Contents Introduction
Compared with traditional current transducers, the all-fiber optic current sensor (AFOCS) possesses the well-known advantages of small size, insensitivity to electromagnetic interference, wide dynamic range, high frequency bandwidth, safety, electrical isolation, and environmental protection [1]–[3]. To date, AFOCS has been widely applied in the electrolytic aluminum industry [4], ultra high voltage DC power system [5], lightning current measurement [6], and plasma current measurement [7], which are the high-current applications. Meanwhile, AFOCS has attracted significant attention from micro-current detection fields, such as ship leakage current [8], [9] and partial discharge measurement [10].
Unfortunately, the operation characteristics of fiber change with temperature, which will alter the polarization of light in the fiber and affect the measurement accuracy of AFOCS. The influence of temperature on AFOCS is mainly divided into three categories. The first is the Verdet constant of sensing fiber. Xu points out that the Faraday effect (the Verdet constant) varies by 0.7% from -40°C to 60 °C [11]. The second is linear birefringence. The linear birefringence in optical fibers changes with temperature by 0.1%/°C [12]. The last is the phase delay of the quarter-wave plate (QWP). The scale factor of AFOCS varies about 4.5% from −40 °C to 60 °C [13]. Therefore, temperature compensation must be carried out to satisfy the required accuracy for DL/T 1789 class 0.2S [14].
The temperature compensation methods can be classified into four categories, i.e., the heat insulation cavity structure, the adaptive temperature compensation scheme, device temperature stability, and the data processing methods. The heat insulation cavity structure can maintain the sensing head within a constant temperature range [15]. However, the external and internal temperatures will be consistent via the heat exchange. This structure is suitable for areas with temperature that vary dramatically but not ideal for areas with temperature changes slowly. Optical devices realize the adaptive temperature compensation scheme with opposite temperature coefficient symbols. The optical devices are extra [16] or parts of AFOCS [17], [18]. However, the accuracy of optical devices is so high that it is difficult to achieve. Improving the optical device temperature stability [19], [20] or the sensing fiber wrapping method [21] is viable. However, the cost and the accuracy are the major obstacles. Compared with these temperature compensation schemes, the real-time temperature compensation method by data processing [5] is more attractive. This method does not alter the optical devices and serves the purpose of temperature compensation. However, there also are some drawbacks. Firstly, the temperature sensing and electric current sensing units share the same superluminescent diode (SLD) light source and signal processing module [5]. However, the other optical devices are independent, which is harmful for integration. The second is the temperature coefficient being very small (about negative 10-3 magnitude [22]). The temperature is obtained by intensity demodulation, which can be submerged in the noise. In this work, we propose and demonstrate a method to measure the temperature and the electric current simultaneously. The electric current and temperature sensing systems share the same light source, transmission fiber line, photodetector (PD), and data processing system, which can improve system integration. The only difference is the sensing units. The temperature coefficient of the Faraday rotation mirror (FRM) is much more significant. The relative error decreases from 14% to 2% by temperature compensation with the data processing method.
The remainder of this paper is organized as follows. Section II describes the principle of operation. The dual-modulation AFOCS and dual-parameter measurement of temperature and current are introduced in this part; In Section III, we model and simulate to explore the influence of modulation parameters on temperature compensation. The experiments are designed to verify the correctness of the theory in Section IV. The experimental results and discussions are also in this section. The last section is the conclusion.
Operating Principle
A. The Principle of Dual-Modulation AFOCS
The acousto-optic modulator (AOM) and electro-optical modulator (EOM) are applied to realize the AFOCS based on the reflected interferometer current sensor, which is called dual-modulation AFOCS [23]. The schematic diagram of AFOCS with dual-modulation is shown in Fig. 1.
The black dotted line, orange line, and solid black line represent the single-mode optical fiber (SMF), the polarization-maintaining fiber (PMF), and the spun highly birefringent fiber, respectively. SMF realizes energy transmission, and PMF can reduce the influence of environmental factors on the polarization state. The spun highly birefringent fiber is applied as the sensing fiber, as shown in Fig. 1. The principle of operation is based on the Faraday effect. AOM is applied to modulate the continuous light of SLD to pulsed light. The initial phase and working frequency of pulsed light are adjustable. The amplitude of pulsed light is the same as continuous light. The pulsed light is linearly polarized after passing through the circulator and the polarizer. The polarized light will convert into two linearly polarized light beams via a 45° splice between the polarizer and PMF. These orthogonal polarization modes convert into left-handed and right-handed circularly polarized waves by QWP. The phase velocities of the two circularly polarized light beams are different, and the difference is proportional to the magnetic field generated by the electric current to be measured. The Faraday rotation angle is applied to represent the rotation angle of the polarization plane. The Faraday rotation angle is doubled when the circularly polarized light beams reflect off the mirror at the end of the sensing fiber and retrace their way through the sensing fiber. The circularly polarized lights are returned to be linearly polarized when they pass through QWP on the return trip. Finally, the two waves are brought back together and interfered at the 45° splice and common input/output polarizer [24]. The light intensity with electric current information is sent to PD through the circulator and processed by the data processing system. EOM is used to modulate the phase and improve the sensitivity of AFOCS. The modulation frequency of EOM is related to the optical path length, which is adjusted by PMF and sensing fiber [25].
The light intensity signal received by PD is given by [23]
\begin{equation*}
{P_{\text{cout}}}(t) = {k_c}{P_{in}} \cdot \frac{{1 + \cos [4\theta - \Delta {\varphi _{\mathrm{C}}}(t)]}}{2} \cdot \frac{{1 + f(t)}}{2} \tag{1}
\end{equation*}
Where \begin{equation*}
f(t) = \left\{ \begin{array}{l} 1\begin{array}{ccc} {}&{}&{n{t_d} + t \leq {t_0} + n{t_d}} \end{array}\\ - 1\begin{array}{ccc} {}&{}&{{t_0} + n{t_d} \leq n{t_d} + t \leq (n + 1){t_d}} \end{array} \end{array} \right. \tag{2}
\end{equation*}
Here,
B. The Principle of Temperature Sensing
FRM is composed of a Faraday rotator and a mirror [27]. The adjustment of the state of polarization (SOP) is shown in Fig. 2.
A permanent magnet provides a constant magnetic field for the Faraday rotator. When the propagation direction of the light is consistent with the magnetic induction intensity, the SOP of the light wave will be rotated with an angle of π/4 rad due to the Faraday effect, as shown in Fig. 2(a) and (b). Then the mirror will reflect the light wave on the far end, and the Faraday rotator will rotate the polarization state with another angle of π/4 rad in the same direction for the non-reciprocity of Faraday effect, as shown in Fig. 2(c) and (d). Therefore, the polarization direction of the beam will rotate π/2 rad when FRM is perfect.
The constant magnetic field of FRM is mainly provided by rubidium iron boron materials, which are sensitive to temperature. Therefore, the SOP is affected by temperature. The rotation angle of SOP due to the Faraday rotator is given by
\begin{equation*}
{\theta _T} = \frac{\pi }{4}(1 + a{}_T\Delta T) \tag{3}
\end{equation*}
Where
The schematic of the temperature sensing optical system is shown in Fig. 3.
The temperature sensing probe is FRM in Fig. 3. The continuous light of SLD is modulated to pulsed light by AOM. The frequency is adjustable, and the amplitude is the same as the continuous light. After passing through the circulator, the pulsed light is sent to the polarizer, and then it will change into linearly polarized light. The polarized light will convert into two linearly polarized light beams when the optic axis of the polarizer and EOM is aligned with a 45˚ offset. The propagation directions are along the fast and slow axes of the polarization-maintaining fiber (PMF), respectively. The state of polarization will change with temperature when FRM reflects them. The polarized beams are brought back together and interfered at the fusion point where the optic axis of EOM and the polarizer is aligned with a 45˚ offset. EOM is used to modulate the phase and improve the sensitivity. The light intensity received by PD is given by
\begin{equation*}
{P_{\text{Tout}}}(t) = {k_T}{P_{in}}\frac{{1 + \cos [4{\theta _T} - \Delta {\varphi _{\mathrm{T}}}(t)]}}{2}\frac{{1 + f(t)}}{2} \tag{4}
\end{equation*}
Where
C. The Principle of Dual-Parameter Measurement
The optical devices are the same except the fiber sensing units, according to Fig. 3 and Fig. 1. Therefore, the temperature and electric current sensing units are connected with a polarization-maintaining fiber coupler, and the temperature and electric current will be distinguished by the time they return to PD. The schematic diagram of the dual-parameter fiber optical sensor is shown in Fig. 4.
The position of FRM and electric current sensing fiber will be illustrated in part C, Section IV. The simulation parameters are as follows. The coupling ratio of the coupler is 50:50, the proportional coefficients, i.e.,
Time domain-waveform simulation. (a): Time-domain simulation of temperature and current; (b): Time-domain simulation of electric-current; (c): Time-domain simulation of temperature.
The modulation signals of AOM I and AOM II are the periodic gate signals, which can be seen as switch signals with different initial phases. When the signal of AOM II is “on” all the same, the pulsed light arrives at PD by order because the optical path is different, as shown in Fig. 5(a). The pulsed light with electric current information will reach PD later because the electric current sensing fiber is much longer than the coupler's pigtail. The gate signal of AOM II is used to select the sensing signal by controlling the switch signal's “on/ off”. The time when temperature and electric current sensing signals reach PD is different, so we can control the delay time between AOM I and AOM II to get the sensing signal that we select to demodulate, as shown in Fig. 5(b) and (c).
Modeling and Simulation Analysis
A. Data Demodulation
The temperature and electric current sensing system share the same data processing system. The optical power of the signal received by the photodetector is the sum of the harmonics of the modulation frequency of EOM if the light source is a continuous light source, as described in previous works [28]. The square wave signals can be expanded into the Fourier series, which is the sum of the harmonics of the modulation frequency of AOM. The relevant demodulation method is applied for demodulation to improve the ability of data processing, and the frequency relationship between the AOM and EOM has been described in detail in previous works [23]. The output of relevant demodulation is given by [23]
\begin{equation*}
R = - \frac{{kRD \cdot {P_{in}} \cdot {J_1}(\delta) \cdot \text{sin}\theta }}{2} \tag{5}
\end{equation*}
Where
B. The Effect of Temperature on Electric Current Sensing
The Verdet constant, QWP, and the linear birefringence of the sensing fiber are related to temperature. The effect of temperature on electric current sensing can be regarded as a polynomial function, and we use second-order polynomials for the sake of simplicity. The relationship between the Faraday rotation angle and the temperature fluctuation is given by
\begin{equation*}
\theta (T) = \theta ({T_0}) + a\Delta {T^2} + b\Delta T + c \tag{6}
\end{equation*}
Where
C. Relationship Between the Length of PMF and Sensing Fiber
The relationship between the eigenfrequency and fiber total length of dual-parameter fiber optical sensor is given by
\begin{equation*}
{f_s} = c/(2{n_0}L) \tag{7}
\end{equation*}
Where \begin{align*}
\Delta \varphi (t) & = \varphi (t){\rm{ - }}\varphi (t{\rm{ + }}\tau) \\
&= - 2A\sin \left({\frac{{\pi f}}{{{f_s}}}} \right) \cdot \cos \left[ {2\pi f\left(t + \frac{1}{{2{f_s}}}\right)} \right] \tag{8}
\end{align*}
Equation (5) will convert into
\begin{equation*}
R = - \frac{{kRD \cdot {P_{in}} \cdot {J_1}(\delta ^{\prime}) \cdot \text{sin}\theta }}{2} \tag{9}
\end{equation*}
Where
We define the normalized scale factor \begin{equation*}
\chi = \frac{{{J_1}(\delta ^{\prime})}}{{max[{J_1}(\delta ^{\prime})]}} \tag{10}
\end{equation*}
We get the maximum for the 1st-order Bessel function of the first kind when
The normalized scale factor will get the maximum when the frequency ratio is an odd multiple of 1/2 and the minimum when the frequency ratio is an even multiple of 1/2, as shown in Fig. 6.
The normalized scale factor of temperature and electric current sensing system get the maximum at the same time when the eigenfrequency and the modulation frequency can meet the relationship
\begin{equation*}
\left\{ \begin{array}{l} {f_T} = \frac{{2f}}{{2{n_1} + 1}}\\
{f_C} = \frac{{2f}}{{2{n_1} + 2{n_2} + 1}} \end{array} \right. \tag{11}
\end{equation*}
Where
According to (7) and (11), the relationship between the length of PMF and electric current sensing fiber can be given by
\begin{equation*}
\frac{{{L_{SF}}}}{{{L_{PMF}}}} = \frac{{2{n_2}}}{{2{n_1} + 1}} \tag{12}
\end{equation*}
Where
Experimental Results and Discussions
A. Modulation Frequency Test Experiment and Discussion
1) Experimental Device and Main Parameters
The relationship between the frequency ratio and normalized scale factor is verified before the temperature and electric current measurement experiment because we must determine the fiber length firstly. We used the electric current measurement results to demonstrate the relationship between the frequency ratio and the normalized scale factor. AOM I and AOM II both adopted the continuous optical working mode, which could be regarded as the fixed loss of the optical path. The dual-modulation AFOCS was equivalent to the reflective interference current sensor. The experimental setup is shown in Fig. 7.
The models and main parameters of optical devices were shown in Table I.
2) Experimental Results and Discussion
The sensing fiber and PFM were 500 m and 200 m, respectively. The eigenfrequency was 151.975 kHz, according to (7). The lock-in amplifier worked at the external modulation mode, and the signal generator provided the modulation signal. The signal generator worked at the sweep mode. The initial frequency was 6 kHz, the termination frequency was 300 kHz, and the frequency step was 2 kHz. The lock-in amplifier was applied for demodulation. The screenshot of the lock-in amplifier is shown in Fig. 8.
The frequency ratio affected the normalized scale factor, as shown in Fig. 8. The normalized scale factor got the maximum when the frequency ratio was an odd multiple of 1/2 and the minimum when the frequency ratio was an even multiple of 1/2, as analyzed in Part C, Section III. Therefore, the length of PMF and the electric current sensing fiber must be optimal to get the maximum normalized scale factor.
B. Temperature Compensation of Electric Current Sensing
The electric current sensing fiber is the spun highly birefringent fibers, which is fabricated by spinning the fiber perform during the drawing process. The manufacturing process is more complex, and the cost is higher than PMF. Therefore, the length of PMF was adjusted to meet (11). The length of PMF was adjusted to 250 m to satisfy (12) with the polarization-maintaining optical fiber fusion machine.
1) Experimental Device
The experimental setup was adjusted based on Fig. 7, as shown in Fig. 9.
Based on the experimental device in Table I, the models and main parameters of newly introduced optical devices were shown in Table II.
The desktop lock-in amplifier was replaced by modularization for the volume. The coupler was the polarization-maintaining fiber coupler.
2) Experimental Results and Discussion
The temperature of the vacuum high- and low-temperature test box was set from 5 °C to 65 °C, and the temperature step interval was 2 °C. When the temperature reached the setting temperature, kept the temperature for 3 minutes before data acquisition to ensure FRM and the sensing head heated evenly. The data acquisition time was 1 min, and the mean value was used as the measurement result to eliminate the influence of random noise. An external current was provided by the DC power supply, which was constant all over the experimental process.
The relationship between the output of the lock-in amplifier and the temperature is shown in Fig. 10.
The sinusoidal function was applied for data fitting. The fitting function was given by
\begin{equation*}
f(T) = a\sin [b(T - 25) + c] + d \tag{13}
\end{equation*}
Where
The output of the lock-in amplifier was collected at different temperatures with the same electric current (1A). After eliminating the zero bias, the observed values and fitted values are shown in Fig. 11.
The relationship between the temperature and the output of electric current sensing (1A).
The room temperature (25 °C) was set as the reference temperature, and polynomial was used for data fitting. The fitting function was given by
\begin{equation*}
y(T) = {p_1}{(T - 25)^2} + {p_2}(T - 25) + {p_3} \tag{14}
\end{equation*}
Where
The relationship between the temperature and electric current was determined by (13) and (14). When the measured current was 2A, we experimented again under the same experimental conditions. The relationship between the output result of the lock-in amplifier and temperature is shown in Fig. 12.
The relationship between the temperature and the output of electric current sensing (2A).
The green dotted line denoted the temperature compensation result using the fitting function described in (14). The dot data represented the observed values when the electric current equaled 2A at different temperatures; The solid red line was the fitted values with a polynomial, and the fitting function was given by
\begin{equation*}
y^{\prime}(T) = {p^{\prime}_1}{(T - 25)^2} + {p^{\prime}_2}(T - 25) + {p^{\prime}_3} \tag{15}
\end{equation*}
Where \begin{equation*}
\eta \, {\rm{ = }} \, \left| {\frac{{y^{\prime}(25) + Y(T) - y^{\prime}(T)}}{{y^{\prime}(25)}}} \right| \tag{16}
\end{equation*}
Where
The relative error fluctuated greatly with the temperature when the temperature compensation was not carried out, as shown in Fig. 13 with a blue circle dotted line. The maximum value declined from 14% to 2% by temperature compensation, as shown in Fig. 13 with a red-point dotted line.
C. Discussion About the Temperature Sensing Unit
1) Installation Position of FRM
The precondition of the Faraday effect is that a light beam traveling in a transparent medium and an external magnetic field is aligned with the light wave propagation vector. Therefore, we should install the FRM in the position where the external magnetic field generated by the electric current is perpendicular to the beam reflected by the FRM. The electric current will have no business on temperature sensing. The installation is shown in Fig. 14
The reflection mirror and the QWP are adjacent to meet the Ampere circuit theorem. FRM is close to QWP to sensing the temperature fluctuation. The extension line of PMF and FRM passes through the center of the electric current sensing ring, as shown in Fig. 14
2) Influence of Electric Current on FRM
The electric current is enormous, especially when the electric current is the impulse current, the magnetic induction intensity generated by the electric current will affect FRM. When the magnetic induction intensity generated by the electric current is far less than the change of permanent magnet magnetic induction intensity by temperature (less than 1%), the influence magnetic field generated by the electric current can be ignored. The temperature coefficient of FRM is 0.1201 rad/°C. The maximum electric current to be measured is 1092.82 A by calculation.
3) The Operating Range of FRM
The magnetic induction intensity of permanent magnet materials is affected by temperature, and there is a demagnetization phenomenon when the temperature reaches Curie temperature. The Curie temperature usually is higher than 300°C [29], which is higher than the normal temperature range of AFOCS. Therefore, the temperature sensing by FRM can be applied for AFOCS temperature compensation all over the operating temperature range. However, the optimal operating temperature range is 14 °C - 40 °C when the output of the lock-in amplifier is linear with the temperature, as shown in Fig. 10. If the temperature exceeds this range, the temperature sensing system needs to be calibrated before operation.
4) Optical Path Loss
The energy of the optical path is attenuated by 3dB based on the original power when we introduce the coupler (coupling ratio 50:50), which will have an adverse impact on the signal-to-noise ratio [30]. The influence of the coupler on the signal-to-noise ratio can be compensated by increasing the input optical power.
Conclusion
We have demonstrated a dual-modulation all-fiber optic current sensor with temperature compensation by FRM. Both theoretical analysis and experimental results indicate that the proposed method is effective. The temperature and electric current sensing units share the same optical devices except for the sensing units, which can meet integration requirements. The relative error of AFOCS declines from 14% to 2% when the temperature compensation is applied. This sensor can be used to ship leakage current, partial discharge measurement, and other micro-current measurement fields.
ACKNOWLEDGMENT
The authors would like to thank anyone for his constructive advice.