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Phasor rotation

  1. Nov 23, 2011 #1
    When phasors are used,for example to illustrate some of the properties of waves,all of the texts seem to emphasise that the phasor rotates anticlockwise.Why anticlockwise?I have always assumed that the direction is just a convention...or am I missing something?If it is a convention then does the choice of anticlockwise have any advantages over clockwise?Thanks to anyone who replies.
    Last edited: Nov 23, 2011
  2. jcsd
  3. Nov 23, 2011 #2
    It's probably a convention, like so many other things.

    By the way, why do degrees start at 3 o'clock and increase counterclockwise? Maybe these degrees are the ones to blame!

    In any case, there ARE phasors that rotate in the clockwise direction.

    I am an electrical engineer and learned about phasors and symmetric components in the power systems class a couple of decades ago...this is what I remember.

    Example, if you have a 3-phase power system, it can be handled and represented with a single phasor per quantity when things are nice and balanced; but when something happens (a short circuit, lightning, etc) and the system becomes unbalanced, it is difficult (impossible with phasors) to handle and so it is decomposed into its 3 symmetric components...these symmetric components can once again be handled with phasors as "things" are balanced within the corresponding frame of reference...the thing is that I said they are 3 symmetric components, they are referred to as the positive sequence, negative sequence and zero sequence components...the positive one rotates counterclockwise, the negative rotates clockwise and the zero does not rotate at all. The linear combination of these symmetric components models the original system.

    A phasor represents a single pure sinusoidal quantity so that when there is a fault and things are momentarily not purely sinusoidal, an n-phase system can be decomposed into its n symmetric components that when combined can represent any state of the original system via these symmetric components which CAN be handle with phasors.

    I hope this help and did not make it too confusing.
  4. Nov 23, 2011 #3


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    I think it's probably because we originally chose Right and Up for our +X and +Y cartesian axes and gradient is the angle 'upwards from the horizontal'. That gives you angles that increase from zero to 90 in an anticlockwise direction. The rest just follows.
  5. Nov 24, 2011 #4
    Thanks gsal and sophiecentaur.
  6. Nov 25, 2011 #5

    Claude Bile

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    We can classify frequencies as being positive or negative depending on what way the phasor rotates; the direction we nominate as being positive is quite arbitrary.

  7. Nov 25, 2011 #6


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    Not quite arbitrary. For a frequency higher than the reference frequency (at which the axes are 'frozen', a higher frequency will be represented by a phasor which is rotating anticlockwise and vice versa because of the rate of change of phase relative to the reference.
  8. Nov 25, 2011 #7
    While the statement above is true for individual signals...

    It is possible to make higher frequency signals show up rotating counterclockwise respect to the frame of reference...this can be accomplished via linear combination of spatially shifted higher frequency signals.

    This is not as weird as it may seem...it is happening right now, somewhere in the world.

    I am talking about a 3-phase electrical generator at some power plant that might not be working under perfect conditions and hence having non-purely sinusoidal waves through its winding...under these conditions, the waves can be decomposed (fourier) into purely sinusoidal ones starting with one at the fundamental frequency (f) and the rest at higher frequencies (2f, 3f, 4f, 5f, 6f, 7f...).

    BUT, when we are talking about a 3-phase system, we have 3 sets of these signals that are (electrically) phase shifted 120 degrees (360/3) and being applied to windings ("mechanically", physically) located 120 degrees (for 2-pole generator) away from each other...when you add the signals vectorially, the resultant may rotate counterclockwise (CCW) or clockwise (CW) respect to the fundamental...

    ...for example, say the fundamental is rotating CCW at an angular velocity of 1f:
    • when you add the 5th harmonics from all 3 phases, the resultant will rotate CW with a velocity of 5f
    • when you add the 7th harmonics from all 3 phases, the resultant will rotate CCW with a velocity of 7f
  9. Nov 25, 2011 #8


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    The way that a sinusoidal signal is generated is not relevant to its rate of change of phase. The 5th harmonic will have a frequency of 250 Hz (or 300 in the US) the phase of such a high frequency signal is advancing five times faster than the fundamental. ω is d∅/dt. It can't be drawn easily on a phasor diagram because the relative phase is increasing so fast but the direction that the phasor points must be anticlockwise and the rate would be at 4X the fundamental (i,e, at the difference frequency). If you have found a simulation that shows you otherwise then the reason is due to sub sampling problems and aliasing. The analysis is pretty clear, however, as shown above.
    Last edited: Nov 25, 2011
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