The four-quadrant diagram in electricity metering

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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.

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

  1. As KVAH is associated with KVARH ,why it is not represented in 4 quadrants?. It is only shown as export and import only but not in 4 quadrants

    1. In this graphical representation the apparent power (S) is considered as constant. With changing of the angle you see that the active power (P) and the reactive power (Q) are in/decreasing. The four quadrant model is used for billing purpose. Each quadrant has its own register. So the utility knows whether it was import or export, inductive or capacitive. The IEC62053-23, annex C gives this simulation as diagram.

  2. Hi!

    Very informative web page, but I would like to highlight some points, perhaps you could clarify these:
    Let us assume the positive current direction is towards the load. As per definition, Q = U*I*sin(theta). When theta in 0..pi, the Q is positive. The standard behind the 4 quadrant picture defines that the power factor is positive in Q1 but negative in Q2 although the reactive power sign is not changing – the load is absorbing reactive power (inductor)in both quadrants. Why they use the capacitor icon in the standard for Q2?

    In Q3 and Q4, theta 180…360, the current is leading and the load is injecting reactive power (capacitor). Still, inductor sign for Q3.

    I’ve seen that in some contexts this 4Q picture is interpreted so that the positive current direction is reversed in Q2 and Q3. That would flip the quadrants, but is not really highlighted anywhere where this 4Q picture is used.

    How do you see it?

    1. Thank you for your comment, Henrik. You have your question nice elaborated. We have a sign-change at 90° respective at 270°. So in this range you need to set your current negative (export). Your last conclusion is right, though the IEC standard doesn’t mention it explicit. You can only refer to the current arrows.

  3. Great stuff. Really helpful in visualising where the voltage and current are for each of the quadrant. I will be back to use your simulation again!

    Thank you

    1. The general information is in the text. If you have a specific question, please let me know.

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