EXPERIMENT NO: 1
Object
To study the single phase series and parallel Inverter.
Apparatus
1. Single phase series inverter kit (10 V/2 Amp)
2. D.C. Power supply (11V/2 Amp)
3. Firing circuit
4. CRO
5. Load
Theory
Basic Series Inverter Circuit
Fig.1 shows the circuit of a series inverter. The commutating elements L and C are such that R, L and C form an under damped circuit. The capacitor has an initial voltage Ec, Thyristor Th1 is turned on first by an external pulse. Since Th1 is already forward biased (due to dc voltage V), Th1 starts conducting and a current I flows in the circuit through Th1, C, L and load.
Because of under damped nature of the circuit the current is not constant but has the wave shapes as shown in fig.2. It rises to maximum value and then decreases to zero. When the current is at its peak value, the voltage across capacitor is nearly equal to supply voltage V. After this the current starts decreasing but the voltage across the capacitor continues to increase as it is still getting charged. When the current becomes zero the voltage across capacitor is maintained at V+Ec. The voltage across L is zero. The time interval ab must be more than time toff of the thyristor. This is necessary to ensure that the stored charges in Th1 are reduced to zero so that at point b Th1 is in completely off state. At point b when Th2 is turned on by an external gate pulse the anode of Th2 is positive (with respect to cathode) due to charge on capacitor Th2 starts conducting. The capacitor discharges and the current I flows through the circuit in the direction opposite to that in the start. The current reaches its negative peak value and then decreases to zero at point c when Th2 is turned off. The above sequence of operation is repeated in the next cycle when Th1 is turned on. The frequency of the output voltage is –
Hz
Where T/2 is the time period of oscillation and Toff the time gap between turn off of one thyristor and turn on of the second thyristor, Also
![](file:///C:/DOCUME%7E1/Student/LOCALS%7E1/Temp/msohtml1/01/clip_image004.gif)
When Th1 is turned on, KVL equation is
![](file:///C:/DOCUME%7E1/Student/LOCALS%7E1/Temp/msohtml1/01/clip_image006.gif)
Where Ec is the initial voltage across capacitor,
Taking laplace transform
![](file:///C:/DOCUME%7E1/Student/LOCALS%7E1/Temp/msohtml1/01/clip_image008.gif)
Since the circuit is under damped, the solution of above equation is
![](file:///C:/DOCUME%7E1/Student/LOCALS%7E1/Temp/msohtml1/01/clip_image010.gif)
Where –
![](file:///C:/DOCUME%7E1/Student/LOCALS%7E1/Temp/msohtml1/01/clip_image012.gif)
![](file:///C:/DOCUME%7E1/Student/LOCALS%7E1/Temp/msohtml1/01/clip_image013.gif)
![](file:///C:/DOCUME%7E1/Student/LOCALS%7E1/Temp/msohtml1/01/clip_image014.gif)
![](file:///C:/DOCUME%7E1/Student/LOCALS%7E1/Temp/msohtml1/01/clip_image015.gif)
![](file:///C:/DOCUME%7E1/Student/LOCALS%7E1/Temp/msohtml1/01/clip_image016.gif)
![](file:///C:/DOCUME%7E1/Student/LOCALS%7E1/Temp/msohtml1/01/clip_image017.gif)
![](file:///C:/DOCUME%7E1/Student/LOCALS%7E1/Temp/msohtml1/01/clip_image018.gif)
![](file:///C:/DOCUME%7E1/Student/LOCALS%7E1/Temp/msohtml1/01/clip_image019.gif)
![](file:///C:/DOCUME%7E1/Student/LOCALS%7E1/Temp/msohtml1/01/clip_image019.gif)
![](file:///C:/DOCUME%7E1/Student/LOCALS%7E1/Temp/msohtml1/01/clip_image019.gif)
![](file:///C:/DOCUME%7E1/Student/LOCALS%7E1/Temp/msohtml1/01/clip_image020.gif)
Fig 1.
This series inverter circuit has the following drawbacks:--
1.) The maximum possible frequency is limited to the damped frequency of oscillation, i.e.
. This is due to the fact that Th1 must be turned off before Th2 is turned on. Otherwise the supply voltage V will be short circuited.
2.) When frequency is less than the damped frequency, the distortion of the output voltage waveform is high because Toff is larger in comparison with ON time of thyristor.
3.) The circuit components carry load current continuously. The capacitor supplies the load current in every negative half cycle. Thus the current rating of the commutating elements L and C is high.
4.) The source supply the load intermittently (only during positive half cycle). Therefore source should have a high harmonic content.
5.) The maximum load current depends on the load resistance. Therefore, output regulation of the inverter is poor.
The drawbacks 1 and 5 can be removed by modifications of the circuit.
Modified Series Inverter:-
Fig. 3 shows a modified series inverter. It has two mutually coupled and exactly similar inductors L1 and L2. when Th1 is turned on, the current I1 begin to increase in the positive half cycle, the voltage across the inductor L1 will be positive with polarity as shown. This voltage induced across L1 will add to the capacitor voltage in reverse biasing Th2. The circuit conditions and analysis is exactly the same as incase of simple inverter. The advantage in having two inductors is that Th2 can be turned on even before Th1 has turned off. Thus the output frequency can be adjusted to a higher value because time Toff in fig 2 can be eliminated, In fig 1 this action results in short circuit is avoided because of the presence of inductors L1 and L2. If Th2 is turned on just before turning off of Th1 the voltage across capacitor C would be somewhat less than the maximum value V+Ec and the current I, will be near to its zero value. Therefore, a voltage equal to capacitor voltage minus the voltage across load will appear across L2 since L1 is mutually coupled with L2 the same voltage will be induced across L1 also, thus the cathode of Th1 will be raised to a higher voltage than the anode and Th1 will be turned off. A similar action will reverse bias Th2 at the end of negative cycle and turn it off. Thus the time interval Toff can be avoided giving a higher output frequency.
Fig 4 shows a further improvement in the series inverter. This circuit uses two mutually coupled inductors and two capacitors. In this circuit power is drawn from the source battery during both half cycles. Thus the intermittent operation of battery is avoided.
Assume that initial charge across C2 is Ec with polarity as shown. Capacitor C1 will be charged to V+Ec in the opposite direction. When Th1 is turned on, the load current iL will have two parallel paths.
Current i1 will flow from battery, through Th1, L1, load and C2. The current i2 will flow from upper plate of C1, through Th1, L1 and load. The driving voltage V+Ec and circuit elements for the currents i1 and i2 are exactly similar. Therefore, current i1 and i2 are equal. At the end of positive half cycle the load current iL would be zero and Th1 would be turned off. Voltage across capacitors would be reversed. An exactly similar operation would occur in the negative half cycle. In each half cycle the load current would be supplied by battery and the other half by one of the capacitors. The maximum forward off state voltage across each thyristor is V+Ec and the peak reverse voltage is Ec.
The waveforms are shown in fig 5.
LOAD
![](file:///C:/DOCUME%7E1/Student/LOCALS%7E1/Temp/msohtml1/01/clip_image029.gif)
PRECAUTIONS
If the inverter frequency increases above the resonant frequency of the power circuit commutation will fail. Then switch off the dc supply, reduce the inverter frequency and try it again if you do not get the results, check the input fuse and try again.