Academy/Tokenization/Basic elements

XP-TOK-E118 · A textbook for energy tokenizers

Basic elements

118 electrical elements: from a physical quantity to a measurable result and an enforceable right.

Download PDF PDF · EN

Where to start

A · 041WeElectrical energyJ; kWh A · 046PActive powerW; kW A · 054WlossEnergy lossesJ; kWh

Colour shows suitability for product design. Issuance and transfer require their own legal basis.

01 / 118

Element map

Letters A, B and C show each element’s role. Open a card for its meaning, unit and application.

Name, symbol or number

118 / 118

Charge and field

1-12

001CqElectric chargeC 002CρVolume charge densityC/m³ 003CσqSurface charge densityC/m² 004CλqLinear charge densityC/m 005BIElectric currentA 006CJCurrent densityA/m² 007CEElectric field strengthV/m 008CBMagnetic flux densityT 009CDElectric displacementC/m² 010CHMagnetic field strengthA/m 011CφElectric potentialV 012CℰElectromotive forceV

Materials

13-24

013CPpolPolarizationC/m² 014CMmagMagnetizationA/m 015CεPermittivityF/m 016CμPermeabilityH/m 017CσConductivityS/m 018CρeResistivityΩ·m 019CχeElectric susceptibility1 020CχmMagnetic susceptibility1 021BtanδDielectric loss tangent1 022BEbdDielectric strengthV/m 023CμcCarrier mobilitym²/(V·s) 024CnCarrier concentrationm⁻³

Electric circuits

25-40

025CΨDElectric displacement fluxC 026CΦMagnetic fluxWb 027CλFlux linkageWb 028BUVoltageV 029BRResistanceΩ 030CGConductanceS 031BCCapacitanceF 032BLInductanceH 033CMMutual inductanceH 034BZImpedanceΩ 035CYAdmittanceS 036CXReactanceΩ 037CBsSusceptanceS 038BτTime constants 039Bf₀Resonant frequencyHz 040CQfQuality factor1

Energy and power

41-55

041AWeElectrical energyJ; kWh 042CWmMagnetic energyJ 043CWemElectromagnetic energyJ 044CuEnergy densityJ/m³ 045Bp(t)Instantaneous powerW 046APActive powerW; kW 047BQReactive powervar; kvar 048BSApparent powerVA; kVA 049CS̲Complex powerVA 050BPFPower factor1 051BcosφDisplacement factor1 052CSpPoynting vectorW/m² 053CpvVolume power densityW/m³ 054AWlossEnergy lossesJ; kWh 055BηEfficiency1; %

Time, waveform and spectrum

56-70

056BfFrequencyHz 057CωAngular frequencyrad/s 058BTOscillation periods 059CθPhaserad 060BΔφPhase differencerad 061CX̂Amplitude[X] 062CXppPeak-to-peak value[X] 063BXrmsRoot mean square[X] 064BX̄Mean value[X] 065CXabsMean rectified value[X] 066BCFCrest factor1 067CFFForm factor1 068BdX/dtRate of change[X]/s 069BXhHarmonic amplitude[X] 070CSX(f)Spectral density[X]²/Hz

Three phases and quality

71-86

071BX₁Positive sequence[X] 072BX₂Negative sequence[X] 073BX₀Zero sequence[X] 074BU₂/U₁Voltage unbalance1; % 075BI₂/I₁Current unbalance1; % 076BTHDuVoltage distortion1; % 077BTHDiCurrent distortion1; % 078BhHarmonic order1 079BΔfFrequency deviationHz 080Bdf/dtRate of change of frequencyHz/s 081BdipVoltage dipV; s 082BswellVoltage swellV; s 083BinterruptSupply interruptions; count 084BtransientTransient overvoltageV; s 085BRVCRapid voltage change%; s 086BPst / PltFlicker1

Waves

87-96

087CλwWavelengthm 088CvpPhase velocitym/s 089CvgGroup velocitym/s 090CγPropagation constantm⁻¹ 091CαattAttenuation constantNp/m 092CβPhase constantrad/m 093CηwWave impedanceΩ 094CδsSkin depthm 095CΓReflection coefficient1 096CVSWRStanding wave ratio1

Power system

97-106

097BZthThevenin impedanceΩ 098BIkShort-circuit currentA; kA 099BSkShort-circuit powerVA; MVA 100BX/RX/R ratio1 101BδpPower anglerad 102BHsysInertia constants 103BKfPower-frequency characteristicW/Hz 104BRdDroop1; % 105BλcModal decay exponents⁻¹ 106BSCRShort-circuit ratio1

Noise and uncertainty

107-112

107CenVoltage noise densityV/√Hz 108CinCurrent noise densityA/√Hz 109CSNNoise power densityW/Hz 110BSNRSignal-to-noise ratiodB 111CL(f)Phase noisedBc/Hz 112Bσy(τ)Allan deviation1

Quantum quantities

113-118

113CeElementary chargeC 114CG₀Conductance quantumS 115CRKVon Klitzing constantΩ 116CKJJosephson constantHz/V 117CΦ₀Magnetic flux quantumWb 118CαfsFine-structure constant1

The catalogue is based on the supplied table and corrected for teaching. The number 118 defines this edition’s scope; no universal physical periodicity is assumed. Editorial corrections.

02 / 8 products

8 products

ENERGY

Energy delivery

41 · We 46 · P 28 · U 63 · Xrms

Subject of the right: A right to an agreed delivery volume or a monetary claim tied to delivery.
Who pays: Buyer under the delivery contract.
Evidence required: Meter, boundary, interval, flow direction, data quality and acceptance record.

W = Σ Pᵢ·Δtᵢ; payment = Σ Wᵢ·cᵢ

Example unit: 1 kWh at a defined point and interval. Delivery rights and payment claims require their respective legal bases.

SAVE

Verified savings

41 · We 54 · Wloss 55 · η 46 · P

Subject of the right: A monetary claim on a contractual share of the verified net benefit.
Who pays: Energy-service customer or another expressly obligated party.
Evidence required: Adjusted baseline, actual consumption, useful output, additional costs and uncertainty.

ΔW = Wbaseline,adjusted − Wactual; claim = share × net benefit

Savings are determined by comparison. Model predictions and meter readings serve different evidence roles.

FLEX

Flexibility and peak reduction

46 · P 38 · τ 64 · X̄68 · dX/dt

Subject of the right: A right to payment for availability and/or delivered load adjustment under programme rules.
Who pays: Aggregator, market operator or customer under the relevant contract.
Evidence required: Resource qualification, command, timestamps, load profile, baseline, response and post-event rebound.

ΔPᵢ = Pbaseline,ᵢ − Pactual,ᵢ; acceptance follows programme rules

10 kW for 2 hours means 20 kWh less consumption during the event. Daily energy savings depend on later operation.

RESERVE

Reserve and available capacity

46 · P 41 · We 38 · τ 55 · η 83 · interrupt

Subject of the right: An obligation to provide power at a specified location, duration and activation speed.
Who pays: Reserve customer or an eligible market counterparty.
Evidence required: Availability test, usable energy, charge state, temperature, degradation, auxiliaries and network limits.

Pavailable ≤ min(Plimit, Eusable,AC / duration)

Battery nameplate kW must be complemented by kWh, response time, state of charge and limits.

QUALITY

Power quality

28 · U 47 · Q 48 · S 50 · PF 51 · cosφ 74 · U₂/U₁ 76 · THDu 81 · dip 83 · interrupt 86 · Pst / Plt

Subject of the right: A service maintaining agreed parameters with measurable acceptance and contractual accountability.
Who pays: Quality-service customer where the contract establishes payment.
Evidence required: Parameters, thresholds, statistics, measurement point, instrument class and unavailable periods.

Payment = service fee ± performance adjustment

Lower THD or higher PF gains a price through a contract. Percentage improvement does not equal percentage energy savings.

GRID

System support

56 · f 79 · Δf 80 · df/dt 97 · Zth 102 · Hsys 103 · Kf 104 · Rd 106 · SCR

Subject of the right: A contractual frequency, voltage or other agreed grid-support service.
Who pays: Operator or service buyer under the applicable market or contract.
Evidence required: Qualification, tests, telemetry, control characteristics and verified response.

Presponse = Kf × Δf; subject to limits and sign convention

Service eligibility is specific to the grid. Network coefficients support the technical assessment.

ORIGIN

Energy origin

41 · We

Subject of the right: A right to a recognized origin attribute under the relevant certificate scheme.
Who pays: Attribute buyer under contract.
Evidence required: Registry, plant, generation period, unique certificate number, transfer and cancellation.

Attribute volume ≤ eligible registered generation

Origin is an additional data layer over no. 41. A token copy must preserve the link to the source registry and cancellation status.

COMPUTE

Energy for computing

46 · P 41 · We 55 · η 83 · interrupt

Subject of the right: A computing service with specified hardware, workload, time and performance.
Who pays: Computing-service customer.
Evidence required: Available power, energy, cooling, connectivity, accelerators, utilization and measured task output.

Energy cost = IT power × PUE × hours × energy price

Converting kW to FLOPS requires specific hardware, numerical precision and operating conditions. PUE defines the infrastructure-energy boundary.

03 / Textbook

Textbook

1. What becomes an asset

A token records a specific right: delivery, service, payment or authorized action. A quantity in the table describes its physical basis. Every product needs a holder, obligated party, deliverable, deadline and acceptance rule.

Working sequence: asset → measurement → verified result → contractual right → entry in the applicable system → settlement. Keep source data and decision grounds at every transition.

A useful minimum accounting unit is asset + point + interval + product + method version + right identifier. Distributed portfolios retain traceability to each asset.

2. How to read the map

The 118 entries are an editorial teaching catalogue based on the supplied poster. They form a selection of quantities, constants and events. There is no universal finite list of all electrical properties; no physical periodicity is claimed.

A marks a useful quantitative product basis: energy, active power and losses. B specifies quality and service conditions. C explains physics and measurement. This is an educational suitability assessment, with no claim of liquidity or permission to issue.

Start with nos. 41, 46 and 54. Add nos. 28, 50, 55, 63, 68, 76 and 83 next. Consult the remaining entries as engineering questions arise.

3. Units and boundaries

kW describes power; kWh describes energy over time. A constant 10 kW load uses 30 kWh in 3 hours. Peak power requires an averaging window: a one-second maximum and a half-hour average produce different values.

For sinusoidal single-phase operation P = UI cosφ, Q = UI sinφ, S = UI, using RMS U and I. For a balanced three-phase system P = √3·Uline·I·cosφ. With distorted waveforms total PF = P/S can differ from fundamental displacement cosφ.

The boundary determines which losses and auxiliary loads enter the calculation. Battery charge and discharge are measured separately; heat and cooling need their own meters and temperature conditions. [X] inherits the unit of the underlying signal.

4. Evidence and certification

A measurement passport includes instrument type and identifier, verification or calibration status under applicable rules, location, connection, timezone, sampling interval, raw data and change log. Missing or substituted data are marked explicitly.

A measurement and verification plan defines the baseline, weather and load adjustments, useful-service preservation, uncertainty and dispute resolution in advance. An intelligence model receives a version and validity range. Its accuracy is checked under new operating conditions. [S2]

For power quality, agree measurement methods and acceptance limits. IEC 61000-4-30:2025 describes measurement methods; limits and applicability depend on the grid, contract and current rules. Equipment certification, result verification, rights registration and tax accounting serve distinct purposes. [S3]

5. Rights, payments and full accounting

First identify the right and obligated party. Then choose a permitted legal form, transfer rules and settlement infrastructure. Russian digital financial assets can include monetary claims; issuance uses the prescribed information-system framework. Utility digital rights, hybrid rights and contractual claims require separate assessment at the transaction date. [S4]

Accounting separates physical volume, gross benefit, costs, tax base, reserve, recognized receivable and cash received. Each measure identifies the accounting party, supporting document, currency and period. There is no single tax rate covering all energy tokens.

Future receipts are disclosed as forecasts. Present value depends on timing, risk, costs and discount rate. Transferring a structure to Serbia or another country requires local legal and tax review.

6. Product compatibility

One asset may provide several services. Prepare a power and energy budget for every interval. Reserve, demand response, computing and native-load obligations must fit the actual constraints simultaneously.

A cancelled origin certificate is removed from the available balance. An allocated share of a receivable keeps its link to the original quantity. Overlap checks cover asset, interval, service, baseline and benefit recipient. [S7]

Reducing consumption by 10 kW, allocating those 10 kW to computing and promising the same 10 kW as reserve requires a compatibility calculation. Revenues are combined only after physical operation and contract rules have been checked.

04 / Worked cases

Worked cases

All worked-case numbers are synthetic. Formulas illustrate the calculation logic; no current tariffs or live issuances are claimed.

Refrigeration savings

Synthetic month: adjusted baseline 100,000 kWh, actual use 82,000 kWh, agreed value RUB 8/kWh. Additional costs RUB 24,000. Provider share 30% of benefit after costs. The temperature service is maintained.

Solution

ΔW = 18,000 kWh. Gross benefit RUB 144,000. After costs RUB 120,000. Contractual share RUB 36,000; customer retains RUB 84,000. Taxes and reserves are outside this example.

Issuance relies on the contractual right and accepted calculation. All input data and the verification statement form the evidence package.

Load reduction with rebound

Load falls by 10 kW for 2 hours. Afterwards the equipment uses an extra 14 kWh. Assumed payment is RUB 5 per accepted event kWh. There is no availability payment.

Solution

Event reduction is 20 kWh; net energy reduction over the full cycle is 6 kWh. If all 20 kWh are accepted, payment is RUB 100. This teaching formula is not a current DR tariff.

Event volume, daily savings and market payment follow separate rules. Programme eligibility is checked separately.

How much reserve a battery provides

Usable AC output energy after all limits is 90 kWh. Maximum output is 40 kW. The customer needs 3 hours of continuous support. All additional losses are already included in the 90 kWh.

Solution

Permitted commitment: min(40, 90/3) = 30 kW for 3 hours. At 40 kW, available duration is 2.25 hours.

The commitment is limited by energy, power and actual condition. Available volume is recalculated when charge falls.

Reactive-power compensation

A sinusoidal 100 kW load. Power factor rises from 0.80 to 0.95 with active power unchanged.

Solution

S falls from 125 to 105.26 kVA. Q falls from 75 to 32.87 kvar; compensation is about 42.13 kvar. At the same voltage, current falls by 15.79%.

The result can support a compensation service. Monetary savings depend on actual losses and billing terms; current reduction does not imply equal load-energy reduction.

Sharing a 10 kW resource

A retrofit frees 10 kW. Computing uses 8 kW in the same interval. An external command then requires another 5 kW reduction in total site consumption.

Solution

The remaining margin relative to the original load is 2 kW. A 5 kW commitment depends on authority and technical ability to curtail computing by at least another 3 kW, plus the programme baseline and rules.

Until compatibility is confirmed, the 5 kW remains a proposal. Computing auxiliaries and cooling must also be checked.

05 / Product passport

Product passport

Complete these ten fields before preparing an issuance. Missing fields identify the evidence still required.

Download PDF

Asset, owner, operator, measurement point and boundary.
Product, physical unit, quantity, interval and timezone.
Useful service, quality parameters, limits and response time.
Instruments, raw data, verification, methodology and uncertainty.
Baseline and version, adjustments, command and intervention logs.
Signed verification statement and dispute-resolution procedure.
Right holder, obligated party, jurisdiction and contractual basis.
Payment formula, price or index, costs, taxes and reserve.
Issuance cap, unique identifier, encumbrances and compatibility.
Transfer, due date, settlement, retirement and failure procedure.

Editorial corrections

The catalogue is based on the supplied table and corrected for teaching. The number 118 defines this edition’s scope; no universal physical periodicity is assumed.

Repeated numbers and duplicate cells are consolidated. Numbers 1-118 serve as learning-card addresses.
No. 11 is electric potential φ; magnetic flux is no. 26. No. 45 is p(t), and no. 46 is P.
Nos. 71-73 use X₁, X₂, X₀: units depend on voltage or current. No. 78 is clarified as harmonic order h; amplitude remains no. 69.
Entries 81-85 show quantities describing the events. No. 103 is Kf in W/Hz. No. 105 is explicitly tied to exp(λc t).
For nos. 114-117 formulas and units are separated: S, Ω, Hz/V, Wb. No. 118 is approximately 1/137 with unit 1.

Original poster · JPEG

06 / Sources

Sources

Official pages and open learning resources. Checked 23 Sep 2026. The A/B/C classification and examples are XPower editorial work.

S1
BIPM · SI Brochure ↗
Units and definitions; ninth edition, 2026 update.
S2
EVO · Measurement & Verification ↗
Savings assessment through comparison and adjustments.
S3
IEC 61000-4-30:2025 ↗
Power-quality measurement methods; official entry, corrected 2026-07. The full standard is paid.
S4
Bank of Russia · Digital financial assets ↗
Digital-rights and infrastructure guidance. Check conditions at issuance.
S5
SO UPS · Demand response ↗
Documents and materials on Russian demand response.
S6
PJM · Regulation Market ↗
An example of a regulation-services market. PJM rules do not automatically apply elsewhere.
S7
AIB · Guarantees of Origin ↗
Origin-registry participation: receipt, transfer and cancellation.
S8
NIST · Fundamental Physical Constants ↗
Fundamental constants and metrology; CODATA 2022 values.
S9
OpenStax · University Physics, Volume 2 ↗
Open textbook for further study of alternating-current circuits.

Catalogue of 118 elements

1. q · Electric charge

C. Amount of charge; q = ∫I dt. Energy also depends on voltage.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

2. ρ · Volume charge density

C/m³. Charge per unit volume, used in field calculations.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

3. σq · Surface charge density

C/m². Charge per unit surface area of a conductor or dielectric.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

4. λq · Linear charge density

C/m. Charge per unit length, useful for a long-conductor model.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

5. I · Electric current

A. Rate of charge flow. Heating and load limits depend on current.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

6. J · Current density

A/m². Current per cross-sectional area; helps assess local heating.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

7. E · Electric field strength

V/m. Force per unit charge, used in insulation design.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

8. B · Magnetic flux density

T. Describes the magnetic field in motors and transformers.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

9. D · Electric displacement

C/m². Combines the electric field and material polarization.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

10. H · Magnetic field strength

A/m. In a linear medium B = μH. Used to design magnetic circuits.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

11. φ · Electric potential

V. Potential energy per unit charge relative to a chosen reference.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

12. ℰ · Electromotive force

V. Source work per unit charge; characterizes a generator or battery.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

13. Ppol · Polarization

C/m². Electric dipole moment per unit volume of material.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

14. Mmag · Magnetization

A/m. Magnetic moment per unit volume, important for magnetic cores.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

15. ε · Permittivity

F/m. Material response to an electric field; affects capacitance.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

16. μ · Permeability

H/m. Relates flux density and magnetic field strength in a material model.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

17. σ · Conductivity

S/m. Ability to conduct current; in a simple model J = σE.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

18. ρe · Resistivity

Ω·m. Inverse of material conductivity; depends on temperature.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

19. χe · Electric susceptibility

1. Dimensionless polarization response to an electric field.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

20. χm · Magnetic susceptibility

1. Dimensionless magnetization response to a magnetic field.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

21. tanδ · Dielectric loss tangent

1. Characterizes dielectric losses; supports insulation diagnostics.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

22. Ebd · Dielectric strength

V/m. Field at which breakdown can occur under specified test conditions.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

23. μc · Carrier mobility

m²/(V·s). Relates carrier drift velocity to electric field strength.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

24. n · Carrier concentration

m⁻³. Number of free charge carriers per unit volume.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

25. ΨD · Electric displacement flux

C. Flux of D through a surface, related to free charge.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

26. Φ · Magnetic flux

Wb. Surface integral of magnetic flux density.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

27. λ · Flux linkage

Wb. Sum of fluxes linked by turns; determines induced voltage.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

28. U · Voltage

V. Potential difference; an essential supply characteristic at the delivery point.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

29. R · Resistance

Ω. At current I, resistive power losses equal I²R.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

30. G · Conductance

S. Reciprocal resistance of a resistive element: G = 1/R.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

31. C · Capacitance

F. Ability to store charge. Ideal capacitor energy equals CU²/2.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

32. L · Inductance

H. Relates current and flux linkage. A linear inductor stores LI²/2.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

33. M · Mutual inductance

H. Magnetic coupling between circuits, central to transformer operation.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

34. Z · Impedance

Ω. Complex opposition to alternating current, with resistive and reactive parts.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

35. Y · Admittance

S. Reciprocal impedance: Y = 1/Z.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

36. X · Reactance

Ω. Imaginary part of impedance, set by capacitance and inductance.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

37. Bs · Susceptance

S. Imaginary part of admittance, used in compensation calculations.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

38. τ · Time constant

s. Characteristic transient time; affects response speed.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

39. f₀ · Resonant frequency

Hz. Resonance frequency; relevant to filters and operating stability.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

40. Qf · Quality factor

1. Describes losses and resonance sharpness in an oscillating system.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

41. We · Electrical energy

J; kWh. Energy transferred over an interval: W = ∫P dt; 1 kWh = 3.6 MJ.

This quantity can define a delivery volume or verified effect. Issuance needs a contract, obligor, methodology and unique rights accounting.

42. Wm · Magnetic energy

J. Energy stored in a magnetic field, for example in an inductor.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

43. Wem · Electromagnetic energy

J. Energy of electric and magnetic fields in the region considered.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

44. u · Energy density

J/m³. Energy per unit volume; useful for fields and storage.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

45. p(t) · Instantaneous power

W. In a single-phase circuit p(t) = u(t)i(t); energy requires integration.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

46. P · Active power

W; kW. Average rate of energy transfer over a specified interval.

This quantity can define a delivery volume or verified effect. Issuance needs a contract, obligor, methodology and unique rights accounting.

47. Q · Reactive power

var; kvar. Describes energy exchange with fields in alternating-current operation.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

48. S · Apparent power

VA; kVA. For one phase S = Urms·Irms; relevant to equipment loading.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

49. S̲ · Complex power

VA. For sinusoidal operation S̲ = P + jQ; its magnitude is apparent power.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

50. PF · Power factor

1. Ratio P/S. Includes waveform effects under the adopted definition of S.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

51. cosφ · Displacement factor

1. Cosine of the phase angle between fundamental voltage and current.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

52. Sp · Poynting vector

W/m². Electromagnetic energy flux density; Sp = E × H.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

53. pv · Volume power density

W/m³. Local energy conversion rate; the resistive contribution equals J·E.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

54. Wloss · Energy losses

J; kWh. Energy lost within a chosen boundary; reduction requires a comparable balance.

This quantity can define a delivery volume or verified effect. Issuance needs a contract, obligor, methodology and unique rights accounting.

55. η · Efficiency

1; %. Useful output energy divided by input energy for a specified boundary.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

56. f · Frequency

Hz. Cycles per second; a system condition and frequency-control parameter.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

57. ω · Angular frequency

rad/s. Rate of phase change; ω = 2πf.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

58. T · Oscillation period

s. Duration of one cycle: T = 1/f. Service duration is specified separately.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

59. θ · Phase

rad. Position within a cycle relative to a chosen reference.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

60. Δφ · Phase difference

rad. Relative phase of two signals; important for power and synchronization.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

61. X̂ · Amplitude

[X]. Maximum signal excursion from the chosen mean level.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

62. Xpp · Peak-to-peak value

[X]. Difference between the maximum and minimum signal values.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

63. Xrms · Root mean square

[X]. Square root of the mean squared signal; used for current and voltage.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

64. X̄ · Mean value

[X]. Average over a stated window. Window length affects peak assessment.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

65. Xabs · Mean rectified value

[X]. Mean of the absolute signal value.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

66. CF · Crest factor

1. Peak magnitude divided by RMS; indicates sharp peaks.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

67. FF · Form factor

1. RMS divided by mean rectified value.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

68. dX/dt · Rate of change

[X]/s. For power, describes the rate of load increase or reduction.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

69. Xh · Harmonic amplitude

[X]. Magnitude of a selected harmonic, used in power-quality analysis.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

70. SX(f) · Spectral density

[X]²/Hz. Distribution of mean-square signal value over frequency.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

71. X₁ · Positive sequence

[X]. Balanced three-phase component with the normal phase order.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

72. X₂ · Negative sequence

[X]. Component with reversed phase order, associated with unbalance.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

73. X₀ · Zero sequence

[X]. Three in-phase components, important for neutral currents.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

74. U₂/U₁ · Voltage unbalance

1; %. Negative-sequence voltage divided by positive-sequence voltage.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

75. I₂/I₁ · Current unbalance

1; %. Negative-sequence current divided by positive-sequence current.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

76. THDu · Voltage distortion

1; %. Total harmonic distortion relative to a specified reference.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

77. THDi · Current distortion

1; %. Current distortion; limits and harmonic range must be specified.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

78. h · Harmonic order

1. Frequency-component index: fh = h·f₁. Amplitude is covered by no. 69.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

79. Δf · Frequency deviation

Hz. Difference between measured and reference frequency.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

80. df/dt · Rate of change of frequency

Hz/s. Describes how quickly frequency changes; needs a defined measurement window.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

81. dip · Voltage dip

V; s. Voltage reduction event, described by residual voltage and duration.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

82. swell · Voltage swell

V; s. Voltage increase event; requires magnitude, duration and threshold.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

83. interrupt · Supply interruption

s; count. Loss of supply under an agreed threshold; count and duration are tracked.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

84. transient · Transient overvoltage

V; s. Short transient event; sufficient instrument bandwidth is required.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

85. RVC · Rapid voltage change

%; s. Change in voltage magnitude defined by the selected measurement method.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

86. Pst / Plt · Flicker

1. Indices of short-term and long-term light flicker severity.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

87. λw · Wavelength

m. Spatial wave period; λw = vp/f.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

88. vp · Phase velocity

m/s. Speed of a constant-phase point in a wave.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

89. vg · Group velocity

m/s. Envelope speed of a narrowband wave packet in the applicable model.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

90. γ · Propagation constant

m⁻¹. Complex parameter γ = α + jβ: attenuation and phase change.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

91. αatt · Attenuation constant

Np/m. Describes amplitude reduction along a propagation path.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

92. β · Phase constant

rad/m. Phase change per unit length.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

93. ηw · Wave impedance

Ω. Ratio of electric to magnetic wave components.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

94. δs · Skin depth

m. Characteristic penetration depth of an alternating field in a conductor.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

95. Γ · Reflection coefficient

1. Ratio of reflected to incident waves at a specified point.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

96. VSWR · Standing wave ratio

1. Maximum-to-minimum standing-wave amplitude ratio.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

97. Zth · Thevenin impedance

Ω. Equivalent network impedance at the chosen connection point.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

98. Ik · Short-circuit current

A; kA. Calculated fault current, determining protection requirements.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

99. Sk · Short-circuit power

VA; MVA. Network-strength indicator at a point; does not express usable load capacity.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

100. X/R · X/R ratio

1. Ratio of reactive to resistive parts of network impedance.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

101. δp · Power angle

rad. Angular position related to power transfer and stability.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

102. Hsys · Inertia constant

s. Stored kinetic energy normalized by rated power.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

103. Kf · Power-frequency characteristic

W/Hz. Slope of active-power change versus frequency change.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

104. Rd · Droop

1; %. Normalized relationship between frequency and controller power changes.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

105. λc · Modal decay exponent

s⁻¹. In exp(λc t), the real part sets decay or growth.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

106. SCR · Short-circuit ratio

1. Short-circuit power divided by the chosen converter rating; a grid-strength indicator.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

107. en · Voltage noise density

V/√Hz. Amplitude spectral density of voltage noise in a measurement circuit.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

108. in · Current noise density

A/√Hz. Amplitude spectral density of current noise.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

109. SN · Noise power density

W/Hz. Noise power per unit bandwidth.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

110. SNR · Signal-to-noise ratio

dB. Describes how clearly a useful signal stands above noise.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

111. L(f) · Phase noise

dBc/Hz. Spectral measure of an oscillator's phase instability.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

112. σy(τ) · Allan deviation

1. Measure of fractional-frequency stability across averaging times.

Helps specify quality, limits or acceptance. A standalone product requires a distinct service and payment obligation.

113. e · Elementary charge

C. Fundamental constant: exactly 1.602176634 × 10⁻¹⁹ C.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

114. G₀ · Conductance quantum

S. Quantum quantity G₀ = 2e²/h, measured in siemens.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

115. RK · Von Klitzing constant

Ω. RK = h/e²; used in quantum resistance standards.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

116. KJ · Josephson constant

Hz/V. KJ = 2e/h; relates frequency and voltage in the Josephson effect.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

117. Φ₀ · Magnetic flux quantum

Wb. Φ₀ = h/(2e); underlies superconducting measuring devices.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.

118. αfs · Fine-structure constant

1. Dimensionless electromagnetic coupling constant, approximately 1/137.

Used in engineering calculations or metrology. Economic value attaches to a service, equipment, licence or proven result.