Method and measurement arrangement for measuring the amperage of an electric current flowing through a conductor

Abstract

The invention relates to a method for determining the amperage of an electric current flowing through at least one conductor (200), wherein the at least one conductor is positioned in a specified measurement region of a measurement arrangement (100), and wherein the measurement arrangement (100) comprises a plurality of magnetic field sensors (101-108), wherein the amperage is determined using an optimisation algorithm. The invention also relates to a measurement arrangement (100) designed to carry out the method.

Description

[0001] Method and measuring arrangement for measuring the current intensity of an electric current flowing through a conductor

[0002] Description

[0003] The invention generally relates to a method and a measuring arrangement for measuring the current intensity of an electric current flowing through a conductor, wherein the measurement is carried out in particular without contact.

[0004] Various measuring methods are known for determining the current flowing in a conductor. For example, the voltage drop across a resistor such as a shunt resistor can be determined, and with the known resistance value, the flowing current can be determined according to Ohm's law. In addition, current measuring arrangements with a ferromagnetic core are known which operate according to the transformer principle. In this case, the conductor with the current to be measured is passed through a core. The conductor with the current to be measured forms the primary conductor of a transformer. Via a secondary winding wound on the core, the primary current can be determined from the current flowing through a resistor connected to the secondary winding, known as a burden. The secondary current is proportional to the primary current and is determined by the turns ratio between the secondary winding and the primary winding.However, the transformer principle is limited in its application to measuring alternating currents.

[0005] Furthermore, it is possible, for example, to measure the magnetic field caused by a current using Hall sensors and use this to infer the current causing it. In this way, currents, including direct currents, can be measured contactlessly. In particular, methods are known that do not require a ferromagnetic core to focus the magnetic field. In particular, the magnetic field strength can be evaluated according to Ampere's law, according to which the measured current is based on the solution of a path integral of the magnetic field. For this purpose, the formula I m = s Hds are used, where I mdenotes the electric current to be measured, S describes a closed path in space that encloses the current, and where H denotes the vectorial magnetic field strength and ds the differential of the integration path. If the magnetic flux density is measured pointwise in one spatial direction using sensors, the approximation is the formula l m where lma denotes the approximate current to be measured and po the permeability of the vacuum and i is a counting index that runs from 1 to N, where N is the number of magnetic field sensors and Bi is the magnetic flux density detected by the i-th sensor in the direction of the path element with the length si. The path elements Si must be arranged in such a way that they form a closed path in space that encloses the conductor to be measured. The approximation of the current is exact when the number of magnetic field sensors tends towards infinity. If the number of sensors is finite, an exact solution can also be obtained if, for example, the magnetic field sensors are arranged equidistantly on a circular path and aligned tangentially to it and the current to be measured passes exactly perpendicularly through the area in which the circular path is located and through which the current passes exactly through the center of the circular path.However, the conditions for an exact solution are usually not met in practice.

[0006] Measuring arrangements which use the measuring principle described above based on Ampere's law are described, for example, in EP 3 589 961 Bl, US 11,150,272 B2, EP 3 958 003 A1 and EP3259603B1.

[0007] Mechanisms for compensating for interfering magnetic fields are described, for example, in US 11029342 B2 and US 2021 / 0231709 A1. EP 3948310 A1 further describes a measuring arrangement which, for this purpose, comprises a filter unit for homogenizing external magnetic fields, i.e., magnetic fields that are not caused by the electric current to be measured. In order to determine the current intensity of the electric current flowing through a conductor based on a magnetic field generated by a current-carrying conductor by measuring the magnetic field using magnetic field sensors, without using the measuring principle based on Ampere's law described above, the position of the current-carrying conductor relative to the magnetic field sensors must be known.

[0008] For this purpose, the measuring arrangements described, for example, in WO 2022030287 A1, EP 2821798 B1, EP 2921864 B1, and EP 3106884 B1 each provide for fixing the electrical conductor to be measured in a predetermined position. WO 2010 / 096344 A1 describes a current measuring device for measuring an alternating current in a conductor, which includes a plurality of measuring coils by means of which the position of the conductor is determined.

[0009] EP 3761044 A1 further discloses a current measuring device with two magnetic field sensors, wherein the conductor position and orientation and the current to be measured are deduced from the measured values ​​of the magnetic field sensors, wherein complex triaxial magnetic field sensors are used for this purpose, i.e. magnetic field sensors that measure the magnetic field in all three spatial axes. A measurement error in the method described in EP 3761044 A1 arises from the fact that the calculation assumes that the components of the magnetic field detected by the respective triaxial sensor in the three spatial directions refer to an identical spatial point, wherein this is only approximately the case due to the design, since a triaxial sensor is constructed from separate, spatially adjacent sensors for the respective spatial direction.

[0010] The invention is based on the object of showing a way in which the current intensity of an electric current flowing through a conductor can be determined in a simplified and / or improved manner, wherein in particular a contactless measurement of both direct and alternating currents is to be made possible, and wherein in particular a corresponding measuring method and a measuring arrangement are to be specified which allow retrofitting, i.e. a retrofit, to existing cables for different cable cross-sections and which dispense with the use of a ferromagnetic core.

[0011] This object is achieved by the features of the independent claims. Advantageous embodiments are the subject of the dependent claims, wherein the stated features and advantages can essentially apply to all independent claims.

[0012] According to a first aspect of the invention, a method is provided for determining the current intensity of an electric current flowing through at least one conductor, wherein the at least one conductor is positioned in a predetermined measuring range of a measuring arrangement, and wherein the measuring arrangement comprises a plurality of magnetic field sensors. The method comprises the following steps: a) measuring, at a first time, by each of the magnetic field sensors, a value for the magnetic flux density along at least one spatial direction at the location of the respective magnetic field sensor; b) setting the values ​​for a plurality of conductor variables to respective starting values, wherein the conductor variables comprise variables that represent the position and orientation of the at least one current-carrying conductor relative to the measuring arrangement;c) Calculating expected values ​​for the values ​​measured by the magnetic field sensors as a function of the values ​​of the plurality of conductor variables; d) Determining a value of a predeterminable first quality function as a function of the values ​​calculated in step c) and the values ​​measured in step a); e) As long as a predeterminable first termination criterion is not yet met, varying the values ​​of the plurality of conductor variables as a function of a predeterminable first optimization algorithm and repeating steps c) and d); f) Upon fulfillment of the first termination criterion, determining a value for the current intensity of the current flowing through the at least one conductor as a function of the values ​​of the conductor variables. According to a second aspect of the invention, a measuring arrangement designed to carry out the method is provided for measuring the current intensity of an electric current flowing through a conductor.which comprises at least one processing unit and a plurality of magnetic field sensors connected to the processing unit, wherein the processing unit is designed to carry out the method described above.,

[0013] A core idea of ​​the invention can be seen in the provision of a method and a measuring arrangement which enables a measurement of the current intensity of a current flowing through a conductor by means of a measuring arrangement with a plurality of magnetic field sensors, wherein the position and orientation of the conductor relative to the measuring arrangement is determined with the aid of an optimization algorithm, so that the conductor can be positioned and oriented as desired relative to the measuring arrangement within a predetermined measuring range.

[0014] The method advantageously enables contactless measurement of AC and DC currents using magnetic field sensors without the use of a ferromagnetic core. It also enables retrofitting to existing cables and can be used for various conductor cross-sections without the conductor having to be fixed at a precisely known position. Furthermore, it is not necessary to position the magnetic field sensors in such a way that a closed measuring path enclosing the conductor is formed. Particularly advantageously, the magnetic field sensors can be used in a variety of possible arrangements, preferably with a minimum number of magnetic field sensors dependent on the number of conductor variables. Furthermore, the method advantageously allows the use of cost-effective sensors that detect the magnetic field in only one spatial direction.

[0015] The invention will be explained in more detail below using exemplary embodiments in conjunction with the drawings. Figure 1 shows a schematic representation of a preferred embodiment of a measuring arrangement according to the invention in plan view,

[0016] Figure 2 is a schematic perspective view of the measuring arrangement shown in Fig. 1,

[0017] Figure 3 is a schematic block diagram of a preferred embodiment of a measuring chain of the measuring arrangement shown in Figures 1 and 2,

[0018] Figure 4 is an exemplary schematic flow diagram of steps of a method for determining the current intensity of an electrical current flowing through at least one conductor,

[0019] Figure 5 is an exemplary schematic flow diagram of steps of a method for determining the current intensity of an electric current flowing through at least one conductor, which comprises determining a predicted value for the value of the current intensity,

[0020] Figure 6 is an exemplary schematic flow diagram of steps of a calibration method for determining parameters relating to the magnetic field sensors of the measuring arrangement shown in Figures 1 and 2,

[0021] Figure 7 shows schematically an exemplary calibration arrangement for carrying out the calibration method shown in Figure 6 in plan view,

[0022] Figure 8 schematically shows an exemplary circuit arrangement for the selective selection of current-carrying calibration conductors of the calibration arrangement shown in Figure 7,

[0023] Figure 9 schematically shows the influence of a current-carrying adjacent conductor on the measurement of the current intensity of an electric current flowing through at least one conductor with the measuring arrangement shown in Figures 1 and 2, and

[0024] Figure 10 schematically shows the influence of a current-carrying neighboring conductor on the measurement of the current intensity of an electrical current flowing through at least one conductor using the measuring arrangement shown in Figures 1 and 2, which additionally has shielding. Fig. 1 shows a plan view of a schematic representation of a preferred embodiment of a measuring arrangement 100 according to the invention for measuring the current intensity of an electrical current flowing through a conductor 200. The measuring arrangement comprises a processing unit 130 and a plurality of magnetic field sensors 101-108 connected to the processing unit, wherein the processing unit is designed to carry out the method described above for determining the current intensity of an electrical current flowing through at least one conductor. In the measuring arrangement shown in Fig.In the embodiment illustrated in Figure 1, the processing unit comprises a microcontroller 130, which is advantageously designed to execute instructions stored in a memory to carry out the method. Instead of a microcontroller, the processing unit can alternatively comprise a microprocessor or a CPU (Central Processing Unit).

[0025] The embodiment illustrated in Fig. 1 shows the measuring arrangement 100 with 8 magnetic field sensors 101-108 arranged on a circuit board 110 in a plan view, and Fig. 2 shows a perspective view of the same measuring arrangement 100. Any magnetically sensitive sensor can serve as the magnetic field sensor, in particular a Hall sensor, a fluxgate sensor, a magneto-resistive sensor, or a magneto-optical sensor. The magnetic field sensors 101-108 illustrated in Figures 1 and 2 are designed to detect the magnetic flux density in a spatial direction, each indicated by arrows. The circuit board 110 has a U-shaped contour, which allows a conductor 200, which carries a current to be measured, to be introduced into the area between the sensors 101-108, this area defining the measuring area.

[0026] The current-carrying conductor 200 does not pass through the exact center of the area, but the point of passage has a displacement x s in a first spatial direction, shown in Fig. 1 as x-axis, and a displacement y s in a second spatial direction, shown in Fig. 1 as the y-axis. In the illustrated embodiment, the magnetic field sensors are arranged in a plane, with the conductor 200 not passing perpendicularly through the plane in which the sensors are located, but rather having a directional angle α and a tilt angle β relative to the plane, with both angles being unequal to 90° in the illustrated embodiment. It should be noted that the tilt angle β is only visible in Fig. 2 due to the limitations of the illustration.

[0027] Fig. 3 shows a schematic block diagram of a measuring arrangement such as the measuring arrangement 100 shown in the figures. The analog output signals of a plurality of magnetic field sensors 101-10n, for example the magnetic field sensors 101-108 shown in Figures 1 and 2, are connected to an analog-to-digital converter 120 and converted there into a digital data stream. The digital data stream represents the sensor signals sampled at discrete time steps in digital form. The digital data stream is passed to a microcontroller 130. The processor of the microcontroller 130 calculates a value for the current intensity of the electrical current flowing in the conductor 200 from the digital data stream, wherein an optimization algorithm is used in the calculation, which is described in more detail below. A signal is generated from the calculated value for the current intensity and output by means of an output unit 140.The output unit 140 outputs, for example, an analog voltage in the range of 0-10V according to the NAMUR standard, with the output voltage value being proportional to the measured current value (e.g., 0V=0A, 10V=1000A). However, it is also possible to output a current proportional to the current in the conductor, e.g., in the range of 0 to 20mA. The output unit 140 can also output the measured current in digital form, for example, via a fieldbus such as Modbus, Profmet, etc.

[0028] The output unit 140 can also evaluate the calculated current value and, for example, issue a warning signal when a threshold value is reached. It is also possible for an analog-to-digital converter and a magnetic field sensor to be integrated into one component. In this case, a digital data stream is sent to the processor from each magnetic field sensor with integrated analog-to-digital converter. The exemplary embodiment shown in Figures 1 and 2 comprises eight sensors, each of which detects the magnetic field in one spatial direction. However, other configurations are also conceivable in which a different number of sensors are positioned in a different arrangement, detecting the magnetic flux density in one, two, or three spatial directions.

[0029] The magnetic field caused by the current to be measured is measured using multiple sensors at different positions and spatial directions. The sensors are fixed in a rigid arrangement, in the illustrated embodiment on a circuit board 110. The arrangement has an opening that allows current conductors to be brought into the measuring range without breaking the circuit. It is not necessary to fix the current conductor in a specific position or a specific orientation; it is sufficient if the conductor is located at any position in any orientation within a defined measuring range. The defined measuring range is predetermined in particular by the design of the measuring arrangement 100, whereby the design of the measuring arrangement 100 can vary depending on the intended use.

[0030] In the embodiment shown in Fig. 1, the measuring arrangement 100 comprises a printed circuit board 110 on which the processing unit and the plurality of magnetic field sensors 101-108 are arranged. The printed circuit board 110 has a U-shape due to a recess provided in the printed circuit board. The recess forms two printed circuit board arms, between which the predetermined measuring range of the measuring arrangement lies, and at least one of the plurality of magnetic field sensors 101-108 is arranged on each of the two printed circuit board arms. In the illustrated embodiment, four of the magnetic field sensors are arranged on each of the two printed circuit board arms in a row along the direction of extension of the respective printed circuit board arm.

[0031] The sensor signals are converted into a digital data stream using analog-to-digital conversion, which can be processed by a processor in the microcontroller or CPU to ultimately output the current to be measured. A core aspect of the invention is the use of an optimization algorithm for the measurement data evaluation. The algorithm's task is to find the combination of values ​​for conductor variables that best "explains" the existing measured values ​​of the magnetic field sensors. The conductor variables include, in particular, the position and orientation of the conductor in the measuring range and, optionally, the current to be measured.

[0032] Optimization algorithms require a cost or quality function that expresses the quality of an estimate in a number. The estimate is then varied to find the value that achieves the highest quality or lowest cost. The optimization algorithm can be terminated after a specified number of optimization iterations or when the quality criterion falls below a predefined threshold.

[0033] In the optimization algorithm used here, the estimated value consists of the combination of the values ​​of the conductor variables and thus represents an N-dimensional vector, where N is defined by the number of conductor variables. Other influencing factors that can be considered include the cross-sectional shape of the conductor as well as the position, orientation, and current strength of any adjacent current conductors. The position and orientation of the conductor are essentially only auxiliary variables that arise as a by-product of the optimization algorithm to increase the accuracy of the current to be measured. Output of these values ​​is typically not provided.

[0034] In order to determine the current intensity of an electric current flowing through at least one conductor 200, which is positioned in a predetermined measuring range of a measuring arrangement 100 with a plurality of magnetic field sensors 101-108, the method provides the following steps: a) Measuring, at a first time, by each of the magnetic field sensors 101-108, a value for the magnetic flux density along at least one spatial direction at the location of the respective magnetic field sensor 101-108, b) Setting the values ​​for a plurality of conductor variables to respective starting values, wherein the conductor variables comprise variables that represent the position and orientation of the at least one current-carrying conductor 200 relative to the measuring arrangement, c) Calculating expected values ​​with respect to the values ​​measured by the magnetic field sensors 101-108 as a function of the values ​​of the plurality of conductor variables,d) determining a value of a predeterminable first quality function depending on the values ​​calculated in step c) and the values ​​measured in step a), e) as long as a predeterminable first termination criterion is not yet met, varying the values ​​of the plurality of conductor variables depending on a predeterminable first optimization algorithm and repeating steps c) and d), f) upon fulfillment of the first termination criterion, determining a value for the current intensity of the current flowing through the at least one conductor depending on the values ​​of the conductor variables.

[0035] It should be noted that the at least one conductor advantageously comprises exactly one conductor. However, the at least one conductor can also comprise a plurality of conductors, each of which is positioned independently of one another in any position and orientation within the predetermined measuring range of the measuring arrangement 100. In this case, the number of conductor variables to be optimized increases accordingly, and thus possibly also the number of required magnetic field sensors. The at least one conductor can furthermore also comprise a plurality of conductors, the position and orientation and, if applicable, current intensity can be represented by conductor variables that satisfy known boundary conditions, for example if, in a cable with several conductors, it is known that the conductors have the same orientation and a fixed distance from one another and, if applicable, also have the same current intensity.These known boundary conditions can advantageously be taken into account when carrying out the method. Furthermore, the at least one conductor can also comprise a plurality of conductors which are, however, treated as a single conductor, for example in the case of a bundled conductor comprising a plurality of individual conductors. For the sake of clarity and better comprehensibility, only one conductor 200 is shown in each of Figures 1 and 2. Fig. 4 shows the current determination algorithm according to the method described above in the form of a schematic flow diagram. First, in step 300, the measured values ​​of the magnetic field sensors 101-108 are recorded at a first time step. Subsequently, in step 310, parameters of a current conductor for which the current intensity is to be determined are initially specified, i.e., values ​​for a plurality of corresponding conductor variables are set to respective starting values.The conductor variables include variables that represent the position and orientation of the at least one current-carrying conductor 200 relative to the measuring arrangement 100. In the embodiment shown in Figures 1 and 2, the conductor variables that represent the position and orientation of the conductor are the passage position in the x-direction, iex s , the passage position in the y-direction, ie y s , as well as the direction angle α and the tilt angle β. Optionally, the current to be determined can also be advantageously considered as an additional conductor variable. For example, the initial values ​​can be the passage position xs=0, ys=0, the current I=100A, the direction angle α=0°, and a tilt angle relative to the plane β=90°.

[0036] Subsequently, in step 320, the expected sensor values ​​of the magnetic field sensors are calculated using the specified values ​​of the conductor variables. The Biot-Savart law is advantageously applied for this calculation. For simplicity, the Biot-Savart law can be applied for an infinitely long straight conductor. In cylindrical coordinates, this is:

[0037] The calculation is also performed depending on information or parameters of the magnetic field sensors, wherein the parameters represent, in particular, the position, orientation, and / or metrological properties of the respective magnetic field sensor. For example, for each magnetic field sensor, information regarding the respective position, the orientation, e.g., as the value of a tilt angle, the gain (i.e., the proportionality between the existing magnetic flux density and the sensor output value), and the offset (i.e., a zero-point deviation) are taken into account. These parameters can advantageously be determined in advance by a calibration method described in more detail below and stored in a memory of the measuring arrangement 100, for example, a memory of the microcontroller 130.Advantageously, the parameters of the magnetic field sensors considered in the calculation can be adapted to the ambient conditions by adjusting the respective parameter values, for example, to achieve temperature compensation and / or compensation for supply voltage fluctuations. In this case, the measuring arrangement advantageously comprises corresponding sensors for temperature measurement and / or voltage measurement. The provision of the parameters of the magnetic field sensors is shown in Fig. 4 as step 330.

[0038] Subsequently, in step 340, a value of a predeterminable first quality or cost function is determined as a function of the values ​​calculated in step 320 and the values ​​measured in step 300, wherein in particular the recorded sensor values ​​are compared with the calculated values ​​in order to determine the value of the quality or cost function.

[0039] Various cost functions are conceivable. A preferred possibility is to calculate which magnetic field would be established at the positions of the individual magnetic field sensors if the estimated conductor variables were present, in particular by applying the Biot-Savart law, whereby in this case the costs result from the differences between the calculated and the actually measured field strengths, whereby, for example, a standard deviation or a difference between minimum and maximum can be calculated. In this variant, the current to be measured is considered as one of the conductor variables. In the flow diagram shown as an example in Fig. 4, such a cost function is used and accordingly the current to be measured is considered as one of the conductor variables. Another possibility for determining the current strength is to use the estimated geometric arrangement of the at least one conductor 200, ieto determine a gain factor from the respective current estimated values ​​of the conductor variables for each of the magnetic field sensors 101-108, which is used to calculate an estimated current strength from the actually measured field strength. If the estimated arrangement of the at least one conductor 200 corresponds to reality, the same current strength results from each measured value. Accordingly, the deviations in the estimated values ​​for the current strength can be used as a cost function.The respective amplification factor is again advantageously calculated using the Biot-Savart law, whereby the calculation of the amplification factors is carried out on the basis of standardized magnetic field measured values. The standardization can, for example, provide for the measured values ​​to be divided by the largest of the measured values. In this case, the standardized values ​​are independent of the current intensity and only contain information about the position and orientation of the conductor, so that the current intensity to be measured does not have to be taken into account as one of the conductor variables in this case.

[0040] Subsequently, in step 350, it is analyzed whether a termination criterion has been met. The termination criterion can be the amount of the costs calculated by the cost function; for example, exceeding or falling below a threshold can be provided as the termination criterion. Another termination criterion can be the number of previous optimization runs. If a limit is reached, the determination process is terminated, and the determined value of the current to be measured is saved in step 370.

[0041] If the termination criterion is not met, the current conductor parameters, i.e., the conductor variables, are optimized in step 360 using a predeterminable first optimization algorithm. This means that the values ​​of the majority of conductor variables are varied depending on the predeterminable first optimization algorithm, with the value of at least one of the conductor variables being changed in particular. Various optimization algorithms known from the literature can be used for the optimization, for example, the simplex method according to Nelder and Mead, particle swarm optimization, the trust region method, the Powell method, and many more.

[0042] When using a total of 5 conductor variables as described in the example, which represent current strength, passage position x, passage position y, direction angle α and tilt angle β, a minimum of 5 measured values ​​of the magnetic flux density are required for optimization. If, for example, magnetic field sensors are provided that each detect only one component of the magnetic flux density, it is advantageous to provide at least 5 magnetic field sensors. Preferably, the number of magnetic field sensors provided is greater than or equal to the number of conductor variables considered in the optimization. Increasing the number of magnetic field sensors leads to an improvement in accuracy, since the determination method is then overdetermined and interference such as sensor noise, interference fields from neighboring conductors and the like have a lesser influence on the accuracy of the current strength to be determined.

[0043] The arrangement of the magnetic field sensors is advantageously chosen so that the current determination algorithm, i.e., in particular, the optimization algorithm, converges well and quickly. The arrangement of magnetic field sensors shown in Figures 1 and 2, and a variety of other arrangements of magnetic field sensors investigated by the inventors, result in convex optimization problems that can be solved with most optimization algorithms, with the use of the Powell method for optimization proving particularly advantageous in this regard. The Powell method is described, for example, in "An efficient method for finding the minimum of a function of several variables without calculating derivatives.", MJD Powell, Computer Journal, 7: 155-162, 1964.

[0044] Additional influencing factors can advantageously be estimated as conductor variables, such as the position, orientation, and current strength of a neighboring current-carrying conductor. Accordingly, the method can advantageously provide that the plurality of conductor variables includes, for example, variables that represent the current strength and / or the position and orientation of at least one conductor located outside the specified measuring range.

[0045] This increases the number of conductor variables to be optimized. Depending on the specific geometric arrangement of the magnetic field sensors, a non-convex optimization problem could arise, characterized by a cost function with multiple local minima. There is a risk that an optimization method will strive for a local optimum while missing the global optimum, resulting in an error in the current to be determined. This can be advantageously avoided by using more complex optimization algorithms that are robust to non-convex cost functions, for example, by using genetic algorithms or stochastic methods.However, since such a problem is already apparent during development, the number and arrangement of the magnetic field sensors, the conductor variables to be considered and the optimization algorithm to be used can each be advantageously selected in such a way that a convex optimization problem results.

[0046] It is also conceivable to estimate the conductor variables, for example, the current strength of the electric current flowing through at least one conductor, as well as the conductor position and orientation, using artificial intelligence via neural networks. For this purpose, a neural network can be trained, for example, using synthetically generated, i.e., simulated, or real measurement data. A current imprinted in the simulation or measurement can be used as a label as an evaluation criterion.

[0047] Referring again to Fig. 4, the conductor variables adjusted using the optimization method are then used in step 320 to calculate the newly resulting magnetic field sensor values ​​and to execute the subsequent steps described above. After the termination criterion has been reached and the estimated current has been saved, a wait step 380 is executed, in which the estimation algorithm pauses until sensor values ​​from the next time step are available. If the current is not part of the conductor variables, the current is first calculated by "denormalization" before saving. This is done by multiplying the sensor values ​​by the inverse of the normalization value.Once the magnetic field sensor values ​​acquired in step 390 for the next time step are available, a value of the predeterminable first quality or cost function is again determined in step 340 as a function of the sensor values ​​measured in step 390 and the values ​​last calculated in step 320. In particular, the acquired sensor values ​​are again compared with the calculated values ​​to determine the value of the quality or cost function. If the measured and calculated sensor values ​​are in good agreement, the termination criterion is met and the estimated current strength is saved. This is particularly the case if the real conductor parameters, which are represented by the conductor variables, have not changed or have changed only slightly compared to the previous time step. If the termination criterion is not met, the optimization of the conductor variables is continued as described above.

[0048] The optimization, and thus the estimation of the ladder variables, is therefore performed continuously during ongoing measurement operations. The last optimization result from the previous time step can advantageously be used as the starting value. For this reason, high convergence rates are not necessary, and a few iteration steps per time step are usually sufficient.

[0049] The method can advantageously provide for each of the magnetic field sensors to measure a value for the magnetic flux density along at least one spatial direction at the location of the respective magnetic field sensor at a second point in time, and for a respective forecast value for the value of the current flowing through the at least one conductor to be determined for the second point in time from the respective current value determined for the first point in time and the measured values ​​determined by the magnetic field sensors at the first and second points in time. The determination of such a forecast value represents a concurrent estimation of the current intensity in the event that the time available between two sampling steps by means of the magnetic field sensors is insufficient to carry out an estimation of the conductor variables, i.e. to satisfy the first termination criterion or to complete the optimization of the conductor variables.

[0050] Fig. 5 shows an exemplary schematic flow diagram of steps of a method for determining the current intensity of an electric current flowing through at least one conductor, which comprises determining a predictive value for the value of the current intensity, ie such a concurrent estimation of the current intensity.

[0051] In the embodiment shown in Fig. 5, weighting factors aio are initially specified in step 400 and stored as weighting factors ai in step 405, where i denotes a counting index from 1 to n, where n is the number of magnetic field sensors. Accordingly, in the embodiment shown in Figures 1 and 2, n=8. Using the weighting factors, the current I P k of the electric current flowing in the at least one conductor 200 at a sampling time k, as predicted by the following equation:

[0052] In the given equation, Uik denotes the measurement signal of the i'th magnetic field sensor at time step k and aik denotes the weighting factor of the i'th magnetic field sensor at time step k, whereby when using Hall sensors as magnetic field sensors the measurement signal is present, for example, as a voltage value.

[0053] The initial weighting factors can be specified, for example, by means of a prior calibration using a conductor carrying an electric current of known magnitude. Subsequently, in step 410, the magnetic field sensor values ​​Uik are recorded for the current time step. Subsequently, in step 415, a check is performed to determine whether a possibly previously initiated current estimation has already been completed. Current estimation at this point refers to performing the method described in connection with Fig. 4 for determining the current magnitude of the electric current flowing through the at least one conductor for a time step.

[0054] If this is the case, the value of the previously estimated current is stored in step 420, and the previously determined weighting factors are updated in step 425 and stored in step 430. Subsequently, a new current estimation is started in step 435. The current estimation process can be performed concurrently, i.e., parallel to the execution of the remaining sequence shown in Fig. 5, which is shown in Fig. 5 as step 440.

[0055] Since, to carry out the described methods, instructions stored in a memory are advantageously executed by a processor of the microcontroller 130, ie, in particular, a program code is executed, a multitasking operating system can advantageously be provided for concurrent execution of the current estimation process, or an event-driven interruption of the program flow, ie, an interrupt-based program execution, can be provided. An event can be, for example, the arrival of a new sample value.

[0056] A check is then performed again in step 415 to determine whether a previously initiated current estimation has already been completed. If the current estimation is not yet completed, a forecast value for the current strength in the current time step k is determined in step 450 based on the currently stored weighting factors ai retrieved in step 445, and a wait step 455 is executed until magnetic field sensor values ​​for the next time step are available.

[0057] The weighting factor aik of the i'th magnetic field sensor at the k'th time step can be determined using the following equation: Ui describes S is the measurement signal of the i'th magnetic field sensor, which was present at time s of the last current estimation, and n is the number of magnetic field sensors. The current les indicates the current value determined using the current estimation, which is present at the time of the s'th time step.

[0058] In this way, a current value can be predicted for each sampling time step, even if the current estimation requires a time span of several time steps. A temporal change in the current to be measured is taken into account by the temporal change in the magnetic field sensor values. The described forecast is therefore essentially an extrapolation, which, however, only takes into account a change in the current in the current conductor to be measured, but not a change in position or direction. Since the change in position and direction of the conductor are not taken into account in the forecast, the forecast provides reliable values, especially when the position and orientation of the conductor change only slightly between two current estimates.Studies have shown that with commercially available microcontrollers, current estimation can often be carried out within a second, so that changes in the position and orientation of a current conductor can be tracked sufficiently well.

[0059] Advantageously, the forecast value determined for the current intensity can also be used as a starting value for the conductor variable representing the current intensity in the method described above for determining the current intensity of an electric current flowing through at least one conductor.

[0060] In the event that the at least one conductor to be measured comprises multiple conductors, it can advantageously be provided to determine a separate forecast value for each conductor, in particular if the individual conductors are positioned independently of one another in any position and orientation within the predetermined measuring range of the measuring arrangement 100. This only provides reliable values ​​if the current intensity in the multiple conductors changes by the same or a similar factor between the first and second points in time. Alternatively, a forecast value for the current intensity of the resulting total current can also be determined, for example in the case of a bundled conductor.

[0061] As already described above, the current determination algorithm described in Fig. 4 requires information on the magnetic field sensors, in particular the position, alignment, offset, and gain of the respective magnetic field sensor. This information can be obtained, for example, from design data for the circuit board and sensors and from the technical data sheets of the sensors. Alternatively, these parameters can be determined by measurement on existing hardware, for example, during a series calibration in final production inspection. Measuring the sensor properties can be complex, and some sensor properties are difficult or even impossible to measure. For example, the position of a magnetic field-sensitive element, such asa Hall plate within a sensor module housing can exhibit specimen scatter, so that non-destructive testing methods such as X-ray analysis with high spatial resolution would have to be carried out to clearly determine the position and orientation of the sensor.

[0062] Alternatively, the present method advantageously provides for determining the sensor parameters using a calibration measurement method. Accordingly, the method advantageously comprises determining parameters of the plurality of magnetic field sensors, wherein the parameters represent, in particular, the position, orientation, and / or metrological properties of the respective magnetic field sensor, using a calibration method. The calculation of expected values ​​with respect to the values ​​measured by the magnetic field sensors, as provided in step c) of the method described above, takes place as a function of the values ​​of the plurality of conductor variables depending on the parameters of the plurality of magnetic field sensors determined for the plurality of magnetic field sensors using the calibration method.

[0063] The calibration method advantageously provides for at least one calibration conductor, through which a current of a predeterminable current intensity flows, to be introduced successively in different arrangements into the predefined measuring range, and for each arrangement the following steps are carried out:

[0064] A) Measuring, by each of the magnetic field sensors, a value for the magnetic flux density along at least one spatial direction at the location of the respective magnetic field sensor,

[0065] B) setting the values ​​for a plurality of sensor variables and calibration conductor variables to respective starting values, wherein the sensor variables represent the parameters of the plurality of magnetic field sensors and the calibration conductor variables comprise variables which represent the position and orientation of the at least one calibration conductor relative to the measuring arrangement,

[0066] C) Calculating expected values ​​for the values ​​measured by the magnetic field sensors depending on the values ​​of the majority of sensor variables and

[0067] Calibration ladder variables,

[0068] D) Determining a value of a predeterminable second quality function depending on the values ​​calculated in step C) and the values ​​measured in step A),

[0069] E) as long as a predefined second termination criterion is not yet met, varying the values ​​of the calibration ladder variables depending on a predefined second optimization algorithm and repeating steps C) and D),

[0070] F) if the second termination criterion is met, saving the values ​​of the calibration ladder variables,

[0071] G) Calculating expected values ​​for the values ​​measured by the magnetic field sensors depending on the values ​​of the sensor variables and the stored calibration ladder variables,

[0072] H) Determining a value of a predeterminable third quality function depending on the values ​​calculated in step G) and the values ​​measured in step A),

[0073] I) as long as a predefined third termination criterion is not yet met, varying the values ​​of the sensor variables depending on a predefined third optimization algorithm and repeating steps G) and H),

[0074] J) if the third termination criterion is met, saving the values ​​of the sensor variables, K) as long as a predefined fourth termination criterion is not yet met, repeating steps C) to J) with the saved values ​​of the sensor variables and calibration ladder variables as starting values,

[0075] L) if the fourth termination criterion is met, using the stored values ​​of the sensor variables as parameters of the magnetic field sensors when calculating the expected values ​​in step c).

[0076] Capital letters are used for the steps of the calibration procedure to distinguish them from the lowercase steps above.

[0077] Advantageously, the calibration conductor variables may comprise at least one variable representing the current intensity of the current flowing through the at least one calibration conductor, wherein in particular the starting value for the current intensity corresponds to the predeterminable current intensity.

[0078] An exemplary calibration procedure or calibration measurement procedure is shown as a schematic flow diagram in Fig. 6.

[0079] The calibration measurement method illustrated by way of example can be divided into three sections. In a first section 510, the calibration is initialized. In a second section 520, the parameters of the magnetic field sensors, i.e., values ​​for the plurality of sensor variables, are determined. In a third section 530, the position and orientation of the at least one calibration conductor relative to the measurement arrangement, i.e., values ​​for the plurality of calibration conductor variables, are determined.

[0080] In the first section, a counter m is first set to 1 in step 511, which indicates which calibration measurement is involved. Subsequently, in step 512, the at least one calibration conductor is positioned in the measuring range of the measuring arrangement and preferably a current strength of the electrical current flowing through the at least one calibration conductor is specified, wherein, as described above, the arrangement of the at least one calibration conductor relative to the measuring arrangement differs for each calibration measurement. The current can, for example, be specified from a current source with a known current strength, or an unknown current can be specified, the current strength of which is determined using a suitable measuring method, for example by means of a shunt measurement, a current transformer or a Rogowski coil.The position and orientation of the calibration conductor are irrelevant. The point of passage of the at least one calibration conductor through the area defined by the magnetic field sensors, in particular the point of passage through a plane in which the magnetic field sensors are arranged, must merely lie within a permitted range located between the magnetic field sensors, in particular within the predetermined measuring range described above in connection with Figures 1 and 2. In the presence of the predetermined current, the sensor signals of the magnetic field sensors are recorded in step 513, corresponding to step A) above.

[0081] Subsequently, in step 514, the values ​​for the plurality of sensor variables and the values ​​for the plurality of calibration conductor variables are initially specified, corresponding to step B) above. The sensor positions and orientations can be assumed, for example, from the design data of the circuit board 110, and the gain can be taken from the data sheet. The offset can initially be assumed to be 0.

[0082] Analogous to the optimization algorithm described above in connection with the method for determining the current intensity of an electric current flowing through at least one conductor, the values ​​for the calibration conductor variables can now be determined in step 515, corresponding to steps C), D) and E) above. It should be noted that, accordingly, in step 515, initially only the calibration conductor variables are optimized with constant sensor variables. In step 516, the determined calibration conductor variables are stored, corresponding to step F) above. The described initialization is repeated for all calibration measurements, for which purpose the counter m is incremented in step 517 and in step 518 it is checked whether the counter m has exceeded a maximum value mm®, where the value m ma x corresponds to the number of calibration measurements. As long as this is not the case, steps 512 to 517 are repeated.

[0083] Each magnetic field sensor is advantageously characterized by a sensor position x, a sensor position y, a sensor tilt angle, a sensor rotation angle, a sensor offset, and a sensor gain. In this case, each magnetic field sensor has 6 degrees of freedom and therefore 6 corresponding sensor variables are provided for each magnetic field sensor. The sensor position x and the sensor position y preferably refer to a defined coordinate system, which is selected, for example, depending on the design of the circuit board 110. The sensor tilt angle and sensor rotation angle preferably indicate the respective angles relative to a plane defined in particular by the circuit board 110, wherein the passage of the conductor 200 through this plane is indicated in Figures 1 and 2 as a circle 210.Since, as described below, the sensor variables are determined separately for each magnetic field sensor, this results in a total of 6 degrees of freedom, so that in this case at least m is required to optimize the sensor variables. m ax=6 calibration measurements are required. A larger number of calibration measurements increases robustness against external influences, such as noise. Preferably, the positioning or arrangement of the at least one calibration conductor differs as much as possible in the individual calibration measurements to ensure a convex cost function for sensor parameter optimization. For an accurate determination of the offset, it is advantageous to perform one of the calibration measurements in the absence of an electrical current.

[0084] The phase 520 of determining the sensor parameters following the initialization phase is now carried out successively for each of the n magnetic field sensors, with n=8 for the measuring arrangement 100 shown in Figures 1 and 2. For this purpose, a sensor counting index i is initially set to 1 in step 521.

[0085] Subsequently, in step 522, the sensor variables are adjusted using a suitable optimization method, corresponding to steps G), H) and I) above. For this purpose, the previously determined values ​​of the calibration ladder variables and the recorded magnetic field sensor values ​​for the respective magnetic field sensor i are specified and the corresponding sensor variables assigned to the magnetic field sensor i, for example, position Xi, position yi, rotation angle a, tilt angle ß t, OFFSETS, and GAIN! are adjusted so that the calculated sensor signals match the measured sensor signals as closely as possible for all calibration measurements m performed. The determined sensor parameters are saved in step 523, corresponding to step J) above.

[0086] The described optimization of the sensor variables is performed for all magnetic field sensors. For this purpose, the sensor count index i is incremented in step 524, and a check is performed in step 525 to determine whether the sensor count index i has exceeded the number n of magnetic field sensors. As long as this is not the case, steps 522 to 524 are repeated.

[0087] Subsequently, in step 526, it is checked whether a termination criterion is met, which in particular corresponds to the fourth termination criterion defined in step K) above. Expediently, the termination criterion can be an exceeding of a predefined number of iterations performed between optimization of the sensor variables and optimization of the calibration ladder variables, or an undershoot of a predefined residual error with respect to the optimized values ​​of the calibration ladder variables and sensor variables. If the termination criterion is met in step 526, the calibration process is terminated in step 527, and the stored sensor variables can be used as sensor parameters for a subsequent current determination, as described above, corresponding to step L) above.

[0088] If the termination criterion in step 526 is not met, the values ​​of the calibration ladder variables for the individual calibration measurements can be optimized again using the determined sensor variables. In the flowchart shown in Fig. 6, the counter m is first reset to 1 in step 528 and the stored sensor variables are then retrieved in step 531 and used to calculate the expected magnetic field sensor values ​​in step 532. Using the newly determined values ​​of the calibration ladder variables, the sensor variables can then be optimized again, corresponding to step K) above. As shown in Fig. 6, steps 533, 534, 535, and 536 are executed to redetermine the values ​​of the calibration ladder variables; these steps correspond to steps 515 to 518.

[0089] Investigations by the inventors have shown that with suitable placement and orientation of the sensors, for example according to the arrangement shown in Figures 1 and 2, with 10 calibration measurements with different arrangements of the at least one calibration conductor, including arrangements in which a calibration conductor is positioned in the center of the U-shaped recess of the circuit board 110 and those in which a calibration conductor is arranged at other positions distributed within the recess, and with 4 iterations of optimizations of the sensor variables and the calibration conductor variables, a calibration of the sensor parameters with sufficient accuracy is achieved.

[0090] As described above, the calibration should preferably be set to m max different configurations regarding the arrangement of the at least one calibration conductor are provided. For this purpose, a calibration conductor can be moved in the measuring area manually or automatically, for example, with the aid of mechanical actuators. Alternatively, a calibration arrangement can be provided for calibration, as shown schematically in Fig. 7.

[0091] In the calibration arrangement shown schematically in plan view in Fig. 7, calibration conductors K1 to K9 are shown as the at least one calibration conductor, which are positioned within the measuring range of the measuring arrangement 100 shown in Figures 1 and 2, wherein a return conductor KR is also provided in the calibration arrangement shown. The calibration conductors K1 to K9 are positioned in the area between the magnetic field sensors 101 to 108, the return conductor KR is positioned outside the measuring range and all calibration conductors run perpendicular to the plane of representation in the illustrated embodiment. A possible displacement in the x and y directions and a current direction that is not perpendicular to the plane of representation, i.e. tilting and / or twisting, of the calibration conductor are possible but are not shown in order to keep the illustration clear.The direction of the currents in the calibration conductors K1 and K3 to K9 runs into the display plane, while the current in the calibration conductor K2 flows out of the display plane. Various calibration configurations with different numbers of calibration conductors and current directions other than those shown are conceivable. It is preferably intended that the position, tilt, and rotation of the individual calibration conductors do not change during calibration. For this purpose, mechanical fixation of the calibration conductors can be provided. The individual calibration conductors can be charged with a current I. m be energized.

[0092] An exemplary circuit diagram is shown in Fig. 8. A controllable current source 620 can be configured for the respective calibration configuration m with m G {1, can be configured via a control input 610 and thus the calibration current I mbe specified. Via a controllable switching matrix 630, the calibration current can be supplied to the calibration conductors Kl to Kn and the calibration return conductor KR, which is located outside the measuring range, via the switches S 1,1 to Sn,l, Sl,2 to Sn,2 and SR. It is possible that no calibration conductor, a calibration conductor and the calibration return conductor, a calibration conductor pair or several calibration conductors and / or the return conductor are connected to the controllable current source. In this way, a large number of calibration configurations can be provided by means of permutations for a small number of calibration conductors. It is also possible for the current in the individual calibration conductor pairs to be equal by connecting the calibration conductor pairs in series. For the sake of simplicity, only one possible parallel connection is shown in Fig. 8. In order to, as described above, to use the 6 degrees of freedom of the individual magnetic field sensors, i.e.In order to determine sensor parameters or the values ​​of the sensor variables, the calibration configurations shown in the following table can be provided with the help of three calibration conductors Kl, K2, K3, the return conductor KR and the switching matrix. The entry "0" means that no current flows into the relevant calibration conductor, + indicates a positive current, i.e. into the representation plane of Fig. 7, and - a negative current, i.e. out of the representation plane of Fig. 7. The conductor parameters determined in configurations 2, 3 and 4, i.e. the values ​​of the corresponding calibration conductor variables, can advantageously be used in configurations 5 to 10, taking into account the current direction and the current amplitude I. m be reused.

[0093] This means that with the help of 3 calibration leads and one return lead, 10 calibration measurements can be carried out. In configurations 8-10, the current in the individual calibration leads is preferably measured, since unequal conductor resistances, contact resistances, etc. can lead to an inexactly equal distribution of the parallel flowing currents. In addition to the sensor parameters described above, position x, position y, tilt and inclination angle, offset and gain, other parameters such as sensor non-linearity, temperature-dependent gain and offset, etc. can be determined by suitable adaptation of the optimization procedure and the inclusion of further calibration conditions such as temperature. It is also possible to assume sensor parameters that do not exhibit large deviations, for example the sensor alignment, i.e. the angle of rotation, as fixed, which reduces the number of required measurements or even eliminates them.increases robustness against noise for a given number of measurements.

[0094] As described above, determining the current flowing through a conductor by optimizing the conductor parameters or corresponding conductor variables allows for any desired positioning and orientation of the magnetic field sensors. This is preferably used to reduce the influence of interference fields, caused, for example, by neighboring current-carrying conductors.

[0095] For illustration purposes, Fig. 9 again shows the same measuring arrangement as was already shown in Figures 1 and 2. In the measuring area defined by the cutout in the circuit board 110, a conductor LI is shown which carries a current that flows into the representation plane. The conductor LI is surrounded by concentric magnetic field lines that form around the conductor, including in the area of ​​the magnetic field sensors. The magnetic field lines of the conductor LI are shown as solid lines 710. If a conductor L2 is located outside the measuring area but in the vicinity of the measuring arrangement 100, the magnetic field lines, shown as dashed lines 720 around the conductor L2, can extend into the area of ​​the magnetic field sensors. In many applications, the conductors LI and L2 are arranged in a common horizontal plane.Examples of this include cable and busbar arrangements in control cabinets and wiring installations on a panel. The magnetic field sensors can be arranged, as shown in Fig. 9, such that the magnetic field lines of conductor LI run predominantly in the sensitivity direction of the sensors, while the magnetic field lines of the neighboring conductor L2 are predominantly perpendicular to the magnetic field lines, i.e., at a 90° angle. The output signal of the magnetic field sensors is therefore more strongly influenced by conductor LI than by conductor L2. In other words, the measurement error when measuring the current flowing in conductor LI, if neighboring conductors are neglected, is smaller in this configuration than in a configuration in which the sensor orientation is not selected as shown.The method accordingly preferably provides that the magnetic field sensors measure the magnetic field strength in one spatial direction, wherein the magnetic field sensors are arranged on the circuit board arms in such a way that they measure the magnetic field strength substantially along the extension direction of the circuit board arms, so that the influence of a magnetic field generated by a current-carrying conductor that is arranged substantially parallel to the conductor to be measured on the measured values ​​supplied by the magnetic field sensors is minimized.

[0096] If the distance between conductors LI and L2 is known, this information can be used to jointly estimate the position of LI and L2, thereby further reducing the error.

[0097] In an advantageous embodiment, the measuring arrangement 100 further comprises shielding elements for homogenizing external magnetic fields within the predetermined measuring range. This is illustrated schematically in Fig. 10, wherein Fig. 10 shows the same arrangement as shown in Fig. 9, but additionally two shielding plates 810 and 820 arranged next to the measuring arrangement 100 are provided as shielding elements. The shielding plates 810 and 820 are preferably made of a ferromagnetic material with a high relative permeability p r , for example a sheet package made of steel or Mu-metal sheet with a p r from approximately 1000 to 50000, ferrite blocks with a p r of approximately 100 to 5000 or a plastic mixed with ferrite particles with a p rfrom approximately 10 to 500. For a material with high relative permeability, the magnetic field lines occur perpendicularly to the interfaces between the environment with low permeability, such as air or plastic with p r =l, and the material with high permeability. As a result, the field lines 720' of the adjacent conductor L2 run approximately perpendicularly between the shielding plates 810 and 820. The magnetic field lines 710' of the conductor L1 to be measured are also distorted by the presence of the shielding plates 810 and 820. It should be noted that the magnetic field sensors are preferably arranged and designed such that they measure the magnetic field strength in a spatial direction perpendicular to the direction of the magnetic field lines 720' of the external magnetic field homogenized between the shielding plates 810 and 820, so that there is no influence on the measured values ​​provided by the magnetic field sensors.

[0098] The method can advantageously provide that the change in the magnetic field generated by the at least one current-carrying conductor caused by the shielding elements is taken into account when calculating the expected values ​​in step c). The distortion can be taken into account when calculating the expected sensor values ​​of the magnetic field sensors, for example, using current mirror methods. Alternatively, the distortion can be reduced to a negligible level by appropriately positioning the shielding plates 810 and 820. Depending on the application, a compromise is then appropriately determined between low distortion, which occurs when the shielding plates 810 and 820 are positioned far away from the measuring arrangement, and a good shielding effect, which occurs when the shielding plates 810 and 820 are arranged as close as possible to one another.

[0099] The shielding plates 810 and 820 are preferably dimensioned and positioned such that the ferromagnetic material does not saturate, i.e., the plates 810 and 820 are preferably provided with a thickness sufficient for the respective application. Saturation effects occur when the magnetic flux density in the ferromagnetic material exceeds a limit value, which is referred to as the saturation flux density, whereby the material loses its shielding effect when the saturation flux density is reached. In addition, the material can heat up considerably when passing through the hysteresis loop until it reaches saturation. This must be taken into account especially with alternating currents in the conductors LI and / or L2. In addition, the length and width of the shielding plates are preferably selected so that the shielding effect is sufficient with the least possible material usage and thus low manufacturing costs and weight.

Claims

Patent claims 1. A method for determining the current strength of an electric current flowing through at least one conductor (200), wherein the at least one conductor is positioned in a predetermined measuring range of a measuring arrangement (100), and wherein the measuring arrangement (100) comprises a plurality of magnetic field sensors (101-108), comprising the steps of: a) measuring, at a first time point, by each of the magnetic field sensors (101-108), a value for the magnetic flux density along at least one spatial direction at the location of the respective magnetic field sensor (300), b) setting the values ​​for a plurality of conductor variables to respective initial values, wherein the conductor variables include variables representing the position and orientation of the at least one current-carrying conductor relative to the measuring arrangement (310), c) calculating expected values ​​with respect to the values ​​measured by the magnetic field sensors as a function of the values ​​of the plurality of conductor variables (320).d) Determining a value of a predefined first performance function as a function of the values ​​calculated in step c) and the values ​​measured in step a) (340), e) as long as a predefined first termination criterion is not yet satisfied (350), varying the values ​​of the plurality of conductor variables as a function of a predefined first optimization algorithm (360) and repeating steps c) and d), f) upon satisfaction of the first termination criterion, determining a value for the current strength of the current flowing through the at least one conductor as a function of the values ​​of the conductor variables (370).

2. The method of claim 1, wherein the conductor variables comprise at least one variable representing the current strength of the current flowing through the at least one conductor (200), and wherein in step c) expected values ​​are calculated for the values ​​measured by the magnetic field sensors (101-108), and wherein determining a value for the current strength of the current flowing through the at least in step f) a conductor (200) of flowing current a determination of the value of the respective variable which represents the current strength as the value of the current strength of the current flowing through the at least one conductor (200) determined for the first time point.

3. Method according to claim 1 or 2, wherein the plurality of conductor variables further comprises variables representing the current intensity and / or the position and orientation of at least one conductor arranged outside the specified measuring range.

4. Method according to one of the preceding claims, wherein the Biot-Savart law for an infinitely long straight conductor is used to calculate the expected values ​​in step c).

5. A method according to any of the foregoing claims, comprising - Determining parameters of the majority of magnetic field sensors (101-108), wherein the parameters represent in particular the position, orientation and / or metrological properties of the respective magnetic field sensor (101-108), using a calibration procedure, wherein the expected values ​​in step c) are calculated as a function of the determined parameters.

6. The method of claim 5, wherein the calibration method provides for successively inserting at least one calibration conductor (K1-K9), through which a current of a predeterminable current strength flows, into the predetermined measuring range in different arrangements, and for each arrangement performing the following steps: A) Measuring by each of the magnetic field sensors (101-108), one value for the magnetic flux density along at least one spatial direction at the location of the respective magnetic field sensor (101-108), B) Setting the values ​​for a plurality of sensor variables and calibration ladder variables to their respective starting values, wherein the sensor variables are the parameters of the plurality of magnetic field sensors (101-108) represent and include the calibration ladder variables, which represent the position and orientation of at least one calibration ladder (K1-K9) relative to the measurement arrangement (100), C) Calculating expected values ​​for the values ​​measured by the magnetic field sensors (101-108) as a function of the values ​​of the majority of sensor variables and calibration conductor variables, D) Determining a value of a predefined second performance function as a function of the values ​​calculated in step C) and the values ​​measured in step A), E) as long as a predefined second termination criterion is not yet fulfilled, vary the values ​​of the calibration ladder variables depending on a predefined second optimization algorithm and repeat steps C) and D). F) upon fulfillment of the second termination criterion, saving the values ​​of the calibration ladder variables, G) Calculating expected values ​​for the values ​​measured by the magnetic field sensors (101-108) depending on the values ​​of the sensor variables and the stored calibration ladder variables, H) Determining a value of a predefined third performance function as a function of the values ​​calculated in step G) and the values ​​measured in step A), I) As long as a predefined third termination criterion is not yet fulfilled, vary the values ​​of the sensor variables depending on a predefined third optimization algorithm and repeat steps G) and H). J) upon fulfillment of the third termination criterion, saving the values ​​of the sensor variables, K) as long as a predefinable fourth termination criterion has not yet been met, repeat steps C) to J) with the stored values ​​of the sensor variables and calibration ladder variables as starting values, L) if the fourth termination criterion is met, use the stored values ​​of the sensor variables as parameters of the magnetic field sensors (101-108) when calculating the expected values ​​in step c).

7. Method according to claim 6, wherein the calibration conductor variables comprise at least one variable representing the current strength of the current flowing through the at least one calibration conductor (K1-K9), wherein in particular the starting value for the current strength corresponds to the predefinable current strength.

8. A method according to any of the preceding claims, further comprising the steps of: - Measure, at a second time point, through each of the magnetic field sensors (101-108), a value for the magnetic flux density along at least one spatial direction at the location of the respective magnetic field sensor (101-108), - Determining a respective predicted value for the value of the current flowing through the at least one conductor for the second time point from the respective value of the current determined for the first time point and the measured values ​​determined by the magnetic field sensors (101-108) at the first and second time points.

9. Method according to one of the preceding claims, wherein the measuring arrangement (100) comprises a printed circuit board (110) on which the majority of the magnetic field sensors (101-108) are arranged, wherein the printed circuit board (110) has a U-shape by means of a recess provided in the printed circuit board (110), wherein the recess forms two printed circuit board arms between which the predetermined measuring range of the measuring arrangement (100) lies, and wherein at least one of the majority of the magnetic field sensors (101-108) is arranged on each of the two printed circuit board arms.

10. The method of claim 9, wherein the magnetic field sensors (101-108) measure the magnetic field strength in a spatial direction, and wherein the magnetic field sensors (101-108) are arranged on the printed circuit board arms such that they measure the magnetic field strength substantially along the extension direction (y) of the printed circuit board arms, so that the influence a magnetic field (720) which is minimized to the measured values ​​supplied by the magnetic field sensors (101-108) by a current-carrying conductor (L2) which is arranged essentially parallel to the conductor (LI) to be measured.

11. Method according to one of the preceding claims, wherein the measuring arrangement comprises shielding elements (810, 820) for homogenizing external magnetic fields within the specified measuring range.

12. Method according to claim 11, wherein the change in the magnetic field generated by the at least one current-carrying conductor caused by the shielding elements (810, 820) is taken into account when calculating the expected values ​​in step c).

13. Measuring arrangement (100) for measuring the current intensity of an electric current flowing through a conductor, comprising - one processing unit (130), and - a plurality of magnetic field sensors (101-108) connected to the processing unit (130), wherein the processing unit (130) is configured to perform a method according to one of claims 1 to 12.

14. Measuring arrangement (100) according to claim 13, wherein the measuring arrangement (100) comprises a printed circuit board (110) on which the processing unit (130) and the plurality of magnetic field sensors (101-108) are arranged, wherein the printed circuit board (110) has a U-shape by means of a recess provided in the printed circuit board (110), wherein the recess forms two printed circuit board arms between which a predetermined measuring range of the measuring arrangement (100) lies, and wherein at least one of the plurality of magnetic field sensors (101-108) is arranged on each of the two printed circuit board arms.

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