Subject : Power Electronics
Unit : DC to AC Converters
Determination Of Load Phase-Voltages
Determination of load phase – voltages:
Fig: Schematic load circuit during conduction of Sw5, Sw6 and Sw1 Fig: Schematic load circuit during conduction of Sw6, Sw1 and Sw2
- The three load terminals are connected to the three output points (A, B, C) of the inverter. The neutral point ‘N’ of the load is deliberately left open for some good reasons.
- The load side phase voltages V_{AN}, V_{BN }and V_{CN }can be determined from the conduction pattern of the inverter switches. For 0≤ωt≤π/3, switches Sw5, Sw6 and Sw1 conduct. Under the assumption of ideal switches the figure of “Schematic load circuit during conduction of Sw5, Sw6 and Sw1” represents the equivalent inverter and load circuit during the time interval 0≤ωt≤π/3.In the equivalent circuit representation the non-conducting switches have been omitted and a cross (X) sign is used to represent a conducting switch.
- For a balanced 3-phase load the instantaneous phase voltage waveforms have been derived below for the following two cases (i) when the 3-phase load is purely resistive and (ii) when the load, in each phase, consists of a resistor in series with an inductor and a back e.m.f. In both the cases the equivalent circuit of “Schematic load circuit during conduction of Sw5, Sw6 and Sw1” has been referred to derive the expression for load-phase voltage.
- For case (i), when the load is a balance resistive load, it is very easy to see that the instantaneous phase voltages, for 0≤ωt≤π/3, will be given by V_{AN }= 1/3 E_{dc}, V_{BN }= -2/3 E_{dc}, V_{CN }= 1/3 E_{dc}.
- For case (ii), the following circuit relations hold good.
Where, i_{A} , i_{B} , & i_{C} are the instantaneous load-phase currents entering phases A, B and C respectively. E_{A} , E_{B} & E_{C} are the instantaneous magnitudes of load phase-emfs.
- R and L are the per-phase load resistance and inductance that are connected in series with the corresponding phase-emf. Since the load is balanced (with its neutral point floating) the algebraic sum of the instantaneous phase currents and the phase emfs will be zero.
- Accordingly
- Rearranging,
- Thus the instantaneous magnitudes of load phase voltages, in case of a more general (but balanced) R-L-E load are same as in case of a simple balanced resistive load.
- During π/3≤ωt≤2π/3, when the switches Sw6, Sw1 and Sw2 conduct. The instantaneous load phase voltages may be found to be V_{AN }= 2/3 E_{dc}, V_{BN }= V_{CN }= -1/3 E_{dc}. The load phase voltage waveforms for other switching combinations may be found in a similar manner.
- Two of the phase voltages, V_{AN} and V_{BN}, along with line voltage V_{AB} have been plotted over two output cycles in Fig. of “Schematic load circuit during conduction of Sw6, Sw1 and Sw2”.
- Voltage V_{BN} is similar to V_{AN} but lags it by one third of the output cycle period. Further, it can be verified that the load phase voltage V_{CN} also has a waveform identical to the two other phase voltages but time displaced by one third of the output time period. V_{CN} waveform leads V_{AN} by 120 degrees in the time (ωt) frame. The fundamental component of the phase voltage waveforms will constitute a balanced 3-phase voltage having a phase sequence A, B, C. It may also be recalled that by suitably changing the switching sequence the output phase sequence can be changed. The phase voltage waveform shows six steps per output cycle and is also referred as the six-stepped waveform.