Page 1
AN-1152
APPLICATION NOTE
One Technology Way • P. O. Box 9106 • Norwood, MA 02062-9106, U.S.A. • Tel: 781.329.4700 • Fax: 781.461.3113 • www.analog.com
Calibrating a Single-Phase Energy Meter Based on the ADE7816
by Aileen Ritchie
INTRODUCTION
This application note describes how to calibrate the ADE7816.
It details the calibration procedure, including equations and
examples of how to calculate each constant.
The ADE7816 is a high accuracy multichannel metering IC that
allows the energy to be measured on up to six current channels.
It provides a variety of energy measurements including active
and reactive energy, along with current and voltage rms readings.
A variety of power quality features, including no load, reverse
power, and angle measurement, are also provided. The ADE7816
can be accessed via an SPI, I
(HSDC) interface.
2
C, or high speed data capture
Rev. 0 | Page 1 of 12
Page 2
AN-1152 Application Note
TABLE OF CONTENTS
Introduction ...................................................................................... 1
Revision History ............................................................................... 2
Calibration Basics ............................................................................. 3
Calibration Steps ........................................................................... 3
Calibration Setup .......................................................................... 3
Required Register Settings .......................................................... 4
Energy Calibration ........................................................................... 5
Current Channel Gain Matching ............................................... 5
REVISION HISTORY
5/12—Revision 0: Initial Version
Phase Calibration ..........................................................................5
Establishing the Wh/LSB Constant—First Meter Only ...........6
Active Energy Gain Calibration ..................................................6
Reactive Energy Gain Calibration ...............................................7
Advanced Energy Offset Calibration (Optional) ......................7
Current and Voltage RMS ............................................................8
Rev. 0 | Page 2 of 12
Page 3
Application Note AN-1152
Calibration Stage
Typical Requirement
VOLTAGE
THE SOURCE P ROVIDES THE
ACCURACY FOR CALIBRATION
SOURCE
CURRENT ×6
10668-001
CALIBRATION BASICS
To obtain accurate readings that do not reflect meter-to-meter
variations in external components or the internal voltage reference,
the ADE7816 requires calibration. Calibration is required on
every meter; however, it is a simple process that can be performed
quickly.
The active and reactive energies, along with current and voltage
rms, must be calibrated for accurate readings to be acquired.
All signal paths are independent and, therefore, perform the
calibration on the measurements that are required in the
completed meter.
Access to the energy metering registers is provided via the SPI
2
or I
C interface (see the ADE7816 data sheet for more details).
When calibrating the active and reactive energy readings, the
line cycle accumulation mode should be used. See the ADE7816
data sheet for details on the line cycle accumulation mode.
CALIBRATION STEPS
When designing a meter using the ADE7816, a maximum of
three calibration stages is required: gain, phase, and offset.
These stages must be performed on each measurement separately. Depending on the external configuration and meter class,
one or more of these stages can be omitted. Table 1 provides
guidance on which calibration steps are typically required for a
particular configuration. Because the requirements and performance can differ on a design-by-design basis, use Table 1 as a
general guideline only. The performance of the meter should be
evaluated to determine whether any additional calibration steps
are required.
Table 1. Typical Calibration Steps
Gain Calibration It is always required.
Phase Calibration
Offset Calibration
It is required when using a sensor that
introduces a phase delay.
If the sensor does not introduce a phase
delay, it is not typically required.
When looking for high accuracy over a
large dynamic range, it is often required.
It is not usually required for all other meter
designs.
CALIBRATION SETUP
Accurate Source
To calibrate the ADE7816, an accurate source should be used.
The accurate source must be able to provide a controllable
voltage and current input with higher accuracy than that
required in the resulting meter. Figure 1 shows a typical setup
using an accurate source.
Figure 1. Accurate Source
Ideally, calibrate all six current channels simultaneously. If this
is not possible, each channel can be calibrated individually. Care
should be taken to isolate and verify the board level channel-tochannel crosstalk for optimum performance.
Required Input Conditions
The gain and phase calibration steps can be performed with a
single set of inputs. Set the voltage to the nominal value, typically 110 V or 220 V. The current should also be set to the
nominal value, for example, 10 A. It is advisable to set the
current around 10 times less than the maximum current for
the meter. The current and voltage inputs should be applied
at a power of around 0.5. The load can be either capacitive or
inductive. The key factor when setting up the calibration inputs
is to determine exactly what is being applied to the meter. For
example, there is no issue in using a power factor of 0.45 as long
as it is known that this is what is being applied to the meter.
If an offset calibration step is required, a second load must be
applied at the minimum current. The voltage should remain at
nominal level and the power factor at 0.5.
Rev. 0 | Page 3 of 12
Page 4
AN-1152 Application Note
0x43B1
PCF_A_COEFF
Phase calibration for Current Channel A
0x400CA4 (50 Hz)
0x4388
DICOEFF
Digital integrator algorithm; required only if using di/dt sensors
0xFFF8000
REQUIRED REGISTER SETTINGS
Prior to calibrating the ADE7816, it is important that a set of
default registers be configured. These registers are listed in
Table 2. Default Registers Required Prior to Calibration
Register Address Register Name Register Description Required Value
0x43AB WTHR1 Threshold register for active energy 0x000002
0x43AC WTHR0 Threshold register for active energy 0x000000
0x43AD VARTHR1 Threshold register for reactive energy 0x000002
0x43AE VARTHR0 Threshold register for reactive energy 0x000000
0x43B2 PCF_B_COEFF Phase calibration for Current Channel B 0x400CA4 (50 Hz)
0x43B3 PCF_C_COEFF Phase calibration for Current Channel C 0x400CA4 (50 Hz)
0x43B4 PCF_D_COEFF Phase calibration for Current Channel D 0x400CA4 (50 Hz)
0x43B5 PCF_E_COEFF Phase calibration for Current Channel E 0x400CA4 (50 Hz)
0x43B6 PCF_F_COEFF Phase calibration for Current Channel F 0x400CA4 (50 Hz)
Tabl e 2. Refer to the ADE7816 data sheet for details on these
registers.
Rev. 0 | Page 4 of 12
Page 5
START
CALIBRATION
ENERGY
CALIBRATION
COMPLETE
CALIBRATE
PCF_x_COEFF
SEE PHASE
CALIBRATION
SECTION
DOES
THE METER
ACCURACY MEET
SPECIFICATION
OVER POWER
FACTOR?
YES
NO
DOES THE
METER
ACCURACY MEET
SPECIFICATION
AT LOW
CURRENT?
YES
NO
SET
IxGAIN
SEE CURRENT
CHANNEL
GAIN MAT CHING
SECTION
SET
Wh/LSB
SEE ESTABLISHING
THE Wh/LSB
CONSTANT–FIRST
METER ONLY
SECTION
CALIBRATE
xWGAIN
SEE ACTIVE
ENERGY GAI N
CALIBRATION
SECTION
CALIBRATE
xWATTOS
SEE ACTIVE
ENERGY OFFSET
CALIBRATION
SECTION
CALIBRATE
xVAROS
SEE REACTIVE
ENERGY OFFSET
CALIBRATION
SECTION
CALIBRATE
xVARGAIN
SEE REACTIVE
ENERGY GAI N
CALIBRATION
SECTION
CALCULATION REQUIRED
ON FIRST M E TER ONLY.
THE SAME VALUE CAN
THEN BE USED ON ALL
SUBSEQUENT METERS
10668-002
−×= 12
23
IxRMS
IARMS
IxGAIN
Application Note AN-1152
ENERGY CALIBRATION
Figure 2 shows the calibration flow for the energy measurements. Use this flow to determine a calibration routine.
Figure 2. Active Energy Calibration Flow
CURRENT CHANNEL GAIN MATCHING
Because the ADE7816 has six current channels, it is convenient
to match them all prior to calibrating. Matching the current
channels results in easier computations because one bit in the
rms and energy registers has the same weight on each channel.
It is recommended that channel matching be performed as the
first calibration step.
To mat ch the six current channels, follow the procedure
outlined in the Setting the IxGain Registers section.
Setting the IxGain Registers
To match all current channel, apply the same fixed input current to
all six channels. This should be the nominal current as described
in the Required Input Conditions section. The current rms
readings can then be used to determine if there is any error
between the six channels. For increased stability, synchronize
the rms register readings to the ZX measurement. This reduces
the effects of ripple in the readings caused by nonidealities of
the internal filtering. See the ADE7816 data sheet for details on
zero-crossing detection.
One channel, for example, Channel A, should be used as a
reference. The IBGAIN (Address 0x4382), ICGAIN (Address
0x4383), IDGAIN (Address 0x4384), IEGAIN (Address
0x4385) and IFGAIN (Address 0x4386) registers can then be
used to correct any mismatch from Channel A. The following
equation describes how to adjust the IxRMS reading to match
that in IARMS using the IxGAIN register:
After all IxGAIN register have been set, all six channels should
produce exactly the same IxRMS reading with a constant input.
PHASE CALIBRATION
Phase calibration is required when the current sensor being
used introduces a phase shift. Current transformers can add
significant phase shift that introduces large errors at low power
factors. Phase calibration should be performed before gain or
offset calibration because large phase corrections can alter the
gain response of the ADE7816.
Phase calibration can be performed with a single inductive or
capacitive load at a power factor of 0.5. If this load is not available,
another power factor can be chosen; however, for best results,
the power factor should be as close to 0.5 as possible. The following
equation outlines how to determine the phase error in degrees:
Error
AWATTHR
−
1
tan)degrees(
=
−
AWATTHRAVARHR
+
AVARHR
where φ refers to the angle between the voltage and the current
(in degrees).
)cos()sin(
ϕϕ
)cos()sin(
ϕϕ
Rev. 0 | Page 5 of 12
Page 6
AN-1152 Application Note
sin)3)(sin(
ωωθ
−+
error
8000
)Hz(
Linefreq
ω
039.0
8000
50
2 ==
πω
sin)3668.0sin(
−+
ωω
(sec))(
×
TimeonAccumulatiWLoad
Wh
36001909
sec5)60cos(A10V220
×
×××
Wh
=
AWATTHR
decimal6981
sec/hr3600109
sec5)60cos(A10V220
4
=
××
×××
=
−
EXPECTED
AWATTHR
For example, if a LINECYC value of 500 half line cycles is set
and the frequency of the input signal is 50 Hz, the accumulation
time is 5 seconds (0.5 × (1/50) × 500). Assuming that a load of
220 V and 10 A at a power factor of 0.5 (inductive) produces an
AWATTHR reading of 1870, and the AVARHR reading is
−3328, the error in degrees can be determined as follows:
)60cos(3328)60sin(1870
−+−
Error
=
tan)degrees(
=
1
−
0.668
o
)60cos(1870)60sin(3328
−+−−
The ADE7816 uses all pass filters to accurately add time advances
and delays to the current channels with respect to the voltage
channels. A separate filter is included on each of the six current
channels. To adjust the time delay or advance, the coefficient of
these filters must be adjusted. Equation 1, Equation 2, and
Equation 3 show how the coefficients correspond to the phase
offset in radians.
PCF_x_COEFF
FRACTION
=
error
(1)
)4)(sin(
ωθ
+
where error(θ) is the phase error in degrees.
To determine the Wh/LSB constant, use the following formula:
/
LSB
=
AWATTHR
×
sec/hr3600
where:
Accumulation Time is the line-cycle accumulation time.
AWAT THR is the energy register reading after this time has
elapsed.
For example, if a LINECYC value of 500 half line cycles is set
and the frequency of the input signal is 50 Hz, the accumulation
time is 5 seconds (0.5 × (1/50) × 500). Assuming a load of 220 V
and 10 A produces an AWATTHR reading of 1909, the Wh/LSB
constant can be calculated as
4
−
/
=LSB
108
×=
To adjust the constant to meet a particular specification or to
make the constant easier to store, the AWGAIN register can be
used. The AWGAIN register can be used to modify the Wh/LSB
constant by ±50%. The AWGAIN register affects the AWATTHR
register as shown in the following formula:
2
π
=
If PCF_x_COEFF ≥ 0, then
PCF_x_COEFF = 2
23
× PCF_x_COEFF
FRACTION
(2)
If PCF_x_COEFF < 0, then
PCF_x_COEFF = (2
23
+ 2328) × PCF_x_COEFF
FRACTION
(3)
Using the previous example, the required phase adjustment, θ,
is 0.668°. The PCF_A_COEFF register setting can then be
calculated as follows:
PCF_A_COEFF
+
PCF_A_COEFF = 2
=
FRACTION
53502x0
=
)4668.0sin(
ω
23
× 0x53502 = 0x447B89
Analog Devices provides a spreadsheet to simplify this
calculation. It is available at
http://www.analog.com/ADE7816_tools_software_simulation.
Depending on the current sensors being used, different phase
calibration values can be required on all six channels.
ESTABLISHING THE WH/LSB CONSTANT—FIRST METER ONLY
When calibrating the first meter, the Wh/LSB constant must be
determined. The Wh/LSB constant is used to set the weighting
of each LSB in the active energy register. This constant allows
the energy register readings to be converted into real-world values.
Once established, the same Wh/LSB meter can be used for each
subsequent meter.
AWGAIN
23
AWATTHR
AWATTHR
EXPECTED
ACTUAL
−×= 12
To achieve a different meter constant, alter the AWATTHR
reading based on the desired Wh/LSB.
EXPECTED
(sec))(××
TimeonAccumulatiWLoad
LSBWh
sec/hr3600/
For example, to alter the previously calculated Wh/LSB constant
−4
to 9 × 10
, the desired AWATTHR reading is:
This adjustment can be made using the AWGAIN register as
described in the Active Energy Gain Calibration section.
ACTIVE ENERGY GAIN CALIBRATION
The purpose of the active energy gain calibration is to compensate
for small gain errors due to part-to-part variation in the internal
reference voltage and external components such as the time error
introduced by the crystal. Gain calibration is required on every
meter and is performed with nominal voltage and current inputs at
a power factor of 0.5 as previously described. For simplicity, it
is recommended that all meters be calibrated to use the same
Wh/LSB value, and this should be set up in the first meter as
explained in the Establishing the Wh/LSB Constant—First
Meter Only section.
Rev. 0 | Page 6 of 12
Page 7
Application Note AN-1152
=
AWATTHR
1600
=
xVARHR
691
3600103
sec05cos(60)A0.1V220
5
=
××
×××
=
−
EXPECTED
AWATTHR
%8.2
169
169165
% −=
−
=Error
kHz8(sec)
%
WHTHR
onTime
Accumulati
AWATTHR
error
AWATTOS
EXPECTED
××−
=
0x18E
kHz8
0x2000000
50
169
0.028 =××=AWATTOS
Use the following formula to determine the expected reading in
the AWAT T H R register:
EXPECTED
(sec))W(××
TimeonAccumulatiLoad
LSBWh
sec/hr3600/
The actual value can then be read from the AWAT TH R register,
and the AWGAIN register can be used to correct any error. The
following formula shows how AWGAIN can be used to adjust
the AWAT T H R reading:
AWGAIN
23
AWATTHR
AWATTHR
EXPECTED
ACTUAL
−×= 12
Using the previous example, at 220 V and 10 A, the expected
AWATTHR reading is 1698 decimal. Assuming that the actual
AWATTHR reading is 1600 decimal, AWG AIN is calculated as
1698
23
2
0x7D70A1
=
−×=AWGAIN
Note that the gain calibration for Channel B through Channel F
is controlled by the BWGAIN, CWGAIN, EWGAIN, and
FWGAIN registers. Assuming that the channels are correctly
matched, as described in the Current Channel Gain Matching
section, the previous procedure does not need to be repeated for
the other channels. Writ e the value calculated for AWGAIN to
BWGAIN, CWGAIN, EWGAIN, and FWGAIN for accurate
results.
REACTIVE ENERGY GAIN CALIBRATION
Because the ADE7816 active and reactive energy measurements
are closely matched, separate reactive energy gain calibration is not
always required. In most cases, the values calculated for AWGAIN
in the Active Energy Gain Calibration section can be written to
the AVARGAIN register to retain the same VARhr/LSB constant.
If a different LSB weighting (that is, VARhr/LSB constant) or
further calibration is required, the reactive energy can be
calibrated separately. Reactive energy calibration should be
performed with nominal inputs at a power factor of 0.5 as
previously described. The reactive energy calibration is performed in a similar manner to the active energy calibration by
first determining the expected xVARHR output.
correctly matched, as described in the Current Channel Gain
Matching section, the previous procedure does not need to be
repeated for the other channels. Write the value calculated for
AVARGAIN to BVARGAIN, CVARGAIN, EVARGAIN, and
FVARGAIN for accurate results.
ADVANCED ENERGY OFFSET CALIBRATION (OPTIONAL)
Active Energy Offset Calibration
Active energy offset calibration is required only if accuracy at low
loads is outside the required specification prior to offset
calibration.
To correct for any voltage-to-current channel crosstalk that may
degrade the accuracy of the measurements at low current levels,
perform active energy offset calibration. A low level current
signal must be applied to allow the offset magnitude to be
measured and then removed.
When performing offset calibration, it is often required to increase
the accumulation time to minimize the resolution error. As the
line-cycle accumulation mode accumulates energy over a fixed
time, the result is accurate to ±1 LSB. If the number of bits
accumulated in the x WAT TH R register is small after this time,
the ±1 LSB error can result in a large error in the output. For
example, if only 10 bits are accumulated in the x WAT TH R
register, the resolution error is 10%. Increasing the number of
accumulation bits to 1000 reduces the resolution error to 0.1%.
In the following example, a LINECYC value of 5000 half line
cycles is set, and an input current of 100 mA is applied. With a
voltage channel input of 220 V at a power factor of 0.5, the
expected AWATTHR reading is determined as
If the actual AWATTHR register reading is 165 at 100 mA, the
percentage error due to offset is determined as
The offset in the watt measurement is corrected according to
The compensation can then be determined by
Note that the gain calibration for Channel B through Channel F
is controlled by the BVARGAIN, CVARGAIN, EVARGAIN,
and FVARGAIN registers. Assuming that the channels are
EXPECTED
AVARGAIN
×
LSBVARhr
23
×
RENERGYA
RENERGYA
(sec))(
TimeonAccumulatiVARLoad
sec/hr3600/
EXPECTED
ACTUAL
−×= 12
Note that, depending on the board layout and the crosstalk on
the meter design, Channel B through Channel F may need a
separate offset calibration from Channel A. This can be achieved
through the BWATTOS, CWATTOS, DWATTOS, EWATTOS,
and FWATTOS registers. These registers correct the respective
Rev. 0 | Page 7 of 12
Page 8
AN-1152 Application Note
=
AVAROS
=
InputVoltage
[V]
InputCurrent
[A]
81x02100
000,400,3
V220
16
AConstantV =××=
000,400
A10
x WAT THR register reading in the same way that AWA T T O S
affects the AWAT THR register reading.
Reactive Energy Offset Calibration
Reactive energy offset calibration is only required if accuracy at low
loads is outside the required specification prior to offset calibration.
To correct for any voltage-to-current channel crosstalk that may
degrade the accuracy of the measurements at low current levels,
reactive energy offset calibration is performed. A low level current
signal must be applied to allow the offset magnitude to be
measured and then removed.
When performing offset calibration, it is often required to increase
the accumulation time to minimize the resolution error. Because
the line-cycle accumulation mode accumulates energy over a
fixed time, the result is accurate to ±1 LSB. If the number of bits
accumulated in the x VA R HR register is small after this time, the
±1 LSB error can result in a large error in the output. For example,
if only 10 bits are accumulated in the xVARHR register, the resolution error is 10%. Increasing the number of accumulation bits
to 1000 reduces the resolution error to 0.1%. The expected
xVARHR reading is determined as
AVARHR
EXPECTED
×
LSBVARhr
(sec))(
TimeonAccumulatiVARLoad
sec/hr3600/
×
The offset in the reactive energy measurement is corrected
according to the following equation:
%
Error
RENERGYA
EXPECTED
TimeomAccumulati
WTHR
××−
kHz8(sec)
Note that, depending on the board layout and the crosstalk on
the meter design, Channel B through Channel F may need a
separate offset calibration from Channel A. This can be achieved
through the BVAROS, CVAROS, DVAROS, EVAROS, and
FVAROS registers. These registers correct the respective x VARHR
register reading in the same way that AVAROS affects the
AVARHR register reading.
CURRENT AND VOLTAGE RMS
Calibrating the voltage and current rms is only required if the
instantaneous rms readings are required. RMS calibration does
not affect the performance of the active or reactive energy.
Perform the rms calibration using the instantaneous rms register readings. The readings can be obtained from the IxRMS
register and the VRMS register. For increased stability, synchronize the rms register readings to the ZX measurement. This
reduces the effects of ripple in the readings caused by the
nonidealities of the internal filtering. See the ADE7816 data
sheet for details on zero-crossing detection.
The current and voltage rms readings require gain calibration to
compensate for any part-to-part variations. Offset calibration
may also be required on every meter to remove crosstalk that
may degrade the accuracy of the readings at low signal inputs.
RMS Gain
Along with compensating for part-to-part gain variations, the
rms gain constant converts the rms reading in LSBs into a
current or voltage value in amps or volts. The voltage and current
rms constants are determined under fixed load conditions by
dividing the number of LSBs in the rms register by the amplitude of the input.
[LSBs]
k
k
ConstantV ×=
ConstantI ×=
[V/LSB]
[Amps/LSB]
VRMS
IxRMS
[LSBs]
If the current channels have been correctly matched by following the procedure described in the Current Channel Gain
Matching section, all current channels, A through F, should
have the same I constant.
To maintain the full resolution when the conversion is taking place
in the firmware, the voltage and current rms constants can be
multiplied by a constant, k. The use of a multiplication factor, k,
allows resolution to be maintained when converting and storing
the rms readings as a hexadecimal number using fixed point
multiplication. Converting the reading to the hexadecimal format
is required prior to performing a hexadecimal-to-binary coded
decimal conversion for display purposes.
An example of how the voltage rms register reading can be
converted into a value in volts, while maintaining resolution of
one digit below the decimal point, is provided in the following
equation. In this example, 220 V is applied, producing a VRMS
register reading of 3,400,000 decimal.
The volts/LSB constant is multiplied by a factor of 100 × 216 to
maintain accuracy when using fixed point multiplication. The
V constant is 0x1A8.
An additional example showing the generation of the current rms
gain constant is provided in the following equation. In this
example, the resulting LCD display measurement is accurate to
two digits below the decimal point. A current input of 10 A is
applied, resulting in an IRMS reading of 400,000 decimal.
16
=××=ConstantI
666x021000
The amps/LSB constant is multiplied by a factor of 1000 × 216 to
maintain the required accuracy during conversion. The resulting
I constant is 0x666.
Rev. 0 | Page 8 of 12
Page 9
Application Note AN-1152
22
2
VRMSVRMS
22
2
IRMSIRMS
NOMINAL RE ADING
ACTUAL RMS
EXPECTED RMS
ERROR
OFFSET
INPUT AMPLITUDE
10668-003
RMS Offset
To obtain accurate readings at low signal levels, the current and
voltage rms offset may have to be calibrated. This calibration is
performed using the internal VRMSOS and IxRMSOS registers
that apply an offset prior to the square root function. The
compensation factor is determined by applying the following
equations:
As illustrated in Figure 3, the rms offset calibration is based on
two points, where the expected reading is derived from the rms
measurement with nominal inputs.
VRMSOS−=
IxRMSOS−=
12
12
ACTUALEXPECTED
ACTUALEXPECTED
Figure 3. RMS Offset Compensation
Rev. 0 | Page 9 of 12
Page 10
AN-1152 Application Note
NOTES
Rev. 0 | Page 10 of 12
Page 11
Application Note AN-1152
NOTES
Rev. 0 | Page 11 of 12
Page 12
AN-1152 Application Note
©2012 Analog Devices, Inc. All rights reserved. Trademarks and
NOTES
I2C refers to a communications protocol originally developed by Philips Semiconductors (now NXP Semiconductors).
registered trademarks are the property of their respective owners.
AN10668-0-5/12(0)
Rev. 0 | Page 12 of 12
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