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

  1. Our billing system is to compute by taking three para meters these are Active energy (kwh), reactive energy (Kvarh) and max. demand ( Kw) .In order to calculate the average power factor of the month, we have to take the reading of Kvarh so where shall we take the reactive component from the first or the fourth quadrant as per the obis cod.

    1. Thank you, now it’s clear. For average power-factor calculation, you take the SUM of Q1 + Q4. You don’t know whether the reactive energy is inductive (Q1) or capacitive (Q4). The load can also sometimes change from Q1 to Q4.

  2. Thank you indeed Mr. LAOARN , We are Electricity seller company so I am expecting to take the reading from positive parameter import quadrant i.e first only . Am I right? Last time when the there was a discrepancy of one phase current connection , we couldn’t take a maximum demand reading . While we changed the connection of the current terminal in the correct way all the reading was displayed including max.demand in Kw . What was reason behind Sir.?
    b.regards,
    Masresha

    1. The quadrants are to capture the reactive power (Q). For consumption billing, you take the active power (P). The import (P+) is always moving horizontal, so the active import doesn’t have a quadrant indication. It’s between Q1 and Q4. You won’t find an active energy register with quadrant indication. Look at the units. Active energy has kWh while reactive energy has kvarh.
      For the display, the best guess is that the meter has rebooted during the connection change and then performed a self-test. This can lead to several display indications. But should be fine after 10 seconds.

Clou Symbol55

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