\(dq\) frame

\(dq\) frame (closeup)

\(\alpha\beta\) frame

waveforms
(ABC)

This is an interactive visualization of three-phase overmodulation.

The two outer frames show the synchronous \(dq\) frame and the stationary \(\alpha\beta\) frame, from the viewpoint of the \(dq\) frame (left) and \(\alpha\beta\) frame (right). The middle frame is a zoomed-in view of the \(dq\) frame. The hexagon represents the limits of applied voltage using a three-phase bridge; the point at the vertex labeled \(\alpha\) represents the A phase switched to full positive voltage (the DC+ node) and the B and C phases switched to full negative voltage (the DC− node). The circumscribed outer circle C2 represents the boundary outside which applied voltages are always unachievable. The inscribed inner circle C1 represents the boundary inside which applied voltages are always achievable. The area between circles may be achievable or unachievable depending on electrical angle.

The small open circle represents a fixed desired point \(P\) in the \(dq\) frame. The small black dot represents the actual applied voltage \(P'\) after zero-sequence modulation (the conventional midpoint clamp SVPWM is used) and clipping. For points inside circle C1, the two are at the same point: actual applied voltage equals desired voltage. For points outside circle C1, the two diverge for part or all of the electrical cycle as the applied voltage is limited to the hexagon boundary. Points \(P\) and \(P'\) are joined to the origin with a solid gray line and to each other with a dashed gray line to highlight two effects of this type of clipping:

- the error between \(P\) and \(P'\) is perpendicular to the hexagon boundary, minimizing the magnitude of error
- the electrical angle of \(P\) and \(P'\) may be slightly different, showing that clipping may cause a change in applied electrical angle

The trajectory of point \(P'\) is highlighted by a dark green curve. At its mean value in the \(dq\) plane is a dark green dot, representing the mean \(dq\)-voltage applied over an electrical cycle for fixed desired voltage \(P\). A light green ellipse is drawn to show the statistical behavior of this trajectory (major and minor axes indicating RMS variation of applied voltage over a cycle, in the \(d\)- and \(q\)-axes).

You can change point \(P\) by clicking or dragging the mouse within the \(dq\) frame, or by using the arrow keys to adjust incrementally. (Click on one of the reference frame graphs first.)

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