Collection of formulas (for UMG measurement devices)

Collection of formulas (for UMG measurement devices)

Effective value of the current for phase conductor p

Effective value of the neutral conductor current

Effective voltage L-N

Effective voltage L-L

Neutral voltage (vectorial)

Effective power for phase conductor

Apparent power for phase conductor p

The apparent power is unsigned.
The apparent power is unsigned.

Total apparent power (arithmetic)

The apparent power is unsigned.
The apparent power is unsigned.

Ordinal numbers of harmonics

THD

  • THD (Total Harmonic Distortion) is the distortion factor and gives the relationship of the harmonic portions of oscillation to the fundamental oscillation.

THD for voltage

  • M = Ordinal number of harmonics
  • M = 40 (UMG 604, UMG 508, UMG 96RM)
  • M = 63 (UMG 605, UMG 511)
  • Mains frequency fund equals n = 1

THD for current

  • M = Ordinal number of harmonics
  • M = 40 (UMG 604, UMG 508, UMG 96RM)
  • M = 63 (UMG 605, UMG 511)
  • Mains frequency fund equals n = 1

ZHD

  • ZHD is theTHD for interharmonics
  • Is calculated in the device series UMG 511 and UMG 605

Interharmonics

  • Sinusoidal form oscillations, whose frequencies are not whole multipliers of the mains frequency (fundamental oscillation)
  • Is calculated in the device series UMG 511 and UMG 605
  • Calculation and measurement processes according to DIN EN 61000-4-30
  • The ordinal number of an interharmonic equates to the ordinal number of the next smallest harmonic. For example, the 3rd interharmonic lies between the 3rd and 4th harmonics.

TDD (I)

  • TDD (Total Demand Distortion) gives the relationship between the current harmonics (THDi) and the effective current value with full load.
  • IL = Full load current
  • M = 40 (UMG 604, UMG 508, UMG 96RM)
  • M = 63 (UMG 605, UMG 511)

Ripple control signal U (EN 61000-4-30)

The ripple control signal U (200 ms measured value) is a voltage measured with a carrier frequency specified by the user. Only frequencies below 3 kHz are taken into consideration.

Ripple control signal I

The ripple control signal I (200 ms measured value) is a current measured with a carrier frequency specified by the user. Only frequencies below 3 kHz are taken into consideration.

Positive-negative-zero sequence component

  • The proportion of voltage or current unbalance in a three-phase system is labelled with the positive, negative and zero sequence components.
  • The symmetry of the three-phase system strived for in normal operation is disturbed by unbalanced loads, faults and operating equipment.
    - A three-phase system is referred to as exhibiting symmetry if the three phase conductor voltages and currents are of an equal size and are phase- shifted at 120° to each other. If one or both conditions are not fulfilled then the system is deemed unbalanced. Through the calculation of the symmetrical components comprising positive sequence component, negative sequence component and zero sequence component a simplified analysis of an unbalanced fault in a three-phase system is possible.
  • Unbalance is a characteristic of the power quality, for which threshold values have been stipulated in international standards (e.g. EN 50160).

Positive sequence component

Negative sequence component

Zero sequence component

A zero sequence component can only arise if a total current is able to flow back via the neutral conductor.
A zero sequence component can only arise if a total current is able to flow back via the neutral conductor.

Voltage unbalance

Downward deviation U (EN 61000-4-30)

Downward deviation I

K-factor

  • The K factor describes the increase in eddy current losses with a harmonics load. In the case of sinusoidal loading of the transformer the K factor = 1. The greater the K factor, the more heavily a transformer can be loaded with harmonics without overheating.

Power Factor (arithmetic)

The power factor is unsigned.
The power factor is unsigned.

Cosphi – Fundamental Power Factor

  • Only the fundamental oscillation is used in order to calculate the cosphi
  • Cosphi sign:
    - = for delivery of effective power
    + = for consumption of effective power

Cosphi sum

  • Cosphi sign:
    - = for delivery of effective power
    + = for consumption of effective power

Phase angle Phi

  • The phase angle between current and voltage of phase conductor p is calculated and depicted per DIN EN 61557-12.
  • The sign of the phase angle corresponds with the sign of the reactive power.

Fundamental oscillation reactive power

The fundamental oscillation reactive power is the reactive power of the fundamental oscillation and is calculated with the Fourier analysis (FFT).The voltage and current do not need to be sinusoidal in form. All reactive power calculations in the device are fundamental oscillation reactive power calculations.

Reactive power sign

  • Sign Q = +1 for phi in the range 0 ... 180 ° (inductive)
  • Sign Q = -1 for phi in the range 180 ... 360 ° (capacitive)

Reactive power for phase conductor p

Reactive power of the fundamental oscillation
Reactive power of the fundamental oscillation

Total reactive power

Reactive power of fundamental oscillation
Reactive power of fundamental oscillation

Distortion reactive power

  • The distortion reactive power is the reactive power of all harmonics and is calculated with the Fourier analysis (FFT).
  • The apparent power S contains the fundamental oscillation and all harmonic portions up to the Mth harmonic.
  • The effective power P contains the fundamental oscillation and all harmonic portions up to the Mth harmonic.
  • M = 40 (UMG 604, UMG 508, UMG 96RM)
  • M = 63 (UMG 605, UMG 511)

Reactive energy per phase

Reactive energy per phase, inductive

Reactive energy per phase, capacitive

Reactive energy, sum L1–L3

Reactive energy, sum L1–L3, inductive

Reactive energy, sum L1–L3, capacitive

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