Phasor Leading and Lagging Angles

[XPTPCREWX]

Consider two voltage phasors:

V1 = 1 volt @ 50°, and
V2 = 1 volt @ 30°.

It follows then that the relative phase shift between these two phasors can be expressed by any of the four following descriptions in terms of leading and lagging angle relationships.

1.) V1 Leads V2 by 20°
2.) V1 Lags V2 by 340°
3.) V2 Leads V1 by 340°
4.) V2 Lags V1 by 20°

My question is: By using the above lead/lag positive angle displacements, does is make any sense or is it possible to instead express these same angles in terms of their corresponding negative angle displacements? If you could express it in terms of negative angles how would it be done? Would it negate a lead or lag?

ie. Modify description 1.) to V1 Leads V2 by 20° OR EQUIVALENTLY -340°

I just want to know if this is legal mathematically/conceptually or even makes sense. Some links or references to conventions or interpretations would be nice. Thanks in advance.

 

[NascentOxygen]

V1 lags V2 by 340°
V1 lags V2 by -20°

V2 leads V1 by 340°
V2 leads V1 by -20°

The sinusiod is cyclic, so the general expression is V1 Leads V2 by (20° + n360°) for any integer n ≥ 0.

 

[XPTPCREWX]

V1 lags V2 by 340°
V1 lags V2 by -20°

V2 leads V1 by 340°
V2 leads V1 by -20°

The sinusiod is cyclic, so the general expression is V1 Leads V2 by (20° + n360°) for any integer n ≥ 0.

1.) Can you provide a reference about this for phasors?
2.) If n≥0 why did you express "V2 leads V1 by -20°"
3.) The terms "Lead" and "Lag" already contain information about which way to traverse the angle from the REFERENCE phasor. What does the negative mean in "V2 leads V1 by -20°"?

Typically V1 lags V2 by 20° means rotate C.W. starting from phasor V2 (REFERENCE) by 20°. So in this case we must traverse the plane in the negative angle (lagging or C.W.) direction, however i don't understand saying both leading or lagging AND -20°. It seems that this would be a double negative. Can you clarify what you mean by this?

 

[NascentOxygen]

For sources, use google.

For any leading angle you can throw in an extra +n360°,
for any lagging angle you can include an additional -n360°.

Double negatives are fine, though best used judiciously. Leading by -20° is equivalent to lagging by +20°. But of course, for clarity it is best to keep to a positive angle and choose the appropriate lead/lag word to fiit.

 

[pmacias]

I can confirm that it is possible to express the angles in terms of negative displacements. This is a common practice in phasor analysis, where the negative angle displacements represent the opposite direction of rotation. In this case, it would be equivalent to saying that V1 lags V2 by 340° or that V2 leads V1 by -340°. This does not change the lead or lag relationship between the two phasors, as the magnitude of the angle difference remains the same.

Mathematically, this is perfectly valid as it follows the principles of vector addition and subtraction. However, it is important to note that the convention for expressing angles in phasor analysis is to use positive angles for lead and negative angles for lag. This convention is widely accepted and used in the field of electrical engineering and power systems analysis.

In terms of references, you can refer to any standard textbook or reference material on phasor analysis, such as "Electric Circuits" by James W. Nilsson and Susan A. Riedel or "Power System Analysis" by John J. Grainger and William D. Stevenson Jr. These resources will provide a more detailed explanation and examples of using both positive and negative angle displacements in phasor analysis.