Method and sensor device for determining current flowing in conductor, and current measuring system

Abstract

A method for determining a current (Imeas) flowing in a conductor (11), comprising: providing a plurality of magnetic sensor elements (HEj) sensitive to a magnetic field (B) generated by the current (Imeas) at respective sensor positions (dj) relative to a predetermined reference point; outputting a sensor signal (sj (t)) indicative of a magnetic field characteristic at each sensor location; receiving the sensor signal by a processing circuit (12); mapping the received sensor signal to an output value (xkk) indicative of the current; and outputting an output value wherein the mapping comprises a multi-pole expansion using a magnetic field B generated by the current, the multi-pole expansion comprising a predetermined number (Mm) of predetermined multi-pole components (m [alpha]) and respective associated predetermined multi-pole coefficients (c [alpha]); a current sensor arrangement (10, 15, 16) and a current measurement system (30, 31, 32) are also included.

Description

Technical Field

[0001] Examples and aspects generally relate to the field of current sensors. More specifically, some examples and aspects relate to methods and sensor devices for determining the current flowing in a conductor. Some examples and aspects also relate to current measurement systems. Background Art

[0002] Sensor devices for estimating the current flowing in a conductor are generally known in the art. The current flowing in a conductor generates a magnetic field. The current in the conductor can be determined by placing a magnetic sensor nearby and sensing the associated magnetic field generated by the current. Current measurement is based on the principle of Maxwell's equations, which states that the strength of the magnetic field generated by the flow of current in a conductor is inversely proportional to the distance from the center of the conductor to the measurement point and directly proportional to the current flowing in the conductor. For example, US2017 / 0184635A1 describes a sensing device for characterizing the current flowing through a conductor, the device including a plurality of magnetic sensors. Summary of the Invention

[0003] A fundamental challenge faced by such sensor devices and systems is their long-term stability. The initially sufficiently precise calibration of the sensor device or system changes over time, for example, due to mechanical displacement or misalignment of components relative to each other, or due to drift in the properties of the electronic sensors.

[0004] In addition, such sensor devices may respond to external fields, such as magnetic fields generated by other / adjacent current-carrying conductors (i.e., crosstalk), stray magnetic fields of other / adjacent magnetic components, the Earth's magnetic field, etc. Without countermeasures, these additional field components cannot be distinguished from the useful field, and thus the external fields limit the precision of the sensor device or system.

[0005] Therefore, there is a need for a method, a sensor device, and a current measurement system for determining the current flowing in a conductor, which are characterized by improved performance, where the evaluation of performance is mainly based on aspects such as operational robustness, numerical accuracy, long-term stability, application flexibility, and simplicity and cost of production / implementation.

[0006] One objective is to provide a method, a sensor device, and a current measurement system for determining the current flowing in a conductor to ensure high operational robustness and long-term stability, for example, with low sensitivity to interference caused by external fields not related to the current flowing in the conductor, such as the above-mentioned fields (e.g., stray fields, crosstalk, etc.), and low sensitivity to displacement or misalignment of components relative to each other, while providing accurate and reliable measurement results. The adaptability of the method, the device, and the measurement system to different usage scenarios and requirements should also be improved, and the complexity and cost of manufacturing and implementation should be reduced, for example, by not requiring a shielding sleeve or a magnetic core.

[0007] Examples, embodiments, and aspects are defined by the independent claims. The dependent claims define advantageous embodiments.

[0008] It should be noted that the individual features listed in the following description can be combined with each other in any technically meaningful way (and can also span different categories, such as devices and methods), and further embodiments are shown. The descriptions of the various examples, embodiments, and aspects are additionally characterized and specified in conjunction with the accompanying drawings.

[0009] Furthermore, it should be understood that if the terms "and / or" or the expressions "at least one" or "one or more" are used herein to combine a first and a second feature, it should be interpreted as disclosing a first embodiment including only the first feature, a second embodiment including only the second feature, and a third embodiment including both the first and the second features. If more than two features are listed, any combination thereof should also be interpreted as disclosed embodiments.

[0010] Furthermore, the terms "about", "substantially", or "approximately" indicate the normal tolerance ranges considered by those skilled in the relevant art. In particular, the above terms should be understood to cover tolerance ranges of the recited numerical values up to + / - 20%, preferably up to + / - 10%.

[0011] In many cases, certain examples, embodiments, and aspects will be described with reference to certain drawings, but the claimed subject matter is limited only by the claims.

[0012] The terms "first", "second", etc. in the specification and claims are used to distinguish similar elements and are not necessarily used to describe an order in terms of time, space, rank, or any other way. It should be understood that, where appropriate, the terms so used may be interchanged, and the embodiments described herein are capable of operating in an order different from that described or illustrated herein.

[0013] Furthermore, the directional terms in the specification and claims, such as top, bottom, front, back, front portion, tail portion, below, above, etc., are described with reference to the directions of the said drawings and are not necessarily used to describe absolute positions. Since the components of the embodiments can be positioned in multiple different directions, unless otherwise specified, the directional terms are for illustrative purposes only and are in no way intended to be limiting. Therefore, it should be understood that, where appropriate, the terms so used may be interchanged, and the embodiments described herein are capable of operating in a direction different from that described or illustrated herein.

[0014] It should be noted that the term "comprising" used in the claims should not be interpreted as being limited to the elements listed thereafter. It does not exclude other elements or steps. Therefore, it should be interpreted as specifying the presence of the features, elements, steps or components mentioned, but not excluding the presence or addition of one or more other features, elements, steps or components or groups thereof. Therefore, the scope of the expression "a device comprising features A and B" should not be limited to a device consisting only of features A and B. This means that the device may include additional elements or features in addition to A and B.

[0015] References throughout this specification to "one embodiment" or "an embodiment" mean that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, the phrases "in one embodiment" or "in an embodiment" appearing in various places throughout this specification do not necessarily all refer to the same embodiment, but may all refer to the same embodiment. Furthermore, as will be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments, the particular features, structures, or characteristics may be combined in any suitable manner.

[0016] Similarly, it should be understood that in the description of the example embodiments, various features are sometimes combined in one embodiment, figure, or description thereof in order to simplify the disclosure and aid in understanding one or more of the various inventive aspects. However, this method of disclosure should not be interpreted as reflecting an intention that the claimed subject matter requires more features than those expressly recited in each claim. On the contrary, as reflected in the following claims, inventive aspects lie in less than all of the features of a single preceding disclosed embodiment. Therefore, the claims that follow the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment.

[0017] In addition, as will be appreciated by those skilled in the art, although some embodiments described herein include some features of other embodiments but do not include other features of other embodiments, the combination of features of different embodiments is intended to be within the scope of this disclosure and form different embodiments. For example, in the following claims, any of the claimed embodiments may be used in any combination.

[0018] In the description provided herein, many specific details are set forth. However, it should be understood that embodiments can be practiced without these specific details. In other cases, well-known methods, structures, and techniques are not shown in detail to avoid obscuring the understanding of this description.

[0019] According to one example, a method for determining a current flowing in a conductor (e.g., a cable, a busbar, etc.) comprises the following steps:

[0020] - Providing a plurality of magnetic sensor elements (e.g., analog or digital sensor elements such as Hall elements, circular Hall elements, horizontal Hall elements, vertical Hall elements, magnetoresistive (MR) elements, AMR elements, XMR elements, GMR elements, TMR elements, etc.) at respective sensor positions relative to a predetermined reference point (also referred to herein as "the origin of the multipole expansion"), which are sensitive to the magnetic field generated by an electric current,

[0021] - Outputting, via the magnetic sensor elements, sensor signals indicative of the characteristics of the magnetic field at the respective sensor positions, e.g., the magnetic field components oriented in a specific direction;

[0022] - Receiving, via a processing circuit (e.g., but not limited to an electronic processor, microcontroller, microprocessor, digital signal processor, etc.), the sensor signals from the magnetic sensor elements or circuits (e.g., a Wheatstone bridge including the sensor elements),

[0023] - Mapping, via the processing circuit, the received sensor signals to an output value indicative of the electric current flowing in the conductor, and

[0024] - Outputting the output value, e.g., as a measured electric current,

[0025] wherein the mapping includes using a multipole expansion of the magnetic field generated by the electric current relative to the predetermined reference point, the multipole expansion including a predetermined number of predetermined multipole components and respective associated predetermined multipole coefficients. These coefficients can be stored in a non-volatile memory (e.g., flash memory) of the sensor device.

[0026] The plurality of sensor elements can be mounted on one or more printed circuit boards (PCBs), e.g., on a single PCB.

[0027] The position of the reference point can be a predefined position in the cross-sectional area of the electrical conductor.

[0028] Some aspects are based on the idea of not only measuring the magnetic field in a spatial point generated by a current flowing through an electrical conductor, but also determining the intensity of the spatial harmonics or spatial patterns of the magnetic field generated by the current. The spatial harmonics / patterns are the mathematical equivalent of a magnetic multipole expansion. The intensity of the spatial harmonics / patterns of the magnetic field generated by the current flowing in the conductor is an attribute of the conductor's shape and does not change over time. Thus, according to some examples, the method for determining the current in a conductor is insensitive to (at least local) variations in the actual sensor position relative to the conductor. Some examples use spatial (solid, fixed, not changeable over time) patterns so as to be unaffected by small relative movements between the sensor element (or the printed circuit board on which the sensor element is mounted) and the conductor. This applies to both direct current (DC) and alternating current (AC) flowing in the conductor. Even in the latter case, alternating currents of different frequencies will generate slightly different spatial patterns (e.g., due to the skin effect), i.e., the multipole expansion shows a frequency dependence that is not time-dependent as it does not weaken over time.

[0029] Likewise, the method is also robust to interference caused by external fields (e.g., stray fields, crosstalk, etc.) that are not related to the current flowing in the conductor. These characteristics allow for the precise determination of the current in the conductor. Thus, some examples can dispense with the magnetic core and / or the shielding sleeve without sacrificing accuracy (i.e., facilitate the use of coreless and unshielded sensor devices), which results in cost savings and an increase in bandwidth as ferromagnetic core materials typically limit the bandwidth to a few tens of kHz, e.g., 200 kHz, 100 kHz, 50 kHz, or even lower, e.g., 30 kHz, 20 kHz, 10 kHz.

[0030] It should be emphasized that the sensor signals together provide the required intensities of the spatial harmonics / patterns of the magnetic multipole expansion.

[0031] The method can include the following additional steps: arranging the sensor elements relative to the electrical conductor in a predefined manner, e.g., by arranging a printed circuit board (PCB) including the sensor elements relative to the electrical conductor in a predefined manner. These sensor elements have fixed positions and orientations relative to each other (since they are mounted on the PCB). After arranging the PCB relative to the electrical conductor in a predefined manner, each sensor element also has a predefined position and orientation relative to the electrical conductor.

[0032] In some embodiments, the method includes the additional step of providing the conductor.

[0033] Alternatively, the method for determining the current flowing in a conductor (e.g., a cable, a busbar, etc.) as described above can be illustrated in terms of aspects including the following steps:

[0034] - Providing a plurality of magnetic sensor elements (e.g., analog or digital sensor elements such as Hall elements, circular Hall elements, horizontal Hall elements, vertical Hall elements, magnetoresistive (MR) elements, AMR elements, XMR elements, GMR elements, TMR elements, etc.) at respective sensor positions relative to a predetermined reference point (also referred to herein as the "origin of the multipole expansion"), which are sensitive to the magnetic field generated by an electric current,

[0035] - Outputting, via the magnetic sensor elements, sensor signals indicative of the characteristics of the magnetic field at the respective sensor positions, e.g., field components of a magnetic field oriented in a specific direction;

[0036] - Receiving, via a processing circuit (e.g., but not limited to an electronic processor, microcontroller, microprocessor, digital signal processor, etc.), the sensor signals from the magnetic sensor elements or a circuit (e.g., a Wheatstone bridge including the sensor elements),

[0037] - Mapping, via the processing circuit, the received sensor signals to an output value indicative of the electric current flowing in the conductor, and

[0038] - Outputting the output value, e.g., as a measured electric current,

[0039] wherein the mapping includes position compensation such that the mapped output value is substantially unaffected by changes in the relative position between the sensor elements and the conductor.

[0040] Generally, the sensor elements may be configured to detect predefined or arbitrary field components of the magnetic field, i.e., the field components B x , B y and / or B z with respect to the three spatial directions x, y, and z.

[0041] Additionally or alternatively, signals from at least some of the sensor elements may be combined (e.g., added, subtracted, linearly combined, etc.) to detect the field gradient of the magnetic field in an arbitrary spatial direction (e.g., x, y, and / or z).

[0042] In any case, it should be noted that sensor elements measuring the same information (i.e., having the same sensor positions and measuring the same spatial field components of the magnetic field) are not counted towards the total number of sensor elements.

[0043] On the other hand, if the sensor elements measure magnetic fields in different spatial directions, a single packaged sensor (e.g., such as one SMD package) measuring magnetic fields in the same position but different spatial directions may be counted as multiple sensor elements. For example, a two-way sensor package (also referred to as a "2D magnetic sensor") in one physical sensor position should be interpreted as two sensor elements.

[0044] The method may include the following additional steps: arranging the sensor elements relative to the electrical conductor in a predefined manner, for example by arranging a printed circuit board (PCB) including the sensor elements relative to the electrical conductor in a predefined manner. The sensor elements have fixed positions and orientations relative to each other (since they are mounted on the PCB). After arranging the PCB relative to the electrical conductor in a predefined manner, each sensor element also has a predefined position and orientation relative to the electrical conductor.

[0045] In some embodiments, the method includes the additional step of providing a conductor.

[0046] In some embodiments, all or some of the sensor elements may detect magnetic fields oriented in the same spatial direction, i.e., detect the same field components or field gradients of the magnetic field.

[0047] In other embodiments, at least some or all of the sensor elements may be configured, or their signals may be combined (e.g., added, subtracted, linearly combined, etc.) to detect magnetic fields in different spatial directions, i.e., detect different field components or field gradients of the magnetic field. Providing sensor elements sensitive to different spatial directions conveys more information to compensate for changes in the spatial position between the sensor elements and the conductor during the service life and to suppress external field interference.

[0048] Preferably, these sensitive directions span a 90° angle.

[0049] In one embodiment, some sensor elements are configured to sense a magnetic field component (commonly denoted as Bx) in a first direction (e.g., X), and some sensor elements are configured to sense a magnetic field component (commonly denoted as By) in a second direction (e.g., Y) perpendicular to the first direction (X), and optionally, some sensor elements are configured to sense a magnetic field component (commonly denoted as Bz) in a third direction (e.g., Z) perpendicular to the first direction (X) and perpendicular to the second direction (Y).

[0050] In other preferred embodiments, the sensor positions are determined such that the spatial distance between at least two sensor elements is greater than the maximum operational spatial position change of the relative position between the sensor elements and the conductor that is desired to be compensated during the service life. In this way, it is ensured that the sensor elements measure the relevant field changes caused by the spatial position change.

[0051] In certain embodiments, the conductor has a rectangular cross-section with a length L and a width W, and the distance between at least two sensor elements is greater than the smaller of L and W.

[0052] In certain embodiments, the conductor has a diameter D or a maximum diagonal D, and the distance between at least two sensor elements is greater than D.

[0053] In other advantageous embodiments, the sensor positions are determined to be at highly symmetric positions, e.g., within a symmetry / mirror plane, which provides for a smaller signal variation (due to the vanishing gradient there) under position changes during the service life for compensation. Optionally, some sensor positions can be chosen at symmetry / mirror points with respect to the symmetry / mirror plane, since the sum or difference of the corresponding signals will inherently provide a first-order compensation for spatial variations, thus providing a more robust system.

[0054] Furthermore, the magnetic sensor elements are configured such that the difference of the signals measured along the same spatial direction must be significantly larger than the typical noise amplitude of the sensor elements used.

[0055] For the following description, bold letters represent vectors or matrices depending on the context.

[0056] In general, the magnetic field B (also referred to herein synonymously as the induction field) generated by a current in a conductor can be described as a superposition of M m multipoles m α in the region of interest (i.e., at the predetermined sensor positions of the sensor elements).

[0057] The multipole expansion of the induction field B in free space (i.e., μ r ≈ 1 = constant) is:

[0058]

[0059] where x represents the position vector, M m represents a predetermined number of multipole components m α , B i (x) represents the i-th vector component of the induction field distribution, c α ∈ R represents the multipole coefficient associated with each multipole component, represents the distribution of the i-th vector component of the α-th multipole. The acceptable multipole components satisfy to comply with Maxwell's equations

[0060] The coefficients c α can be determined by simulation or measurement.

[0061] According to a further advantageous embodiment, the multipole coefficients c αis determined as the solution vector c of the linear equation system Mc = b, where the equation system is given by the system matrix M, which consists of the number of said multipole components evaluated at the sensor positions and the right-hand side vector b formed by the received sensor signals, and where, if the number of magnetic sensor elements is equal to the number of multipole components, the linear equation system is solved by the inverse of the system matrix M, if the number of magnetic sensor elements is greater than the number of multipole components, the linear equation system is solved by the least squares equation, and if the number of magnetic sensor elements is less than the number of multipole components, the linear equation system is solved by selecting the minimum norm solution, i.e., by using the pseudo-inverse of the system matrix M.

[0062] In other words, the multipole coefficients are the elements of the vector c, which is determined by the square of the minimum norm ||M c - b||, where the system matrix M consists of the number of multipole components evaluated at the sensor positions and the vector b formed by the received sensor signals, and where, if the number of sensor elements is less than the number of multipole components, the minimum value can be found by an additional side condition of the minimum norm ||c|| of the solution vector c.

[0063] In some embodiments, the multipole coefficients c α are determined during a calibration phase of an electrical component comprising an electrical conductor and magnetic sensor elements, during which the processing circuit receives the sensor signals while injecting a predetermined calibration current into the conductor. The multipole coefficients can be stored in a non-volatile memory (such as flash memory) mounted on a PCB or embedded in the sensor device.

[0064] In a further embodiment, the multipole coefficients are determined entirely by calculation based on the geometric relationship of the sensor positions relative to the conductor, for example by using finite element (FE) simulation. The fully pre-calculated multipole coefficients can be used as a starting point before the calibration phase, during which the multipole coefficients are determined more precisely, for example, according to the actual manufacturing tolerances of the current sensor device or current measurement system.

[0065] The magnetic field of the conductor is linearly related to the current flowing in the conductor. This can be reflected in the multipole expansion by:

[0066]

[0067] where, denotes the predetermined calibration current I injected into the conductor during the calibration phase of the magnetic sensor element cal of the expansion coefficient, and is a linear factor (also referred to herein as the relative current amplitude), which provides the current I to be determined in the conductor during the expected measurement phase after the calibration phase meas of the multipole coefficients.

[0068] For a given sensor position d j (which may be partly identical, i.e., for some n≠m, d m ≡d n ) at a given number N s of sensor elements, if the current in the conductor equals I cal , the measurement signal can be characterized as:

[0069]

[0070] In the calibration phase, the sensor elements are positioned relative to the electrical conductor in a predefined manner (e.g., by arranging the PCB containing the sensor elements relative to the electrical conductor in a predefined manner), and the sensor elements measure the sensor signal cal for a predetermined fixed calibration current I To calibrate the sensor elements, Equation 1 becomes:

[0071]

[0072] which is used to solve for c α value.

[0073] Preferably, the solution is then stored in the non-volatile memory (e.g., flash memory) of the sensor device or connected to a processing circuit from which it can be retrieved.

[0074] If the number N s of sensor signals is greater than the number M m of multipole components, this presents a linear least squares (LS) fitting problem. Since the sensor positions d j are predefined by the actual design, the system matrix M jα ≡m α (d j ) is considered known. The solution to the problem is given by the LS normal equations. Using the matrix A≡(M T M) -1 M T we obtain:

[0075]

[0076] The same formula also applies when the number of sensor signals is less than the number of unknown multipole coefficients, i.e., N s <M m . Then, the solution is characterized as the minimum norm in the infinite solution set of an underdetermined linear system of equations The corresponding matrix A αj is the matrix M jαThe pseudo-inverse. From a physical perspective, it is reasonable to assume that this solution is the correct answer. Nevertheless, it is advisable to use as many sensor signals as there are independent multipole components.

[0077] According to a further advantageous embodiment, the mapping further comprises the steps of: predicting the sensor signal as a predicted sensor signal from a previous output value using a linear combination of multipole components evaluated at respective sensor positions and weighted with the respectively associated multipole coefficients, and correcting the output value based on the difference between the predicted sensor signal and the received sensor signal.

[0078] This prediction is based on a predefined measurement model that describes the underlying physical system for which the current is to be determined. For example, using the multipole coefficients known from the calibration phase The measurement model can be obtained from Equation 1 and Equation 2 to predict the unknown current I meas = γ·I cal The sensor signal for:

[0079]

[0080] Experiments have shown that the Kalman filter method provides a very suitable solution for signal processing to determine the current in a conductor. The Kalman filter depends on a state vector (also referred to herein as the output value) that contains state variables that completely define the state of the underlying physical system, settings of a dynamic model that describes the time variation of the state variables that form the state vector, and a measurement model that links the (raw) sensor signal to the system state.

[0081] In the above case, the only state variable is γ, which completely defines the physical system to derive all relevant physical properties.

[0082] In a further embodiment, the mapping further comprises the step of determining the actual translational and / or actual rotational displacement of the sensor position relative to the sensor position in the calibration phase.

[0083] If, in addition to the current to be determined, there is an unknown translation t between the actual sensor position and the sensor position in the calibration phase, the measurement model given above can be extended as follows to account for the translational displacement:

[0084]

[0085] This is because the multipole coefficients represent the magnetic field of the conductor, which does not change except for the linear scaling factor γ and possibly the translation vector t. Equation 4 provides a basis for robustly determining the current in a conductor under (small / local) spatial distortions.

[0086] If the relative position of the sensor element and the conductor also includes rotational displacement, the measurement model can be generalized to:

[0087]

[0088] where R(θ) corresponds to the rotation matrix for rotating by an angle θ along the longitudinal axis of the conductor, which requires including θ as an additional state variable.

[0089] The magnetic sensor elements can be mounted on a common rigid body (e.g., a printed circuit board, PCB) such that the translational and / or rotational motion of the sensor elements relative to the conductor is substantially the same for all sensor elements.

[0090] It should be noted that, as will be further described below, the update rate of the actual displacement of the sensor position and the update rate for determining the current in the conductor can be different. Optionally, the update rates can be the same.

[0091] For example, in the case of the translational displacement of the sensor element relative to the conductor described above, the most basic state vector is given by (γ,t x ,t y ). T If these state variables are known, the system is fully defined, and all relevant properties of the underlying physical system can be deduced. Some variations of this system state that lead to more efficient methods will be introduced below.

[0092] In this case, the simplest dynamic model of the state vector assumes that all state variables are constant, but are affected by white noise:

[0093]

[0094] where the vector η = (η γ ,η tx ,η ty ) T represents white noise random variables with vanishing mean, and its covariance is given by:

[0095]

[0096] The so-called process variance σ γ etc. corresponds to the time variation of unmodeled and a priori unknown state variables.

[0097] The measurement model is given by Equation 4, i.e.,

[0098]

[0099] where a white noise random variable ν j of sensor element j is added to account for measurement noise (also with zero mean and variance characterization). The model is typically non-linear because the multipole m α (x) may depend non-linearly on the translation vector t (see the multipole components m 5 given further below), and furthermore, they are multiplied by γ. This approach can correspond to an extended Kalman filter.

[0100] To this end, an estimator-corrector-scheme can be provided to update the state vector based on new evidence (i.e., new measurements and received sensor signals s j ). The covariance cov(η) allows the correct attribution of changes in the signal to the most likely cause in cases where it is not possible to determine given due to measurement noise. If the system only undergoes slow spatial position changes (e.g., during its service life), then compared to changes in the translation t, changes in the conductor current (i.e., the state variable γ) are a more likely cause of changes in the (raw) sensor signal.

[0101] On the other hand, a system affected by vibrations may undergo position changes on a time scale similar to or even faster than the current variables. Then, this situation can be characterized by a larger value of the process variance (e.g., etc.).

[0102] Therefore, different update rates may be appropriate for the determination of translational and / or rotational displacements as well as for the current in the conductor, and will be considered in various embodiments.

[0103] According to a further advantageous embodiment, the reference point is preferably determined in the symmetry plane of the conductor (or actually a small part of the conductor). Such a symmetry plane can be a mirror plane, for example, a plane containing the longitudinal axis of a long straight conductor. For example, the conductor can be a relatively long straight busbar with a rectangular cross-section, but even if the busbar is short or curved, the reference point is preferably selected relative to the shape of the cross-section in a plane perpendicular to the local current flow direction.

[0104] Optionally or additionally, the reference point can be determined to be located on the inversion symmetry line of the conductor or at its inversion point.

[0105] In both of the above cases, the number of multipole components that must be considered in the multipole expansion for determining the current in the conductor can be reduced. This is because the magnetic field generated by the current cannot contribute to a specific spatial direction in this symmetry plane or symmetry point since the corresponding associated multipole coefficients of this multipole component become zero. Therefore, choosing a highly symmetric point or plane as the reference point is beneficial for reducing the computational workload of the processing circuit, for example, this allows the use of less powerful hardware.

[0106] In addition, by using the symmetry of the conductor, the spatial dimensions to be considered in the multipole expansion can also be reduced. For example, it may be sufficient to consider a multipole expansion in only two spatial dimensions (2D) instead of three spatial dimensions (3D), because the field of interest is presented as 2D through the symmetry of the conductor (such as a long straight conductor, e.g., a bus bar). This further reduces the computational workload for processing the circuit.

[0107] Additionally or alternatively, the reference point or origin of the multipole expansion can be chosen to be at a relatively short distance from the sensor position of the sensor element. Placing the sensor element close to the reference point will result in a rapid convergence of the multipole expansion. Thus, the contributions of the higher-order multipole components quickly vanish and do not need to be considered to obtain accurate and robust results.

[0108] It has been found that in some embodiments where the multipole expansion includes up to a second-order maximum (i.e., 0th, 1st, and 2nd orders in the spatial coordinates), accurate and robust results can be obtained.

[0109] For example, in the 2D case, the number M of multipole components up to the second order m = 6 (given as vectors of the induced field in the plane perpendicular to the longitudinal axis of the conductor (e.g., a bus bar)) is:

[0110]

[0111] where x1 represents the first spatial direction in the plane (also referred to as the x-direction in this text), and x2 represents the second spatial direction in the plane (also referred to as the y-direction in this text). If the conductor extends linearly along its longitudinal axis and has a uniform cross-section, the third spatial direction, i.e., the x3 or z-direction, does not need to be considered.

[0112] In addition to considering the choice of the expansion order, the origin (i.e., the reference point) of the multipole expansion can also be advantageously selected. For example, this point can be chosen to be located at the geometric center (i.e., the centroid) of the sensor element. This ensures that the distance between the reference point and the sensor element is short. Then, the values of the input coordinate variables (i.e., x, y, z or x1, x2, and x3 respectively) will be small, i.e., for higher-order multipole components, the relative contributions will quickly become small.

[0113] The above-mentioned number of multipole components corresponds to the case where the magnetic field at the origin of the multipole expansion does not exhibit any symmetry. If there is symmetry, such as a mirror plane formed due to the symmetry of the conductor geometry, the number of multipole components will be reduced. For example, if the conductor has a flat and elongated geometry, there is no field component of the magnetic field in the y-direction in the middle plane (i.e., the symmetry plane) along the longitudinal axis of the conductor. If the origin is chosen in the middle plane, this corresponds to the vanishing of the multipole coefficient c2.

[0114] In some embodiments, the current to be determined is a direct current (DC).

[0115] In other embodiments, the current to be determined is an alternating current (AC) and the mapping further includes the step of determining the instantaneous phase of the alternating current.

[0116] In this case, the dynamic model of the current variable γ can be extended to describe the alternating current, where the state variable is no longer a constant but corresponds to a harmonic variation. Using the parameterization of the alternating current given by I meas (t) = γ sin(φ)·I cal The dynamic prediction model will be improved (see Equation 5)

[0117]

[0118] where ω represents the angular frequency of the determined alternating current and φ represents its instantaneous phase.

[0119] According to a further embodiment, more than one conductor is provided and determining the current includes determining the individual currents flowing in each conductor respectively, where a separate multipole expansion is used for each conductor.

[0120] The principles disclosed herein can also be used to determine three-phase alternating current. For each of the three phases, a set of sensor signals is measured where X ∈ U, V, W. For the B-field generated by three conductors, separate multipole expansions are performed. Introduce the three-phase relative current amplitude vector γ = (γ U , γ V , γ W ) T to describe the relative current amplitudes of the three phases instead of the scalar variable γ.

[0121] If there is interference between phases (i.e., crosstalk occurs in the system), then the corresponding measurement model must include, for example, the influence of phase U on phase V. Since different phases are separated by a greater distance compared to the sensor positions of the sensor elements for each phase, this crosstalk will only include the lowest-order multipoles (e.g., up to linear in the spatial coordinates) to reduce the workload of signal processing.

[0122] The dynamic model of the three-phase current can incorporate the specific correlations inherent in this situation. Thus, since the measurement signal makes full use of the prior knowledge resulting from the three-phase characteristics, the measurement accuracy will be improved.

[0123] In certain embodiments, a single PCB is mounted at a predefined position relative to three electrical conductors (e.g., three busbars), and the single PCB contains two sets of sensor elements, each set of sensor elements being located in the space between two electrical conductors (e.g., as Figure 4as shown). Each group may include, for example, at least two or at least three magnetic sensor elements. In this case, only a single translation and rotation vector applies to all magnetic sensors.

[0124] In a variant, two PCBs are mounted at predefined positions relative to three electrical conductors (e.g., three busbars), and each PCB contains a group of sensor elements, with each group of sensor elements located in the space between two electrical conductors. Each group may include, for example, at least two or at least three magnetic sensor elements. In this case, a first translation and rotation vector applies to the magnetic sensors of the first PCB, and a second translation and rotation vector applies to the magnetic sensors of the second PCB.

[0125] Depending on the mechanical structure of the conductor arrangement, the number of mechanical degrees of freedom (i.e., translation vectors, rotation angles) can be increased to separately handle the relative position changes of each conductor. This is of course necessary if they do not behave as a rigid body as a whole.

[0126] All sensor signals can be determined uniformly in time (i.e., simultaneously) to provide concurrent state variable updates. This results in complex matrix operations that need to consider all cross-correlations. However, the measurements can also be made non-uniformly or non-simultaneously, i.e., one sensor element after another, and the state variable updates can be carried out step by step accordingly.

[0127] Especially for three-phase alternating current, a hybrid method seems particularly advantageous: one of the sensor signals of the individual sensor elements for each phase is received simultaneously, and the relative current amplitudes of the three phases are updated. However, the remaining state variables that describe the spatial position are only updated after all sensor signals are received again. In this way, the computational effort will be minimized, and at the same time, the fluctuations in the relative current amplitudes will also be minimized.

[0128] According to a further advantageous embodiment, the signals from various sensor elements can be combined to correspond to the magnetic field gradient relative to a predetermined spatial direction at each sensor position. From the gradient, more precise information about the position changes (i.e., translation and / or rotation) of the actual sensor position can be obtained.

[0129] In a further embodiment, the number of magnetic sensor elements is equal to or greater than the number of multipole components.

[0130] Generally, the minimum number N of sensor signals required to determine the current in the conductor s corresponds to the maximum value of the number of degrees of freedom of the system given by the number of current phases N p and the mechanical rigid body motion N r i.e.,

[0131] N s ≥N p+N r

[0132] For maximum accuracy, the multipole components M involved should also be considered m in number. Although the pseudo-inverse method described herein can be used to calibrate M m >N s , if M m ≤N s , i.e., N s ≥max(M m ,N p +N r ), the calibration accuracy will be improved.

[0133] Some examples are given below.

[0134] Example 1

[0135] For a long straight conductor (such as a busbar or cable), the B-field components to be considered are only those in the plane perpendicular to the conductor. For the number M of multipole components up to the first order m =4 (i.e., m α (x), α = 1, …, 4), a single current phase (N p =1) and two translational degrees of freedom of the relative displacement of the sensor element with respect to the sensor position of the conductor (N r =2), we find that:

[0136] N s ≥3

[0137] Example 2

[0138] By placing the origin of the multipole expansion (i.e., the reference point) in the symmetry plane of the conductor. For example, for a strip busbar, it can be determined that the origin is in the middle plane of the busbar cross-section. Due to symmetry, neither m 1 (x) nor m 2 (x) contributes to the magnetic field. Therefore M m =3, N p =1 and N r =2, and

[0139] N s ≥3,

[0140] where the number of such sensor signals allows for a comprehensive characterization of the multipole coefficients during calibration.

[0141] Example 3

[0142] For the system according to Example 1, but with an additional rotational degree of freedom in two translational degrees of freedom, i.e., N r =3,

[0143] N s ≥ 4

[0144] However, in this case, since the required information cannot be provided by the sensor elements first, the origin of the multipole expansion is not determined to be in the symmetry plane of the conductor.

[0145] Example 4

[0146] Furthermore, choosing an appropriate origin for the multipole expansion will reduce the number of excited multipole components to, for example, M m = 4, thereby allowing the system to have N r = 3 rigid body degrees of freedom (including rotation here) and a single current phase N p = 1, according to

[0147] N s ≥ 4

[0148] According to another aspect, a current sensor device for determining the current flowing in a conductor (e.g., a cable, a busbar, etc.) includes:

[0149] - a plurality of magnetic sensor elements sensitive to the magnetic field generated by the current (e.g., analog or digital sensor elements such as Hall elements), wherein each magnetic sensor element is arranged at respective sensor positions relative to a predetermined reference point (also referred to herein as the "origin of the multipole expansion") and is configured to output sensor signals respectively indicating the field components of the magnetic field at the respective sensor positions, and

[0150] - a processing circuit (e.g., and not limited to, an electronic processor, a microcontroller, a microprocessor, a digital signal processor, etc.), which is configured to receive the sensor signals from the magnetic sensor elements,

[0151] wherein the processing circuit is configured to map the received sensor signals to an output value indicating the current flowing in the conductor and output the output value, wherein the mapping includes using a multipole expansion of the magnetic field generated by the current with respect to the predetermined reference point, the multipole expansion including a predetermined number of predetermined multipole components and respective associated predetermined multipole coefficients.

[0152] It should be noted that regarding the effects and advantages of the features of the sensor device disclosed herein, all refer to the corresponding similar features of the method disclosed herein and their effects and advantages. Therefore, unless otherwise clearly stated, the features of the method should also be regarded as applicable to defining the embodiments of the sensor device, and vice versa. Therefore, for the sake of brevity of this specification and better understanding of the principle, the repeated explanations of these similar features, their effects and advantages may be omitted, and any such omission should not be construed as a limitation.

[0153] The sensor device for determining the current flowing in a conductor (e.g., a cable, a busbar, etc.) as described above can optionally be described in terms of an aspect that includes:

[0154] - A plurality of magnetic sensor elements sensitive to the magnetic field generated by the current (e.g., analog or digital sensor elements such as Hall elements, circular Hall elements, horizontal Hall elements, vertical Hall elements, magnetoresistive (MR) elements, AMR elements, XMR elements, GMR elements, TMR elements, etc.), wherein each magnetic sensor element is arranged at respective sensor positions relative to a predetermined reference point (also referred to herein as the origin of the multipole expansion), and is configured to output a sensor signal indicating the characteristics (e.g., field components) of the magnetic field at the respective sensor positions, and

[0155] - A processing circuit (e.g., and not limited to, an electronic processor, a microcontroller, a microprocessor, a digital signal processor, etc.), which is configured to receive the sensor signals from the magnetic sensor elements,

[0156] wherein the processing circuit is configured to map the received sensor signals to an output value indicating the current flowing in the conductor, and output the output value, wherein the mapping includes position compensation such that the mapped output value is invariant with respect to changes in the relative position between the magnetic sensor elements and the conductor.

[0157] In an advantageous embodiment, the magnetic sensor elements are mounted on a common rigid body. In this way, for all the sensor elements, the translational and / or rotational movements (i.e., position displacements) of the sensor elements relative to the conductor are substantially the same, which reduces the computational workload of the processing circuit.

[0158] In some embodiments, a first subset of the sensor elements is mounted on a first rigid body (e.g., a first PCB), and a second subset of the sensor elements is mounted on a second rigid body.

[0159] In some embodiments, signals from one or more magnetic sensor elements are combined (e.g., added, subtracted, linearly combined, etc.) to respectively output the gradient of the magnetic field as the field component at the respective sensor positions with respect to a predetermined spatial direction.

[0160] In a further embodiment, the number of magnetic sensor elements is equal to or greater than the number of multipole components.

[0161] According to another aspect, a current measurement system includes at least one conductor and a current sensor device that is used to determine the current flowing in the at least one conductor according to any one of the embodiments disclosed herein.

[0162] Furthermore, it should be noted that with regard to the effects and advantages of the features of the measurement system, reference is made in full to the corresponding analogous features of the methods and sensor devices disclosed herein. Accordingly, unless otherwise explicitly stated, the features of the method and sensor device should also be regarded as applicable to define the features of embodiments of the measurement system, and vice versa. Therefore, for the sake of brevity of this specification and better understanding of the principles, repeated explanations of these analogous features, their effects and advantages may be omitted, and any such omission should not be construed as a limitation.

[0163] In some embodiments, the magnetic sensor element is arranged in a plane oriented perpendicular to or parallel to the longitudinal axis of the conductor.

[0164] In a further embodiment, the reference point (also referred to herein as the origin of the multipole expansion) is determined to be in a plane including the longitudinal axis of the conductor.

[0165] In a further advantageous embodiment, the magnetic sensor element is arranged along a virtual sensing line around the conductor, the virtual sensing line including an angular range between 20 degrees and 45 degrees, more preferably between 20 degrees and 90 degrees, and still more preferably up to 180 degrees.

[0166] In some embodiments, the magnetic sensor element is arranged on a PCB oriented perpendicular to the direction of the current flowing through the electrical conductor, and the angle formed between a first branch defined by one of the sensor positions and the geometric center of the cross-section and a second branch defined by another sensor position and the geometric center is an angle of at least 20°, or at least 30°, or at least 45°, or at least 60°, or at least 90°, or at least 120°, or at least ≤150°.

[0167] In other embodiments, the magnetic sensor element is arranged along a virtual sensing line around the conductor, the virtual sensing line spanning an angular range greater than 180 degrees.

[0168] In other advantageous embodiments, the current measurement system includes more than one conductor, for example three conductors, and determining the current includes determining the individual currents flowing in each conductor separately, where a separate multipole expansion is used for each conductor.

[0169] Further advantageous embodiments are defined in the drawings and the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0170] These and other features and advantages will be apparent from the following description of non-limiting embodiments, which will be illustrated with reference to the accompanying drawings.

[0171] The accompanying drawings are merely schematic, i.e., for illustrative purposes, the dimensions of some elements may be exaggerated and not drawn to scale. The absolute and relative dimensions do not necessarily correspond to the actual implementation of various embodiments and examples.

[0172] In the figures, schematically:

[0173] Figure 1 A cross-sectional view of a conductor carrying a current to be determined is shown according to an example embodiment.

[0174] Figure 2 A perspective view of an example embodiment of a sensor device and a current measurement system is shown.

[0175] Figure 3 A perspective view of another example embodiment of a current measurement system is shown.

[0176] Figure 4 A cross-sectional view of another example embodiment of a current measurement system is shown.

[0177] Figure 5 A functional diagram of an example embodiment of a sensor device is shown.

[0178] In the various figures, elements that are equivalent with respect to their functions generally have the same reference numeral / identification, and thus these elements are generally described only once. Detailed Description

[0179] When referring to a "conductor" in this document, it means an electrical conductor.

[0180] When referring to a "magnetic field gradient oriented in a certain direction" in this document, it refers to the magnetic field gradient of the magnetic field component oriented in the specified direction along a non-specified direction, or the magnetic field gradient of the magnetic field component oriented in the non-specified direction along the specified direction.

[0181] When referring to a "symmetry plane of the conductor" in this document, it refers to the symmetry plane of the cross-section of the conductor in a plane perpendicular to the current flow direction, unless otherwise clearly indicated from the context.

[0182] Various embodiments will now be described with reference to the accompanying drawings.

[0183] Figure 1 Schematically shown is a cross-sectional view of a conductor 11 (e.g., a long flat bus bar) carrying a current I to be determined meas according to an example embodiment of a method. According to the described embodiment, the method includes the following steps:

[0184] - Providing N at respective sensor positions d j relative to a predetermined reference point (not shown)s a magnetic sensor element HE j , the magnetic sensor element HE j is sensitive to the magnetic field B generated by the current I meas and outputs an indication of the field component, e.g., B of the magnetic field B at respective sensor positions d

[0185] - via the magnetic sensor element HE j and / or B j and / or B x and the sensor signal s of B y and / or B z j ,

[0186] - the processing circuit 12 receives the sensor signal s from the magnetic sensor element HE j j ,

[0187] - the received sensor signal s is mapped by the processing circuit 12 (e.g., an electronic processor, a microcontroller, a microprocessor, a digital signal processor, etc.) to an output value x indicative of the current I flowing in the conductor 11 j meas and k|k - the output value x is output

[0188] k|k ,

[0189] wherein the mapping includes a multipole expansion of the magnetic field B generated by the current I with respect to a predetermined reference point, the multipole expansion including a predetermined number M meas of predetermined multipole components m m and the respectively associated predetermined multipole coefficients c α α .

[0190] In some embodiments, the method further includes the additional step of providing the conductor 11

[0191] As Figure 1 shown in the equation, the magnetic field B is a superposition of M j multipoles m m in the region of interest 13 (i.e., the region where the sensor element HE α is arranged and distributed). The multipole coefficients c α are determined during the calibration phase of the magnetic sensor element HE j , during which a predetermined calibration current I j is injected into the conductor 11 while receiving the sensor signal s cal .

[0192] The sensor element HE j ​​​​​can be configured to detect any field component of the magnetic field B, i.e., B x , B y or B z (where the latter is perpendicular to Figure 1 the drawing plane). In fact, any two spatial field components that do not point in the same direction can be selected as the field components to be detected. It does not necessarily have to be along the coordinate system x, y, z depicted in the figure and does not even have to be perpendicular to each other.

[0193] Additionally or alternatively, signals from at least some of the sensor elements HE j can be combined (e.g., added, subtracted, linearly combined, etc.) to detect the field gradient of the magnetic field B in any spatial direction x, y, or z.

[0194] In Figure 1 , the output value is shown as the output vector x k|k , which includes the relative current amplitude γ of the current I meas to be determined and the translation vector t, where the translation vector t represents the translational displacement between the actual sensor position dj and the sensor position during the calibration phase. In this example, the current I meas to be determined is a direct current, but it is not necessarily limited to this.

[0195] Figure 2 Schematically shows a perspective view of an exemplary embodiment of a sensor device 10 and a current measurement system 30 for determining the current I meas flowing in the conductor 11. This current sensor device 10 includes magnetic sensor elements HE1, HE2, HE3, HE4, HE5, and HE6 that are sensitive to the magnetic field B (see meas ) generated by the current I Figure 1 . In this example, the number of sensor elements HE1, HE2, HE3, HE4, HE5, and HE6 is six. However, it should be understood that Figure 2 the numbers shown in j are only an example, and more or fewer sensor elements HE

[0196] In Figure 2 the exemplary sensor device 10 shown, in each case, two sensor elements, namely HE1 and HE2, HE3 and HE4, HE5 and HE6, are substantially arranged at the same position d j, but they detect the magnetic field B in two different spatial directions (here, for example, in the x and y directions, but not necessarily limited to the x and y directions). The magnetic field B in the z direction can also be detected, either as an alternative to the x or y direction, or as a supplement to the x and y directions. For example, each pair of sensor elements can be encapsulated in a single encapsulated sensor assembly, such as an SMD package.

[0197] The sensor device 10 further includes a processing circuit 12 configured to receive the sensor signals s from the magnetic sensor elements HE1-HE6 j . In the present sensor device 10, the processing circuit 12 and the sensor elements HE1-HE6 are mounted on a common rigid body, such as a common printed circuit board (PCB), however, it is not necessarily limited thereto. The processing circuit 12 and the sensor elements HE1-HE6 can all be mounted on multiple separate bodies (such as multiple PCBs), or only the processing circuit 12 can be mounted separately from the sensor elements HE1-HE6, where the sensor elements HE1-HE6 are mounted together on a common rigid body (such as a PCB).

[0198] Although not shown, the PCB may also include a non-volatile memory (such as a flash memory). The non-volatile memory can be embedded in the sensor device or the processing circuit, or can be a discrete component mounted on the PCB but communicatively connected to the processing circuit 12.

[0199] In Figure 2 it is shown that in this example, the sensor elements HE1-HE6 are located in a plane perpendicular to the longitudinal axis 14 of the conductor 11, and this plane corresponds to the cross-section of the conductor 11.

[0200] The reference point (not shown), i.e., the origin of the multipole expansion, can be determined in the plane including the longitudinal axis 14 of the conductor 11 (see Figure 5 ), however, it is not necessarily limited thereto. Generally, the reference point can be selected at any spatial position.

[0201] Figure 3 A perspective view of another exemplary embodiment of a current measurement system 31 using a sensor device 10' similar to Figure 2 is schematically shown. Figure 3 The main differences between the measuring device 31 shown in Figure 2 and the measuring device 30 shown in Figure 3 are the orientation of the PCB, and the position and orientation of the sensor elements HE1-HE6. As Figure 2An example of the current measurement system 30 depicted in the figure. In this current measurement system 31, pairs of two sensor elements, namely HE1 and HE2, HE3 and HE4, HE5 and HE6, detect the magnetic field B in two different spatial directions, for example, in the x and y directions. Furthermore, the magnetic field B in the z direction can also be detected, either as an alternative to the x or y direction, or as a supplement to the x and y directions. For example, each pair of sensor elements can be encapsulated in a single packaged sensor assembly, such as an SMD package. Each SMD package can also be referred to as a 2D magnetic pixel.

[0202] Figure 4 A cross-sectional view schematically showing another exemplary embodiment of the current measurement system 32, which uses the sensor device 15 to determine the current I flowing in the three conductors 11 U meas , I V meas and I W meas . In this example, the current I U meas , I V meas and I W meas are three-phase alternating currents (AC). For each conductor 11, a separate multipole expansion is used.

[0203] In Figure 4 the example case shown, the sensor device 15 includes three sensor elements HE1,, HE2, HE3 arranged between the leftmost conductor 11 and the middle conductor 11, and HE4, HE5, HE6 arranged between the middle conductor 11 and the rightmost conductor 11. The sensor elements HE1,, HE2, HE3 mainly detect the superimposed magnetic field generated by I U meas and I V meas , while the sensor elements HE4, HE5, HE6 mainly detect the superimposed magnetic field generated by I V meas and I W meas . Since the sensor elements detect the magnetic field of I U meas +I V meas and / or I V meas +I W meas , in order to determine the current I V meas , all the signals HE1 to HE6 will be used to calculate the output value.

[0204] In Figure 4 the illustrated embodiment, the sensor elements HE1, HE2, HE3, HE4, HE5 and HE6 and the processing circuit 12 are located in a plane perpendicular to the longitudinal axis of the electrical conductor 11, where the longitudinal axis extends parallel to the z-direction. Each sensor element HE1-HE6 can be configured to detect a magnetic field B in one or more different spatial directions, for example, in the x, y, and / or z directions.

[0205] Figure 5 A functional diagram of an exemplary embodiment of the sensor device 16 is schematically shown. The sensor device 16 for determining the current I meas flowing in the conductor 11 includes N meas magnetic sensor elements HE s sensitive to the magnetic field B j ( Figure 5 HE1 and HE2 are shown in, there may be more, but not shown), where each magnetic sensor element, including HE1 and HE2, is arranged at respective sensor positions d j relative to a predetermined reference point (not shown, but in this example selected within the mirror plane 17 containing the longitudinal axis of the conductor 11), such as d1 and d2, and is configured to output sensor signals s j (t), i.e., s1(t)…s r (t), which indicate the field components of the magnetic field B at the respective sensor positions d j , such as B x and / or B y and / or B z . In practice, any two spatial field components that do not point in the same direction can be selected as the field components to be detected. It may not necessarily be along the coordinate system x, y, z depicted in the figure, and may not even be perpendicular to each other. The sensor device 16 further includes a processing circuit 12, which is configured to receive the sensor signals s j from the magnetic sensor elements HE j (t).

[0206] As Figure 5 shown, the processing circuit 12 is configured to map the received sensor signals s j (t) to an output value x meas indicating the current I k|k flowing in the conductor 11, and output the output value x k|k . This mapping includes using a multipole expansion of the magnetic field B generated by the current I meas relative to a predetermined reference point, and the multipole expansion includes a predetermined number M m of predetermined multipole components m α and respective associated predetermined multipole coefficients c α .

[0207] The sensor device 16 uses the Kalman filter method to generate an output value x from the (raw) sensor signal s j (t), which will be described below. k|k

[0208] The sensor device 16 includes a system state corrector 18, which is configured to determine the actual output value of the physical system, i.e., the system state x, at a given state update period k k|k . The state update period k corresponds to a moment t k , where t k = kT, and T is the sampling period. As shown in Figure 5 , in this example, the system state vector x k|k includes the relative current amplitude γ and the translation vector t. As described above, in the case of determining an alternating current, the system state vector x k|k may include other information, such as the angular frequency ω and its instantaneous phase φ.

[0209] In addition, Figure 5 the sensor device 16 shown in k-1|k-1 also includes a system state predictor 19, which is configured to determine the predicted system state x of the physical system at a given prediction period k from the previous system state x of the previous state update period k - 1 k|k-1 . As shown in Figure 5 , the previous system state x from the previous state update period k - 1 k-1|k-1 is provided by the delay unit 20. In a simple implementation, the delay unit can be a storage unit (such as a register of a RAM, μP, or μC, etc.), and at least one system state is stored after being output by the system state corrector 18 so that it can be used as the previous system state x in subsequent state update periods k-1|k-1 .

[0210] In addition, the sensor device 16 includes a sensor signal predictor 21, which is configured to determine the predicted sensor signal at a given prediction period k from the predicted system state x using the measurement model of the physical system (for example, the model described in Equation 7) k|k-1 .

[0211] In addition, Figure 5 the system state corrector 18 of the sensor device 16 in j (t) is configured to obtain the received sensor signal according to the received sensor signal obtained from the sensor signal s at a given prediction period k j,k and the corresponding predicted sensor signal of each received sensor signal s The difference between them is used to predict the system state x k|k-1 Apply the Kalman filter operation to determine the actual system state x at a given state update period k k|k .

[0212] In Figure 5 In this example of the sensor device 16, the collected sensor signal s j,k always includes simultaneously the sensor signals s from all sensor elements HE j of j (t), that is, each collected sensor signal s j,k is related to the same given moment t at a given prediction period k k (this is also referred to herein as uniform sampling or simultaneous sampling). For this purpose, a multi-channel analog-to-digital converter ADC is provided. Each channel of the multi-channel ADC is connected to a corresponding one of the sensor elements HE j in order to simultaneously collect all sensor signals s k (t) at the moment t j . After A / D conversion, the multi-channel ADC outputs the digital representation of the sensor signal s j (t) as the collected sensor signal s j,k .

[0213] In an alternative embodiment (not shown), the sensor device may include non-uniform sampling or non-simultaneous sampling of the sensor signal s j (t). In this case, the N j channels of the sensor signal s s (t) are multiplexed and discretized in a single-channel ADC to sequentially obtain the signals s j,k , j = 1, …, N s . As in the case of the simultaneous sampling method before, each of the N s sensor signals s j,k is then used for a related sequence of prediction and correction steps.

[0214] Although various examples, embodiments, and aspects have been shown and described in detail in the drawings and the foregoing description, these illustrations and descriptions should be considered illustrative or exemplary, rather than restrictive.

[0215] Other modifications will be apparent to those skilled in the art upon reading this disclosure. These modifications may involve other features known in the art, and these features may be used to replace or supplement the features already described herein.

[0216] By studying the drawings, the present disclosure, and the appended claims, those skilled in the art can understand and implement variations of the disclosed embodiments. The fact that certain measures are recited only in different dependent claims does not mean that combinations of these measures cannot be used to obtain advantages.

[0217] Any reference signs in the claims shall not be construed as limiting their scope.

[0218] Reference sign

[0219] 10 Sensor device

[0220] 11 Electrical conductor

[0221] 12 Processing circuit

[0222] 13 Region of interest

[0223] 14 Longitudinal axis

[0224] 15 Sensor device

[0225] 16 Sensor device

[0226] 17 Symmetry / mirror plane

[0227] 18 System state corrector

[0228] 19 System state predictor

[0229] 20 Delay unit

[0230] 21 Sensor signal predictor

[0231] 30 Current measurement system

[0232] 31 Current measurement system

[0233] 32 Current measurement system

[0234] ADC Analog-to-digital converter

[0235] B Magnetic field

[0236] d j Position vector j of the sensor element

[0237] HE j Sensor element

[0238] I meas Current to be determined

[0239] k State update period

[0240] N s Number of sensor elements

[0241] PCB circuit board

[0242] Vector of the predicted sensor signals

[0243] s j (t) Continuous-time sensor signal

[0244] s j,k Discrete-time sensor signal

[0245] t Translation vector

[0246] x k|k Output value

[0247] x k|k-1 Predicted output value

[0248] x k-1|k-1 Previous output value

[0249] U The first phase of the three-phase alternating current

[0250] V The second phase of the three-phase alternating current

[0251] W The third phase of the three-phase alternating current

[0252] x The first spatial direction

[0253] y The second spatial direction

[0254] z The third spatial direction

[0255] γ Relative current amplitude

[0256] θ Rotation angle

[0257] φ DC current phase

[0258] ω Alternating current angular frequency

Claims

1. A method for determining a current (I meas ), the method comprising the following steps: - at each sensor position (d j ) provides multiple (N s )Magnetic sensor element (HE j ), the magnetic sensor element is connected by the current (I meas ) is sensitive to the magnetic field (B) generated by - through the magnetic sensor element (HE j ) output indicates the position of each sensor (d j ) at the characteristic sensor signal (s j (t)), for example, the field component (B) of the magnetic field (B) x ,B y ,B z ) sensor signal (s j (t)), - receiving, via a processing circuit (12), from the magnetic sensor element (HE j ) of the sensor signal (s j (t)), - The received sensor signal (s) is processed by the processing circuit (12) j (t)) is mapped to an indication of the current (I) flowing in the conductor (11) meas )’s output value (x k|k ),as well as - Output the output value (x k|k ), The mapping comprises relative to the predetermined reference point, using the current (I meas ) generated by the multipolar expansion of the magnetic field (B), the multipolar expansion comprising a predetermined number (M m ) of the predetermined multipole components (m α ) and the respective associated predetermined multipole coefficients (c α ).

2. The method according to claim 1, wherein the multipole coefficient (c α ) is determined as the solution vector c of the linear system of equations Mc=b, which is given by the system matrix M, which is determined by the sensor position (d j ) evaluated at the multipole component (m α ) m ) and the sensor signal (s j (t)) is composed of the right-hand side vector b, where If the magnetic sensor element (HE j ) s ) is equal to the multipole component (m α ) m ), then the linear equations are solved by the inverse of the system matrix M. If the magnetic sensor element (HE j ) s ) is greater than the multipole component (m α ) m ), then the linear equations are solved by the least squares method, and if the magnetic sensor element (HE j ) s ) is smaller than the multipole component (m α ) m ), then the linear equations are solved by selecting the minimum norm solution.

3. The method according to claim 1 or 2, wherein the mapping further comprises the following steps: Using the various sensor positions (d j ) and are respectively related to the multipole coefficients (c α ) weighted multipole components (m α ), from the previous output value (x k-1|k-1 ) predicts the sensor signal (s j,k ) as the predicted sensor signal And according to the predicted sensor signal and the received sensor signal (s j ) to correct the output value (x k|k ).

4. A method according to any one of the preceding claims, wherein: The mapping also includes determining the sensor location (d j ) relative to the sensor position (d j )'s actual translation (t) and / or actual rotational displacement (θ), and optionally also includes the step of storing the rotational displacement in a non-volatile memory.

5. A method according to any one of the preceding claims, wherein: The reference point is determined to be located in a symmetry plane (17) of the electrical conductor (11).

6. A method according to any one of the preceding claims, wherein: Determine the sensor position (d j ) so that at least two of the sensor elements (HE j ) is greater than the spatial distance between the sensor elements (HE j ) and the maximum operating space position change of the relative position between the electrical conductor (11).

7. A method according to any one of the preceding claims, wherein: The sensor position (d j ) is determined to be located in the symmetry plane (17) of the electrical conductor (11) or at a symmetric point relative to the symmetry plane (17) of the electrical conductor (11).

8. A method according to any one of the preceding claims, wherein: The multipole expansion includes at most second order maxima.

9. A method according to any one of the preceding claims, wherein: A plurality of conductors (11) are provided, and determining the current comprises determining a separate current (I U meas ,I V meas ,I W meas ), wherein a separate multipole expansion is used for each conductor (11).

10. A method for determining a current (I meas ) of a current sensor device (10, 15, 16), comprising: -Multiple (N s ) is the current (I meas ) generates a magnetic field (B) that is sensitive to the magnetic sensor element (HE j ), wherein each magnetic sensor element (HE j ) are arranged at each sensor position (d j ) and are configured to output indications at the respective sensor positions (d j ) at the magnetic field (B) x ,B y ,B z ) sensor signal (s j (t)), and a processing circuit (12) configured to receive signals from the magnetic sensor element (HE) j ) of the sensor signal (s j (t)), The processing circuit (12) is configured to receive the sensor signal (s j (t)) is mapped to an indication of the current (I) flowing in the conductor (11) meas )’s output value (x k|k ), and output the output value (x k|k ), wherein the mapping comprises mapping the current (I meas ) generated by the multipolar expansion of the magnetic field (B), the multipolar expansion comprising a predetermined number (M m ) of the predetermined multipole components (m α ) and the respective associated predetermined multipole coefficients (c α ).

11. The current sensor device according to claim 10, wherein: The magnetic sensor element (HE j ) are mounted on a common rigid body (PCB).

12. The current sensor device according to claim 10 or 11, wherein: One or more magnetic sensor elements (HE j ) are configured to output the gradient of the magnetic field (B) as the gradient of the magnetic field at each sensor position (d j ) relative to a predetermined spatial direction (x, y) x , B y , B z ).

13. A current measuring system (30, 31, 32) comprising at least one electrical conductor (11) and a current sensor device (10, 15, 16) according to any one of claims 10 to 12, the current sensor device (10, 15, 16) being configured to determine a current (I ) flowing in the at least one electrical conductor (11). meas ).

14. The current measurement system according to claim 13, wherein: The reference point is determined to lie in a plane (17) that includes the longitudinal axis (14) of the electrical conductor (11).

15. The current measurement system according to claim 13 or 14, comprising a plurality of conductors (11), and determining the current comprises determining a separate current (I ) flowing in each electrical conductor (11) respectively. U meas ,I V meas ,I W meas ),in, A separate multipole development is used for each conductor (11).

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