Clustered magneto-optical current sensor to eliminate the interference of a phase-to-phase magnetic field

Zhao Xiaojun; Liang Zhuohang; Li Yansong; Liu Jun

doi:10.1364/OPTCON.447649

1. Introduction

Optical current sensors have the advantages of a large dynamic range, wide frequency response, and high accuracy [1,2]. These advantages not only compensate for the operational defects of traditional electromagnetic current sensors, such as large volume, ferromagnetic resonance, and poor transient characteristics [3,4], but also facilitate the transmission of information as digital output, which conforms to the digital and networked development trend of smart grids [5].

The optical current sensor uses the Faraday magneto-optical effect to measure current [6,7]. As one of the research direction for optical current sensors, straight-through magneto-optical current sensors have the advantages of simple structure, high long-term operational reliability, low cost, and easy fabrication [8], which have attracted the attention of many scholars and researchers. However, because the path of the sensing light is not closed, it cannot meet Ampere's circuital law and cannot resist the interference of the external magnetic field, especially interference by the interphase magnetic field [9,10]. In addition, the occurrence of reclosure and other actions in the power system often lead to the displacement of the sensor [11], which affects its measurement accuracy and makes it difficult to meet the requirement of an accuracy grade of 0.2 for the sensor in the power system.

In view of the weak ability of magneto-optical current sensors to resist phase-to-phase magnetic interference, a discrete loop magnetic field integration model was established in Ref. [12]. It was proposed that if the power system wiring mode could meet the mutual convenience conditions of the model, the phenomenon of phase-to-phase magnetic field interference could be avoided. However, this method requires magneto-optic glass to be placed at a specific angle, and requires a large number of magneto-optic glass, which has many inconveniences in practical application. In [13], the magnetic field of the target was enhanced by the magnetic field of the solenoid to indirectly suppress the interference between phases. In Ref. [14], a parallel placed double MOCS group was initially proposed, which is the prototype of a differential optical current sensor, and in Ref. [15], the differential optical current sensor was formally proposed. By subtracting the outputs of two symmetrically distributed current sensing units, the obtained signal had no common mode interference and eliminated the common-mode interference signal in the phase magnetic field interference. However, this structure can not eliminate the differential mode interference in the interphase magnetic field, but will enhance it. Reference [16] proposes a splicing magneto-optical current sensor that can satisfy the ampere loop law and reduce measurement error by optimizing the structure of the strip magneto-optical current sensor. The above research has played a role in suppressing and weakening the interference of the phase-to-phase magnetic field of magneto-optical current sensors, but it does not fundamentally solve the problem of phase-to-phase magnetic interference.

In order to fundamentally solve the problem of phase-to-phase magnetic field interference, it is necessary to comprehensively deal with the multi-dimensional sensing measurement of three-phase conductors. The method of extracting corresponding physical quantities from multiple field sensor signals is widely mentioned in power system, such as the detection technology of transmission line in Ref. [17] and [18], which measured the electrical and spatial parameters of the line at the same time. Similarly, in the field of MOCS measurement, as described in Ref. [19], where a MOCS three-phase current measurement with three sensors was proposed, a three-dimensional coefficient matrix is used to connect the three sensor signals with the three measured currents. However, in some real-world situation, the coefficient matrix is not a constant matrix, and the calibration of coefficient matrix is difficult, which limits the wide application of this measurement method [20].

Therefore, this study first analyzes the principle of phase-to-phase magnetic field interference in traditional magneto-optical current sensors, proposes a structure for clustered magneto-optical current sensors, and establishes the mathematical model of phase-to-phase magnetic field coupling by analyzing its sensing mechanism. Then, an iterative algorithm is used to decouple the measurement of the mathematical model and eliminate the interference of the phase-to-phase magnetic field. At the same time, the position of the sensor is also corrected, which improves the ability of the sensor to resist the interference of the phase-to-phase magnetic field and reduces the measurement error caused by changes in the position of the sensor.

2. Principle of traditional magneto-optical current sensor and analysis of the interference between phases of the magnetic field

2.1 Sensing principle of traditional magneto-optical current sensor

The Faraday magneto-optical effect refers to the fact that when linearly polarized light propagates in magneto-optical sensing material under the force of a magnetic field, its polarization plane rotates, resulting in an angle between the incoming polarization plane and outgoing polarization plane. This angle is also called the Faraday rotation angle θ [21]; this principle is shown in Fig. 1.

Fig. 1. Schematic diagram of Faraday magneto-optical effect.

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The calculation formula of Faraday rotation Angle is as follows:

(1)$$\theta = V\int {\overrightarrow H \cdot d\mathop{l}\limits^{\rightharpoonup} }$$

where V : Verdet constant;$\overrightarrow H$: magnetic field intensity;${d\mathop{l}\limits^{\rightharpoonup}}$: the integral path. From formula (1) we can draw a conclusion that there is only one Verdet constant difference between the rotation angle θ value and the magnetic field integral value of the corresponding path. Therefore, the rotation angle can be obtained by analyzing the magnetic field path integral part.

When the Faraday effect is used as the basic principle for current measurement, it actually converts current information to magnetic field intensity H. When the current in a power system is measured, the magnetic field generated by the current in the conductor is superimposed in space, as shown in Fig. 2. The three-phase conductors are positioned in a horizontal arrangement that is commonly used in power systems [22]. To highlight the influence of the superimposed magnetic field on the optical sensing part of the magneto-optical current sensor, the magneto-optical current sensor is simplified to its optical sensing part.

Fig. 2. Magnetic field superposition relationship of traditional magneto-optical current sensor.

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Figure 2 shows a schematic diagram of the traditional magneto-optical current sensor and three-phase current with the magnetic field generated from a top view. In the figure, the yellow, green, and red solid circles represent the A, B, and C three-phase conductors respectively. And the currents inside the conductors are I_A, I_B, and I_C respectively. The yellow, green, and red dotted circles represent the magnetic field generated by currents I_A, I_B, and I_C in the conductor, respectively. The left rectangle is the optical sensing part of the traditional magneto-optical current sensor

As shown in Fig. 2 and its partially enlarged drawing, the magnetic field generated by the adjacent conductor, also known as interphase magnetic field interference, will be superimposed on the local magnetic field. But the current sensor reflects the magnetic field information here as the measurement value of phase A current, which makes the current sensor produce measurement error.

2.2 Analysis of phase-to-phase magnetic field interference of traditional magneto-optical current sensor

The influence of the magnetic field interference between the traditional magneto-optical current sensor over one cycle of the power system is analyzed below. The positional relationship between the magneto-optical current sensors and conductors is shown in Fig. 3. In the figure, m is the optical path length of the magneto-optical sensing materials in a traditional magneto-optical current sensor; a is the distance between the phase of the current sensor and the phase of the conductor; and d_AB, d_BC, and d_AC are the horizontal distances between phase A and phase B, between phase B and phase C, and between phase A and phase C, respectively.

Fig. 3. Location of traditional magneto-optical current sensor and three-phase conductor.

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In a power system, the conductors are generally arranged horizontally, and the distance between adjacent two-phase conductors, which is expressed as d in this study, is generally equal and constant. Therefore, d_AB, d_BC, and d_AC are d, d, and 2d, respectively.

The calculation formula for the measured value I’ of the current sensor in Fig. 3 is as follows:

(2)$$\begin{aligned} I^{\prime} &= \int_{ - \frac{m}{2}}^{\frac{m}{2}} {\frac{{{I_A}}}{{2\pi }}} \cdot \frac{a}{{{a^2} + {y^2}}}dy + \int_{ - \frac{m}{2}}^{\frac{m}{2}} {\frac{{{I_B}}}{{2\pi }}} \cdot \frac{{d + a}}{{{{({d + a} )}^2} + {y^2}}}dy + \int_{ - \frac{m}{2}}^{\frac{m}{2}} {\frac{{{I_C}}}{{2\pi }}} \cdot \frac{{2d + a}}{{{{({2d + a} )}^2} + {y^2}}}dy\\ &= \frac{{{I_A}}}{\pi }\arctan \frac{m}{{2a}} + \frac{{{I_B}}}{\pi }\arctan \frac{m}{{2(d + a)}} + \frac{{{I_C}}}{\pi }\arctan \frac{m}{{2(2d + a)}} \end{aligned}$$

To distinguish the actual value from the measured value, the variable with ‘ is the measured value, and the variable without ‘ is the actual value.

Equation (1) shows that the measured value I’ of the magneto-optical current sensor not only reflects the magnetic field of the local phase, but also reflects the magnetic field of the adjacent phase. The interphase magnetic field interference coefficient α is defined to measure the interference of the adjacent phase magnetic field on the local phase magnetic field.

(3)$$\alpha = \frac{{{I_\textrm{s}}}}{{{I_\textrm{t}}}}$$

where

(4)$$\begin{aligned} {I_\textrm{t}} &= \frac{{{I_A}}}{\pi }\arctan \frac{m}{{2a}}\\ {I_\textrm{s}} &= \frac{{{I_B}}}{\pi }\arctan \frac{m}{{2(d + a)}} + \frac{{{I_C}}}{\pi }\arctan \frac{m}{{2(2d + a)}} \end{aligned}$$

The larger the value of α, the greater the interphase magnetic field interference, whereas the smaller the value of α, the weaker the interphase magnetic field interference.

The instantaneous values of three-phase symmetrical currents I_A, I_B, and I_C are

(5)$$\left[ {\begin{array}{*{20}{c}} {{I_A}}\\ {{I_B}}\\ {{I_C}} \end{array}} \right] = {I_m}\left[ {\begin{array}{*{20}{c}} {\sin (100\pi t)}\\ {\sin (100\pi t - \frac{2}{3}\pi )}\\ {\sin (100\pi t + \frac{2}{3}\pi )} \end{array}} \right]$$

where I_m is the magnitude of the current and t is the time.

By substituting Eq. (4) into Eq. (2), the interphase magnetic field interference coefficient α can be simplified as follows:

(6)$$\alpha = \frac{{\arctan \frac{m}{{2(d + a)}}\sin (100\pi t - \frac{2}{3}\pi ) + \arctan \frac{m}{{2(2d + a)}}\sin (100\pi t + \frac{2}{3}\pi )}}{{\arctan \frac{m}{{2a}}\sin (100\pi t)}}$$

Equation (5) shows that the interphase magnetic field interference coefficient α has nothing to do with the current amplitude I_m, but has only to do with the optical path length m, interphase distance d, sensor position a, and time t. Taking the conventional design of a 220 kV substation in the power system as an example, the phase-to-phase distance d is generally 3 m when the conductors are horizontally arranged, and the length m of the optical sensing part of a traditional magneto-optical current sensor is generally designed as 0.1 m, and the distance a from the measuring conductor is generally designed as 0.05 m. Assuming these parameter values, the change in the interphase magnetic field interference coefficient α with time t is shown in Fig. 4.

Fig. 4. Variation in interference coefficient over one cycle.

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Based on the analysis in Fig. 4 and Eq. (5), t = 0 s, t = 0.01 s, and t = 0.02 s are the zero points of the local phase current. At these points, the interphase magnetic field interference coefficient α appears as an infinite breakpoint. In other words, in a power system cycle, the smaller the local phase current value, the greater the interphase magnetic field interference coefficient α. Therefore, it is difficult for a traditional magneto-optical current sensor to meet the 0.2 accuracy grade measurement requirements of the power system over the entire cycle without interference from the phase-to-phase magnetic field.

3. Structure and mathematical model of clustered magneto-optical current sensors

At present, the improvement and optimization of the anti-magnetic interference structure of magneto-optical current sensors are based on the measurement of a single-phase current. According to the analysis in the previous section, the so-called phase-to-phase magnetic field interference is caused by ignoring other phase magnetic fields and treating the superimposed magnetic field as the local phase magnetic field. This type of neglect inevitably affects measurement accuracy. Therefore, to completely eliminate the interference of the phase-to-phase magnetic field, the single-phase current cannot be separated, and the three-phase current must be regarded as a whole. At the same time, because reclosing and other operations often occur in the power system and it is difficult to avoid vibration and other factors, the position of the magneto-optical current sensor often deviates to a certain extent, and the position stability cannot be guaranteed.

Considering the bottlenecks and potential problems of traditional magneto-optical current sensors, this study proposes clustered optical current sensors, which overcome the limitations of the previous single-phase current measurement method. According to the positional relationship between the sensor and the conductor, the magnetic field between each single-phase current sensors is coupled, which not only ensures the measurement of each phase current, but also addresses the influence of the deviation in conductor position on the current sensor.

3.1 Structure of clustered magneto-optical current sensors

The optical sensing device of the clustered magneto-optical current sensor is shown in Fig. 5. The optical sensing device is composed of a fixing bracket and magneto-optical sensing materials that are fixed at both ends. The device is U-shaped. The bottom of the U is a fixing bracket, and the two sides are magneto-optical sensing material. The fixing bracket is composed of an insulating nonmagnetic material. The effective length of the optical path of the magneto-optical sensing material is m, and the length of the fixing bracket is l.

Fig. 5. Structure of optical sensing device.

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The optical sensing device of the clustered magneto-optical current sensor and the spatial position relationship of the conductor are shown in Fig. 6. An optical sensing device surrounds each phase conductor, and the conductor is located inside the U-shaped optical sensing device. To correct the influence of the positional deviation of the instrument sensor on its measurement accuracy, the positions of the optical sensor device were regarded as variable factors in this study. Here, the distance between the magneto-optical sensing material on the left side of the optical sensor device and the local phase conductor was set as a variable.

Fig. 6. Spatial position relationship of optical sensors.

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Figure 6 shows that when the conductors are horizontally arranged, the horizontal distance between phases is d, and the distance between each of the three phase conductors and the left side of their optical sensing device is a, b, and c.

The complete clustered magneto-optical current sensor consists of three optical sensing devices, each of which contains two current sensors made of magneto-optical sensing materials. For the convenience of description, current sensors of our model in Fig. 6 are labeled A-left, A-right, B-left, B-right, C-left, and C-right respectively. And their current measurement values I’ are expressed as I₁’, I₂’, I₃’, I₄’, I₅’, and I₆’, respectively.

3.2 Mathematical model of phase-to-phase magnetic field coupling

To facilitate the expression of the mathematical model, the magneto-optical sensing material is simplified as a line segment along the direction of the optical path. The mathematical model of the optical sensing part of the clustered magneto-optical current sensor is shown in Fig. 7 in a top view. The horizontal direction is the x-axis direction, the vertical direction is the y-axis direction, and the position of I_B is at the coordinate origin.

Fig. 7. Mathematical model of spatial optical path for optical sensing part of clustered magneto-optical current sensors.

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The measured value I₁’ of the A-left current sensor was analyzed using Eq. (1) above, i.e.,

(7)$${I_\textrm{1}}^\prime = \frac{{{I_A}}}{\pi }\arctan \frac{m}{{2a}} + \frac{{{I_B}}}{\pi }\arctan \frac{m}{{2(d + a)}} + \frac{{{I_C}}}{\pi }\arctan \frac{m}{{2(2d + a)}}$$

The current measurement values for the other magneto-optical current sensors I_i’ (i = 2,3,4,5,6) are

(8)$${I_2}^\prime ={-} \frac{{{I_A}}}{\pi }\arctan \frac{m}{{2(l - a)}} + \frac{{{I_B}}}{\pi }\arctan \frac{m}{{2(d - l + a)}} + \frac{{{I_C}}}{\pi }\arctan \frac{m}{{2(2d - l + a)}}$$

(9)$${I_3}^\prime ={-} \frac{{{I_A}}}{\pi }\arctan \frac{m}{{2(d - b)}} + \frac{{{I_B}}}{\pi }\arctan \frac{m}{{2b}} + \frac{{{I_C}}}{\pi }\arctan \frac{m}{{2(d + b)}}$$

(10)$${I_4}^\prime ={-} \frac{{{I_A}}}{\pi }\arctan \frac{m}{{2(d + l - b)}} - \frac{{{I_B}}}{\pi }\arctan \frac{m}{{2(l - b)}} + \frac{{{I_C}}}{\pi }\arctan \frac{m}{{2(d - l + b)}}$$

(11)$${I_\textrm{5}}^\prime ={-} \frac{{{I_A}}}{\pi }\arctan \frac{m}{{2(2d - c)}} - \frac{{{I_B}}}{\pi }\arctan \frac{m}{{2(d - c)}} + \frac{{{I_C}}}{\pi }\arctan \frac{m}{{2c}}$$

(12)$${I_\textrm{6}}^\prime ={-} \frac{{{I_A}}}{\pi }\arctan \frac{m}{{2(2d + l - c)}} - \frac{{{I_B}}}{\pi }\arctan \frac{m}{{2(d + l - c)}} - \frac{{{I_C}}}{\pi }\arctan \frac{m}{{2(l - c)}}$$

From Eqs. (6)–(11), it can be seen that the measured value of any clustered magneto-optical current sensor contains the relevant expressions of I_A, I_B, I_C, and a, b, c; that is, the clustered magneto-optical current sensor couples the three-phase current with the positional relationship of the sensor. Equations (6)–(11) are referred to as the coupled equations of measurement. Obviously, the equations are six-dimensional nonlinear equations.

4. Decoupling strategy for measurement of clustered magneto-optical current sensors

In the previous section, a mathematical modeling analysis of the sensor structure was used to obtain the coupled equations of measurement. In this section, an iterative algorithm is applied to solve the nonlinear equations, and a strategy for the decoupling measurement is proposed: by inputting d, m, l, and I_i’ (i = 1,2,3,4,5,6), the position offset of the sensor can be corrected, and the three-phase current measurement values I_A’, I_B’, and I_C’ can be obtained.

In a power system, the phase-to-phase distance d is a fixed parameter, and the structural parameters m and l of the optical sensor are fixed. Therefore, after obtaining the current measurement value I_i’ of each magneto-optical current sensor (i = 1,2,3,4,5,6), the coupling equation system of measurement is represented as a six-dimensional equation group containing only six variables, namely I_A, I_B, I_C, and a, b, and c, and the equations have solutions. Newton’s method is a classical algorithm for solving nonlinear equations. Therefore, the decoupling strategy is illustrated using the Newton method. The solution process is as follows:

The initial values of the given variables are I_A⁽⁰⁾, I_B⁽⁰⁾, I_C⁽⁰⁾, a⁽⁰⁾, b⁽⁰⁾, and c⁽⁰⁾, and their corrections are ΔI_A⁽⁰⁾, ΔI_B⁽⁰⁾, ΔI_C⁽⁰⁾, Δa⁽⁰⁾, Δb⁽⁰⁾, and Δc⁽⁰⁾.

Let the number of iterations k = 0, and begin the iteration:

(1) Calculate the unbalanced variables
(2) Calculate the Jacobian matrix J
(3) Calculate the corrections ΔI_a^(k),ΔI_b^(k), ΔI_c^(k), Δa^(k), Δb^(k), and Δc^(k).
(4) Correct the variables.
(5) The new variables are taken as the initial values, and the next iteration is repeated according to (1)–(4) till the iteration accuracy is satisfied.

See the Supplement 1 for the detailed calculation process and formula expression. A program block diagram is shown in Fig. 8.

Fig. 8. Flow chart for solving the measurement decoupling strategy.

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The a’, b’, and c’ obtained from the solution are the measured values for the position of the sensor, which are used to correct the position of the sensor. I_A’, I_B’, and I_C’ are output as the measured values of the three-phase current.

5. Clustered magneto-optical current sensors and their measurement decoupling strategy verification

5.1 Construction of experimental platform

In this section, the experimental platform of the cluster magneto-optical current sensor is built. The experimental platform includes three-phase current conductor, light source generation equipment, photoelectric acquisition equipment and optical sensing part. The overall structure of the experimental platform is shown in Fig. 9 below. Figure 9(a) shows the spatial arrangement of the three-phase conductor, and Fig. 9(b) shows the name of the single-phase conductor and related measuring instruments. The polarized light needed for the experiment is generated by a light source and enters the magneto-optical glass. The photoelectric detector converts the light signal into electrical signal, and the data is collected by the data acquisition card. Due to laboratory equipment and space problems, the conductor phase to phase distance d of the experimental platform cannot achieve the space distance of 3 m described in section 2.So, the d of the experimental platform is set to 1.2 m.

Fig. 9. The experimental platform of clustered magneto-optical current sensor.

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The optical path length m of magneto-optical current sensors is 0.1 m, and the position (a, b and c) of sensor is 0.05 m. In order to ensure the stability of the magneto-optical sensing structure, the magneto-optical sensing elements used in the experimental platform are encapsulated elements, and the magneto-optical sensing material is a magneto-optical glass with a length of 0.1 m. The internal structure of the magneto-optical sensing element is shown in Fig. 10.

Fig. 10. Internal structure of magneto-optical sensing element (3-Magneto-optical glass, 1 and 5-Collimator, 2 and 4-Polarizer).

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Because the non-magnetic fixed support in the optical sensing device needs a long time to manufacture, and this test focuses on the performance of the clustered magneto-optical current sensor, the experimental platform does not provided with a fixed support. And the position of the sensor is simulated by fixing the distance of each magneto-optical sensing unit in advance. It is assumed that when the sensor is not offset, the distance between each transformer and the conductor is 5 cm, that is, a = b = c = 5 cm. Taking the phase A as an example, the following Fig. 11 simulates the relative position relationship between the sensors and the conductor when the length l of the fixed support is 10 cm.

Fig. 11. Spatial position relationship between optical sensing part and conductor of cluster magneto-optical current sensor.

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In the subsequent simulation of the position offset of the sensor, the experimental platform is realized by moving the position of the magneto-optical current sensing unit to keep the distance between the two magneto-optical sensing units consistent. Figure 12 shows the relative position relationship between the sensor and the current conductor when simulating the position offset of the sensor, that is, a = 5.5 cm when the length l of the fixed support is 10 cm.

Fig. 12. Spatial position relationship between optical sensing part of sensor offset and conductor.

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In the cluster magneto-optical current sensor, the laser transmitter emits light with a wavelength of 850 nm. The light is input into the magneto-optical glass through the polarization maintaining fiber, and then output to the photoelectric converter through the polarization maintaining fiber. The photoelectric converter converts the optical signal into an electrical signal, and finally collects and processes the electrical signal. We set the acquisition frequency to 20kHz, write the data analysis program, and get the final light intensity signal through AC / DC separation, band-pass filter and oscilloscope. The light intensity output results of A-right magneto-optical current sensor in a certain period and the results after denoising and filtering are shown in Fig. 13 below.

Fig. 13. Light intensity measurement results of A-right sensor in a period.

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Adjust the photoelectric conversion output signal to current value at room temperature of 25 ℃, and the measured value of A-right after adjusting is shown in Fig. 14 below.

Fig. 14. Sensor measurement signal after adjusting.

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5.2 Experimental test and analysis

The RMS value of the three-phase current was set to 200 A, and a, b, and c were set to 5, 5, and 5 cm respectively by the method shown in Fig. 11 to simulate the situation that the sensor does not deviate. After denoising, filtering and setting conversion, the measured value signals of sensors in one cycle of power system is shown in Fig. 15.

Fig. 15. Sensor measurement signal.

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Substitute the above measurement signals into the program shown in Fig. 8 for iteration. The instantaneous values I_A’, I_B’ and I_C’ after iteration are shown in Fig. 16 below.

Fig. 16. Calculation results.

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The initial values of the iterative procedure are selected as follows. Because the position offset of the sensor is small, the initial values can be set as 5 cm. The initial values of current is the current measurement value of the previous data point, that is, the calculation result of a data point is used as the initial value of the next data point calculation. Through the repeated verification of the relevant data of the experimental platform of the clustered magneto-optical current sensor and its decoupling strategy, it is found that when the current is measured in Ampere, the iterative accuracy of the instantaneous value is within 0.001, and the final RMS(Root Mean Square, RMS) result can basically meet the requirements of 0.2 accuracy of the power system. The number of iterations is shown in the Fig. 17 below.

Fig. 17. Number of iterations.

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Most data points can reach the set accuracy within 3 iterations. Some data points may need 9 iterations. At the same time, in order to avoid too many iterations caused by non- convergence of a data point, this test limits the number of iterations to 10 at most. The calculation of the instantaneous value of a data point may be inaccurate, and because the final calculation is the RMS value, the data point will not have too much impact on the RMS value when the sampling frequency is large enough. Figure 18 shows the RMS values and relative errors of each phase current after continuous operation for multiple cycles.

Fig. 18. RMS value and relative error of three-phase current.

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It can be seen from Fig. 18 that the RMS value of current fluctuates around 200A. Since the final consideration is the RMS values of current, some data points that deviate far from the real value have little impact on the overall RMS value of current. After calculating the relative error of the RMS value of three-phase current and selecting its maximum value, it can be seen from the maximum relative error that the relative error can be controlled within 0.2%.

When the sensors shift its position, for example, as shown in Fig. 12, (a), (b) and c change to 5.5, 5.5 and 5.5 cm. If the position of the sensors is not corrected, that is, the current sensors position is still calculated with the original value of 5 cm, the coupling equations of measurement will be considered as overdetermined equations. At this time, the iterative algorithm is not used for calculation. The calculation results are shown in Fig. 19 below.

Fig. 19. Measurement result before the correction of sensor position.

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It can be seen from Fig. 19 that without correcting the position of the sensor, the RMS value of phase A and phase C current is significantly higher than 200A, and the current of phase B is significantly lower than 200A. The measured value of each phase current deviates greatly, and the current measurement accuracy is poor. In other words, the displacement of the position of the sensor will have a great impact on the current measurement value. Therefore, it is extremely necessary to correct the position of the sensor in time during the operation of the sensor.

After the decoupling strategy is used to correct the position of the transformer and calculate the current value, the instantaneous value, RMS value and relative error results of three-phase current are shown in the Fig. 20 below.

Fig. 20. Measurement results after the correction of sensor position.

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According to the analysis of Fig. 20, the value of three-phase current measured by the combined quantity measurement decoupling strategy of cluster magneto-optical current sensor is basically consistent with the real value, the RMS value is close to 200A, and the relative error is less than 0.2%, which meets the requirements of measurement accuracy of power system.

Comparing Fig. 19 and Fig. 20, it can be seen that the decoupling algorithm can correct the position deviation factor of the sensors. Before the correction of the position, the measured value of the three-phase current deviates greatly from the true value, and the measurement accuracy of some of the measured values decreases significantly; the relative error exceeds 0.2%, which cannot meet the measurement accuracy requirements of the power system. After the position of the sensor is corrected, the accuracy of the current measurement is greatly improved, and the relative error meets the measurement accuracy requirement of 0.2 level.

The above test results show that the clustered magneto-optical current sensor not only eliminates the phase-to-phase magnetic field interference, but also corrects the position offset of the sensing device. The results verify the effectiveness of the clustered magneto-optical current sensor and its decoupling strategy.

6. Conclusion

In this study, the reason for the magnetic field interference between the phases of a traditional magneto-optical current sensor was investigated, and a cluster magneto-optical current sensor was proposed. Based on a mathematical model of the magnetic field coupling between phases, the coupling equations of measurement were derived to describe the relationship between the measured values of the magneto-optical current sensor and the actual values of the three-phase current and the position of the sensor.

A measurement decoupling strategy was proposed based on a mathematical model of phase-to-phase coupling. By inputting the phase-to-phase distance d, as well as the structural parameters m and l of the optical sensing device and the current measurement value I_i’ (i = 1,2,3,4,5,6) of each magneto-optical current sensor, the phase-to-phase magnetic field interference is eliminated, the position offset of the mutual inductor was corrected, and the three-phase current measurement values I_A’, I_B’, and I_C’ were obtained.

Finally, an experimental platform of the cluster magneto-optical current sensor was established. By comparing the measured current value with the real value, and analyzing the relative error of each measured value, the ability of the cluster magneto-optical current sensor to resist the interference of the phase-to-phase magnetic field was verified.

Funding

National Natural Science Foundation of China (51277066).

Acknowledgments

Funding from the Natural National Science Foundation is gratefully acknowledged. We would also like to thank Editage (www.editage.cn) for English language editing.

Disclosures

The authors declare no conflicts of interest.

Data availability

No data were generated or analyzed in the presented research.

Supplemental document

See Supplement 1 for supporting content.

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Clustered magneto-optical current sensor to eliminate the interference of a phase-to-phase magnetic field

Abstract

1. Introduction

2. Principle of traditional magneto-optical current sensor and analysis of the interference between phases of the magnetic field

2.1 Sensing principle of traditional magneto-optical current sensor

2.2 Analysis of phase-to-phase magnetic field interference of traditional magneto-optical current sensor

3. Structure and mathematical model of clustered magneto-optical current sensors

3.1 Structure of clustered magneto-optical current sensors

3.2 Mathematical model of phase-to-phase magnetic field coupling

4. Decoupling strategy for measurement of clustered magneto-optical current sensors

5. Clustered magneto-optical current sensors and their measurement decoupling strategy verification

5.1 Construction of experimental platform

5.2 Experimental test and analysis

6. Conclusion

Funding

Acknowledgments

Disclosures

Data availability

Supplemental document

References

Supplementary Material (1)

Data availability

Cited By

Figures (20)

Equations (12)

Optics Continuum