Chapter 2
Rogowski coil: construction and applications
2.1 Introduction
In this chapter we introduce Rogowski coil, it’s applications, advantages, operation
Theory, and the equivalent circuit.
2.2 Rogowski coil
The Rogowski coil is flux-to-voltage transducer for non-intrusive current measurement.
In some application iron core replaced by air core due to disadvantages of iron core which is the CT (iron core) is a non-linear element that saturates whenever flux inside the CT core exceeds the saturation level, resulting in distorted and reduced secondary current as shown in fig.2.1
Fig.2.1: comparison between secondary current in two cases saturation and non-saturation
2.3 Theory of operation
Rogowski coil theory is based upon Faraday’s law that states the total electromotive force induced in a closed circuit is proportional to the time rate of change of the total magnetic flux linking the circuit. A simple flexible Rogowski coil is shown in Fig.2.2
Fig.2.2: simple flexible Rogowski coil
A voltage can be induced in a wire loop by moving the conductor through a magnetic field or by placing the wire loop in a time varying magnetic field
When a Rogowski coil is placed on a current-carrying conductor, the coil generates a voltage, e0proportion to the coil’s mutual inductance M, and the time rate of change of current.
To obtain a measure of current, the coil’s output voltage must be integrated, and then scaled by the reciprocal of the value of mutual inductance.
2.4 Construction of Rogowski coil
-A Rogowski coil is a current transformer. It consists in an air-cored (no ferromagnetic material) toroidal coil through which the current to be measured circulates.
-Rogowski coils may be wound having a single-layer winding or multiple-layer windings.
- Single-layer coils will have lower values of mutual inductance, series self-inductance, series resistance, and distributed capacitance.
-The winding is wound on a toroidal core made of dielectric material.
-A typical single-layer Rogowski coil is shown in Fig.2.3
Fig.2.3 construction of Rogowski coil
-The coil is wound as a continuous helix of round wire around the core form.
-Single- layer-type Rogowski coils typically have several hundred turns for practical-sized forms. The mutual inductance that is usually obtainable ranges from about 0.1-1 μH
2.5 Equivalent circuit of rogowski coil
Fig.2.4: equivalent circuit of rogowski coil
The corresponding equivalent circuit consisted of a coil’s equivalent resistanceRc, self-inductancelc, mutual inductanceMc, self-capacitance Cc, terminal resistanceRt, and voltage source end, which is acting as a coupling circuit, is shown in Fig.2.4
2.6 Characteristics depending on geometry of the Rogowski coil
As mentioned earlier, the electrical response of the coil model is configured by its geometrical parameters. Following overview is presented for the assessment of coil’s most critical characteristics that are directly dependent on the coil geometry. Such characteristics are mutual inductance, self-resistance, self-inductance and self-capacitance of the Rogowski coil as shown in fig.2.5.
Fig.2.5
1-Mutual inductance
Mutual inductance determines the self-inductance and is a decisive parameter for assessment of coil’s sensitivity.
Its value depends on the shape of the cross section of the core used for coil winding.
The most common selections of cross-section of the core are circular, oval or rectangular .
in case cross-section of the core are circular.
where M is the mutual inductance of the Rogowski coil, H,
1) μo, is the permeability of air, which equals 4π×10-7
2) n is the number of turns of the coil,
2) n is the number of turns of the coil,
3) W is width (thickness) of the toroid in meters,
4) b is the outside diameter in meters, and
5) a is the inside diameter in meters.
2-Self resistance
The coil’s self-resistance is made up from the resistance of the wire that is used for making the winding.
Resistance depends on the wire cross-section areaAw, length of wire used lwand material’s characteristic resistance.
Fig.2.6: Calculation of coil’s Pitch Pw
The wire length of a single turn on the Rogowski coil depends on the turn pitch Pw as show in Fig.2.6 of the winding and diameter of the core drc.
For a coil with N number of turns, the total coil wire resistance Rc is
Whereρ is the electrical resistivity of the conductor.
3- Self inductance
Inductance of a single circular loop L loop of wire can be found as
It can be seen that the inductance is dependent on the square of number of turns. This should be kept in mind for the analysis on the frequency response of the Rogowski coil.
4- Self capacitance
The capacitance of the Rogowski coil can be divided into two categories; the capacitance between the winding and the central return loop Cc (turn-to-return capacitance) and the coil’s turn-to-turn capacitance Ct as shown in Fig.2.7
The turn-to-return capacitance has been suggested to be calculated as a coaxial system, with winding perimeter as the outer electrode and the return wire as the center electrode.
-The turn-to-return capacitance can be calculated as:
Fig.2.7: Self-capacitance of rogowski coil
-The turn-to-turn capacitance can be calculated as:
This assumes that capacitance between turns would be the same as wire rings (turns) placed side-by-side, making up a chain of series-connected capacitors. Therefore equivalent turn-to-turn capacitance for a coil with higher number of turns would become very small and could be neglected.
2.6.1. Effect of geometrical parameter on the performance NCEEFF
1. Decreasing the coil diameter (dm) is the most favorable alternative for improved performance of the coil.
Both sensitivity and bandwidth increase by reducing the coil diameter.
Additional advantages are the smaller size, lower weight and more possibility of the under test line to be placed in the center of the rogowski coil.
2.Core diameter seems the second preferred option to improve the electrical performance.
3. Adding the number of turns to increase the sensitivity would not be recommended, as it decreases the operating bandwidth significantly.
Additional disadvantage is the increased weight.
4. It has been observed that variation in wire diameter is not very effective towards the electrical response.
5. Mechanical strength and weight of the coil might be the criteria to select the wire diameter.
6. The conductor diameter is more influential for the measurements in the mains frequencies, as the low frequency measurements (50 Hz) would need higher number of turns.
7. The return loop is preferable over the return winding.
The return winding provides basically the same sensitivity, however there is a significant increase in capacitance which results in remarkable reduction.
2.7 Advantages of Rogowski coil
1- Suitable to measure currents from mA to hundreds of kA
2- High linearity as shown in Fig.2.8
Fig.2.8: Comparative V-I Characteristics for Iron-Core CTs, Linear Couplers, and rogowski Coils
3- Wide dynamic range
4-Very useful with large size or awkward shaped conductors or in places with limited access
5- No danger from open-circuited secondary
6-Not damaged by large overloads
7-Non-intrusive, no power drawn from the main
8-Thanks to its light weight, it can be changed on the measured conductor
9- Totally shielded
10- Very thin coil diameter: down to 8 mm
11-Newly designed and enhanced bayonet connector including possibility to regulate calibration
12- Improved accuracy
13-Measurement uniformity at any position of the conductor inside the coil
14- Excellent degree of rejection to the external current conductor.
2.8 Rogowski coil application design
Rogowski coils have been designed and applied at all voltage levels (low, medium, and high voltage).
They have been designed for indoor and outdoor installations and applied for metering, protection, and control.
2.8.1 Low voltage application design
Fig.2.9 shows low-voltage switchgear that uses Rogowski coils for metering and protection. Circuit breakers are equipped with self-powered, microprocessor-based trip-devices to sense overload and short circuit conditions.
Rogowski coil accuracy is better than 1%.
Fig.2.9: Rogowski Coil Applications in Low Voltage Switchgear
Energy monitoring flexible Rogowski coils for energy measurements in applications such as industrial production machines, supermarkets, data centers, schools, and TV studios. as shown in fig.2.10
Fig.2.10: Rogowski Coil Application for Energy Measurements
2.8.2 Medium voltage application
Fig.2.11 and Fig.2.12show applications of Rogowski coils combined with voltage sensors on design
Fig.2.11: Outdoor Application of Rogowski Coils Combined with Voltage sensors
Fig.2.12:
Rogowski Coil Applications in Medium Voltage Switchgear (combined current and voltage sensor)
Applications in Industrial Complexes.Fig.2.13 shows two different designs of Rogowski coils applied in steel companies for protection of electric arc furnace transformers.
Coils in Figure are non-split core style installed on the primary side of transformers.
Split-core style coils are installed on the secondary side of transformers because secondary conductors cannot be opened for the coil installation 
Fig2.13: Rogowski Coil Applications fir Electric Arc furnace Transformer Protection
Motor Protection. Rogowski coil technology provides a lighter and more compact solution compared to overload protection based on conventional CTs, and improves fault diagnosis, motor protection, and reductions in inventory.
In addition, the units are considerably easier to install. Electronic integrators accurately reproduce primary current waveforms. Fig.2.14. shows a motor protection solution based on rogowski coils.
Fig2.14: Application of Rogowski Coils for Motor Protection
The motor-protective system applies for motor currents from 1A to 820A.
Relays provide the standard functions of protection in the event of phase failure, overload, or current imbalance.
Relays provide the standard functions of protection in the event of phase failure, overload, or current imbalance.
Other advantages include:
- Small control panel design with a volume reduction of 58:1 compared to conventional transformers
- Small light-weight sensors with wide current ranges
- A small number of devices, resulting in reduced storage costs
- Simple installation. Fixing bands enable Rogowski coil sensors to be easily mounted.
2.8.3 High voltage application design
Fig.2.15 shows a stand-alone Rogowski coil design.
Performance characteristics include:
- Continuous Current: 600 A, 1200 A, 2000 A
- Voltage: 7.5 kV - 500 kV (line-to-line)
- BIL Rating: 95 kV - 1470 kV
- Accuracy: +/- 0.15%
Fig.2.15: Stand-Alone Rogowski Coil for Current Measurements at 69 k, 1200A
This figure illustrates a stand-alone Rogowski coil design using the Optically Powered Data Link (OPDL) technology.
OPDL transmit data from the Rogowski coil and remote unit that are located at high-voltage potential to ground potential using fiber-optic cables and laser technology.
Recent applications include current measurement for protection and metering with metering accuracy.
Recent applications include current measurement for protection and metering with metering accuracy.
Rogowski coils are installed at high-voltage levels, suspended from the primary conductor or a busbar.
This eliminates the need for a supporting insulator.
This eliminates the need for a supporting insulator.
The advantages of these methods as compared to the conventional solutions that use free-standing iron core CTs are: no oil or SF6 gas, light weight, no seismic or explosion concerns, and use of low-voltage insulation class RCs.
In this solution, the Rogowski coil output signal is fed into the remote unit of the OPDL.
The remote unit is interfaced to the ground unit over two fiber-optic cables.
One cable provides power for the remote unit and the second cable transmits data from the Rogowski coil.
Mobile substations require that the equipment tolerate the motion and vibration associated with movement over the road on a trailer.
The Rogowski coil approach offers much less weight and size in the sensor when compared to conventional CTs — along with improved protection system performance. Fig.2.16 shows a 20 MVA, 161/13.8 kV, delta/grounded-wye power transformer with Rogowski coil based differential protection. The 161 kV side Rogowski coils are mounted at the base of the primary bushings on the transformer. The 13.8 kV side Rogowski coils are mounted on the front of the trailer in the existing support structure.
An additional Rogowski coil is mounted around the neutral bushing on the secondary side of the transformer for monitoring neutral current and for restricted earth fault protection.
Fig.2.16: Rogowski Coil Installation around Bushings in a Mobile Substation
2.9 GIS application designs
The combined electronic voltage and current transducer (EVT/ECT) shown in Fig.2.17 is designed according to IEC 60044-7 and IEC 60044-8.
It consists of two fully independent measurement systems, each with protection and metering data.
- Current: 100 – 4000 A, 0.2S / 5P TPE
- Voltage: 330 – 550 kV/√3, 0.2 / 3P
A single-phase primary converter contains two independent sets of voltage sensors and Rogowski coils.
Two redundant secondary converters are mounted directly on the primary converter, containing signal acquisition, signal processing, and digital transmission circuits.
Merging units provide interfaces to IEDs over Ethernet link according to IEC 61850-9-1 / 9-2.
Separate devices are used for metering and control, and protection applications.
Fig.2.17: Rogowski Coil designs for GIS Applications (example 1)
Fig.2.18 shows a GIS that uses Rogowski coils for metering and protection.
The coils have an accuracy class of 0.1 in a temperature range from –40 °C to +90°C.
Fig.2.18: Rogowski Coil implementations in GIS (example 2)
Fig.2.19 shows the system configuration of a 245 kV I-AIS with ECT.
The Rogowski coil and sensing unit are mounted at top of the circuit breaker. Power to supply the sensing unit at the high-voltage potential is provided by a Laser Diode Unit (LDU) at ground potential.
The Rogowski coil and sensing unit are mounted at top of the circuit breaker. Power to supply the sensing unit at the high-voltage potential is provided by a Laser Diode Unit (LDU) at ground potential.
The sensing unit at the high-voltage potential and the merging unit at ground potential are interfaced by a fiber-optic link within an insulator.
The analog signal from the Rogowski coil is converted into 16-bit digital signal by the sensing unit, and is transmitted to merging unit through the fiber-optic cable.
Fig.2.19: Rogowski Coil Integration with High Voltage Circuit Breakers (example)
2.10. Future protection application
Faults in power systems cause traveling waves (TW) that propagate through the system near the speed of light away from the fault location and reflect at points where impedance changes.
Traveling waves have a fast-rising front and a slower-decaying tail.
Magnitudes of consecutively reflected waves decrease (attenuate).
Magnitudes of consecutively reflected waves decrease (attenuate).
When TW are generated, both traveling wave voltages (TWV) and traveling wave currents (TWC) exist.
Here, applications of traveling wave currents for protective relaying purposes and determining fault locations in power systems are considered.
For relay protection applications, detection of the TWC polarity is more important than their magnitudes.
The TWC magnitudes only determine thresholds to initiate protection algorithms. The TWC polarity determines the fault direction.
If the polarity is positive, the fault is in the forward direction, and if the polarity is negative (180 opposite), the fault is in the reverse direction.
By comparing input signals from all terminals of a Zone (two or more terminals), it is possible to determine if the fault is inside Zone or outside Zone.
However, when a fault occurs near or at the voltage zero, TWC are not generated. In those events, TWC-based relays may not operate and protection should be provided by a backup protection for phasor-based protective relays, signal processing is required to extract the power frequency signal. However, for TW-based protective relaying, all lower.
However, when a fault occurs near or at the voltage zero, TWC are not generated. In those events, TWC-based relays may not operate and protection should be provided by a backup protection for phasor-based protective relays, signal processing is required to extract the power frequency signal. However, for TW-based protective relaying, all lower.
Frequency components of the line current are not relevant Rogowski coils can be designed to have a frequency response exceeding 100 MHz since they inherently amplify high-frequency components, Rogowski coils generate a pulse resulting from the step change in current magnitudes caused by TWC reflections and refractions.
Magnitudes of generated pulses can be different for different events and can also quickly attenuate. Therefore, TW-based protective relaying uses pulse magnitudes only for thresholds.
The protection and fault location algorithms use the time difference between successive pulses and their polarity.
Method using different algorithms, such as phasor-based.
2.11. Disadvantages of Rogowski coil
Low Sensitivity means not able to measure very small partial discharge current.
So we will be working on Sensitivity improvement as shown in next chapter.
