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Re: [Phys-L] Power loss in transmission lines

On 05/23/2014 04:42 AM, Folkerts, Timothy J wrote:
The "loss fraction" on the page you mention is the ratio of
(power lost) / (power delivered)

Aha. Good catch.

If we take my formula out of context

Ploss / P = ΔV / V [1]

it could be interpreted either way. It could be

Ploss / Psource = ΔV / Vsource [2]

which what I intended. This is what we normally call
the fractional loss. It is also equal to (1-efficiency).
See also diagrams below.

I didn't notice it at first, but the reference
uses the same symbols (at least on the LHS) but with
a different meaning, equivalent to

Ploss / Pload = ΔV / Vload [3]

The reference calls this the loss fraction, but IMHO that
is not a wise definition. The best I can say is that when
the efficiency is not low, it doesn't much matter whether
you interpret [1] as [2] or [3].

OTOH, when the efficiency is low, equation [3] produces a
counterintuitive and unhelpful result. It can greatly
exceed unity ... but for the most trivial of reasons.
It's just not a good way to define fractional loss.


I assume the original question meant to ask about equation
[2]. In that case I stand by the "spirit" of the answer I
gave on 05/23/2014 02:11 AM.

In any case, it would have been a much better answer if I
had been more explicit, writing equation [2] instead of
equation [1]. I also should have drawn the diagram:

Vsource ----------ZZZZZ-------------Vload
Z [4]
ground ----------------------------ground
return leg

ΔV := Vsource - Vload [5]

This assumes there is negligible loss in the return leg, which
is possibly reasonable in a two-phase distribution scheme. If
this is not negligible, we can draw a different diagram and
redefine things such that equation [2] remains true:

Va ----------ZZZZZ-------------Vc
Z [6]
Vb ----------ZZZZZ-------------Vd

Vsource := Va - Vb
Vload := Vc - Vd [7]
ΔV := Vsource - Vload
ground := undefined and unnecessary

If the intent was to ask about equation [3], then we have
*two* valid explanations for why the ratio can exceed unity:
-- one trivial reason, having to do with the peculiar
definition, and
-- one nontrivial reason, having to do with the possibility
of non-passive loads.


Pedagogical and practical lesson: It pays to be really
explicit about what the symbols mean. In simple cases the
meaning can be conveyed by using sufficiently elaborate names,
such as Vsource (rather than simply V). In other cases this
quickly becomes unwieldy, and it becomes necessary to have
a /legend/ or /glossary/ or /diagram/.

As a corollary: In electronics problems, it pays to draw the
circuit diagram.

Students don't believe this the first eleventeen times you
say it, but it's true: Draw the diagram!

Note that sometimes you need both a diagram (e.g. [6]) and
a legend (e.g. [7]).

Pedagogical remark: On exercises and quizzes, require students
to exhibit an explicit legend, glossary, and/or diagram. Make
it part of the grading scheme. Mention this in the instructions
the first eleventeen times, but by the end of the course is
should go without saying.