Thursday, December 9, 2010

Single Phase Drives - Low Speed Control Mode

Power circuit for single phase drive - low speed control mode

At low speeds, motor voltage V should not have lower-order harmonics. An ideal would be a pure sinusoidal voltage but a compromise is acceptable.

The square wave voltage used in the high speed mode contains lower order harmonics of order 3,5,7,9...etc. So we con not use it for low speed operations. If attempted we will get some wobbling speed perturbations at low speeds.

We use switching strategy known as PWM (Pulse Width Modulation) to deliver near sinusoidal voltage for the motor. We have two operations of PWM.

(a). Bipolar PWM
(b). Unipolar PWM

(a). Bipolar PWM

In this PWM, we treate Q1 and Q2 as one pair and Q3, Q4 as the other pair. These pairs are operated in complementary way, so only one switching signal is necessary.

Bipolar switching signal

Switching signal is generated by a PWM modulator. This contains a high frequency triangular waves generator (carrier), a low frequency sinusoidal wave generator (reference signal) and a comparator.

Bipolar PWM modulator circuit

Ec - Carrier amplitude
Er - Reference amplitude
fc - Carrier frequency
fr- Reference frequency

Ec is constant and fixed.
Er is adjustable such that 0 <= Er <= Ec.
fc is fixed (but provisions exist to change it in steps).
fr is adjustable (fr will be frequency of output voltage V, so a range about 0 -200 Hz will be adequated).

Modulator has two important parameters

1. Depth of modulation m
2. Carrier ratio p

m = Er/Ec

p = fc/fr

Range of m is 0 to 1. Value of p should be an odd integer for best results and its values should be as large as possible. (A figure around 100 would be sufficient).

                                   Vd    if S is High (e.g. Vr > Vc)
V (Motor voltage)
                                  -Vd    if S is Low (e.g. Vr < Vc)

Fundamental components of V

The motor voltage V has a dominant fundamental components and very high order harmonics (which are less influencing the motor operation). Current wave form I produce by V is almost sinusoidal due to the filtering by motor induction L.

We can quote mathematical expressions for the amplitude of fundamental V, and the order of harmonics in V.

r.m.s value of fundamental component of  V =

Order of harmonics present in V =
n+k = Odd integer

Harmonic spectrum of bipolar PWM

To control output voltage we adjust m
To control motor frequency we adjust fr
To regulate harmonics we use p

Software program for PWM modulator

Note: We have PWM integrated circuits to implement the PWM modulator in hardware. If necessary we may implement in software tool.

(b). Unipolar PWM

This PWM produces still better quality motor-voltage. It removes the clusters of harmonics present at the first-multiple of p, so the significant harmonics start at the second-multiple of p.

In unipolar PWM we move away from the pairing switches, instead treat-inverter-legs separately. Leg A needs switching signal Sa and leg B need Sb, so two switching signals are necessary. These are generated in the PWM modulator, now containing 2 numbers of comparators (among other units).

Unipolar PWM switching circuit

              Vd         if Q1 ON and Q2 ON
V      =   -Vd       if Q3 ON and Q4 ON
              0           Otherwise

     Unipolar PWM modulator switching signals

Typical motor voltage wave form produced by uniform PWM
Unipolar PWM motor voltage waveform removes negative excursions during the positive half cycle and positive excursions during the negative half cycles.

r.m.s value of fundamental component of V =

Same as in bipolar PWM.

So we get equivalent r.m.s. voltage (as in bipolar PWM) and lesser harmonics. Switching frequency is however now two times carrier frequency.

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