What is the difference between vectorial- and arithmetic VA calculation?

There are two commonly used methods to calculate the apparent power (VA).
The traditional method is the vectorial calculation. Here we are adding the active power (W) from each phase and the reactive power (var) from each phase. As the reactive power vector has a 90° angle vers. the active power we can calculate the hypotenuse (VA). Old meter installations are using this method.
With electronic meters with microprocessor we are able to calculate the VA for each phase individually and then add the VA values. This method is called arithmetic calculation. It is more accurate.
CLOU meters are using the arithmetic calculation. Some meters can be set to vectorial calculation mode.

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What is Maximum Demand Measurement?

Demand is a measure of average power consumption over a fixed time interval. Maximum (or peak) demand is the highest demand recorded over the billing period. The billing period is mostly end of the month.

Non-domestic electrical power users often have to pay a maximum demand charge in addition to the charge for the consumed energy. This additional charge is based on the highest amount of power used over a period (e.g. 15 minutes) during the billing period.

CLOU meters can operate with a fixed window or with a sliding window. Please note that not all meters have this function.

What is the difference?

The fixed window is defined in certain steps (e.g. 15 minutes), starting at the full hour. It can be programmed for the following fixed intervals:

  • 5 minutes
  • 15 minutes
  • 30 minutes
  • 60 minutes

At the end of each fixed window period, the average power for that period is calculated. If this value is higher than the already existing value, it is stored as the MD (maximum demand).

The sliding window is the CLOU default setting. For sub integration period the default is 1 minute.

At the end of a sub integration period the average power is calculated for one integration period. If this value is higher than the already existing value then this is stored as MD. The integration period slides by a window of the sub integration period.

sub periods
Sub periods for sliding window
Integration period 1 min 2 min 5 min 6 min 12 min
5 min 5 1
15 min 15 3
30 min 30 15 6 5
60 min 60 30 12 10 5

The maximum demand register MD will be reset at the set transferring time of each month (1stof each month).
Demand value measured in 6 digits, including 4 integers and 2 decimals.

Which impact has the measurement with fixed- or sliding window on the result?
We take a simple example:
Below we see the energy consumption for a time period from 9 o’clock to 9:30. The reading is once per minute.
energy consumption
The diagram below shows the calculated demand for above load profile between 09:15 and 09:33. We can see that the sliding window calculation shows a MD of 157 kW (blue line) while the fixed window shows a MD of 141 kW (red line).
maximum demand
What do we learn?
With the same load profile the maximum demand values can be different. If the customer has to pay an additional penalty for exceeding 150 kW, he does not have to pay by calculation with fixed window.
With sliding window calculation he needs to pay, because with 157 kW he is exceeding his limit.
The benefit for utilities is that the consumers will not switch-on all machines and appliances at the same time to avoid the penalty. This effect has also big influence on minimizing of peak loads in the grid.
We recommend to use our default setting with 15 minutes interval, sliding by one minute.

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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 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

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How long does a no-load test take?

First we take a look at the IEC standards.

The run-time depends on several factors like

  • accuracy class
  • meter constant
  • number of elements
  • Nominal Voltage
  • Maximum Current

Test criteria
When the voltage is applied with no current flowing in the current circuit, the test output of the meter shall not produce more than one pulse.
For this test, the current circuit shall be open-circuit and a voltage of 115 % of the reference voltage shall be applied to the voltage circuits.

Minimum Required Time for No-Load Test
nominal voltage V
maximum current A
meter constant i/kWh
IEC62053-21 class 2
IEC62053-23 class 2

IEC62053-21 class 1
IEC62053-22 class 0.5S

IEC62053-22 class 0.2S

For MID meters according to DIN EN BS 50470-3 the calculation formula is different.

Minimum Required Time for No-Load Test EN50470-3
nominal voltage V
nominal current A
meter constant i/kWh
Direct connected class A
Direct connected class B
Direct connected class C
CT connected class A
CT connected class B
CT connected class C
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Which standard is applicable for acceptance tests for energy meters?

From time to time there are some questions regarding the acceptance inspection for energy meters. This paper is to clarify the legal and metrological matters.

The IEC 61358 (later referred to old) was published in May 1996 and withdrawn in September 2008. The old standard has been replaced by IEC 62058-11 and IEC 62058-31.
This new standards take special care about the electronic energy meters while the old standard was written at a time where electromechanically energy meters have been wide spread.

For full wording see introduction of IEC 62058-11
This standard (IEC 62058-11)… and IEC 62058-31… cancels and replaces the following standards..
IEC 61358 Acceptance inspection for direct connected alternating current static watt-hour meters for active energy (classes 1 and 2).

While IEC 62058-11 is dealing with the General Acceptance Methods, for this document the relevant part is the IEC 62058-31 (later referred to new).

Means, the old standard is already cancelled since > 8 years.
The guaranteed stability date of the new standard is 2018. Soon we can expect either a updated release of the IEC 62058 family or a “very new” standard.

From the legal point of view a end-customer (the domestic user) can claim that the initial verification done by the old standard is not valid. The comparison table below covers only the essential part for the metrology. Differences in the sampling methods are not covered. Comments are cursive.

IEC 61358, old IEC 62058-31, new
Item 8.2, Test No.1, AC voltage test

Parameters: 4 kV for 1 minute

Item 5.3, Test No.1, AC voltage test Parameters: 3.2 kV for 2 seconds
The IEC committee had certain reasons to reduce the time and voltage:

1. The electronic meters have a plastic housing together with a printed circuit board. The historical events of poor wiring insulation versus a metal housing are not occurring anymore.

2. The lifetime of e electronic meter is increasing by putting less stress on the PCB board.

Item 8.5, Tests No. 4…9 (values for cl.1)

Accuracy limits for meters class 1

Item 5.6, Tests No. 4…9

Accuracy limits for meters class 1

Test No.4 +/- 2.5 % Test No.4 +/- 1.5 %
Test No.5 +/- 1.5 % Test No.5 +/- 1.0 %
Test No.6 +/- 2.0 % Test No.6 +/- 1.0 %
Test No.7 +/- 2.5 % Test No.7 +/- 2.0 %
Test No.8 +/- 2.5 % Test No.8 +/- 2.0 %
Test No.9 +/- 1.5 % Test No.9 +/- 1.0 %
Electronic energy meters are much more accurate than electromechanical meters, therefor all error tolerances are reduced.
Item 8.6, Test No.10,

verification of the meter constant


Difference between metrological pulse output and display increment

Allowed error: +/- 0.2%

Item 5.7, Test No.10,

verification of the register


Difference between injected energy and incremented energy on display

Allowed error: +/- 1 %

Here we have a comparison of pulses generated by the rotating disk or pulse output with the recorded energy. This means, on top of the error evaluation limits (Tests No.4…9) an additional +/-0.2% error for display incrementing is allowed on top of the +/-1.5% error (considering tests are done with Imax).

The reason behind is a possible additional error coming from the gear-driven mechanical counters.

Here the register increment is compared with the real injected energy by the source.

There is no additional error allowance. The +/- 1% limits for class 1 on Imax are still valid.

This measurement is gives the utilities the evidence that the billing is aligned with the meter accuracy.

Nevertheless we expect that also this standard will change in future because of the rapidly increasing higher meter accuracies.

Thank you for interest.

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