Phase Control of Delta

Phase Control of Delta-Configured Motors

In a previous article, six-step phase control of Y-configured motors was worked out in detail. Vector control of delta-configured windings is the dual, and details of phase control are presented here.

The D three-phase motor winding configuration is the dual of the Y configuration. Around the D loop, shown above, the polarities of the induced-voltage generators of the phase-windings aid, so that the + terminal of one connects (through the winding resistance) to the – terminal of the next generator. Drive is applied directly to phase-winding vectors A, B, and C, accessed by terminals X, Y, and Z. A is driven when drive voltage, v, is connected to terminal X and terminal Z is grounded. This leaves terminal Y open, with open-node voltage v_x to ground.

The difference of phase-winding vectors B and –C are sensed at the open node. Phase-windings B and C are in series, shunting A. At the connection between them - the open node, Y - the voltage, v_x is:

By adding Y and Z phase-winding voltage vectors algebraically, as shown on the vector diagram below, YZ = Y – Z corresponds to waveform v_YZ but is shown vectorially as an amplitude and phase. Half of v_YZ and half of the PWMed drive to winding X appears as v_x.

The driven winding-pairs are shown between vectors in the 60-degree phase intervals on the diagram. A winding pair is driven so that the step driving it is centered about its peak induced voltage. For instance, A crosses zero at 0° on the vector diagram. Then 60° later, its drive step occurs because its induced voltage is maximum for the interval from 60 to 120 degrees. The diagram is marked during this interval with XZ as the driven terminals, which correspond to an opposing voltage drive to A. Similarly, each of the other phase-windings and their opposites correspond to drive terminal-pairs.

The drive-steps (60° phase intervals) of the vector diagram above and the +zc-sensed vector that correctly advances the phase-step for CCW rotation to the next step is listed in the following table.

Drive Vector	Terminals	Sense Vector
A	XZ	B
–C	YZ	–A
B	YX	C
–A	ZX	–B
C	ZY	A
–B	XY	–C

The vectors sensed on the open nodes appear 90° ahead of the driven phase-windings. For example, when phase-winding pair ZY is driven, the +zc of A is (somehow) sensed to start the next step, the drive to XY. Unfortunately, the voltage vectors appearing at the open nodes occur midway through the steps, and as such, are not directly useable for advancing phase steps. For instance, when A is being driven by XZ, the zero crossing that occurs is BC which is midway through the XZ step. The desired phase for a zero-crossing is at B, which starts drive to –C across terminals YZ.

To use the open-node sensed voltage v_x to advance phase to the next step, which should occur at the phase of Y, two problems exist:

The positive zero-crossing (+zc) of v_x occurs 30 degrees early.
The waveform is corrupted by PWM noise.

The second problem can be solved by constructing a virtual neutral node with equal-value resistors connected each to one of the three motor terminals. Their common node is the virtual neutral node, N'. It has a voltage of:

Then by using v_N' as the reference input to the phase-advance comparators, and comparing to v_x, the transitions occur at the zero-crossing of the two waveforms, or when their difference is zero. Substituting and subtracting,

The PWM noise of v has been common-moded out, though the "mid-step zero-crossing" problem still exists. This problem is easily solved by a new method of six-step phase control developed by Innovatia, to be revealed in the future.

Closure

The same circuitry can drive both D and Y-configured motor windings, but the phase tables differ by a phase offset, and must be taken into account in the design. A microcontroller input bit-line can be jumpered to indicate Y or D, and the corresponding phase table for drive advancement and sensing can be used.

Why use the D configuration at all if it is the dual of the Y? Although the two are functionally equivalent, the D has 1/3 the impedance and is better suited for low-impedance (low voltage, high current) applications. When used with winding-sensed (sensorless) control, the hardware for both configurations is identical.