Flexible Rogowski Coil: A Technical Review
Read Our Review of The Flexible Rogowski Coil Below
Sam Seyfi
Magnelab, Inc.
600 Weaver Park Road
LongmontCO 80503
OCT 2007
Abstract
A flexible Rogowski coil is an air core toroidal transformer which has been a very useful and innovative tool in the transformer industry due to its ease of use and primarily due to its lack of saturation at high currents.
A technical review of the operating principles surrounding the design and operation of the Rogowski coil as it has been designed and productized by Magnelab will be discussed in this document.
The advantages of this measurement tool are based on its wide range linearity for differential field detection and frequency range, made possible by its lack of magnetic core structure that allows the exclusion of saturation effects. Also, other important factors are ease of use and add on electronics which allow for signal refinement and integration. The disadvantages associated with this technology application are also going to be discussed.
Finally, data summaries tracking the development and finalized product stages will be presented.
Introduction of the Rogowski Coil
The basic operating principle of a Rogowski coil was first postulated in 1912 by Rogowski et al (1). It described that a closely wound coil over a nonmagnetic former of constant cross sectional area and closed loop configuration, will detect an induced voltage which is proportional to the rate of change of the current flowing in the wire surrounded by the coil. In Figure 1 the generalized schematic of such a configuration is shown.
In terms of physical formulation,
V=M dI/dt,
Where V=voltage detected; M=mutual inductance of the coil or coil sensitivity, (Vs/A); and dI/dt= rate of change of current.
Figure 1: Generalized diagram of a Rogowski coil set up
Recapping, the basic function of a Rogowski coil is to measure current through a conductor placed within its loop and reproduce the current fluctuations over a given time interval of
observation. For accurate replication of the current, the raw voltage output needs to be integrated in order to account for the rate of change proportionality that is generating the voltage read out. Amplification of the signal output above noise is also achieved with integration.
The utilization of the Rogowski coil as a viable current sensing device for commercial applications has been hampered by the electronics availability for the integrator design. However, since the early 90’s (2, 3) wide bandwidth Rogowski coils have been available for commercial use.
Technical Aspects and Considerations
Magnelab applications were initiated based on the wide range linearity of the flexible Rogowski coil, and the flexibility it offers the customer with diverse current sensing requirements. Figure 2 shows a picture of one of the Magnelab Rope CTs and Table 1 lists the specifications associated with the product without an integrator transforming the output.
The choice of test ranges in the data charts was primarily driven by the specification requirements of the customer base. However, testing is ongoing to determine the full spectrum capability of the device.
Figure 2: Physical configuration of a Magnelab flexible Rope CT system
The inherent lack of saturation constraints makes the coil almost indestructible due to over current conditions. In addition, this allows for a wide range of current measurements (100A to 100kA) without the requirement of physical size changes which makes the Rogowski coil easily adaptable to a variety of physical shapes of transducers, as well as their respective current ratings. However, in order to achieve this wide bandwidth, the coil sensitivity has to be low enough to minimize the coil inductance. At the same time, it has to be high enough to accommodate low frequency, low amplitude currents.
The use of appropriate integration allows for precise and repeatable measurements to be generated. In the past, the use of passive RC (resistor-capacitor network) integrators, limited the use of the Rogowski coil to the detection of large, high frequency current pulses which required increased currents in the wire in order to provide adequate accuracy, thus limiting the low frequency applications.
On the other hand, the introduction of active integrators which are generally variable RC systems allows for the same Rogowski coil to cover a wide range of currents and frequencies by just changing its integration time constant.
Flexible Rope CTcoils are less accurate than their rigid counter parts due to the non uniformities introduced by flexing the former onto which the windings rest, as well as due to the difficulty of screening and calibrating against fixed positions.
End matching is another liability of flexible coils but, the utilization of concentric, aligned connectors improves the end matching and prevents interference pick up from stray fields.
Table 1: Functional Parametrics of Magnelab
RopeCT: Raw Data
| Product ID |
RopeCT |
| CurrentRange |
5A – 10 kA |
linearity error for current sense range
|
up to 5% of range <2%
6- 100% of range <0.2% |
| FrequencyRange |
45 Hz – 100KHz. |
| Vout range (mV) |
0.7-125 |
| Coil Sensitivity (mV/A) |
0.07-0.08
(av. integrated S=0.35mV/A) |
Product checks during the development of the Rope CT at Magnelab have shown that for the particular Rogowski coil length and arrangement developed, the end matching configuration is very robust, with a small error shift in the repeatability of measurement if the current carrying line and the connector site overlapped during the measurement. This is easily controlled by not allowing the connector center to be in contact with the current line during the measurement.
Preliminary data on the stability and linearity of the Rogowski coils are shown in figures 3 and 4. Figure 3 plots show the raw data collected for a Rope CT system as measured under a range of input currents and at constant frequency of 60Hz. The linearity is the typical response expected over the current range, 100A to 1500A, used.
A slight offset is observed which could be fixed by the introduction of the appropriate integrator filtering. In addition, the very close matching of the two sets of data is indicative that positioning errors are not an issue for the geometries studied.
Figure 4 shows the linearity of the center point measurement for Rope CT 2 as measured over the 5-200 Amp range. The linear fit has an R2 factor of 0.99 and the standard deviation percentage is less than 2% in the low end of the range with sub 0.2% values for the majority of the plot.
Frequency range dependencies in the product spec range and positioning accuracy studies are shown in figure 5.
The data have been collected on raw Vout measurements and the linearity of output is characteristic of consistent winding counts and cross sectional uniformity.
Position dependencies were determined by contact measurements at 8 uniformly distributed sites along the coil’s length. Points 1 and 8 are the locations adjacent to the connectors at each end of the coil. No end effects were detected in either of the coil ends, as well as no matching issues with the connector arrangement.
The diameter of the former in the coil for the measurement is 0.235”. The insert in figure 4 shows the approximate measurement locations with respect to coil length.
Integrated data of the product have also been reviewed with signal amplification of one order of magnitude, and no significant changes in the overall performance. The particular integrator has been structured to fit the customer’s unique application.
Figure 3: linearity of raw output voltage for Magnelab Rope CT as measured at 60Hz
Figure 4: Linearity and repeatability response of center point measurement for Rope CT 2
Figure 5: Frequency and positioning accuracy data for Magnelab prototype Rope CT as measured at Iin=500A.
Rogowski Coil Summary
The basic operation principles of a Rogowski coil have been reviewed and summarized as it pertains to Magnelab product.
Basic characterization data and product physical configuration are also presented.
The Rope CTs studied have shown good low and high current and frequency responses. This makes them good candidates for a wide range of applications using appropriate integration.
References
- Rogowski, W and Steinhaus, W; Arch Electrotech 1, pp141-150 (1912)
- Ray, WF and Davis RM; EPE Journal, vol 3, no 1, pp51-59 (1993)
- Ray, WF and Davis RM; EPE Journal, vol 3, no 2, pp116-122 (1993)