Current sensing for energy metering, William Koon, Analog Devices, Inc.
Abstract
Solid-state electric energy meters contain both voltage and current sensing elements.
The current sensing requirement is a more difficult problem. Not only does the current
sensor require a wider measurement dynamic range, it also needs to handle a wider
frequency range because of the rich harmonic contents in the current waveform.
This paper shows how a digital integrator can be used to convert the di/dt signal
output from Rogowski coil current sensor to an appropriate signal and how it can be
combined for a high-current energy meter.
电能计量中的电流感应，William Koon, Analog Devices, Inc.
电子式电能计量仪表需对电压与电流两信号进行采集，而对电流互感器要求相
对来说更严格一些。不仅因为电流互感器需要更宽的计量范围以应付不同的负
载，电流波型中含有的众多谐波成分决定了它还必须有更宽的频率范围。
本文阐述了怎样采用一个数字积分器结合Rogowski线圈式电流互感器，将线圈
输出的电流对时间微分(di/dt)的信号还原，并如何成功使用在大电流电能计量仪
表中。
Introduction
Today, most advanced solid-state energy meters adopt mixed-signal architecture,
using high accuracy A/D converter front end and DSP back-end. Some
implementations use discrete components while the majority uses ASIC designed
specifically for energy measurement. This mixed-signal architecture offers superb
accuracy and long-term stability. Before voltage and current are sampled, both
signals need to be conditioned to the appropriate signal level. All energy meters
contain both voltage and current sensing elements. Current sensing is a more difficult
problem. Current sensor requires wider measurement dynamic range, it also needs to
handle a much wider frequency range because of the rich harmonic contents in the
current waveform. As the energy consumption in a household continue to increase,
the needs for measuring high current is no longer limited to industrial applications.
For example, the new energy meters installed in the U.S. residential market need to
measure maximum current up to 200A. Today’s current sensing technologies can no
longer measure current as high as this very cost-effectively.
Rogowski coil has long been used for high current measurement such as in sub-station
transformers and arc wielding machines. It offers numerous advantages comparing
with the other current sensing solutions. However, the difficulty for building an
analog integrator which is stable over a long period of time has kept Rogowski coil
from being used in metering applications. This article introduces the basic principle
of a Rogowski coil and a recent digital implementation of an integrator. This
combination has enabled this current sensing technology to be successfully used in a
recent high-current electric energy meter design. Because of the many advantages to
this technology, this could be the sensor of choice for the next generation electric
energy meters.
Today’s current sensing solutions
The three most common sensor technologies today are the low resistance current
shunt, the current transformer (CT), and the Hall effect sensor.
Low Resistance Current Shunt
Current shunt is the lowest cost solution available today. A simple model for this
current measurement device is shown in Figure 1.
Figure 1. A simple model of the shunt with parasitic inductance
Low resistance current shunt offers good accuracy at low cost and the current
measurement is simple. When performing high precision current measurement, one
must consider the parasitic inductance of the shunt. The inductance is typically in the
order of only a few nH. It affects the shunt’s impedance magnitude at relatively high
frequency. However, its effect on phase is significant enough, even at line frequency,
to cause noticeable error at low power factor. Figure 2 shows the phase shift resulting
from a 2nH inductance in a 200µΩ shunt.
Figure 2. Phase shift caused by the self-inductance of a shunt (2nH in a 200µΩ shunt)
The percentage measurement error caused by any phase mismatch between the
voltage and current signal paths can be approximated by the following formula:
Measurement error≈Phase mismatch ( in radian ) × tan(φ)× 100% (1)
In the above expression, φ represents the power factor phase angle between the
voltage and current. As one can see, a phase mismatch of 0.1° will result in about
0.3% error at power factor of 0.5. Therefore, special care needs to be taken to ensure
phase are precisely matched between the internal signal paths for the voltage and
current.
Shunt is rather low cost and reliable. It is a popular choice for energy metering
applications. However, because the current shunt is fundamentally a resistive
element, the heat it generates is proportional to the square of current passing through.
This self-heating problem makes shunt a rarity among high current energy meters.
Current Transformer (CT)
Current Transformer (CT) is a transformer which converts the primary current into a
smaller secondary current. CT is the most common sensor among today’s high
current solid-state energy meters. CT can measure up to very high current and
consumes little power. Because of the magnetizing current, CT typically have a small
phase shift associated with it (0.1°-0.3°). If un-calibrated, it will lead to noticeable
error at low power factor (see earlier discussion on parasitic inductance in current
shunt). In addition, the ferrite material used in the core can saturate at high current.
Once magnetized, the core will contain hysteresis and the accuracy will degrade
unless it is demagnetized again. Figure 3 shows a typical hysteresis curve of a ferrite
material.
Figure 3. Hysteresis curves of a ferrite material
CT saturation can occur when current surges beyond a CT’s rated current, or when
there is substantial dc component in the current (e.g. when driving a large half-wave
rectified load). Today’s solution to the saturation problem is to use ferrite material
with very high permeability. This typically involves using Mu-metal core. However,
this type of CT’s have inconsistent and larger phase shift comparing with the
conventional iron core CT’s. Energy meters based on Mu-metal core CT’s would
require multiple calibration points for both current level and temperature variations.
Hall Effect Sensor
There are two main types of Hall effect sensors: open-loop and closed-loop
implementation. Most Hall effect sensors found in energy meters use open-loop
design for lower system cost. Hall effect sensor has outstanding frequency response
and is capable of measuring very large current. However, the drawbacks of this
technology include that the output from Hall effect sensor has a large temperature
drift and it usually requires an stable external current source. Hall effect sensors are
somewhat less common comparing with the CT.
Rogowski coil
A simple Rogowski coil is an inductor which has mutual inductance with the
conductor carrying the primary current. Rogowski coil is typically made from aircore coil so in theory there is no hysteresis, saturation, or non-linearity.
If current i(t) passes through a long straight wire on z-axis, the magnetic field at a
random point P which has coordinate (ρ, θ, z) in cylindrical coordinate is:
B=
µ i(t)
Φ (2)
×
2π
ρ
The electromotive force (EMF) generated by the magnetic field in any area in space
can be calculated using Maxwell’s equation:
Electromotive force (EMF) = ∫∫
∂B
• d S (3)
∂t
Figure 4 shows an example of Rogowski coil current sensor. It consists of N-turns of
rectangular air-core coil arranged around a long straight wire and perpendicular to the
magnetic field generated by the current in the wire.
Figure 4. Rectangular air-core Rogowski coil
The EMF of the coil in this arrangement is:
EMF =
µ air NL
di
c di
(4)
ln( ) = M
dt
b dt
2π
The constant term M represents the mutual inductance of the Rogowski coil, and it
has a unit of Henry (H). It indicates the signal level from the output of the coil per
unit di/dt. The voltage output of the coil relies only on the di/dt changes in primary
current. Because EMF is only generated when there is changes in the magnetic field,
Rogowski coil cannot be used to measure dc component in the current. In addition,
this type of sensor can easily measure ac current up to thousands of Amps. That is
why it is so useful in many high current measuring applications. It has no iron core so
there is no non-linearity over a very wide measurement range (from hundreds of amps
to milliamps).
The basic operating principle of a Rogowski coil is to measure the primary current
through mutual inductance. Because Rogowski coil relies on measuring magnetic
field, it makes this type of current sensor susceptible to external magnetic field
interference comparing with the CT. The following highlights a few important
aspects to minimize external magnetic field interference.
Minimizing unwanted loop area
Any loop formed by conductor will pick up magnetic field. It is therefore important
to minimize unwanted loop area to reduce interference pick-up. For example, figure 5
shows a toroidal air-core Rogowski coil. It is intended to detect the magnetic field
around the circular ring. However, the winding itself makes up an undesirable loop
and makes this design susceptible to interference perpendicular to the ring.
Figure 5. Undesirable loop can cause susceptibility to interference
Design with interference cancellation
Interference is generally far field in nature and therefore will be more uniformly
distributed throughout the sensor. It is important for the Rogowski coil to
differentiate between the far field interference and the near field signal, and design the
coil in such a way that the far field interference will cancel out within the coil. For
example, the circular shape of the toroidal coil ensures that there is opposing EMF
when a far field interference is applied to the coil.
Figure 6. Far field interference generate opposing EMF in different part of the coil
However, note that perfect cancellation will require a perfectly uniform winding and
zero impedance of the coil. In practice, the small non-uniformity of the winding and
non-zero coil wire impedance will create some interference susceptibility in the
Rogowski coil.
Shielding
Shielding can be used to add extra protection. However, to shield magnetic field of
frequency as low as the power line frequency requires thick shielding or high
permeability in the shielding material to be used. If care is taken when designing the
Rogowski coil, shielding can be avoided.
Designing the Integrator
The analog approach
Because the output from the Rogowski coil is proportional to the time derivative of
the current, an integrator is needed to convert the di/dt signal back to the format of i(t)
for further processing. Traditional approach has been to use high performance op-
amps and build an analog integrator. Figure 7 shows a simple integrator design using
an op-amp.
Figure 7. Implementing an integrator using an op-amp
The biggest challenge of this analog implementation has been to design an integrator
that is accurate over the long operating life and the hostile operating environment of a
meter. This was one of the major drawback which had prevented Rogowski coil from
being widely adopted, even among the traditional high current industrial meters.
Digital Integrator
To overcome this problem. A digital implementation has recently been introduced.
In frequency domain, an integration can be viewed as a -20dB/decade attenuation and
a constant –90° phase shift. A digital implementation can implement this with
outstanding accuracy. Figures 8 and 9 are the frequency response and the detailed
phase response of the digital integrator implemented in Analog Devices’ ADE7759
energy measurement ASIC.
Figure 8. Magnitude response of a digital integrator from 10Hz to 10kHz
(with gain normalized to 0dB at 60Hz)
Figure 9. Phase response of a digital integrator (from 40Hz to 70Hz)
As shown, the phase and magnitude response of a digital integrator is very close to
ideal. When interfacing with an IC which has on-chip digital integrator, building a
meter with the Rogowski coil is just as simple as using current sensors such as CT or
shunt. The air-core coil has no hysteresis, saturation, or non-linearity problem. In
addition, it has outstanding ability to handle large current. The added benefit of the
digital implementation is that it is more stable over time and environmental changes.
These are very important for energy metering application because of the hostile
operating condition and long operation life of an energy meter. A residential energy
meter with maximum current of 200Amps that is based on the Rogowski coil and
ADE7759 has recently been introduced. Extensive in-house experiments has shown
that this new meter design outperforms meters that are based on traditional current
sensing technologies in many areas.
Figure 10 below shows a linearity accuracy plot of the ADE7759 with a Rogowski
coil current sensor over a 1000:1 (60dB) dynamic range. It has less than 0.1% over
this wide dynamic range.
0.2500%
Full-Scale = 0.5V
Gain = 4
Integrator ON
0.2000%
0.1500%
% Error
0.1000%
0.0500%
0.0000%
25C, PF=1
-0.0500%
-0.1000%
-0.1500%
-0.2000%
-0.2500%
0.01
0.1
1
10
Current (Amps)
Figure 10. Linearity accuracy of Rogowski coil
100
The following table summarizes the strength and weakness of the technologies
described:
Current Sensing
Low resistance
Current
Hal Effect
Technology
current shunt
Transformer
Sensor
Cost
Very Low
Medium
High
Linearity over
Very Good
Fair
Poor
measurement range
High Current
Very Poor
Good
Good
measuring capability
Power consumption
High
Low
Medium
DC/high current
No
Yes
Yes
saturation problem
Output variation
Medium
Low
High
with temperature
DC offset problem
Yes
No
Yes
Saturation and
No
Yes
Yes
Hysteresis problem
Table I. Comparison of various current sensing technologies
Rogowski
Coil
Low
Very Good
Very Good
Low
No
Very Low
No
No
Conclusion
As the energy consumption in a household continue to rise, there is much interest in
finding new current sensor which can measure large current without saturation
problem. Rogowski coil, combining with digital integrator, offers a cost competitive
current sensing technology and could become the technology of choice for the next
generation electric energy meters.
Author Autobiography:
William Koon is an Applications Engineer for the Energy
Measurement Group at Analog Devices, Inc. located in Wilmington,
MA, USA. He holds a MSEE from the University of Illinois and a
BSEE from the Ohio State University. You can contact William
directly by mail at MS-626, 804 Woburn Street, Wilmington, MA
01867, USA, or via email at william.koon@analog.com. For further information on
Analog Devices’ energy measurement products, please visit
http://www.analog.com/energymeter.