Patent Description:
This invention was made with government support under Award No. DE-OE0000877, awarded by the Department of Energy. The government has certain rights in the invention.

The various embodiments of the present disclosure relate generally to current sensors. More particularly, the various embodiments of the present disclosure are directed to current sensors employing Rogowski coils.

Electric utilities are installing various sensors for advanced situational awareness into the sub-transmission and distribution networks. Current sensors are critical for recording steady state and fault currents in different parts of the grid. Current transformers have typically been used by utilities. Limitations of cost and dynamic range, however, are causing utilities to adopt newer solutions like Rogowski coils. The typical implementation of a Rogowski coil is shown in <FIG>. Rogowski coils exhibit several advantages over current transformers (CTs) and other magnetic effect sensors like Hall effect or even shunt-based current transducers. Rogowski coils, which encircle the conductors, are typically air-cored, and hence do not saturate due to the absence of magnetic elements. A high bandwidth can be achieved, along with a linear response over a wide dynamic range, compared to CTs with magnetic cores. Rogowski coils are also resilient to thermal, conducted, and radiated noise. Additionally, they offer isolation and need minimal signal conditioning, making them ideal for power electronics applications. Compared to Rogowski coils, CTs can be bulky and expensive.

Utilities have used various sensors for capturing waveform signatures which are a useful resource for utility operations, particularly in protective relaying. These fault current signatures can also help in identifying faulty equipment, perform predictive maintenance, or post-event analysis. For instance, it has been shown that the waveform data can be used to recognize fault types in overhead distribution lines. Additionally, Rogowski coils have been used for stator fault diagnosis in machines.

With recent advances in manufacturing techniques, designers have integrated the toroidal windings on printed circuit boards (PCBs), thus achieving a compact form-factor, low cost and good reproducibility. The availability of precision-trimmed operational amplifiers (op-amps) has helped in achieving low drift, fast settling analog (active) integrator circuits. The Rogowski coil outputs a signal proportional to the differential of the current enclosed in it (di/dt sensor). Analog integrators can condition the signals from the Rogowski coil and feed them into a data converter and microprocessor-based unit that can record the data or perform certain control actions based on it. PCB-based Rogowski coils have been developed for both power-line frequencies (<NUM>/<NUM>) as well as switched mode power converters.

However, there are certain limitations on these conventional devices that need to be improved. For example, the dynamic range of Rogowski coils is limited by the signal conditioning circuitry. This is because the associated op-amps saturate at finite signal levels, causing signal distortion and clipping. These circuits can also add some phase shift in the signal, which can add to significant errors when the signal is used for power metering or for operating protection equipment.

With micro-processor and digital signal processor (DSP) based systems, the integration function can be performed digitally, using filters to achieve better phase response. An FPGA based digital integrator and a programmable gain amplifier (PGA) has been used to control the gain and ensure that the coil voltage is scaled for the ADC (analog to digital data converter) stage. Both time-domain and frequency-domain digital compensation techniques have been proposed for reconstructing the input current signals. These approaches, however, add costs in hardware, computation, and power consumption.

Additionally, with a traditional closed-coil structure, it is difficult to install these sensors on conductors already present in the field. Rather, utilities must de-energize the circuits, sever the conductors, and pass them through the Rogowski coil as part of the installation process-a task that significantly adds to the overall costs. Thus, retrofit capability is important for a low cost, commercially viable design. But while several designs have been proposed, the solutions are still significantly expensive (> $<NUM>) with no other advantages.

Several PCB-integrated Rogowski coil sensors have been proposed in literature, with precise tuning for frequencies of interest. The bandwidth of the Rogowski coil is determined by self-resonant frequency (fr), which depends on the lumped parameters (L, C, R) of the coil. Thus, an understanding of the dependence of the parasitics on the coil construction is important. At lower frequencies, the coil can act as a self-integrating coil if the terminating resistance Rt < ωL, and a di/dt sensor if Rt > ωL; thus, coil termination is also important.

The integrator design at lower frequencies also can be challenging because a low frequency offset-drift can accumulate; or the capacitor in the RC feedback can discharge causing errors. It is difficult to design a wide bandwidth integrator that can measure both power line (<NUM>/<NUM>) as well as high frequencies (several kHz range) like those encountered in switching power converters. Often times, conventional PCB Rogowski coil implementations meet either power line or high frequency requirements. The combination of the frequency response of the PCB coil itself along with the <NUM>st order analog integrator are shown in <FIG>. The +<NUM> dB/dec due to the coil and <NUM> dB/dec from the integrator result in a relatively flat gain response over the integration bandwidth. Careful tuning of the integrator can result in a wide bandwidth design, which is limited only by the integration gain and the coil self-resonant frequency, as discussed below.

As such, an ideal signal conditioning circuit may entail a precise analog design with wide bandwidth, near-zero phase shift over frequencies ranging from power-line to several <NUM>'s of kHz, and can scale and track the signal according to the current being measured. This would make it possible to capture fast transients and fault currents without the limitations imposed by the signal conditioning circuitry.

An important limitation of the Rogowski signal conditioning system is the dynamic range. Even though Rogowski coils (air-cored) themselves do not saturate and offer higher dynamic range than the magnetic core based CTs (that can saturate), the primary limitation in conventional Rogowski coil-based sensors is the signal conditioning circuit. Active integrator-based signal conditioning can have a limited dynamic range and starts saturating (causing signal distortion and clipping) when the signal levels start hitting supply rail voltages. With a static integrator gain, the dynamic range is dictated by the rail voltages. This results in a significant level of selection and tuning in the field for matching the currents flowing to the sensor itself. As a consequence, utilities are forced to employ different sensors depending on the current rating of the asset, e.g., from <NUM>-<NUM>,000A for steady state in five distinct steps, not including fault currents.

As shown in <FIG>, most conventional asset monitoring solutions based on Rogowski coils have a coil, an analog front end, an ADC, an MCU (micro-controller unit) and a radio. Some applications involve specialized sensors like µ-PMUs (micro-phasor measurement units) for advanced visibility into the grid or extracting d, q, and zero sequence currents in <NUM>-phase systems. The radio includes a cellular network or a standard Internet of Things (IoT) protocol, with a wireless gate-way device for cloud connectivity. Today's sensors tend to be very expensive, with a typical current/voltage sensor costing over $<NUM> to monitor a transformer asset that is of similar value, making cost justification very challenging. These costs do not include the back-end system for data management that needs to be customized, installed, and maintained. As a result, even though the need for ubiquitous sensing is well recognized, the high cost has limited the deployment of such sensors only to high value applications.

Therefore, there is a desire for improved current sensors that address the one or more of the issues discuss above. Various embodiments of the present disclosure address this desire.

Document <CIT> discloses an electronic transformer within a wide current inspection range where a control circuit control uses the magnitude of the detected analog signal to adjust the gain of a variable amplifier. The control circuit comprises an analog circuit, an analog-to-digital converter and a microprocessor. <CIT> discloses another system where a rogowski coil current sensor is used together with a similar control circuit that adjusts the gain based on the magnitude of the detected analog signal.

Document <CIT> discloses a device comprising a circuit board, a Rogowski coil on the circuit board, persistent data storage on the circuit board, and a control circuit on the circuit board for collecting values representing current sensed by the coil, and storing the values in the persistent memory.

The present disclosure relates to current sensors and methods of measuring current.

These and other aspects of the present disclosure are described in the Detailed Description of the Invention below and the accompanying figures. Other aspects and features of embodiments of the present disclosure will become apparent to those of ordinary skill in the art upon reviewing the following description of specific, exemplary embodiments of the present disclosure in concert with the figures. While features of the present disclosure may be discussed relative to certain embodiments and figures, all embodiments of the present disclosure can include one or more of the features discussed herein. Further, while one or more embodiments may be discussed as having certain advantageous features, one or more of such features may also be used with the various embodiments of the disclosure discussed herein. In similar fashion, while exemplary embodiments may be discussed below as device, system, or method embodiments, it is to be understood that such exemplary embodiments can be implemented in various devices, systems, and methods of the present disclosure.

The following Detailed Description is better understood when read in conjunction with the appended drawings. For the purposes of illustration, there is shown in the drawings exemplary embodiments, but the subject matter is not limited to the specific elements and instrumentalities disclosed.

The components, steps, and materials described hereinafter as making up various elements of the invention are intended to be illustrative and not restrictive. Many suitable components, steps, and materials that would perform the same or similar functions as the components, steps, and materials described herein are intended to be embraced within the scope of the invention. Such other components, steps, and materials not described herein can include, but are not limited to, similar components or steps that are developed after development of the invention.

As shown in <FIG>, various embodiments of the present disclosure include a Rogowski coil <NUM> positioned on a substrate <NUM>. The substrate <NUM> can be many different substrates. In an exemplary embodiment, the substrate <NUM> can be a printed circuit board (PCB). In some embodiments, the PCB comprises multiple layers.

The substrate comprises an aperture <NUM>. The aperture <NUM> is configured to permit a conductor <NUM> to pass therethrough. As shown in <FIG>, the Rogowski coil <NUM> is positioned along the perimeter of the aperture <NUM>. For example, the coil traces can be embedded in the substrate <NUM>. The Rogowski coil <NUM> can have an inner radius and an outer radius. As also shown in <FIG>, the coil <NUM> can comprise coil terminals <NUM>. When the conductor <NUM> passing through the aperture <NUM> carries an alternating electrical current, the Rogowski coil <NUM> generates an analog voltage signal at the coil terminals <NUM> proportional to the magnitude of the current carried by the conductor <NUM>.

The substrate <NUM> can be either a continuous piece, meaning the conductor <NUM> is typically inserted through the aperture <NUM>, or the substrate can be a "clip-on," which is shown in <FIG>. In the "clip-on" configuration, the substrate <NUM> comprises a first portion <NUM> and a second portion <NUM>. A first portion of the Rogowski coil <NUM> can be positioned on the first portion of the substrate <NUM>, and a second portion of the Rogowski coil <NUM> can be positioned on the second portion of the substrate <NUM>. In some embodiments, the first and second portions of the substrate <NUM>, <NUM> can comprise one or more connectors (not shown) for detachably connecting the portions <NUM>, <NUM> together. The connectors can be many different connectors known to those skilled in the art. Thus, the first and second portions of the substrate <NUM>, <NUM> can be separated from each other and positioned around an existing conductor <NUM>. The first and second portions <NUM>, <NUM> can then be connected to each other, such that the first and second portions of the Rogowski coil <NUM>, <NUM> are in electrical communication with each other. The "clip-on" configuration can be beneficial for measuring current carried by a conductor <NUM> without having to disconnect one end of the conductor <NUM> and run it through the aperture <NUM>, i.e., operation of the conductor <NUM> is uninterrupted.

As discussed above, various current sensors of the present disclosure make use of Rogowski coils. Specifically, various embodiments employ a printed circuit board (PCB) which has coil traces embedded therein forming a toroidal structure. The top view and side view of such a PCB are shown in <FIG> (with an equivalent circuit shown in <FIG>). If h is the thickness of the PCB, and a, b, are the inner and outer diameters of the PCB coil, a closed form expression can be derived, relating the mutual inductance of the primary current-carrying conductor to the coil as shown in Equation <NUM>: <MAT> where H is the magnetic field strength, B is the magnetic flux density and µ<NUM> is the permeability of free space, 4π <NUM>-<NUM>H/m <MAT>.

With N number of turns on the PCB; by Faraday's law, voltage induced on the coil, vo is shown in Equation <NUM>: <MAT>.

The mutual inductance M, can be represented by Equation <NUM>: <MAT>.

Typically, for power line applications, Equation <NUM> holds true: <MAT>.

It can be seen that the voltage induced varies directly with the frequency of the primary current, making the Rogowski coil suitable for high frequency current measurements, as vo is proportional to ω.

The frequency characteristics of the coil also depend on the lumped parameters. The coil can be approximated as an LCR circuit and the self-inductance Ls and series resistance Rs can be estimated as shown in Equations <NUM> and <NUM>: <MAT> <MAT> where ρ is the electrical resistivity of PCB traces (for copper, ρ = <NUM> x <NUM>-<NUM> Ω m), dl, dh and dw are length, height and width of PCB traces and t:<NUM> is the permittivity of free space, <NUM> x <NUM>-<NUM> F/m.

A closed-form expression for the lumped capacitance Cs for a PCB embedded coil can be derived from finite element methods, and measured values are used in the model presented herein.

It is evident that the bandwidth of a PCB-based coil itself is greater than several hundred kHz as determined by the lumped parameters, Ls and Cs. The resonant frequency fr is shown in Equation <NUM>: <MAT>.

Based on these principles, four PCB embedded coils were manufactured to compare the performance. These coils are shown in <FIG>. Two of these coils (coils A and B) had a closed structure and were identical to each other, with only the PCB thickness being different. Coils C and D were "clip-on" Rogowski coils (discussed below), with similar structures but different number of turns.

For the parameters of the coils shown in <FIG>, experimental data using an impedance analyzer (<FIG>) on the four constructed coils show that fr > <NUM>, making them suitable for us in frequencies up to <NUM>. The expected values using Equations <NUM>-<NUM> and measurement results from an impedance analyzer are provided in Table I.

To evaluate the performance of the coils, they were excited with the same current (ip = <NUM> ARMS at <NUM>) and the coil output voltage (Mdip/dt) compared. <FIG> shows that the responses of the clip-on coils are comparable to the closed core coils, with the mutual inductance M being the dominant governing factor. It can be concluded that the clip-on versions (coils C and D) are equivalent to the PCB-based coils (coils A and B). The step response for coil D is shown in <FIG>, showing a fast setting dip/dt output for an excitation current of ip = <NUM> mApk-pk.

For a Rogowski coil with an air gap without any compensation, the mutual inductance M varies as little as <NUM>% when the conductor is near the airgap. It also has little variation in other arbitrary locations inside the coil which is confirmed from our findings.

A test to measure the variation of the mutual inductance due to the conductor position within the coil was carried out. The test setup is shown in <FIG>, with the positions marked. Based on the primary current excitation and Rogowski coil output voltage, mutual inductance was measured using Equations <NUM> and <NUM>. It was seen that the normalized mutual inductance M varied within ±<NUM>% as the position of the conductor was changed. However, it is important to note that the exemplary sensor was designed for utility grade cables (ACSR or <NUM>/<NUM> gauge), so that the positional variance is minimal.

The experimental results show that the open-core, clip-on configuration (used in coils C and D) has a performance comparable to that of the closed core designs (used in coils A and B). It can also be seen that the connectors do not introduce significant noise or parasitics into the lumped model of the Rogowski coil, as concluded from Table I. It can also be seen that the dynamic performance is within specifications, making the clip-on configuration beneficial for a wide bandwidth application.

As shown in <FIG>, current sensors of the present disclosure also comprise a controller. The controller comprises components for processing the analog signal generated by the Rogowski coil. The controller comprises an analog circuit, an analog-to-digital converter (ADC), and a microcontroller unit (MCU) (or microprocessor). The analog circuit can be divided into three sections: a front-end amplifier, a low noise integrator, and an adaptive programmable gain amplifier.

Front End Amplifier: Rogowski coils can be very sensitive (e.g., approximately <NUM> µV/A at <NUM>), the signal generated by the coil can be first amplified, before integrating it. This can be achieved by a programmable gain instrumentation amplifier, to remove any common mode noise, offset error, and unwanted signal couplings. To match the Rogowski coil's sourcing capability, this stage is desirably a high impedance input stage. Hence, in an exemplary embodiment, an instrumentation amplifier with <NUM> nA bias current was chosen, and converted into a programmable gain amplifier with the use of solid-state analog switches, with an ultra-low insertion loss. The dynamic range added due to this stage is <NUM> : <NUM>, i.e. +<NUM> to +<NUM> dB.

Low Noise Integrator: The front-end amplifier can condition the incoming di/dt signal and feed it into a low-noise, low-drift integrator circuit, tuned for operation over a frequency range, e.g., <NUM> to <NUM>. Op-amps with ultra-low offset voltage can be used to minimize the drift. Additionally, a high-pass filter stage can be used to remove any remnant DC offset that can cause distortions in the signal.

Adaptive Programmable Gain Amplifier: In the third state of the analog circuit, a programmable gain amplifier (PGA) can be used to condition the signal for the ADC. The PgA can be digitally controlled over a gain range, e.g., <NUM> to <NUM>, which can add another <NUM>: <NUM> to the dynamic range (i.e., -<NUM> to +<NUM> dB). In addition to the gain, this stage can level-shift the signal and center it around half of the voltage rail (+<NUM>. 65V), setting it up for both single ended and differential ADCs.

Analog-to-Digital Conversion and Microcontroller: In the exemplary sensor shown in <FIG>, the MCU used was the mixed signal processor MSP432P401R which has ultra-low power consumption, fast speed (<NUM>), and excellent ADC integration. The on-board ADC has a successive approximation architecture, featuring up to <NUM> kS/s sampling rate. For the purpose of the experiment, it has been configured to sample at <NUM> and a <NUM> oversample and average architecture to generate and store the waveform data (<NUM> samples/cycle) to the on-board flash memory in a cyclic memory buffer.

The specifications for the exemplary analog design are summarized in Table II. The sensor can achieve -<NUM> to +<NUM> dB range correction to the incoming current waveforms. The MCU can capture data from the ADC and drive the gains for the preceding stages through seven general purpose I/Os. An exemplary algorithm for driving the gains is discussed below.

In various embodiments of the present disclosure, the gain applied to the analog signal generated by the Rogowski coil can be varied allowing for the sensor to achieve a high resolution while maintaining a high degree of accuracy. For example, in some embodiments, the current sensor can be configured to measure the alternating electric current relative to a full scale at a resolution of <NUM>:<NUM> and at an accuracy within <NUM>%, wherein the full scale can range over <NUM>:<NUM>.

As used herein, "full scale" refers to the maximum current that the combination of the signal conditioning circuit and the data acquisition stage of the sensor can support while functioning without non-linearity or distortions. The "resolution of <NUM>:<NUM>" defines the range of discrete, valid measurements that can be successfully made with the help of the data acquisition stage. A "resolution of <NUM>:<NUM>" refers to <NUM> discrete steps in which the measurements can be assigned a digital or discrete value using the data acquisition stage. "Accuracy within <NUM>%" sets an upper bound on the error to be <NUM>% of true value when operating at rated, full scale of the current. The phrase "full scale can range over <NUM>:<NUM>" refers to the fact that the adaptive signal conditioning stage can vary the full scale of operation over a range from 1x to 5000x.

For example, let an embodiment of the sensor be configured to measure full scale of <NUM> amperes at a resolution of <NUM>:<NUM> and at within <NUM>% accuracy. This indicates that the maximum current that can be measured with the sensor is <NUM> amperes, and the minimum current measured is <NUM> amperes. With <NUM>% accuracy, the maximum error when measuring <NUM> amperes current is <NUM> amperes. With the adaptive signal conditioning, the full scale (i.e., the maximum measurable input) can be varied over a range of <NUM>:<NUM> indicating that the sensor can change the full scale from <NUM> amperes to <NUM>,<NUM> amperes, while maintaining the <NUM>% accuracy, i.e. maximum error of <NUM> amperes at the full scale of <NUM>,<NUM> amperes and a resolution of <NUM>:<NUM>, i.e. being able to measure <NUM> amperes as the lowest measurement.

In embodiments of the invention, the gain applied to the analog signal generated by the Rogowski coil is varied using a Dynamic Range Correction using Edge Intelligence. The Dynamic Range Correction method can adjust the gain of the analog circuits so that the current being measured is mapped into the full-scale range of the ADC (e.g., <NUM>-<NUM>. 3V), especially when the current changes drastically in fault scenarios. An illustration of this concept is shown in <FIG>, where the current changes suddenly from <NUM> Apk to <NUM> Apk. In this scenario, with a finite rail to rail swing on the analog integrator, the analog stage can saturate and clip the signal, resulting in distortion. However, by dynamically adjusting the gains of the analog stage, to match the current levels, the analog signal can be "compressed" to maintain the signal within rail to rail swing, and can be "uncompressed" during post-processing. This effectively creates a mapping between the input current i(t) and the sensor output voltage v(t) and can be used to switch the gains as shown in <FIG>. However, in some embodiments, magnitude alone is not used for range correction because it can lead to chattering. Thus, according to the invention, the di/dt information is also used, as follows:.

Consider a steady state input current i(t) flowing in the utility conductor. From Equation <NUM> voltage induced in the Rogowski coils is vo(t) = Mdi(t)/dt. The integrator with a gain G produces an output represented in Equation <NUM>: <MAT>.

It can be seen that the integrator output dv/dt is related to the incoming di/dt through a constant, K which is the overall gain of the system. Thus, when the incoming di/dt changes drastically (e.g., increases above a predetermined threshold) in the event of a fault, the MCU can calculate dv/dt, and knowing the gain of the integrator, estimate the current level on the primary conductor. Based on these values, a new gain can be calculated so that the analog stage does not saturate, as shown in <FIG>.

The dv/dt can be calculated in the discrete domain by dv/dt = (v[n] - v[n - <NUM>]). fs where fs = <NUM> kS/s; and used to generate the next gain value G[n + <NUM>], which depends on the present gain value G[n], the RMS trend of the voltage vrms and the calculated dv/dt. There can exist a pre-set mapping of gains corresponding to different current levels for which the current variation maps into the full-scale range of the ADC. For instance, i(t) ∈ [<NUM>, <NUM>] A → dv/dt ∈ [K. w]; i(t) ∈ [<NUM>, <NUM>] A → dv/dt ∈ [<NUM>. w] and so on. The MCU then sets the gain K so that v[n + <NUM>] will be maintained within <NUM>-<NUM>. This exemplary procedure is summarized in Algorithm <NUM>. Thus, the exemplary sensor can intelligently detect high di/dt signals and adjust the gain to obtain full scale mapping to the ADC.

Sensors disclosed herein can also include a transceiver. The sensors can use the transceiver to communicate with a remote device. In some embodiments the transceiver is a wireless transceiver, i.e., a transceiver configured to communicate with a remote device (e.g., remote computer, server, cloud, and the like) via a wireless signal. In some embodiments, the sensor can receive a command signal from a remote device, which can indicate the sensor should transmit a response signal to a remote device indicative of the current measured by the current sensor. In some embodiments, the current sensor can be configured to transmit such a signal to a remote device according to a predetermined schedule.

Sensors disclosed herein can also include a power supply to provide electrical power to the current sensor. The power supply can be many power supplies known in the art, including, but not limited to, batteries, a solar panel, wired connection to an electrical grid/generator, and the like.

Performance of an exemplary current sensor will not be described. The exemplary current sensor was manufactured on a compact <NUM> by <NUM> PCB and the bench test setup is shown in <FIG> illustrates a schematic of the tested exemplary sensor, <FIG> illustrates the test setup, and <FIG> illustrates the manufactured prototype. A Pearson current probe was used as a reference measurement to validate the performance of the proposed sensor.

Transient Response of the Integrator: For fault current capture, the integrator stage can be tuned for fast transient response, ideally settling to the expected values within a few line cycles, and not having a large overshoot. <FIG> shows the simulated and experimental transient responses of the integrator stage to di/dt signals at <NUM> and <NUM>, respectively. It can be seen that the integrator transient settles within <NUM>-<NUM> cycles over a bandwidth accommodating <NUM> harmonics, without significant phase error.

Frequency Response: The response of the exemplary sensor at various frequencies is shown in <FIG>. As seen, the sensor output tracks the current waveform as expected, with a phase error < <NUM>° at <NUM>. Measured bandwidth was observed to be between <NUM> and <NUM>, accommodating good harmonic content for analyzing faults in power conductors. <FIG> illustrates the frequency response of the exemplary sensor from ip(t) to sensor output v(t), in which the magnitude of the response can be adjusted a dynamic range correction process as discussed below.

Dynamic Range Correction: For higher currents, a current circulating loop was created as shown in <FIG>. The sensor output at various current levels is shown in <FIG>, with the output continually being within ADC full scale range. Test results from the dynamic range correction process are shown in <FIG>, where di/dt signals corresponding to different fault current levels were applied and varied with time. The sensor adapted the gains to keep the analog output within the full scale of the ADC, without any distortion. The sensor output was effectively compressed from t = <NUM> - <NUM> and uncompressed from t = <NUM> - <NUM> as seen from the discrete ADC output. Effectively, the sensor was capable of measuring currents from <NUM> mA up to <NUM> kA without saturation or distortion. Thus, a dynamic range of <NUM>:<NUM>,<NUM>,<NUM> was achieved by the exemplary sensor.

Fault Current Capture and Waveform Reconstruction: In order to demonstrate the exemplary dynamic range correction algorithm along with waveform reconstruction using edge intelligence, a transient test was carried out using only di/dt signals corresponding to different fault currents. A di/dt signal corresponding to 410ARMS steady state was applied and then switched to the di/dt level corresponding to <NUM> kARMS fault current state as shown in <FIG>. The sensor intelligently adjusted the gain to maintain signal integrity and prevent distortion as seen from the ADC sampled signal in <FIG>. The waveform was reconstructed by the sensor and streamed to a computer for visualization as shown in <FIG>. Similar test showing recovery from a <NUM> kARMS fault current to the <NUM> ARMS steady state is shown in <FIG>.

Next, to show that the Rogowski coil and the dynamic range correction integrator did not saturate at a high current level, an impulse test was carried out using the setup shown in <FIG>. A capacitor bank (<NUM> mF) was discharged into the primary winding of a <NUM>:<NUM> turns-ratio co-axial winding transformer (CWT). The secondary terminal was shorted to generate a high impulse current across the single turn and the proposed sensor clipped onto this terminal as shown in <FIG>. The resulting di/dt signal generated by the clip-on Rogowski coil, and the integrated sensor output are shown in <FIG>. The sensor output did not saturate.

The <NUM>° phase error depends on the integrator parameters and was constant across the different gain stages. The gain stages switch within <NUM> ns, which is sufficiently fast for accurately capturing <NUM> fault currents, while the transient response ensures fast settling. Thus, the same overall accuracy and phase error is maintained across the full dynamic range.

Auto-Triggering Circuit for Gain Adjustment: One approach for dynamically adjusting the individual gains of the analog front-end is to use the incoming di/dt signal itself. Level-triggered circuits can be used to switch gains when the incoming di/dt signals (the output of the Rogowski coil) vary beyond certain values. However, a look at the noise-spectra at individual stages reveals that this may not always be feasible. The signal-to-noise ratio (SNR) at the output of the exemplary Rogowski coil sensor was <NUM> dB at <NUM>, i.e. the Mdi/dt signal was <NUM> dB above the noise floor when ip = <NUM> ARMS. The signal was not strong enough to guarantee auto-triggering if it were to be used to drive a gain switching stage before the integration stage. Since the exemplary coil itself has a +<NUM> dB/dec gain response, it can be seen that the SNR improves at higher frequencies.

As seen in <FIG>, the combined analog stages can ensure a flat gain response across the bandwidth of interest and the overall system was able to achieve the same SNR of approximately <NUM> dB at the input of the ADC, across all frequencies. In the signal chain, the SNR at <NUM> was seen to improve from <NUM> dB to <NUM> dB.

Drift Errors: The exemplary current sensor was operated continuously over <NUM> hours in order to quantify the drift errors in the system. Over this extended run, the system output had a drift of <NUM> mV in the output and a <NUM>° drift in phase. This was resolved by periodically resetting the integrator so that the errors do not accumulate significantly. In the exemplary system, the MCU can shut down the front-end amplifier and the adaptive PGA, thereby driving the integrator output to zero and resetting it.

Immunity to External Interference: Since Rogowski coil sensors encircle the conductor, they are relatively immune to the stray magnetic fields produced by conductors around them. This can be seen by the definition of mutual inductance due to external current-carrying conductor, Mex shown in Equation <NUM>: <MAT> where N is the number of turns in the coil, and <MAT> is the vector potential field over the jth turn. It can be seen that since the encircled area becomes zero as N becomes large enough, Mex is approximately zero. To verify this, an experiment to quantify the external interference was conducted using the setup shown in <FIG>. As seen from Table III, the effect of interference, in the worst case (i.e., when i<NUM>/i<NUM> = <NUM>) is less than <NUM>%.

Claim 1:
A current sensor comprising:
a substrate (<NUM>) comprising an aperture (<NUM>) configured to receive a conductor (<NUM>) carrying an alternating current to be measured; and
a Rogowski coil (<NUM>) positioned along a perimeter of the aperture;
wherein the current sensor further comprises:
an analog circuit, an analog-to-digital converter, and a microprocessor;
wherein the Rogowski coil is configured to generate an analog signal proportional to a magnitude of the current carried by the conductor;
wherein the analog circuit is configured to receive the analog signal from the Rogowski coil and apply a variable gain to the analog signal to generate a gain-amplified analog output;
wherein the analog-to-digital converter is configured to receive the gain-amplified analog output and generate a digital signal; and
wherein the microprocessor is configured to:
receive the digital signal and generate an output indicative of the magnitude of the current carried by the conductor;
decrease the variable gain applied to the analog output if both the magnitude of the analog signal exceeds a first value and a rate of change of the magnitude of the analog signal exceeds a second value; and
increase the variable gain applied to the analog output if both the magnitude of the analog signal falls below a third value and the rate of change of the magnitude of the analog signal falls below a fourth value.