Displacement vs. True Power Factor: Harmonics and THD
Most power quality textbooks introduce power factor as a single number, the cosine of the angle between voltage and current. That definition holds perfectly for linear loads like resistors and incandescent lamps. Add a variable-frequency drive, a switch-mode power supply, or a bank of LED drivers, and a second, lower number appears on the meter: true power factor. Understanding why the two differ starts with harmonics.
What displacement power factor actually measures
Displacement power factor (DPF) is defined as the cosine of the phase angle φ between the fundamental voltage and current waveforms. Electrically, it captures the lag or lead introduced by reactive elements, inductors and capacitors, at the supply frequency (50 or 60 Hz).
For a purely linear, inductive load such as an uncompensated motor:
- Voltage and current are both sinusoidal at the supply frequency
- Current lags voltage by some angle φ
- DPF = cos φ, typically 0.7 to 0.9 for a lightly loaded motor
A capacitor bank tuned to raise DPF toward unity does exactly this: it shifts the current phasor closer to the voltage phasor. That correction works well as long as current stays sinusoidal.
The limitation surfaces the moment current stops being sinusoidal.
Where true power factor comes in
True power factor (TPF), sometimes called total power factor, accounts for everything the current waveform does, not just its fundamental component. The formal relationship is:
TPF = P / S
where P is real power (watts) and S is apparent power (volt-amperes). When a nonlinear load draws current in sharp pulses, that current contains harmonic components at 3×, 5×, 7× the fundamental frequency. Those harmonics contribute to the RMS current magnitude, increasing apparent power S without contributing useful real power P. The result is a lower ratio, a lower true power factor.
The quantitative bridge between the two metrics is total harmonic distortion (THD):
TPF = DPF / √(1 + THD²)
THD here is expressed as a per-unit ratio (not a percentage). A THD of 0.30 means 30%, entered as 0.30.
This formula shows that even a load with DPF = 1.00 (no phase lag at the fundamental) can have a true power factor well below unity if harmonic currents are significant.
How nonlinear loads introduce harmonic distortion
A VFD, or variable-frequency drive, draws current in two short pulses per half-cycle, once during each peak of the voltage waveform as its DC bus capacitors recharge. A six-pulse rectifier front-end typically produces THD of 30 to 50%. Twelve-pulse and eighteen-pulse rectifiers reduce that to roughly 10 to 15%.
Switch-mode power supplies in computers and servers are similar offenders. A single desktop machine draws negligible harmonic current in the broader scheme, but a data center housing thousands of servers accumulates enough distortion to matter at the utility connection point.
LED drivers, electronic ballasts, and battery chargers fall into the same category. Their rectifier stages all create non-sinusoidal current draws.
What makes this practically important is that power-factor-correction capacitors do not fix harmonic-driven TPF shortfalls. Capacitors shift the fundamental phasor but cannot absorb or cancel harmonic currents. Worse, they can amplify certain harmonics through resonance. Addressing harmonic distortion requires passive harmonic filters, active front-end converters, or detuned reactor-capacitor banks.
Comparing displacement and true power factor
| Characteristic | Displacement PF | True PF |
|---|---|---|
| What it measures | Phase angle at fundamental frequency | Real power / apparent power, all harmonics included |
| Relevant load type | Linear (motors, transformers) | Nonlinear (drives, SMPS, chargers) |
| Affected by capacitor correction | Yes | Partially (DPF component only) |
| Meter type needed | Standard power factor meter | True-RMS power analyzer |
| Utility billing impact | Standard kVAR penalties | May undercount penalty on nonlinear sites |
Standard utility meters measure DPF. A site with a DPF of 0.95 might simultaneously have a TPF of 0.82 if harmonic distortion is high, and only a true-RMS analyzer reveals the gap.
Worked example: VFD bank at a packaging plant
A packaging line runs eight 22 kW VFDs, each with an input DPF of 0.97 and a measured current THD of 38% (0.38 per unit).
Applying the formula:
TPF = 0.97 / √(1 + 0.38²)
TPF = 0.97 / √(1 + 0.1444)
TPF = 0.97 / √1.1444
TPF = 0.97 / 1.0698
TPF ≈ 0.907
Total connected load: 8 × 22 kW = 176 kW. At TPF = 0.907, apparent power S = 176 / 0.907 = 194 kVA.
If the plant had assumed DPF = TPF and sized its transformer and cabling for 176 / 0.97 = 181 kVA, it would have underestimated conductor current by about 7%. That gap matters during motor starting and when additional equipment is added.
A passive 5th/7th harmonic filter on each drive reduces THD to roughly 8% (0.08), giving:
TPF = 0.97 / √(1 + 0.08²) = 0.97 / 1.0032 ≈ 0.967
The apparent power demand drops from 194 kVA to 182 kVA, reducing peak demand charges and freeing transformer headroom.
For a broader look at how real, reactive, and apparent power relate to each other, the kVA, kW, and kVAR explainer covers the triangle geometry in detail.
Why utilities and facility engineers track both
Utility tariffs have historically penalized low power factor based on measured DPF, because that was what meters could read. As smart metering becomes standard, some utilities now measure apparent power demand directly, which implicitly captures true power factor. Facilities that corrected DPF with capacitor banks but left harmonic distortion unaddressed may find their next meter upgrade exposes a hidden TPF problem.
On the facility side, engineers sizing transformers, cables, and switchgear for data centers or other high-density compute loads need TPF rather than DPF to calculate actual current. Undersized conductors overheat; undersized transformers hit thermal limits under loads that appear modest on a DPF meter.
Frequently asked questions
Can a capacitor bank improve true power factor?
A capacitor bank corrects displacement power factor by canceling reactive current at the fundamental frequency. It has no effect on harmonic currents, so it does not directly improve true power factor when THD is the dominant issue. In fact, an improperly designed bank can resonate with harmonic currents and amplify distortion. Active power factor correction or harmonic filtering is required to address the THD component.
What THD level makes the difference between DPF and TPF significant?
At THD below 5%, the gap is small: a DPF of 0.95 becomes a TPF of roughly 0.949. At 20% THD the gap widens to about 0.932. At 40% THD it reaches 0.879. The crossover point where engineers should track both numbers is generally around 10 to 15% THD, which is common on sites with multiple VFDs or large quantities of electronic equipment.
How do I measure true power factor versus displacement power factor?
Standard clamp meters and older panel meters report DPF. True power factor requires a true-RMS power analyzer that samples voltage and current waveforms at high speed and computes real power from the instantaneous product. Instruments from Fluke (435 series), Hioki, and Dranetz are commonly used for this. Some modern energy meters now report both values simultaneously.
Does a high-DPF, high-THD load still cause distribution problems?
Yes. Harmonic currents flow through transformers, cables, and neutral conductors regardless of the fundamental phase angle. They cause additional heating (I²R losses at each harmonic frequency), can saturate transformers designed for sinusoidal loads, and create voltage distortion that affects other equipment on the same bus. Correcting DPF alone does not resolve those issues. See what is power factor for the foundational concepts that underpin both metrics.