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1. True power factor (PF) and displacement power factor (DPF) are
commonly available on power analyzers and loggers. At first glance (and in
POWER QUALITY & RELIABILITY
Power Factor Vs. Displacement Power
Factor
What’s the difference?
Chris Mullins 1 | Jun 28, 2017

2. some situations), they appear to measure the same thing, but there is an
important difference. A review of their definitions and an explanation of
when to use each are presented here.
PF and DPF are both measures of the “efficiency” of power delivery, in the
sense that they are ratios of the useful energy delivered to a load versus the
“effort” or “burden” on the electrical system by that load. PF, or “true
power factor,” has the most straightforward definition, but DPF is perhaps
more familiar in terms of the traditional power triangle relating watts,
VARs (Volt-Amps-Reactive), and VA (Volt-Amps).
Displacement power factor
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The DPF is the “power factor” of just the 60-Hz portion of the waveform
for voltage and current. Harmonic effects are inherently excluded from the
calculation and have no direct effect on the result. DPF is computed as the
cosine of the phase angle between the current and voltage fundamental
sine waves:
DPF = cos
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3. Figure 1 shows a sample voltage (red) and current (blue) waveform,
where the current is shifted in phase from the voltage. This phase shift is
typically caused by inductive loads such as motors. Instantaneous real
power is the voltage times the current. Portions of the waveforms where
the V × I product is positive contribute to positive real power flow (energy
delivered to the load), while negative values represent reactive power,
which subtracts from the net real power over a 60-Hz cycle. If there is no
phase shift, the V × I product is always positive, and every sample
contributes to the real power. On the other hand, if the phase shift is 90°,
the positive values exactly cancel with the negative values, and no real
power is delivered. The familiar power triangle relations quantify this
effect (Fig. 2).
Fig. 1. Voltage and current waveforms with current (blue line) shifted in phase from the voltage (red line).

4. A low DPF is often mitigated with power factor correction capacitors
(PFCs). These capacitors are sized based on the amount of VARs needed to
cancel out the inductive VARs of typical loads. Another equivalent
interpretation is that they shift the lagging current back into phase with the
voltage. In either case, the net VARs is reduced, thus increasing the real
power for a given VA, according to the triangle relation:
VA = √(W + VAR )
Since harmonic currents don’t contribute significantly to real or reactive
power flow, they should not be included in sizing a PFC — or in judging
PFC effectiveness in lowering VARs. For this purpose, DPF is the best
choice. If harmonics are present, DPF is still useful for measuring PFC
effectiveness. But another metric is needed for overall system efficiency —
true power factor.
Power factor
PF is the ratio of real power to apparent power, and is given by the
Fig. 2. The relationship of real power, reactive power, and power factor are presented in this power triangle.
2 2

5. formula:
PF = (W ÷ VA)
Where W is the real power over at least one 60-Hz period, and VA is the
apparent power. The apparent power (VA) is simply the RMS voltage times
the RMS current (over the same period as the real power calculation). This
is called “true” power factor because it’s valid and equally meaningful
regardless of the waveform shape of the voltage or current. Waveform
distortion, or deviation from the ideal 60-Hz sine wave, can be quantified
by harmonics. The RMS computations (and thus VA) and the real power
calculations include the effects of any harmonic (and even interharmonic)
distortion that may be present in the voltage or current.
The PF can be viewed as an efficiency metric, with the real power (W)
representing the power actually delivered to a load and the apparent power
(VA) representing the burden of that load on the system. The real power
may be reduced due to phase shift between the voltage and current
waveforms (also captured by DPF, as described above), thus reducing the
PF value. More significantly for PF, harmonic currents will increase the VA
measurement without appreciably increasing the real power — again,
reducing the PF. In Fig. 3, a typical electronic load is shown with the
Fig. 3. Typical nonlinear electronic load shows the relationship between voltage (red line) and current (blue line).

6. voltage in red and very non-sinusoidal current in blue. The harmonic
breakdown of these waveforms is shown in Fig. 4, along with harmonic
power. The top chart is voltage, where the fundamental is large, and the
3rd and 5th harmonics are just barely visible. The current (middle plot)
shows severe distortion — the 3rd and 5th harmonics are almost as tall as
the 60 Hz fundamental (circled in orange). The harmonic real power in the
bottom plot reveals that only the fundamental shows any significant
power. The 5th harmonic power is the highest of the harmonics, and it’s
still very small. Mathematically, harmonic currents can only produce
harmonic real or reactive power if the corresponding voltage harmonic is
high.

7. In general, harmonic current components deliver very little real power,
and their presence only increases the RMS current. Thus, as harmonics
increase, the VA increases and the PF worsens. The burden on the
distribution network is quantified by VA (transformer heating, resistive
Fig. 4. Harmonic breakdown of the nonlinear load from Fig. 3 reveals the 3rd and 5th harmonics are almost as large as
the 60-Hz fundamental.

8. losses at a fixed nominal voltage, etc.) so the PF value is a good metric for
overall system efficiency, valid for all waveform shapes and harmonic
levels.
PF or DPF?
If the actual waveforms are pure 60-Hz sine waves with no harmonics,
then the PF and DPF measurements will be equal. As harmonics (or
interharmonics) are added, the PF gets smaller, but the DPF stays the
same (all else remaining equal).
Use DPF for 60-Hz reactive power issues, primarily for PFC investigations.
If the DPF is low, there is an opportunity to improve efficiency by installing
(or adjusting) a PFC. If the DPF is different on three phases, a phase on an
existing capacitor bank may be blown. A strip chart graph of DPF may be
used to help set timers or trip points on an adjustable PFC (the VAR strip
chart may also be used for this).
Use PF for quantifying overall system efficiency, including the effects of
harmonics. If the PF is low but the DPF is high, a PFC will probably not
help. A low PF may indicate increased transformer heating or other losses
due to high harmonics. Improving this requires harmonic mitigation, a K-
rated transformer, or upsizing/derating a regular transformer. With low
PF and high DPF, harmonics are present, and a full IEEE 519 harmonic
investigation may be warranted.
In conclusion
PF and DPF are both measures of system efficiency that are equivalent in
non-harmonic situations. Although superficially similar, they are best used
for very different purposes. DPF is a good measure of phase shift and PFC

9. Source URL: http://www.ecmweb.com/power-quality-reliability/power-factor-vs-displacement-power-
factor
performance, while PF is better for overall system efficiency determination
in the presence of harmonics. When DPF and PF differ numerically,
harmonics are present, and a deeper investigation may be
required.
Mullins is VP of operations and engineering for Power Monitors, Inc. He
can be reached at cmullins@powermonitors.com .