Metering System Accuracy

This is the published version, checked on 27 February 2012.

Accuracy	Basic
Depth	Basic
Readability	Basic

Overview

Continental Control Systems, LLC sells WattNode^® electric energy meters, as well as current transformers (CTs). Each have accuracy specifications, but it is not always clear how to combine the accuracy specifications of the meter and the CTs to determine an overall system accuracy; this article tries to clarify that computation and provide some general system accuracy information for energy and power measurements made using our products.

This article does not address the accuracies of other reported values, such as voltage, current, power factor, or reactive power.

General Results

Meters: WattNode LonWorks^® and Modbus^® (WNC Series), WattNode Pulse (WNB Series)
Line VAC: 80% to 115% of nominal
Line Frequency: 60 Hz nominal
Current: 10% to 100% of nominal
Ambient Temperature: 25°C ± 5°C
Measurements: Real power and energy
Current Transformers:
- ACT family: all models
- CTM family: all models
- CTB family: all models
- CTS-0750 family: all models 100A and higher
- CTS-1250 family: all models 150A and higher
- CTS-2000 family: all models
- CTT family: all models

Notes

Conditions as described by ANSI C12.1-2001 Section 3.10.1 General Test Conditions.
All accuracies are ± unless specified otherwise.
All accuracies are percentage of reading.

Combined Accuracies

Power Factor	1.00	0.866 Leading	0.50 Lagging
WattNode Accuracy (%)	0.5%	0.5%	0.5%
System Accuracy (%)	2.0%	3.0%	4.5%

Computations

The accuracy for real power and real energy is the same, since energy is just the integral of power over time. There are three primary sources of power errors:

WattNode gain / linearity error
CT gain / linearity error
CT phase angle error

For purposes of this computation, we are using rated accuracies, which should generally be the worst-case; the actual accuracy will generally be better than the rated accuracy.

Most current transformers have a phase angle error where the output waveform is shifted in time from the measured current. This is generally measured in degrees or minutes (of degrees). The phase shift is almost universally leading. This is counter-intuitive, because it would seem to imply that the CT is predicting the future and because CTs are inductive devices and inductors normally cause lagging phase shifts; nevertheless, a leading phase angle is correct. Standard WattNode meters are calibrated to compensate for CTs with a 1.0 degree leading phase. This is too much compensation for some solid-core low-phase angle CTs and is not enough compensation for many of the split-core CTs, which tend to have larger phase angle errors, but it provides a good compromise, reducing the average error due to the phase angle error.

$M_g = 0.5%$	Meter gain / linearity error (percent of reading)
$C_g$	CT gain / linearity error (percent of reading)
$M_p = 1.0$	Meter phase adjustment (degrees). Lagging = positive value
$C_p$	CT phase angle error (degrees). Leading = negative value
$P_f$	Load displacement power factor
$T_p = C_p + M_p$	Phase angle error after applying WattNode meter correction (degrees)
$L_p = \arccos(P_f)$	Phase angle between voltage and current in the load (degrees). Positive = lagging, which is more common for inductive loads like motors.
$L_p' = L_p + T_p = \arccos(P_f) + C_p + M_p$	Measured V-I phase angle including CT phase angle error and meter adjustment
$P_g = \frac{\cos(L_p')}{P_f} - 1$	System error due to phase angle error
$E = M_g + C_g + \|P_g\|$	Combine worst-case error

Sample Calculations

The following table uses the above equations to compute system accuracies for a few sample cases.

Mg	Cg	Mp	Cp	Pf	Tp	Lp	Lp'	Pg	E
±0.5%	±1.0%	1.0°	-2.0°	0.500	-1.0°	60.0°	59.0°	3.0%	4.5%
±0.5%	±1.0%	1.0°	-1.0°	0.500	0.0°	60.0°	60.0°	0.0%	1.5%
±0.5%	±1.0%	1.0°	-0.3°	0.500	0.7°	60.0°	60.7°	-2.1%	3.6%
±0.5%	±1.0%	1.0°	-2.0°	0.866	-1.0°	30.0°	29.0°	1.0%	2.5%
±0.5%	±1.0%	1.0°	-1.0°	0.866	0.0°	30.0°	30.0°	0.0%	1.5%
±0.5%	±1.0%	1.0°	-0.3°	0.866	0.7°	30.0°	30.7°	-0.7%	2.2%

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