## 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 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.

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.

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

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).

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.

Editor's note: This article was originally published in July 2019 and has been updated for comprehensiveness.

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74 Replies to “The four-quadrant diagram in electricity metering”
1. Masresha Asfaw says:

Dear Mr.LaoreN
Greetings, This is Masresha from Ethiopia ,years before in China CLOU you shared us a lot of deep knowledge while visiting the company inline with you gave us some solution to solve the problem of our Zera machine .
Today the question what we have faced in our utility billing is in some condition the reactive energy reading is more than active energy , Is it possible to be occurred ?The other question is if we only sell energy in fourth quadrant measurement energy meter ,do we usually collect energy measurement and others sum of first and fourth quadrant (I+IV) ?
B. regards,
Masresha

1. Reinhard Günther says:

Dear Masresha,
Greetings! It's wonderful to hear from you again, and I'm glad to know that our previous interactions were helpful to you and your team in Ethiopia.

1.Reactive Energy Reading More Than Active Energy:
Yes, it is possible for the reactive energy reading to be higher than the active energy under certain conditions. This typically occurs in systems with poor power factor, where there is a large amount of reactive power relative to active power. Such scenarios are common in installations with heavy inductive loads, such as motors and transformers, operating under light load conditions. Ensuring proper power factor correction can help mitigate this issue.
Another common problem is the wiring, read the related article here.

2.Energy Measurement in the Fourth Quadrant:
Primarily, you bill for the import of active energy (kWh). If, however, you also bill for reactive energy (kVArh), especially for industrial customers, the standard practice is to use the sum of the reactive energy registers from Quadrant I and Quadrant IV (Q1 + Q4). This approach ensures accurate accounting and billing for both active and reactive energy consumption.

I hope this clarifies your questions. If you need further assistance or more detailed information, please feel free to reach out. It's always a pleasure to assist you.

2. Bizuhan Kebede says:

Dear Mr.Laoren
I came back to agene for asking about aquation. What we have faced in this project is that after we implement it, each AMI meter will send inverse current occurrence events and the starting time and ending time of these events to the head-end system (HES). Some meters have a long-time occurrence event, which means, for example, a 10-day event, and some of them have 8, 7, 6, and 3-day events. Is it a normal condition? in this kind of technology.? Even when we investigated some meters on site, we could not get that much of a result. So is it related to the customer machine, power factor corrector, and so on?

1. LaoRen says:

Bizuhan, if the meter is properly connected, prolonged occurrences of reversed current events should not persist for days. This is highly unusual and abnormal. I recommend that you directly read the event log from the meter using an optical head. Additionally, please verify the energy export register simultaneously. Extended durations of such events should be evident in the registers. It is possible that your meters are reporting another event, such as under-voltage, as reverse current. Alternatively, there may be an issue with how your HES (Head-End System) is mapping the events. I advise you to communicate with both the meter and HES vendors to ensure that the events are correctly assigned.

3. Bizuhan Kebede says:

Dear Mr. Loren,
Thank you for your proper answer. I appreciate that. but we are now implementing the new technology in our country through the AMI project. What we have faced in this project is that after we implement it, each AMI meter will send inverse current occurrence events to the head-end system (HES). We annualized this event and checked the AMI meter status on site and the wiring connection. Some meters have wiring connection errors, but the majority of meters do not have this kind of problem. Because of this, we are now confused, so I am asking you this question. Still, I need your support in more detail on this, please.

1. LaoRen says:

Bizuhan, thank you for additional information. Since you get the events at the HES, you might be able to see also the start- and end time. If an electro-motor is switched off, you can have an electromagnetic force in reverse direction for a short period (<30 s). Our meters are triggering reverse current events after 30 seconds to avoid false messages to the HES. Maybe your meters have a related setting, which you can adjust. If your difference between start and end time of the event is longer, I recommend using a data logger at a meter where it happens frequently.

4. Bizuhan Kebede says:

Dear Mr. LAOREN
I have question what is the main reason? AMI meters show the inverse current occurrence event without any R, S, or T-phase or R, S, and T-phase CT (current transformer) wiring connection error. Is it depending on the customer load? I want to know the reason, please, if you have any concerns about this.

1. LaoRen says:

Thank you for your question, Bizuhan. Actually electronic energy meters have better sensing technonogies that the old Ferraris meters. Therefor such events are noticed more likely now. Without knowing more details, my first guess is, that the neutral conductor has a too high resistance. Together with unbalanced load your can get reverse currents. This is a well-known problem. Please take a look at my related article. The second guess, non-linear loads are causing harmonics and are leading to reverse flow. To pinpoint the exact reason for the inverse current events in your specific situation, it is recommended to involve a qualified electrician or a professional from your utility company. They can perform a thorough investigation, examine the metering setup, assess the customer's load, and identify any potential contributing factors.

5. Mark says:

So quadrant 2 is considered to be Capacitive Generator?
In this case the reference vector from 0 degrees goes to 180 degrees and then what kind of reference is this that is not fixed?
I think it is not enough to say that our diagram conforms to the IEC 62053-23 standard, we need to explain why we have this type of notation.
We know that angles are always measured from current to voltage.
Positive angles are always inductive and negative angles are capacitive.
In the diagram on this site, this contradiction appears in quadrants 2 and 3.
In quadrant 2 the angle is positive (displacement of vector U in the trigonometric sense), but the quadrant has a capacitor drawn.
In quadrant 3 the angle is negative (the displacement of the vector U in the trigonometric sense but the angle is measured from current to voltage – so the direction is clockwise), but the quadrant has an inductor drawn.
How can you explain these things?

1. LaoRen says:

Referring to a standard is an invaluable resource for resolving disputes and gaining clarification, particularly in the field of electrotechnology. The International Electrotechnical Commission (IEC) standards are globally recognized and widely adopted in over 90 countries. Therefore, the previous answer was traceable and sufficient.
To provide further information, it's important to note that the four-quadrant model according to the IEC is based on the current as the reference axis (horizontal), while ANSI (American National Standards Institute) utilizes the voltage as the reference axis (vertical). As a result, when the current transitions from import to export, a previously leading voltage becomes lagging. In other words:

– Quadrant 1: Positive active power, positive reactive power. This quadrant represents a load that consumes both active power and inductive reactive power, which is the most common scenario for many loads.
– Quadrant 2: Negative active power, positive reactive power. This quadrant represents a load that exports active power back to the grid while still consuming capacitive reactive power. It indicates a power factor leaning towards the capacitive side.

The distinctions between the IEC and ANSI standards in terms of reference axes should be taken into consideration when interpreting the quadrants in power factor diagrams.

6. Mark says:

Hello mister LAOREN
What do you think about the following diagram?
Are the notations there correct?
If the answer is 'yes', why does quadrant 2 and 4 have a capacitor drawn in your diagram?

1. LaoRen says:

Hi Mark, thank you for your comment and link. Our diagram shows the geometric representation of active and reactive power according to IEC 62053-23:2020 (Static meters for reactive energy), where it's clearly stated that the quadrants 2 and 4 are capacitive. (see annex C in the standard)