noc19-ee65-lec08

Hello and welcome to this lecture on fundamental electric drives. The last lecture we were discussing about the characteristic of DC motor, especially Shunt motor and Series motor. Now today we will be discussing about the speed control of separately excited DC motor fed from control rectifier. So let us see how the speed can be controlled by using controlled rectifiers Now let us see that how many types of control rectifiers we have. We have especially two types of control rectifiers. One is called a full control rectifier and other is called half controlled rectifier. So let us see the topology of these two kinds of rectifiers. This is a thyristor bridge, so we have the SCRs and this is feeding the armature of a DC motors. The field is apparently excited it is a field binding and we have the AC supply, which is the input to the bridge. Now the current here is Ia, the output current and output voltage across this is Va. Now If we see that in this case the current can only flow in one direction. Because this is a controlled rectifier SCRs can only deliver current in one direction. It means the current here can only come from SCR to like this. There cannot be any reverse current flow. However, the voltage Va can be positive. It can be negative because the input here is an AC supply. This is Vs, so Vs can be expressed as Vm, sin omega t. So if we plot this input voltage, it will be an alternating voltage like this. S, x axis omega t axis this is pi and this is 2 pi. So the input is an alternating supply the output in this case is we will see that this, this is the average will be DC. However the average can be positive or it can be negative because it is a full control rectifier. So this is called a full controlled rectifier. And seeing the input is single phase. We can call this to be a single phase full controlled rectifier. Now if we plot the average voltage and average current in a xy plane we will take the voltage in the y axis and the current in the x axis here. This converter can operate in the 1st quadrant and the 4th quadrant. So this is a 2 quadrant converter, which can operate in the 1st quadrant and the 4th quadrant. The voltage can be positive or negative current can only be positive. Now let us see another type of controlled rectifier here also we have 4 devices. However 2 of the devices are SCRs and 2 are diodes. This field the armature of a separately excited DC motor the field is separately excited. The current here is Ia hour average current average voltage here is a. The input is again an AC supply so here this is called a half controlled rectifier . And since we are talking about single phase, it is called as single phase half controlled rectifier. Now what are the operating quadrants here? The output voltage because we have these 2 diodes here. This diode will be giving a free willing path. So whenever the voltage will try to be negative, these two diodes will be forward biased. So that is a freewheeling path here which is existing. So the voltage Va can never become negative. so this, this is why this is called a half controlled converter. And this operates only in 1st quadrant. So, let us see the operating quadrant here. So if we plot the operation of this converter in VI plane, Va is in the y-axis and Ia is in the x axis. So the operation only happens in the 1t quadrant. Because in this case the voltage can never be negative current of course cannot be negative because we have SCRS and we have diodes. Similarly, this is for single phase converters. Now single-phase convertors are used for lower power applications specifically when the power is less than 10 kilowatt typically these are used for those applications low power applications. But when the power is higher maybe more than 10 kilowatt or more. We go for 3 phase converters. So in case of a 3 phase converter, we can also have a similar topologies we have the 3 phase converters and this is the bridge we are talking about bridge converter and these are all SCRS and this we are feeding the armature of a DC machine. The field is separately excited and the input here is 3 phase. So 3 phase AC input and the output current here is Ia and output voltage here, average voltage is Va we are putting the average voltage. Now if we see this bridge, the input is a 3 phase balanced voltage supply and output voltage, will be can be positive can also be negative the average voltage. So as we have seen in a single phase case in 3 phase, also this can operate in 1st quadrant and the 4th quadrant. So if we see the operating quadrants here, this is the voltage in the y axis and current in x-axis. So we see the operating quadrants. So this, these also a 2 quadrant converter. This can operate in the 1st quadrant as well as the 4th quadrant. So we call this to be a 3 phase full controlled converter and this is usually this is a bridge converters. This is the form of a bridge so we call this to be a bridge converter. Now similarly we can also have half controlled converter, 3 phase converter. So what we have here is we have 6 devices as before so we have in this case 6 devices. 3 of these devices are SCR and 3 are diode. So half of the devices are controlled rectifier and half of the devices are uncontrolled rectifier. Diode is an uncontrolled rectifier, the input supply here is again 3 phase so 3 phase AC supply and the output here feeds the armature of a DC motor. The field is separately excited we have this current here, Ia and the armature voltage here is Va. Now if we see the operation of this converter, this converter also operates in 1 quadrant only. We have the xy plane where we have plotted the voltage and current, but this converter can only operate in 1 quadrant and that is why this is called a half controlled converter. The voltage here cannot be negative because that the freewheeling path with the existing here, through 1 diode and 1 SCR. So whenever the voltage is negative, the freewheeling starts between the diode and the SCR. That is a path of freewheeling which will bring the voltage down to 0. So the voltage Va, the minimum value can be 0 and this can only be positive. This cannot be negative so this operates on lean 1st quadrant. So this is quadrant 1 so this is called a 3 phase half controlled converter and see this is a bridge we can sometimes call this to be 3 phase half controlled bridge converter. Now let us see how we can analyse the operation of a separately excited DC motor when fed from a single phase full control converter. So we are feeding from a single phase full control converter and this is separately excited DC motors. Now let us first draw the circuit diagram here so we have a single phase bridge here. We have 4 SCRs and what we do here, we replace the motor by its equivalent circuit and this is the armature of the motor. The armature consist of resistance and inductance and a back Emf. So this is a representation of the motor so you call this armature of DC motor. So the input is fed from an AC source so this AC source is having the magnitude or the, the value of the voltage is Vs now Vs is the instantaneous value. And this Vs is expressed in terms of its various voltages. So, we can, we can say that Vs is Vm sin omega t. So this is a single phase full control bridge. Now we can control the output voltage by controlling the triggering angle of the SCR. So SCRs can be triggered at a certain angle alpha and the current here is Ia and the voltage which is here is Va the armature voltage Va. Now when we write this small letters, we mean the instantaneous values, the current which is instantaneous. The voltage also, which is instantaneous. Now this particular converter can operate in 2 different modes. One is called a continuous current operation, other is called a discontinuous current operation. Now we will try to see this too in different parts of the lecture. Now let us first see discontinuous current operation. So we call this to be discontinuous armature current when the armature current is discontinuous. So, so what happens Ia comes down to 0 so in this case, suppose we want to plot the output voltage. We have the input which is the sign wave so this is 0, 2 pi this is pi and then this is 2 pi, 3 pi an so on. And we have a back EMF this is the motor back EMF and we triggered this SCR at an angle which is alpha and this happens in every half cycle. So this is the rectified waveform, so here also we triggered alpha so this value is pi+alpha . So the current rise from 0 when we trigger the SCR the corner starts from 0. Now we see that we have an RLE circuit So when we are triggered the SCR. Let us say we have T1, T2 this T1 and T2 are triggered in the positive half cycle because they have followed by us in the positive half cycle and T3 and T4 are triggered in the negative half cycle. So at this instant we trigger T1 and T2. So they are forward biased, they will go into conduction so when they go into conduction we will have a current. The current will start from 0 and will somehow come down to 0 before the triggering of the next pair of SCRs. At pi+alpha at this instant we trigger the next pair of SCRs the next pair of SCR which are triggered in the negative half cycle are T3 and T4. So we have T3 and T4 are triggered in the negative half cycle. So the current will again start from 0 and will die down to 0 before the commencement or before the triggering of the next pair of SCR which is again T1 and T2 because the operation is periodic so this is the nature of the current. So we have i, ia, ia that is like this. So this is our current which we are seeing here this is Ia okay. So the current starts from 0 and goes down to 0 again and this angle at which the current again goes down to 0 is called the extinction angle. This angle is called beta. What about the output voltage? output voltage will be rectified voltage no doubt but this will have a typical wave form. Now when we trigger the SCRs, the output voltage will be same as the input voltage okay, because when we trigger, let us say this to SCRs, this SCRs will go on conducting and so the input is connected to the output. So this is the path of the current and it will be basically returned back like this back to the source. So when we trigger T1 and T2, the output Va will become Vs, Vs the source voltage. So this is the output here okay at omega t=pi is still continues because the current continues to flow beyond omega t=pi so we have continuity of current and the current only comes down to 0 at beta. So the current flows still beta so output Va is same as the input that is Vs. Now at beta, the current comes down to 0. So when the current comes down to 0 this current is 0 now, circuit is disconnected so this part of the circuit is disconnected, the source is disconnected from the load. So the output voltage will be same as the back EMF. So in this case, the voltage here same as the back EMF so it will be like this. And then at pi+alpha, T3 and T4 are triggered, again the current will be diverted from this branch. We have the current, which will now flow through T3 and T4. This tool wave taking the current, so T3 and T4 will be taking the current. So the voltage across the load will reverse so this is the voltage which will be appearing across the load. So this phenomenon is periodic so the output voltage will look like this so even here also the output voltage will have the similar pattern because we have the periodic waveform so the output will be of this sort. So this is the output voltage Va so we have here 2 distinct interval, one is called the powering interval, other is called the 0 current interval or coasting interval. So let us see that we have two intervals when omega t> alpha < beta from this part to this part, the output voltage is the same as the input voltage so this is called the powering interval. This is called the powering interval. And in this case what happens here that the output voltage is same as the input voltage and we have another interval in which omega t is >beta but is < pi+alpha this small interval during which the output voltage is same as the back EMF. So this interval is called the 0 current interval or this is also sometimes called as coasting interval. Now during the coasting interval, the output voltage= back EMF. Now we have 2 different modes here, one is called the powering interval other is called the coasting interval. We will try to analyse these two interval separately. Now let us take the powering interval. In powering interval what happens is the following, this interval is omega t >alpha<beta. Now in this case, what is the input? input is same as output, output is in fact equal to the input voltage Vs. So what is this voltage here Va? Now, if we see this armature voltage Va, armature voltage consists of 3 different voltages, one is the drop occur at the resistance, other the drop occur at the inductance and the third drop is the back EMF. So we can say here that Va=the resistance drop Ra ia+inductance drop La dia/dt +the back EMF, which is E, now this is the equation for the powering interval. Now the input is a sinusoidal supply, the input Vs is a sine wave so we can rewrite this equation by substituting for input voltage Vm sin omega t= Ra ia+La dia/dt+E, now this is a first order linear differential equation and we assume that the back EMF is constant. So we have to find out the solution of this differential equation. Now this differential equation, if we solve this differential equation this differential equation will have 2 parts. Now ia will have a steady state component in the steady state + ia will also have a transient component. Now what is the steady state component? the steady state component is a component when T tends to infinity. So it means in the steady state, the inductive voltage will be the inductive reactants into the current. So in the steady state we have an RLE circuit. Now if you apply the steady state component here, this is Vm/Z sin omega t-theta-E/Ra. So this part is the steady state part and we have a transient part that is A exponentials is we have an RL circuit, we have an exponential part which is t/tau, now this part is the steady state part and this part is the transient part. Because the t tends to infinity, this part will be equal to 0. Now the steady state part has got 2 voltages, one is Vm, the applied voltage that is Vm sin omega t and we have a theta here, theta is called the power factor angle which is equal to tan inverse of omega L/R is called the power factor angle or impedance angle. And we have another voltage that is E that is a DC voltage, the DC voltage will only see the resistance in the steady state. So we have this E here and E is opposing the flow of current. If you see Vs is helping the flow of current and E is opposing the flow of current here. So E will have -E/Ra and then we have a transient component which is A e to the power -t/tau and tau here is the time constant this is omega La/Ra and time constant which is La/Ra. We can call this to be the armature time constant which is tau a. So this is the solution of this equation. We have a steady state component and we have a transient component and the transient component will die down to 0 as t tending to infinity. So we stop here for todays lecture. We will try to find out this constant A in the next lecture.