APPLICATION
The meaning of P, Q, S, η, cos ϕ, PF
and THD for energy efficient lighting
by Chris Yelland, EE Publishers
In studying the recent “Electricity Regulations for Compulsory Norms and Standards for Reticulation Services” published in Government
Gazette No. 31250 on 18 July 2008, one has to wonder whether the input of technical experts has been seriously considered.
In the face of the severe generation capacity
shortages in South Africa, presumably these
regulations were promulgated with the
intention of ensuring stability of electricity
networks, avoiding emergency load
shedding and blackouts, saving electrical
energy [kWh], and facilitating the control
and reduction of active and apparent
power demand.
However in doing this, one may wonder
if the basic concepts and definitions of
real power P [W], reactive power Q [var],
apparent power S [VA], energy [Wh],
efficiency η, displacement power factor
cos ϕ , apparent power factor PF and
total harmonic current distortion I THD are
understood and appreciated.
Take, for example, the new energy efficiency
regulation in respect of lighting, which states
in just one compact sentence:
“Energy efficient fittings must be used in all
buildings except where a specific fitting is
required for some purpose and the nature
of the purpose does not allow for an energy
efficient fitting.”
Vague? Indeed! And moreover, nowhere
in the regulations is the term “energy
efficient” actually defined. One may expect
that perhaps the efficiency of light fittings
should be specified in terms of luminous flux
emitted per watt of electrical power input
[lumens/W] at a defined minimum power
factor. Or is this too complex a concept?
The public may even (wrongly) believe
that a compact fluorescent lamp (CFL) is
the most efficient light source out there,
whereas, in fact, high pressure sodium and
metal halide light sources are far more
energy efficient.
Some people may also confuse energy
efficiency with reducing power demand
and energy consumption by reducing
the power rating and light output of the
light source. They forget that improving
the energy efficiency means reducing the
power demand and energy consumption,
while maintaining (or even improving) the
light output.
Furthermore, the regulation does not specify
any implementation time-frame, whether
the regulation applies to new installations
or must be retro-fitted toexisting installations,
or the persons or bodies responsible for its
implementation (building owners, lessors,
users, electricity distributors, etc.)
Whatever, if the term “energy efficient” isn
not somewhere defined and referenced
in the regulations, it strikes me that this
is a vague, unenforceable and truly
meaningless regulation! But let us investigate
this subject just a little further...
Sinusoidal fundamental frequency
voltages and currents, and displacement
power factor
In considering sinusoidal power frequency
currents and voltages (50 Hz in South Africa),
we have the concept of displacement
power factor cos ϕ, where ϕ is the phase
angle between the sinusoidal voltage and
current waveforms.
When the current waveform “lags” the
corresponding voltage waveform, as in the
inductive circuit of Fig. 1a, the power factor
Fig 1a: Lagging inductive circuit.
Fig 1b: Leading capacitive circuit.
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(which which always ranges from 0 to 1) is
said to be “lagging”, while if the current
waveform “ leads ” the corresponding
voltage waveform, as in the capacitive
circuit of Fig. 1b, the power factor is said
to be “leading”.
From the definition of instantaneous power
p(t) = i(t) . v(t), some mathematics reveals
that for a sinusoidal voltage and current, the
following equations apply for the average
values:
Active power P [W]:
(1)
Reactive power Q [var]:
(2)
Apparent power S [VA]:
(3)
Displacement power factor cos ϕ
(4)
These equations can be shown
diagrammatically in Fig. 2.
Harmonics, total harmonic current distortion
ITHD and apparent power factor PF
The power systems concept of displacement
power factor cos ϕ, with ϕ being the phase
angle between a sinusoidal fundamental
frequency AC current and voltage
waveforms, and Eqns. 1 to 4 (above),
APPLICATION
apply in environments where the harmonic
distortion is relatively low.
The mathematics gets much more complex
when there is significant distortion of the
waveforms from sinusoidal, and where
Fourier analysis reveals significant higher
frequency harmonic content.
In fact, the traditional concepts of leading
and lagging displacement power factor
cos ϕ and reactive power Q become
somewhat meaningless outside of the
mains frequency domain, and in particular
where the voltage is essentially a mains
frequency sinusoid while the current
waveform is highly distorted.
Fig. 2: Vector diagram showing the relationship between of active power P, reactive power Q, apparent
power S and displacement power factor cos ϕ, for AC sinusoidal current and voltage waveforms.
In this case, the phase angle ϕ between the
fundamental frequency rms voltage V1 rms,
and corresponding fundamental frequency
rms current IIrms, and displacement power
factor cos ϕ , is of limited value and
meaning, and one should rather consider
the following definitions:
Power P [W]:
Rms voltage [V]:
(5)
Rms current [A]:
(6)
Fig. 3: Vector diagram showing the effect of the power factor correction capacitor in improving the
displacement power factor cos ϕ, and reducing the apparent power S (and therefore the current
drawn from the supply I1 rms).
Apparent power S [VA]:
(7)
(8)
Total harmonic current distortion ITHD
(9)
Apparent power factor PF
(10)
Where the voltage waveform is sinusoidal
(with little or no harmonic distortion) then the
apparent power factor PF is dependent on
both the displacement power factor cos ϕ
and the total harmonic current distortion ITHD,
according to the following equation:
Apparent power factor PF:
(11)
Thus it can be seen that where the current
and voltage are sinusoidal fundamental
frequency waveforms only, the total
harmonic current distortion ITHD is zero, and
the apparent power factor PF = cos ϕ.
However, when the current waveform is
non-sinusoidal, the total harmonic current
Fig. 4: The current waveforms of a typical, low-cost CFL.
distortion I THD increases above zero, and
this causes the apparent power factor PF
to decrease lower than the displacement
power factor cos ϕ , as indicated in
Eqn. 11.
This is consistent with Eqns. 7, 8 and 10.
As the harmonic content of the current
waveform increases, this causes I rms to
increase above that of the fundamental
rms current I 1 rms (Eqn. 7), and thus the
apparent power S increases (Eqn.8), while
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the apparent power factor PF decreases
(Eqn. 10) below the displacement power
factor cos ϕ.
Linear fluorescent lamps with magnetic
ballasts
About 50% of the South African market for
new linear fluorescent lamps comprises the
old fashioned, common-or-garden type
with magnetic (inductive) ballasts.
This presents a typical inductive (lagging)
APPLICATION
circuit as shown in Fig. 1a, where the
displacement power cos ϕ is about 0,4.
The total harmonic current distortion ITHD is
relatively low at about 0,1.
In the “old” days, the relevant compulsory
standard required that light fittings should
have a displacement power factor cos ϕ
greater than 0,85. For this reason a power
factor correction capacitor was required in
parallel with the inductive ballast, and this
served the purpose of significantly reducing
the apparent power S and therefore the
current drawn I1 rms [A], noting that S = I1 rms.
V1 rms, with the supply voltage V1 rms being
essentially constant at 230 V.
This is illustrated further in Fig. 3.
However, a few years ago, this mandatory
requirement was dropped, as it was not
considered by the regulator y authority
(SABS) to be a safety issue, but rather a
performance issue.
Unfortunately, the drafters of the recently
gazetted new efficiency regulations
(referred to above) have not seen fit to
re-instate the minimum power factor
requirement.
Thus we now see low-cost tubular fluorescent
luminaires with magnetic ballasts being
imported from China and installed in
South Africa, complete with the SABS Mark
of quality and safely, all perfectly legal
and certified, but without a power factor
correction capacitor fitted.
The difference? Well, with or without the
capacitor, the active power P [W], energy
consumption [Wh] and lighting efficiency
[lumens/W] of the florescent light fitting is
the same. The difference, however, is that
without the capacitor the displacement
power factor cos ϕ is about 0,4, while the
apparent power S [VA] and thus the current
drawn I1 rms [A], (and thus the loading
on the distribution network and Eskom's
generators), is about twice (2x) as high! Do
the “regulators” out there understand this?
Not only this, but because the current is
doubled, the distribution network losses
(wasted energy) thus caused by the
fluorescent luminaire without the capacitor,
are four (22) times as high.
Linear fluorescent lamps with separate
electronic ballasts
A more modern development is to replace
the traditional magnetic ballast of the linear
fluorescent luminaire with an electronic
ballast.
A good quality electronic ballast can
operate the linear fluorescent luminaire
at a displacement power factor cos ϕ
greater than 0,95 while maintaining the
total harmonic current distortion I THD at
reasonably low levels of less than 0,1.
At the same time, the active energy losses
of a good quality electronic ballast can be
significantly lower than those of the cheaper
magnetic ballasts, without reducing the
luminous flux emitted.
Thus the use of linear fluorescent luminaires
Active power P
13,76 W
Apparent power S
27,0 VA
Apparent power factor PF
0,51
Voltage Vrms
230 V
Current Irms
0,1174 A
Harmonics
[%]
I1
100
I3
80,0
I5
58,9
I7
54,7
I9
55,9
I11
48,8
I13
37,1
I15
29,2
I17
25,2
I19
20,2
ITHD
149,3
Table 1: Harmonic content of a typical 13 W low-cost “Eskom spec” CFL.
with good quality electronic ballasts
can meaningfully increase the lighting
efficiency [lumens/W], while maintaining
a high displacement power factor cos ϕ
and an acceptable total harmonic current
distortion ITHD.
Disadvantages of linear fluorescent
luminaires with electronic ballasts may
be their increased cost and complexity,
and greater vulnerability to the effects of
over-voltages (such as power surges and
lightning transients) and high ambient and
operating temperatures.
Compact fluorescent lamps (CFLs) with
integral electronic ballasts
Following the generation capacity crisis
resulting from the low generation reserve
margins in South Africa, millions of low-cost
CFLs are being rolled out and installed
throughout the country in efforts to save
energy and power demand. Currently,
Eskom has installed some some 5-million
such CFLs in the Western Cape, some
4-million in KZN, and has a further 10-million
on order (without too much thought given
to disposal – that will be someone else's
problem and cost!).
The current waveform of a typical, lowcost
CFL is shown in Fig. 4.
The CFL current waveform demonstrates
a current pulse ever y half cycle, with
the current peaks occurring just prior
to (i.e. slightly leading) the sinusoidal
voltage waveform peaks. This results from
a DC capacitor charging each half cycle
through a full wave rectifier, all within the
integral electronic ballast circuit of the
CFL. This DC capacitor then supplies the
capacitive stored energy to the fluorescent
tube via a “DC to high frequency” inverter
and coupling transformer.
A typical harmonic current content of
the common-or-garden 13 W lowcost
“Eskom spec” CFL is shown in Table 1, and
demonstrates a total harmonic current
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distortion I THD of about 1,5 (i.e. 150% of
fundamental), well above the harmonic
current limits specified in the NRS 047
quality-ofsupply standard prepared by
Eskom some 10 years ago for the Regulator.
It seems that when it suits Eskom, it can
break its own quality of supply requirements
with impunity!
From the above, it can be determined
that the 13 W CFL has an apparent power
S of 27 VA and an apparent power factor
PF = P/S = 13,67 / 27 = 0,51
In addition to potential quality-of-supply
problems, the high levels of harmonic
currents of low-cost CFLs cause significant
extra loading on distribution circuits, feed
circuit breakers, lighting transformers and
ultimately on Eskom’s generators, and also
significantly increase distribution system
losses.
One can justifiably ask the question as
to how many 13 W 27 VA CFLs can be
connected to say a 1000 VA lighting
transformer (a) from a thermal/loading point
of view, and (b) before the voltage quality
of supply exceeds the limits specified by
the Regulator?
Response by the Department of Minerals
and Energy (DME)
Regarding the new lighting efficiency
regulations referred to above, it surprises
me that issues with such huge economic
impact are covered so vaguely and with
such brevity.
The DME responds by saying that the
definitions, specifications and requirements
relating to energy efficient lighting will
be detailed (later) in the applicable
standards under preparation by the SABS.
But these standards are still to be finalised,
published as Draft South African Standards,
promulgated through a public process, and
then referenced in the energy efficiency
lighting regulations.
APPLICATION
It’s like putting the cart before the horse – having a charade of a democratic
public process and promulgating farreaching mandator y regulations
with huge economic impact, before the public and the industry are
allowed to know and comment on what actually is being suggested. The
details (standards) are not yet ready, and are not even referenced in the
regulations.
Thus presumably, if the DME is true to the democratic process, the regulations
will have to be amended in due course to reference the applicable
standards, and then re-issued again for comment and response following
another public process.
In the meantime, I believe that the energy efficiency lighting regulations as
they now stand are quite meaningless.
Conclusions and recommendations
To be meaningful and effective, requirements for energy efficient lighting
necessarily include a careful definition of what is meant by the term “energy
efficient fittings”, which requirement should perhaps be specified in terms of
the luminous flux emitted per watt of electrical power input [lumens/W] at a
defined minimum apparent power factor PF, which incorporates both the
concepts of displacement power factor cos ϕ and total harmonic current
distortion ITHD.
Other regulated requirements should also limit electromagnetic interference
(EMI) to acceptable levels to ensure electromagnetic compatibility (EMC) with
other electrical and electronic equipment, as well as the operating life [hours]
requirements of the light sources, ballasts and complete light fittings.
For both the regulations and the referenced standards, an open and
democratic public promulgation process should be followed to ensure
scrutiny, comment and response by the affected public and industry
experts, and the standards referenced within the regulations should be
promulgated before being made mandatory through the promulgation of
the accompanying regulations.
Contact Chris Yelland, EE Publishers,
Tel 011 543-7000, chris.yelland@ee.co.za v
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