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Published onPosted on by LaoRen Last updated on August 26th, 2021 Reading time: 2 min, 0 images, 2131 views

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The four-quadrant diagram in electricity metering

When we talk about power we always need to indicate the direction and which sort of power. We can have:

Active power, P Active power is expressed in watt (W). Sometimes this power is also called “real power” This is the power you are actually consuming.

Reactive power, Q Reactive power is expressed in volt-ampere reactive (var) This power is stored in components, then released again back to the source through the AC cycle. Capacitors and inductors do this.

Apparent power, S Apparent power is expressed in volt-ampere (VA) (RMS voltage times the RMS current). A power supply must be capable to output the full apparent power delivered to a circuit, not just the active power.

Quadrant I Quadrant I is defined as an area where both powers flow positively. Both are delivered to the consumer load. In many cases the CLOU terminology is forward. The power factor is lagging, we have inductive influence. The IEC literature is using the term import. In this quadrant we have Import of active power and Import of reactive power.

Quadrant II In quadrant II, reactive power is positive and active power flows negatively. In many cases the CLOU terminology is reversed. The IEC literature is using the term export.

Quadrant III In quadrant III, reactive and active power flow negatively (both powers are received from the customer). This is also a export condition.

Quadrant IV In quadrant IV, reactive power flows negatively, and active power flows positively. This is a import condition.

The interactive diagram below shows the relationship between the phase angle φ, apparent-, active- and reactive power respective energy. The diagram is in accordance with clauses 12 and 14 of IEC 60375. Reference is the current vector (fixed on right-hand line, 0°). The phase angle φ between voltage V and current I is taken to be positive in the mathematical sense (counter clockwise).

Four Quadrant Simulation (IEC62053-23)

Geometric representation of active and reactive power

Note: The sine-wave diagram was changed to mathematical expression with reference on current (green). The oscilloscope view with reference on voltage was leading to misunderstanding. (24.11.2020)

Thank you for taking a look and for valuable comments.

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30 Replies to “The four-quadrant diagram in electricity metering”

I’d like to revisit a question asked earlier. In Quad1 and Quad2 the voltage leads the current (current lags the voltage). Why are not both of these two quadrants labeled inductive?

Thanks for coming back, William.
The IEC IEC62053-23 model is based on current as reference.
In quadrant 1 we have import (P+) with a lagging current.
In quadrant 2 the flow direction is export (P-).
So the current is leading the voltage.

Hi,
In what circumstance the export can happen, considering a power factor correction capacitor bank with the series reactor. Sometimes analyzer showing -92 Deg. and export in one of the phases. Is it a tuning issue?

Seems you have overcompensated the system. Best praxis is to compensate only by 95 %. If you have a 100 % compensation, you will face reverse currents on low inductive loads. Some fine-tuning is recommended.

Mike, you are right. You can also take a look at the vectorial representation for voltage and current. When we look at the formula (S = U * I) we see that S is following U and I.

I’d like to revisit a question asked earlier. In Quad1 and Quad2 the voltage leads the current (current lags the voltage). Why are not both of these two quadrants labeled inductive?

Thanks for coming back, William.

The IEC IEC62053-23 model is based on current as reference.

In quadrant 1 we have import (P+) with a lagging current.

In quadrant 2 the flow direction is export (P-).

So the current is leading the voltage.

Hi,

In what circumstance the export can happen, considering a power factor correction capacitor bank with the series reactor. Sometimes analyzer showing -92 Deg. and export in one of the phases. Is it a tuning issue?

Seems you have overcompensated the system. Best praxis is to compensate only by 95 %. If you have a 100 % compensation, you will face reverse currents on low inductive loads. Some fine-tuning is recommended.

MUY CLARA SU REPRESENTACION, GRACIAS

Thanks for taking a look and kind comment.

So the vector Ua (voltage L1) follows the vector of the apparent Power S. Is my opinion correct?

Mike, you are right. You can also take a look at the vectorial representation for voltage and current. When we look at the formula (S = U * I) we see that S is following U and I.