--- title: "Unity Displacement Power Factor Can Coexist with a Lower True Factor" description: "Leviathan Systems — Technical content Published 2026-10-21; updated 2026-10-21." canonical: "https://www.leviathansystems.co/articles/true-displacement-power-factor-waveform-basis" last-updated: "2026-10-21" --- # Unity Displacement Power Factor Can Coexist with a Lower True Factor Leviathan Systems — Technical content Published 2026-10-21; updated 2026-10-21. Unity displacement power factor means the fundamental current and voltage are in phase. True power factor compares active power with apparent power using the complete waveforms. Harmonic current can therefore coexist with displacement factor 1.0 and true factor 0.8. The two fictional waveforms below both produce 1200 W and 1500 VA, but only one has unity displacement. A supplier's factor supports a conclusion only after its quantity is identified. ## Identify what the reported factor describes A displacement-factor claim concerns the fundamental, the base-frequency component of each waveform. Its value is cos φ₁, where φ₁ is the phase difference between fundamental voltage and fundamental current. Unity means that phase difference is zero for the consuming-load cases considered here. True power factor uses a different comparison: active power P divided by apparent power S. For a single-phase load, S is RMS voltage multiplied by RMS current. Those RMS quantities include the waveform's harmonic components. A fundamental phase relationship alone therefore does not determine the true factor. Schneider Electric's PM5500 documentation explicitly distinguishes these quantities. It also says that, unless specified otherwise, the meter's displayed power factor is true factor. That is a convention for the documented product, rather than a definition to assign to an unidentified report. References: [PF1](https://www.electrical-installation.org/enwiki/Harmonic_distortion_indicators_-_Power_factor), [PF3](https://productinfo.se.com/pm5500/viewer?docidentity=PowerFactorPF-7D7051E2&extension=xml&lang=en&manualidentity=UserManualSeriesHRB1684301-06-2247347A) ## State the voltage assumption before using the relationship For both examples, stipulate a periodic single-phase load supplied by exactly sinusoidal voltage of 100 V RMS. There is no DC component, and every current component not named is zero. The values are invented mathematical inputs, rather than equipment specifications or observations. All stated component amplitudes are RMS values. Write the voltage as v(t) = 100√2 cos(ωt) V, where ω is the fundamental angular frequency. Averaging over complete periods makes the products of this voltage with different-frequency current harmonics cancel. Active power is consequently P = 100 × I₁ × cos φ₁, while apparent power is S = 100 × Iᵣₘₛ. Dividing gives true PF = (I₁ / Iᵣₘₛ) × cos φ₁. This equality uses the exact sinusoidal-voltage premise. Schneider's guide presents its corresponding approximation with a sinusoidal or virtually sinusoidal voltage condition. The simplified relationship here must not be transferred unchanged to distorted-voltage or unbalanced multiphase reports. References: [PF1](https://www.electrical-installation.org/enwiki/Harmonic_distortion_indicators_-_Power_factor) ## Waveform A: unity displacement with harmonic current Let the fundamental current be 12 A RMS and in phase with the voltage. Add a third-harmonic current of 9 A RMS. One explicit waveform is iA(t) = √2[12 cos(ωt) + 9 cos(3ωt)] A. The third harmonic oscillates at three times the fundamental frequency; it does not change the phase difference between the two fundamentals. The component squares add for the total RMS calculation: Iᵣₘₛ = √(12² + 9²) A = √225 A = 15 A. Adding the amplitudes as 12 + 9 = 21 A would give the wrong RMS result. This calculation includes the fundamental, whereas a harmonic-only RMS quantity excludes it. The fundamental produces 100 V × 12 A × 1 = 1200 W of active power. The third-harmonic current's product with the stipulated sinusoidal voltage averages to zero. Its contribution to RMS current remains present, however, so apparent power is 100 V × 15 A = 1500 VA. Displacement factor is 1.0, but true factor is 1200 W / 1500 VA = 0.8. The same result follows from (12/15) × 1.0. A unity displacement claim is fully consistent with this distorted current waveform. References: [PF1](https://www.electrical-installation.org/enwiki/Harmonic_distortion_indicators_-_Power_factor), [PF2](https://www.electrical-installation.org/enwiki/R.m.s._values) ## Waveform B: the same true factor without current harmonics Keep the same voltage and replace the current with a pure fundamental of 15 A RMS. Let it lag the voltage by an angle φ for which cos φ = 0.8. Its waveform is iB(t) = 15√2 cos(ωt − φ) A. There are no higher-frequency current components in this case. Total RMS current is now simply 15 A. Active power is 100 V × 15 A × 0.8 = 1200 W, and apparent power is again 100 V × 15 A = 1500 VA. Both true factor and displacement factor are 0.8. The active-power and apparent-power totals match Waveform A exactly. Nevertheless, A has harmonic current and unity displacement, while B has sinusoidal current and a displaced fundamental. References: [PF1](https://www.electrical-installation.org/enwiki/Harmonic_distortion_indicators_-_Power_factor), [PF2](https://www.electrical-installation.org/enwiki/R.m.s._values) ## See what the shared ratio leaves unresolved The conditional relationship contains two factors. In A, the fundamental-to-total RMS current ratio is 12/15 = 0.8 and the displacement factor is 1.0. In B, the current ratio is 15/15 = 1.0 and the displacement factor is 0.8. Multiplying gives the same true factor through different waveform properties. A true factor of 0.8 alone therefore cannot establish the presence of current harmonics: B is a counterexample. A displacement factor of 1.0 alone cannot establish true factor 1.0: A is a counterexample. Equal P/S values also do not establish equal fundamental phase relationships. Neither case supplies a conversion-efficiency result. Power factor compares active and apparent power at the input boundary. Conversion efficiency compares useful output power with input power. A true factor of 0.8 does not mean that a power supply loses 20% of its input energy. References: [PF1](https://www.electrical-installation.org/enwiki/Harmonic_distortion_indicators_-_Power_factor), [PF3](https://productinfo.se.com/pm5500/viewer?docidentity=PowerFactorPF-7D7051E2&extension=xml&lang=en&manualidentity=UserManualSeriesHRB1684301-06-2247347A) ## Interpret a supplied claim without changing its quantity Consider an invented submission showing 1500 VA and displacement PF 1.0 for one load. Entering 1500 W would silently substitute unity true factor for unity displacement factor. Waveform A satisfies both supplied numbers while producing only 1200 W, so the submitted evidence does not justify that entry. Suppose the supplier instead supplies active power of 1200 W and apparent power of 1500 VA for the same electrical boundary, operating condition and time basis. Their ratio establishes true factor 0.8 on that basis. Those totals alone still do not distinguish A from B. If displacement factor 1.0 is also supplied on the same basis, B no longer matches that additional premise. When two offers respectively quote unity displacement factor and true factor 0.8, their headlines do not establish which has the higher true factor. The two statements could even describe the same waveform A. Ask which quantity the supplier means, retain the applicable documentation and keep its sign convention with the value; the examples here use positive consuming-load magnitudes. The related rack-PDU article covers real/apparent units and metering boundaries. The harmonic-current article explains percentage denominators, including the distinction between THD and TDD. Those separate questions should be resolved using their own definitions rather than inferred from a power-factor headline. References: [PF1](https://www.electrical-installation.org/enwiki/Harmonic_distortion_indicators_-_Power_factor), [PF3](https://productinfo.se.com/pm5500/viewer?docidentity=PowerFactorPF-7D7051E2&extension=xml&lang=en&manualidentity=UserManualSeriesHRB1684301-06-2247347A) ## Connect a separate physical requirement to the installation scope Where the project also has an identified requirement to mount selected IT equipment, the related Rack-and-Stack Installation service and project inquiry address that physical package. Provide the equipment references, approved rack positions, mounting instructions, site constraints and requested IT cabling, labels or handoff records. Leviathan can discuss those physical tasks within an agreed engagement. Electrical analysis, design, live power-quality measurements and energization remain with the customer's appointed qualified electrical and facility parties. ## Primary sources - [PF1 — Schneider Electric Electrical Installation Guide — Harmonic distortion indicators: Power factor](https://www.electrical-installation.org/enwiki/Harmonic_distortion_indicators_-_Power_factor). Checked 2026-10-21. Defines active/apparent power factor and fundamental displacement factor. Its sinusoidal-voltage condition is essential to the relationship used in the fictional single-phase examples. - [PF2 — Schneider Electric Electrical Installation Guide — R.m.s. values](https://www.electrical-installation.org/enwiki/R.m.s._values). Checked 2026-10-21. Combines harmonic-component RMS values by the square root of their squared sum, including the fundamental. Supports the total-current arithmetic. - [PF3 — Schneider Electric PowerLogic PM5500-series manual — Power factor (PF)](https://productinfo.se.com/pm5500/viewer?docidentity=PowerFactorPF-7D7051E2&extension=xml&lang=en&manualidentity=UserManualSeriesHRB1684301-06-2247347A). Checked 2026-10-21. The displayed manual revision is HRB1684301-18. Distinguishes true and displacement quantities and states the named meter's default display convention. ## Related Leviathan resources - [Rack PDU metering, real/apparent units and supplied power records](/articles/rack-pdu-selection-metering-gpu) - [Harmonic current percentages and their reference denominators](/articles/harmonics-power-quality-gpu-density) - [Rack-and-Stack Installation: separately agreed physical work](/services/rack-and-stack) - [Discuss an identified physical IT installation requirement](/contact?service=rack-and-stack&from=%2Farticles%2Ftrue-displacement-power-factor-waveform-basis) - [2N vs N+1 Power Redundancy for AI Clusters: What's Worth Paying For](/articles/2n-vs-n-plus-1-redundancy-ai) ## Discuss a separate physical installation requirement Share the selected IT equipment, approved rack positions, site constraints and requested mounting, IT cabling or installation records. Our team can discuss scope, requirements and availability for the physical work. [Discuss the scope](/contact?service=rack-and-stack&from=/articles/true-displacement-power-factor-waveform-basis)