Subject : Power Electronics
Unit : DC to AC Converters
Smoothly Rotating Space Voltage Vector From Inverter
Smoothly Rotating Space Voltage Vector from Inverter:
Fig: The voltage space-vectors output by a 3-phase inverter
- The continuously varying sinusoidal waveforms results in a space voltage vector of fixed magnitude rotating at fixed (synchronous) speed in the space.
- If the inverter could have produced ideal sinusoidal 3-phase voltages, the resultant space voltage vector would have also moved smoothly in space with constant magnitude and constant angular speed. However by now the reader would know that the practical power electronic inverter could never produce the perfectly ideal sinusoidal voltages.
- In fact when the inverter switches from one active state to another, the space voltage vector changes its direction abruptly, the abrupt change in direction being in multiples of 60 electrical degrees. If at a time only one bit of the inverter switching word changes (i.e., only one leg of the inverter changes the switching state) the abrupt change in space vector direction is by 60 electrical degrees.
- Knowing that the inverter cannot produce ideal sinusoidal voltage waveforms, a good PWM inverter aims to remove low frequency harmonic components from the output voltage at the cost of increasing high frequency distortion. The high frequency ripple in the output voltage can easily be filtered by a small external filter or by the load inductance itself.
- In terms of voltage space vectors the above trade-off between low and high frequency ripples means that the resultant voltage vector will have two components;
- A slowly moving voltage vector of constant magnitude and constant speed superimposed with
- A high frequency ripple component whose direction and magnitude changes abruptly.
- The space-vector PWM technique aims to realize this slowly rotating voltage space vector (corresponding to fundamental component of output voltage) from the six active state voltage vectors and two null state vectors. The active state voltage vectors have a magnitude = E_{dc }and they point along fixed directions whereas null state vectors have zero magnitude.
- The voltage space-vector plane formed by the active state and null state voltage vectors. The null state voltage vectors V_{7 }and V_{8 }are each represented by a dot at the origin of the voltage space plane. The switching word for V_{7 }is 000, meaning all lower side switches are ON and for V_{8 }is 111, corresponding to all upper side switches ON.
- The active-state voltage space vectors point along directions. A regular hexagon is formed after joining the tips of the six active voltage vectors. The space-plane can be divided in six identical zones (I to VI). The output voltage vector from the inverter (barring high frequency disturbances) should be rotating with fixed magnitude and speed in the voltage plane.
- Now it is possible to orient the resultant voltage space-vector along any direction in the space plane using the six active vectors of the inverter. Suppose one needs to realize a space voltage vector along a direction that lies exactly in the center of sector-I of the space-plane.
- For this the inverter may be continuously switched (at high frequency) between V_{1 }and V_{2 }active states, with identical dwell time along these two states. The resultant vector so realized will occupy the mean angular position of V_{1 }and V2 and the magnitude of the resultant vector can be found to be 0.866 times the magnitude of V_{1 }or V_{2 }(being the vector sum of 0.5 V_{1 }and 0.5 V_{2}). Further, the magnitude of the resultant voltage vector can be controlled by injecting suitable durations of null state.