DK178113B1 - System for measurement of multible electrical current magnitudes, based on detection of multible conductor positions - Google Patents

Abstract

This invention concerns non-invasive measurement of the electrical current of individual conductors in a multi-conductor cable arrangement, through discrete measurements of the magnetic field in the vicinity of such an arrangement, combined with a system model involving estimation of the positions of said conductors.

Description

Title

System for measurement of multiple electrical current magnitudes, based on detection of multiple conductor positions

Introduction

As the electric power industry moves towards increasingly decentralized electrical power production, the related power transmission and distribution systems face an increasing monitoring need. E.g., in order to identify segments of said systems which become overloaded, or in order to correctly identify fault locations in the power grid (being either at the transmission or distribution level), with an appropriate level of granularity.

A vital prerequisite for such monitoring is the ability to measure the electrical current magnitudes of each conductor in a given segment of the power grid. Such a segment may e.g. be in the form of a power cable with multiple internal conductors/current paths.

Typical examples would be in the form of 3 or 4 integrated conductors in a cable, used for the 3 phases and a possible shield/ground conductor used in an AC-based power grid system. See figure 1 and 3 for cross section examples of multi-conductor cables.

In power grid nodes, such as switchgears, it is often difficult and/or costly to integrate and calibrate electrical current sensor systems. In part, because many such systems require a separate sensor unit per phase, resulting in 3 or 4 units per power line/section.

The system proposed according to the invention offers novel, non-invasive, high accuracy, cost-effective means of measuring the individual electrical current magnitude of multiple conductors in e.g., a single power cable or a bundle of individual conductor cables, using a single sensor unit, with no need for calibration in the field.

Areas of use

The system may be utilized in any setup where one or multiple conductors are placed in the vicinity of the sensor system, with the goal of obtaining electrical current magnitude measurements of the individual conductors, and/or derived measurement parameters. The system is well suited for a measurement setup which may not be well defined (in terms of the number of conductors, conductor positions, and shape of the conductors). The system presents a significant installation advantage in needing no on-site calibration in order to obtain full possible accuracy for the sensor system.

A particular area of use is on a shielded 3 phase power cable (4 conductors), where the system is capable of producing electrical current magnitudes of the individual conductors, optionally including derived measurement parameters, such as RMS amplitude, phase, main harmonic frequency, frequency content, evaluation and reaction to fault events, etc.

The output of the system may encompass anything from a basic analog output signal to any high level (possibly digital) evaluation of the characteristics of the current signals.

The system may be used in conjunction with a voltage sensing system, enabling further possible outputs, with apparent power being a simple example.

Prior art

Many electrical current sensor systems have been realized today, where the systems determine either the electrical current magnitude of a single conductor/current path or as a sum-total current of a cable with multiple conductors. Of the systems that are based on magnetic field measurements, many rely on the implications of the use of Ampere's circuital law, which results in the ability to measure only the sum of the current flow within the cable, but with no knowledge of the magnitude of individual conductors. In a 3 phase cable system with similar amplitudes and 120° degrees phase separation between conductors, the electrical current sum-total is 0A, and is thus of limited monitoring use.

A magnetic field based sensor system for determining the currents of multiple conductors based on a single sensor unit, has previously been realized in e.g. the 'Compact' sensor system offered byJomitek ApS, Denmark, since 2008. However, this system relies on a calibration specific to the exact environment it is placed in. More specifically, it is factory calibrated initially to match a static model of the positioning of the conductors to be measured on, whereas the proposed system according to the invention determines the position of conductors autonomously as part of an internal system estimator model. A basic difference of properties is thus, that the proposed system is able to produce correct current measurements, even if the unit should be moved about after installation (e.g. by vibrations, which are common in power grid nodes near transformers).

The patent US 7,755,347 B1 presents a measurement and signal processing system with similarities to the present system, but with a number of significant differences in the basic measurement processing premise, and thus the measurement accuracy and/or need for calibration. The system described in the patent targets a power cable for domestic use, consisting of 2 or 3 conductors, where these would be a phase, a null and an optional ground conductor (p. 3 lines 42-45), where only the first 2 would be current carrying. The measurement methodology described relies on either (a) assumptions on the distance from a particular sensor to the conductors of the system, see e.g. p. 5 lines 56-59, or (b) a calibration of the sensor system with respect to the specific measurement setup using a known load, see p. 6 lines 22-29. It is assumed that a sensor pair among a plurality of sensors are determined to have the greatest measurement differential. Based on this detection it is assumed that the pair of sensors closest to the current carrying conductors have been determined, where then the assumptions on distances to the current carrying wires are applied (see Claim 1 of the patent). Given that only a pair of sensors with the greatest measurement differential is found implies a system with the following properties for (a): • The number and configuration of conductors must be known in advance • The phase of the current in the conductors with respect to each other must be known in advance alternatively for (b): • Calibration of the specific measurement setup, using known loads on the conductor must be carried out jointly for the measurement scenarios: • The current of the individual conductor will not be known, only the combined magnitude of the conductors • The position of the conductors will not be determined, since only 1 degree of freedom are obtained, when basing the measurements on the differential signal of only 1 sensor pair.

As a note, it is estimated that the measurement system in the mentioned patent would be very difficult to use in practice for scenarios with 3 or more current carrying conductors with any degree of accuracy.

Patent US 7,755,347 B1 does thus not present an invention with the properties of the present system, see e.g. Claim 1 of the present document, nor will a person skilled in the art be capable of extending the described principles in Patent US 7,755,347 B1 to obtain the capabilities of those presented by the present invention.

Patent EP 0 597 404 A2 details a current measurement system with the capability of measuring the current of individual conductors in a multi-conductor cable. However the processing principle (which requires only m-1 sensors for m conductors), relies on prior knowledge of the number and configuration of conductors in order to derive the conductor-to-sensor sensitivity (Claim 1, section e.). In addition, a particular phase difference is assumed (0/120/240 degrees), whereas the present invention may measure arbitrary current signals (no assumptions on the relationship between the current flow in the conductors). Arbitrary current waveforms will only be mathematically possible to assign to a particular conductor given that the number of sensors is at least m+1 for m conductors, as specified in the present invention. While EP 0 597 404 A2 does allow for m+1 sensors being used, the methodology described will not lead to the capabilities of the present invention, and thus would a person skilled in the art not be immediately able to extend these principles to include the capabilities stated in claim 1 of the present document.

US patent 5,473,244 covers a great variety of applications for non-contacting measurement of voltages and currents. As such, the claims of said patent are not specific in a way which seems to imply the capabilities of the present invention. For the sake of disregarding possible overlap in the patented application, a main difference in particular is that claim 1 of said patent specifies a calibration source, which is not a requirement of the present invention. Concerning the detailed description of the preferred embodiments, it is noted that the description relating to fig. 5A and 5B may seem similar to the present invention.

See p. 7 line 27 to p. 10 line 15. On p. 7 lines 49-50, it is implied that the spacing of the wires of a multi-conductor arrangement is used as an input parameter for the processing of sensor data, which is not needed for the present invention. Furthermore, the method described for determining the current of the individual conductors is vague in that it indicates calculations which iteratively reduces a system error, but with no exemplification of how an expression for such a system error may be obtained. Since the system described in said patent seem to assume equal conductor spacing, it will be difficult to obtain reasonably accurate measurements given a conductor system with differing spacings, as is also noted in the 'Special considerations' section on page 9 to 10. The present invention needs no input with regards to conductor spacing, and handles asymmetrically placed conductors as well as symmetrically placed ones.

A pending patent application, US 2012/0253726 Al, suggests calibration principles similar to those used in the 'Compact' sensor system, but where the scope is to arrive at a calibration methodology with an unknown position of the conductors, and based on a need to inject known currents using an automated 'calibrator' device. This technique does not result in the detection of conductor positions as such, but merely deduces the sensitivity of a current running in a particular conductor with respect to a particular magnetic field sensor. In addition it is a requirement to use an external calibration unit during installation, and should the device move about, it will lose its calibration.

Another patent document within the field of multi-conductor current measurement is US 6,310,470 Bl, where differences in magnetic field strength is used to determine excess current and/or fault current situations. This method is not able to detect the magnitude of the individual currents of the m conductors to be measured, as the patent specifies m-1 magnetic field sensors. It basically tries to measures the difference between the currents of neighboring conductors, somewhat similar to US 7,775,347 Bl. Additionally it does not detect conductor positions.

A pending patent application, US 2012/0319676 Al, addresses a multi-conductor current sensor (seemingly for domestic use), with a detachable sensor housing, and circumferentially mounted magnetic field sensors on said housing. According to claim 1, the sensors provide 'outputs indicative of the properties of the currents that differbut with seemingly no inferred intention of detecting the conductor positions, or the current magnitude of the individual conductors. In addition the present invention will be a fixed installation (i.e., not detachable).

It is, among others, an object of the invention to provide an improved measuring system, which involves a number of advantages over the above cited prior arts, as it will be further elucidated in the following.

The technical problem to be solved A sensor principle measuring the magnetic field in a closed loop (Ampere's circuital law), would only reveal the sum of the current running in the conductors. In order to gain information on the electrical current running through the individual conductors, another measurement principle must be established.

In a multi-conductor cable, the proposed sensor system according to the invention can, non-invasively, accurately measure the electrical current magnitude of the individual conductors, without physically splitting up the cable into its constituent conductors.

This principle applied in accordance with the invention should preferably result in a long term stable (e.g. 20+ years), calibration free, rugged, easy- to-install, single sensor unit (see figure 4), of a physical size that allows an easy fit into the majority of relevant points of access for such measurements in a power grid.

The new technology

In accordance with the implementation of the invention, the magnetic field must be measured on discrete parts of the magnetic field circulating a multi-conductor cable, or bundle of conductors. Ideally (but not necessarily) these discrete parts should be possible to model as point measurements of the magnetic field in a given measurement setup.

Given sufficiently many such point measurements (partly or wholly surrounding the conductors to be measured on) a model of the physical parameters to be estimated can be established, leading to accurate estimation of the electrical current magnitudes of the system. Part of the model consists of parameters describing, directly or indirectly, the positions of the conductors of the system.

The inventive features thus lies in the combination of discrete magnetic field measurements in the vicinity of a multi-conductor arrangement, and a model with current magnitudes and conductor positions as the dynamic parameters (as a minimum), resulting in measurement of the electrical currents of individual conductors.

In addition, the estimation of conductor positions may be realized in a semi-static format. E.g., position estimates are only established when the sensor system is powered up, or at specific intervals in time, or when some other parameter triggers the need for an update of the positioning estimates.

With such a system it will be possible to extract the estimated positions from the sensor system as well; however this information is of secondary interest to the electrical current magnitude measurements themselves. More importantly, since the conductor positions are part of the estimation model, the sensor is able to autonomously detect the type and internal orientation of a given multi-conductor cable, and any subsequent changes of these positioning parameters, enabling no need for external calibration efforts of the system.

One example of such a model for a 2 conductor case is shown in the following. Figure 2 may be used as a reference for some of the notation and indicative sensor positions in the example.

To simplify the example, a coordinate system definition as depicted in Figure 2 is assumed, where the sensors are placed in the X,Y-axis plane, meaning all Z-axis coordinates are 0. The Z-axis is not shown on figure 2, but it is perpendicular to the figure (a Cartesian 3 dimensional coordinate system). Denotation definitions are as in the following examples; v is a scalar, v is a vector, v is a unit vector, and v is a matrix. All position coordinates are in the following treated as vectors.

We define [1] as the 3 dimensional known position of the sensor elements in the sensor system, where the n-index here and in the following denotes the number of the sensor.

Furthermore [2] is the 3 dimensional vector of the current flow of the individual conductor current, where we for the sake of example simplicity assume that the current flow is Z-directional only. The m-index here and in the following denotes the number of the conductor.

[3] is defined as the 3 dimensional position of the conductor. In this simple representation, we assume that the current can be modeled as having a single geometrical point where the current flows through. In reality the current will often flow in the outer parts of a conductor due to the skin effect, and depending on the conductor shape a modeling using a single geometrical point of current flow may not suffice. In such cases, the model may e.g. be expanded to include several current flow points per conductor.

The magnetic field vector applied by the current flow in conductor m on sensor n, will be assumed to follow Biot-Savarts law used on an infinitely long conductor, [4],

The main property of [4] is to express a (usually linear) relation between a unit current flow,

in a conductor with a specific position,

with respect to the magnetic field produced at a specific point outside the conductor,

, where

in [4] illustrates this. This property can be obtained e.g. in the form of an analytical expression, such as the example of [4], or as a point-to-point sensitivity mapping of the unit current in a conductor in a particular positions with respect to a particular sensor position, performed for all sensors, and all applicable conductor positions. In case of significant nonlinear effects, these may be modeled as a Taylor series of sensitivity coefficients to the extent found needed.

We define a known scaling factor for each sensor, kn, which represents the scaling and unit conversion between the magnetic field vector size applied to a sensor, and the finally processed sensor output, yn, for said magnetic field size. Assuming magnetic field sensors measuring 1 dimensionally, and that the orientation, pn, of sensitivity will be in the X,Y-axis plane, we may express above sensitivity as a vector mapping

see [5]

The system, defined as the relationship between sensor outputs

(scalar values of all sensor outputs, arranged as a vector) and currents

(scalar values of all conductor currents, arranged as a vector), as a function of conductor positions, sensor positions, orientations and input-to-output scaling factors may be defined as in [6],

Where

is [7]

Assuming a sufficient amount of sensors for a given number of conductors, possibly in combination with a sufficient amount of successive measurements, M will have a left inverse resulting in [8]

Specifically the sufficiency of sensors depends on the number of degrees of freedom to be determined in M, including the number of conductor currents. In this example, assuming a single sensor signal sample,it is the x and y coordinates of the two conductors, including the currents in these, which are to be determined, and thus a total of 6 sensors are needed as a minimum. By adding more sensors, or more measurements, than the minimum, increased system stability is obtained. As examples erroneous measurements from a sensor may be discarded, and cases of unfortunate placing of sensors with respect to the conductors, seen from a sensor noise level perspective, are reduced.

Determining [8] is considered a well described linear algebra exercise, e.g. in the form of applying the methods involved when determining a Moore-Penrose pseudoinverse.

The system error may e.g. be calculated using [9]

Inserting and reducing the expressions [1],[2], [3], [4], and [5] of the example 2 conductor system, as depicted on Figure 2, into the form of [6] (using [7]), one obtains [10], from which the inverse matrix of [8] can be determined.

Note that the variables to be determined in [10] are Clx, Cly, C2x, C2y,/i,/2 and given the 6 sensor inputs, and appropriately placed sensors, it will be possible to solve the equation system for these variables. An example case of inappropriately placed sensors would be if one or more sensors are placed with the same coordinates, thus making the system underdetermined.

With regards to the sufficiency of sensors, note that a system where the coordinates of the conductors are considered static over a given time frame, and the conductor currents can be considered uncorrelated within said time frame, reveals a minimum of m+1 sensors in order to estimate the positions and currents of m conductors. This property follows from linear algebra, and is exemplified with reference to the 2 conductor system.

Single sample: Given the parameters^ ,(^ , C2 ,C2 , IiA, I2At0 be determined, and a x y x y single sensor signal sample (denoted sample A), 6 sensors are needed to solve for the 6 parameters, assuming none of these are underdetermined.

Two samples: Given the parameters Cx ,C1 ,C2 , C2 , Iia- I2A- Iib*l2Bt0 be determined, and x y x y two sensor signal samples (denoted samples A and B), 4 sensors are needed to solve for the 8 parameters, assuming none of these are underdetermined.

n samples: Given the parametersClx, Cly, C2x, C2y, I1A, I2A, I1B, I2B,..., Iln, I2n to be determined, and n sensor signal samples (denoted samples A, B,..., n), 2+4/n sensors are needed to solve for the 2n+4 parameters, assuming none of these are underdetermined.

The technical effect

By enabling individual electrical current measurements of a multi-conductor setup non-invasively, it is not only possible to use just one sensor unit for a particular power line/section, but also there is no need for having the individual conductors split out from the cable. The device may thus be installed not only at established nodes in the power grid, but also at any point in between (where the multi-conductor cable runs un-split). Additionally, in cases where the cable is shielded, the shielding itself provides a more secure installation environment, while at the same time imposing no limitation on the measurement capability of the sensor system.

Having the conductor positioning as an integral part of the sensor estimation system removes the need for in-the-field calibration both at the time of installation, and at any future point, where the conductors might have changed their position with respect to the sensor system. Additionally, the system will not require any prior calibration for the type of cable to be measured on.

Description of figures

Figure 1: Cross section examples of 2, 3, and 4 conductor systems, where lc is the special case of a 4 conductor system, where one of the conductors acts as shielding. Note, that the physical shape of the conductor cross sections may be sector shaped or some other shape than circular. The conductor cross sections are shown without any insulation material.

Figure 2: Cross section example of a 2 conductor system, with notation according to the modeling example. 'S' is used as notation for the sensor elements, and 'C for the conductors.

Figure 3: Cross section example of a shielded medium voltage sector shaped 3 phase cable, including insulation. As indicated the shielding may consist of many individual wires, but it can often be modeled as a single conductor.

Construction examples

Figure 4: An exemplification of a sensor box layout, and positioning with respect to a 3 phase, shielded cable. Internally, magnetic field sensors are placed on a PCB, e.g. in a fashion similar to the indications in figure 2, such that they are lying on a plane perpendicular to the length of the cable.

Figure 5: Block diagram of the measurement system, where a given number of conductor currents are measured by means of a number of magnetic field sensors, and following this the output of the sensors are used to calculate the conductor positions and currents running in the individual conductors. The conductor position calculations may be running continuously or triggered by e.g. a system error calculation, an event, or a timer. The current calculation results may be further processed and categorized into higher level results, such as the RMS of each signal.

Glossary

Description Patent claims electrical conductor = conductor electrical current = current

Claims (10)

1. A system for measuring electric current, which measures individual currents on a multi-conductor arrangement, with m conductors, where m> = 2, consisting of • m + 1 or more sensors capable of measuring the magnetic field in 1 or more dimensions discrete, e.g. in a point, line, small area, or small volume, as well as processing means configured to operate according to a framework model implemented in hardware and / or software, characterized by the ability to break down sensor measurements into estimates for manager positions and measurement of the magnitude of the electrical current in the individual conductors where the said frame model can be expressed in a form where the sensor output is determined as a linear combination of the flows of the leaders, designated and vice versa where the key property is the ability to express, a typical linear relationship between a unit current running in a conductor with a specific position as compared to the magnetic field produced at a specific point outside the conductor. This property can be expressed in the form of an analytical term, or as a point-to-point sensitivity mapping of a unit current for a conductor in a particular position, viewed in relation to a particular sensor position, performed for all sensors, and all relevant leadership positions. In cases with significant nonlinear effects, these may be broken down into a Taylor series of sensitivity coefficients to the extent deemed necessary to achieve a given level of precision. A system for measuring electric current according to claim 1, wherein the position estimates can be obtained with a semi-static approach, e.g. by positioning the conductors evaluated when the sensor system is turned on, at specific intervals in time, or started via another parameter or event. An electrical current measurement system according to claim 1 or 2, wherein a multi-conductor arrangement consists of a plurality of individual conductors assembled in a bundle in proximity to the measurement system, understood so that the conductors are not integrated into one physical cable. An electrical current measurement system according to claim 1 or 2, wherein an arrangement of multiple conductors is assembled in one physical cable, with a plurality of integrated conductors, one of which may constitute a shield. A system for measuring electrical current according to any one of claims 1 to 4, wherein the sensors measuring a magnetic field are all integrated in the same sensor system box. A system for measuring electric current according to any one of claims 1 to 5, wherein said processing means, based on the mathematical model, can also produce an expression of the model error as an output. A system for measuring electric current according to any one of claims 1 to 6, wherein processing of the sensor measurements, according to the mathematical model, is treated as an integral part of the sensor system. An electrical current measurement system according to any one of claims 1 to 7, with processing means further configured to perform high-level evaluation of the individual current signal characteristics, e.g. RMS, phase, the main harmonic, frequency content, event detection, or quality characterization. A system for measuring electric current according to any one of claims 1 to 8, with processing means further configured to correlate voltage measurements with current measurements, in order to obtain additional high-level evaluation results, such as apparent and reactive power levels. A system for measuring electric current according to any one of claims 1 to 9, with processing means further configured to trigger error handling operations autonomously, e.g. by triggering a power switch.