introduction
Monitoring electricity consumption has become a key element in managing electrical installations in industrial and commercial sectors, such as manufacturing plants, data centers, food processing plants, retail, and medical or educational institutions. Three years ago, LEM launched its Wi-LEM system, which uses the wireless auxiliary metering component EMN to dynamically measure electricity consumption (lighting, HVAC, motors, heating equipment, etc.) at equal intervals. Initially, its measurement range seemed wide enough, reaching 100A. However, it was quickly discovered that this range was far from sufficient for the measurement needs of industrial or high-load electricity consumption sectors. Energy monitoring typically starts by measuring the total energy consumption at the energy input end—requiring a range of up to 2000A, a point that was overlooked during the initial development.
Therefore, LEM developed the RT series of current sensors suitable for these EMN devices. These sensors offer installation flexibility comparable to open-core current transformers with lower measurement ranges, but achieve the Class 1 accuracy required in auxiliary metering applications. Rogowski coils have long been known for their ease of installation, and they provide a suitable solution once their main drawback—the error caused by the sensitivity to the position of the conductors within the loop—is overcome.
RT Series Rogowski Coil Current Sensor
From theory to practice
Here's a brief explanation of the Rogowski coil principle ("Die Messung der magneticischen Spannung", Archiv für Elektrotechnik, 1912). The Rogowski coil is a self-closing coil winding, wound around the conductor being measured, just like any helical current transformer. The only crucial difference is that it lacks a magnetic core. This coil still uses Ampere's law, but the equation is slightly different because we find that the voltage at the sensor's output is not proportional to the primary current, but rather to its derivative: U = M * di/dt. M is the mutual inductance coefficient between the primary conductor and the coil, reflecting, to some extent, the coupling between the primary and secondary loops. The difficulty in achieving good accuracy based on this principle lies in the fact that the simplified analytical expression of this equation assumes absolute symmetry of the coil (M must be constant). In reality, this is impossible, and we will explain this by analyzing three key factors that cause M to become a variable.
Turns density: The coil windings must be absolutely uniform to ensure completely consistent winding density. Unequal turns spacing leads to structural asymmetry, which in turn causes the mutual inductance coefficient M to vary with the position of the primary conductor. This introduces actual errors originating from the position of the cable or busbar under test. For coil segments with turns density different from the average distribution value, the smaller the distance between the conductor and the coil, the greater this error.
Coil cross-section: Similar to turns density, if the cross-section of the entire coil wound around the conductor is inconsistent, the mutual inductance M will also be inconsistent, and changes in conductor position will also introduce errors. Likewise, in this case, for coil segments with cross-sections significantly different from the average distribution, the smaller the distance between the conductor and the coil, the greater this error.
Coil retainer: The main advantage of flexible Rogowski coils is that they provide ends without electrical connections; feedback signals are transmitted through the metal wire wound inside the coil. This is precisely the main cause of asymmetry due to discontinuities within the coil winding, which in turn affects the turns density, as theoretically, the coil needs to be absolutely continuous and homogeneous. This is a particularly critical factor, and it also produces the greatest error.
Actual data:
To date, the best positional error offered by Rogowski coils is 2%. However, there are limitations in most cases; it doesn't cover certain areas of the conductor within the loop, particularly the closure at the front of the retainer. This can be quite fatal, resulting in an error of approximately 6% near the front of the retainer. Therefore, it's easy to understand why energy metering equipment manufacturers consistently avoid this technology. However, LEM recognizes the potential value of this technology for energy measurement, but the key lies in their ability to manufacture coils with a minimum positional error of less than 0.75%. In fact, developing a Class 1 energy meter requires achieving an overall accuracy of over 1% across the entire measurement chain, which includes current sensors, voltage sensors, and signal processing.
Measurement error caused by conductor position within the loop: Conventional Rogowski coil vs. LEMRT
Challenges facing LEM
For nearly 100 years, multiple solutions based on electrical or mechanical principles have been sought to address the main problem of Rogowski coil current sensors: errors caused by imperfect sensor closure, although with very limited success. Considering this situation, LEM engineers decided to delve deeper into the principle to better understand why these attempts had failed. Our latest approach was completely successful – errors caused by coil retainers have become virtually negligible. Naturally, this scientific concept was patented in 2007.
The sensor head retaining ring adopts a new type of "magnetic sleeve".
Hidden Challenge
When the main problems with the split-core Rogowski coil were finally resolved, other issues surfaced. Errors previously associated with the coil retainer system design had been so significant that they had, to some extent, masked other causes of asymmetry. LEM continued its efforts to improve this current sensor, and after two full years of development, LEM was able to develop processes and methods that significantly reduced symmetry defects.
result
The image below compares the accuracy of LEM's split-core Rogowski coil with other products on the market based on this technology, demonstrating the progress LEM has made in this area.
Measurement error caused by the position of the conductor within the loop:
New LEMRT sensor compared to traditional Rogowski coil
It has now been determined that for a conductor with a diameter of 15mm, regardless of its position, even if it is located near the coil retainer, the positional error will not exceed 0.65% of the measured value.
To better evaluate the results, another graph shows the maximum error values for 210 RTRRogowski coil samples. For the new LEM sensor, the typical position error is 0.31% of the measured value.
Maximum position error distribution of 210 RT sensor samples
We should also learn about Rogowski coil sensors.
External conductor
The performance of a Rogowski coil is typically expressed by the positional error of the conductor being measured, but a good sensor must also remain unaffected by interference from all other nearby external conductors. When there is a relationship between these two characteristics, a more perfect loop is better for both. This is consistent with Ampere's law; any error associated with any form of asymmetry will have an effect both inside and outside the loop. For example, if we take a conductor with a 100A current applied and place it inside a Rogowski coil, making it contact a loop that produces a +0.5% error, the resulting measurement will be 100.5A. Placing the same conductor in contact with the same loop segment outside the loop will also produce a 0.5A error, but this will be superimposed on the current measured inside the loop due to the immunity of the external magnetic field.
absolute precision
Typically, Rogowski coil sensors have low absolute accuracy because their gain (denoted by the technical term M) depends on physical parameters that are difficult to control during mass production. In short, attempting to manufacture sensors with gain dispersion of less than a few percentage points (say, 2-5%, depending on the technology employed) is impractical. This means that the pitch of the coil winding machine must be controlled at the micrometer level, and a coil base of equivalent precision must be produced. Therefore, it is customary to connect Rogowski coils to active or passive circuits so that they can be calibrated to achieve good absolute accuracy.
On the other hand, it is essential to ensure the outstanding stability of sensor characteristics, especially with respect to temperature, to prevent any drift that must be corrected by recalibrating to compensate for changes in operating conditions. For example, LEM's RT series has proven its excellence in this regard at 30 ppm/°C.
No measurement limitations
When defining a measurement system, a common question arises: will the sensor saturate if the current exceeds its nominal value? The answer is "no" when using a Rogowski coil, as this type of coil has no magnetic core and therefore does not saturate. Theoretically, there is no limit to the measurable current! In practice, the diameter of the closed loop determines the nominal current value, independent of the measurement range, and related to the specifications of the primary conductor. In specific cases where di/dt (pulse) is high, the current limit is determined by the voltage generated at the coil's ends.
linearity
Of course, linearity is important for sensors intended for precise measurements. Similarly, because Rogowski coils do not saturate, insufficient linearity is impossible, as this is an inherent advantage of such coils. If insufficient linearity is still found, then the measurement method and whether a Rogowski coil is indeed used must be questioned!
Phase shift
Phase shift is a crucial parameter in energy measurement, calculated from current and voltage measurements. Like its performance in saturation and linearity, the Rogowski coil exhibits excellent phase performance, meaning it does not cause phase shift. However, it's important to remember that this is always related to the amplification stage (described below under the heading "Integrator") that itself generates phase shift. In summary, the phase error is essentially zero when the coil is not connected, but it reaches a higher value when a load is connected. However, this error can be easily quantified by calculation or simulation using an equivalent RLC circuit, and can be compensated for through special methods.
LEM Selection
Today, Rogowski coil sensors are fully capable of competing with the best current intensity transformers in the energy measurement field. LEMs need to maximize the performance of this technology, where net profit is generated when measuring large currents, namely weight, overall size, flexibility, and manageability, which becomes very apparent. A 5mm cross-section is almost considered a "standard" size, and when measuring this cross-section, the RT series sensors are the lightest and thinnest Rogowski coil sensors on the market.
The EMN energy meter is installed in an electrical cabinet equipped with three RTRogowski coils.
The coil retainer (patented) is also very compact (28x30x16mm), allowing for reliable connection of the loop to its coaxial signal cable. Here, the coaxial cable is directly connected to the small cross-section of the coil. In fact, because gain is proportional to cross-section, the voltage generated by the precision coil is very small, making it suitable for controlling the signal-to-noise ratio by initially eliminating interference between the loop and the amplification stage.
Finally, to ensure the stability of the RT coil in terms of time and temperature, a novel process developed by LEM engineers integrates the coil into the PU resin. This winding technique also helps to firmly hold the different parts together and provides assembly stability, which is needed in difficult-to-install applications.
So, should you choose a current transformer (CT) or a Rogowski coil (RT)? LEM has already made its choice, but is ready to share it with you!
Application Note: Rogowski Coil Integrator Design
The voltage supplied by the Rogowski coil is proportional to the derivative of the primary current generated at its terminals. Therefore, an electronic integrator must be used to convert this signal into a signal proportional to the value of the primary current.
An integrator is a fundamental component for current measurement using a Rogowski coil, and the amplification method of the amplification stage has a significant impact on the electrical performance of the sensor (linearity, phase shift, and frequency bandwidth). The following lists various key factors for such integrators and some possible solutions:
Very low signal levels (e.g., 20mV/kA, LEM's RT series sensors).
→ We recommend using the very low noise OpAmp to optimize the signal-to-noise ratio.
→ We must try to minimize the PCB surface area or shield the amplification stage as much as possible to reduce its sensitivity to external magnetic fields.
low cutoff frequency
When the integrator is connected to the Rogowski coil, the two together form a high-pass filter. Because it suppresses very low frequencies, a cutoff frequency must be defined to optimize performance at the nominal operating frequency while still obtaining the shortest possible response time.
Disorder of inhibition
The main problem with pure integrators is that they integrate even the weakest parasitic offsets (such as those caused by AmpOp), making the output always unstable and eventually drifting to saturate at a higher or lower level. Therefore, static gain or an active compensation stage must be used to limit this drift.
Total Disorder of Inhibition
The residual offset can be completely eliminated simply by adding a capacitive coupling device between the integrator and the measurement stage.
Phase shift
The offset suppression circuit described above introduces a phase angle error of a few degrees, which becomes a major problem for energy measurements. Therefore, in such applications, a phase shift compensation stage must be added, which typically includes a low-pass filter. Unfortunately, this correction is not constant but frequency-dependent, meaning the design must be optimized to minimize the fundamental frequency phase difference, which is typically 162/3, 50, 60, or 400 Hz.
Calibration: Active gain adjustment
Rogowski coils require calibration against a reference signal for fine-tuning of their gain because unavoidable manufacturing defects prevent perfectly precise coil construction. Typically, engineers use an integrating stage with analog components, such as a potentiometer. Modern digital calibration solutions are similar to those using microcontrollers or a combination of microcontrollers and PGAs (programmable gain amplifiers). In all cases, the calibration of each Rogowski coil is specific and must always employ the same circuitry used in previous calibrations.
Calibration: Passive Gain Adjustment
Historically, Rogowski coils have always been used solely for RMS current measurements, without phase limitations. Many loops offer factory calibration based on pure resistance or resistor/capacitor circuits (RC circuits). This method has always been simple and economical, but it cannot be used for energy measurements because it introduces very large phase errors, and it can also be affected by frequency (if an RC circuit is used).
In developing the new Rogowski coil, LEM aimed to provide a simple and versatile product, confident in the well-known and effective method of integrator technology for achieving optimal performance. Therefore, the RT series sensors do not undergo factory calibration, require no additional electronic components or housing, and do not require a power supply. Using a dedicated integrator connected to the Rogowski device, such as an energy, power quality, or pulse power monitor, provides an economical and high-performance solution.
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