of an induction machine so it means this capacitive current which is which is leading in nature is being given by the motor motor is drawing equivalently a lagging current which is I am i M is called the magnetic current of the induction motor magnetization current of the induction motor now since I have we have a little back EMF here so this will self excite just like a haunt generator and it will finally settle down at full speed full value of the voltage so this how the self excitation takes place okay so now the motor is now having some induced EMF and it is circulating a current in the rotor and the stator there is a losses so because of the losses the motor power will be dissipated in I square R loss and the motor will gradually dissipate so this is called the braking now when the motor speed comes down the induced EMF also comes down the frequency also comes down so let us draw the magnetizing characteristic and the capacitance load line for a reduced frequency now if the frequency reduces what happens if the frequency reduces we will get a different magnet a statistic this is for a reduced value of frequency frequency has reduced so the frequency has reduced the the magnetization characteristic also reduce proposed Netley so this is a this is a value for reduced frequency there may be maybe this is f1 this is f2 so f2 is less than F 1 when the when the speed or frequency reduces we have a reduced value of the induced EMF and if the frequency reduces the slope will increase the capacitance a load line is inversely proportional to Omega Omega is 2 pi F so if the frequency reduces XC will go high so we will have a load line which is which will go up so this is the capacitance load line which is now a different value so the intersection was earlier at this point this is operating point earlier now the operating we'll be at a reduced value of voltage so the voltage reduces so it means as the frequency reduces the voltage decreases the current also decreases because the effective current here is now reduced in this case so the current corresponding to this is now a reduced value if this was I am 1 this value is im2 so I am 2 is less than I am 1 the current is reduced in the losses are also reduced the braking torque also reduces and gradually the motor comes down to zero speed and after certain speed below a certain speed there will not be any self excitation so this is one way of breaking of induction machine which is called a self excited braking of induction motor now we have discussed about the motoring and breaking of a conventional induction machine now let us discuss about the speed control of induction motor using solid state devices the past type of speed control is by using a voltage regulator so let us discuss about the speed control of an induction motor using a voltage regulator or voltage controller speed control of induction motor sometimes called this as I am induction motor by AC voltage controller now let us see what is application this type of speed control is usually applied for fan and palm type of application now what happens here is the following that we have the tox pika district of the Machine of the motor speed in the y axis torque in the x axis the origin now this is the normal top speed kaduk of an induction machine so we have the maximum torque which is occurring here the max at certain value of and this is corresponding to applied voltage that is v1 now the voltage is reduced if the voltage is reduced the torque will also reduced because we have seen that the torque is proportional to v square so if you reduce the voltage torque reduces as v square so if you if we reduce the voltage we we get a reduced torque this is for but the peak torque is occurring at the same value of speed now this is for v2 and v1 is greater than v2 now how is the speed control happen here now the load in this case is a fan or pump type of load in fan or pump type of load the torque is proportional to speed square let us draw the load characteristic here so if we have a fan type of load we get the load characteristic which is like this this is TL TL is equal to K into Omega M Squared the torque is proportional to the speed speed of the fan or speed of the pump the fast intersection is here we see that the intersection for the first characteristic is here so we have the corresponding speed which is here now you when we reduce the voltage the intersection happens at this point so if this is omega m 1 so we can reduce the speed by reducing the voltage to Omega M two and so on if you further reduce the voltage we get different characteristic which is here and and this will lead to the intersection at this point and this point is still a stable point so this is omega M 3 and thus we have good range of speed control by by using voltage controller now how do we use the or how do we implement the voltage controller we can have a three phase circuit or we can have a single phase circuit because this is also applicable to single phase induction motor so let's see and single phase circuit first so we have a single phase circuit in this case what we have here is the following that we have the input AC and we use track what we use here in the track it's a low power circuit and this our induction motor so this is output current this output voltage this is the input AC so the output voltage and the current waveform will look like this this is a input supply with sinusoidal Omega T in the x-axis and in the y-axis we can have the voltage so this is alpha alpha is the triggering angle so we trigger this this triac in both the cycle both the half cycle in the positive half cycle they said alpha the negative half cycle this is that at PI plus alpha so the current starts from zero here and the current comes down to zero are some value that is equal to beta and here the current reverses and this is the current in the negative half cycle so this angle is beta here and this angle is pi plus beta so the output voltage waveform will look like this this is the output voltage waveform so beyond pi also there is conduction because the the current is conducting up to beta so this will be like this and this will continue in the negative half cycle so the voltage reverses and the conduction will be like this and since this is a periodic we have the conduction like this so this is the output voltage V naught and we have the output current the voltage and currents are alternating in nature but however by controlling alpha we can control the RMS of the output voltage so when we control the RMS of the output voltage the torque is reduced and hence the speed is controlled similarly we can extend this to a three phase voltage controller you if we have a three phase circuit which is meant for higher power application single phase is commonly used for fan type of application whenever when we have a single phase motor a single phase fan we use a simple voltage regulator a triac base regulator to control the speed for higher power we go for three phase voltage controller which consists of not triac but anti parallel thyristors let us see three phase AC voltage controller so a three phase AC voltage controller are used for higher power applications now here what we have instead of triac we go for anti parallel thyristors or ecr's this is for phase a similarly for phase B we have another anti parallel thyristors and for phase C we have AC ours so the input is three-phase AC supply we apply the AC here and then this is our induction motor which is connected to a fan or pump type of load so the load in this case is Vanderpump type of load is connected to fan or pump type of load here now the SES in this case a triggered in a particular sequence the sequence is t1 t2 t3 t4 t5 and t6 and the triggering pulse are delayed by 60 degrees t1 t2 t3 t4 t5 t6 and the delay between two successive triggering pulses is 60 degree so the triggering sequences in this case is t1 and then we we trigger t2 then t3 t4 t5 and t6 in fact when we trigger t2 we apply also the triggering pulse to t1 to maintain the continuity we apply to t2 t1 then t3 t2 t4 t3 t5 t6 t4 t6 T 1 and T 1 T 6 so what we do we overlap the triggering pulse the reason is if we just apply a single pulse the voltage controller may not start at all so the controller - or the triggering pulse to each SCR is a pair of pulses like this if you say that t1 is being triggered by this pair of pulses this t2 is being triggered by the pair of pulses and so on and this this distance is 60 degree so this is how AC voltage controller is triggered to control the output voltage now let us find out the efficiency in case of voltage control so we have we have to calculate the efficiency efficiency of induction motor under voltage control so we neglect the stator impedance neglecting stator impedance for simplicity we can draw the equivalent circuit which is consisting of the rotor only so we have the equivalent circuit which is X R Prime and this is our prime y is for simplicity we have ignored the stator resistances the stator resistance stator leakage reactance now here the current which is flowing in the rotor circuit is ir Prime and the input here is there is the input in this case P input and P input is same as the air gap power which is PC so we can say that P input is same as P air gap is equal to this is a single-phase equivalent circuit so for three-phase we write here IR square into RR by s since we have a circuit where we have the resistance only the power will be consumed only in the resistance and in the rotor also we have copper loss the rotor copper loss so the rotor copper loss is equal to 3 PI R square into R prime now the output power which is coming out of this is P out so that's equal to P out is equal to P air gap - the rotor copper loss that is equal to 3 PI R square or R 1 by s minus 1 that's equal to 3 PI R square into RR prime into 1 minus s by now when we calculate efficiency efficiency is the ratio of output power by the input power so we calculate the efficiency is P out by P in that's equal to 3 PI R square R R 1 minus s by s divided by the input is 3 PI R square R a prime basis now that's equal to 1 minus s so the efficiency in this case for voltage controlled induction motor is 1 minus s so it means if we have higher slip the efficiencies are going to be less so if sleep is close to 1 efficiency is less if sleep is close to zero efficiency is high so when we have a fan which is being controlled by a voltage regulator we should operate it at higher speed to get higher efficiency so efficiency decreases with with reduction in speed so efficiency decreases efficiency decreases with decrease in speed so this is the control of induction motor by voltage control which is applied for low power application primarily for fan application where efficiency is not a very big issue for high power the voltage control is not preferred because when we use voltage control and the speed is low efficiency decreases so for higher power use it have better ways of speed control so what we do at higher power is voltage and frequency control so we control both voltage and frequency so let us see what is the voltage and frequency control for an induction motor so let us see that the the torque equation is given as 3 by Omega MS into v square divided by RS plus RR by s whole square plus XS plus XR square into RR prime a s now we know that the maximum torque occurs at this slip xmax T is equal to RR prime by RS square plus XS plus XR prime whole square under root so we have a plus minus the plus is for the motoring action and the minus is for the generating action so this is a normal guy district of induction motor we we have maximum value of torque and the maximum value of torque occurs at a sleep of X max T if we substitute this X max T in this torque equation we get the maximum torque value so T max is given us 3 by 2 Omega M s into v square divided by RS plus minus re square plus XS plus XR whole square so we can also rewrite this in the particular form K into V by F square divided by RS by F plus minus RS by a full square plus 4 PI square into LS plus L R square so the torque spec a district of an induction motor can be expressed in terms of voltage and frequency as given by this equation so in this case what we do we vary the voltage as well as the frequency so that is called the variable voltage and variable frequency control of induction motor so we have an advantage that we have adding voltage and frequency we can maintain the peak torque constant and we can also have higher efficiency so we'll be discussing more about variable voltage and variable frequency control of induction motor in the next lecture [Music] [Music]