|
High resolution and large measurement range voltage sensing based on an optoelectronic oscillator utilizing an unbalanced Mach–Zehnder interferometer
|
1. Introduction .
Voltage is one of the essential parameters for the electrical power system that must be monitored to keep the electrical power facilities working reliably, safely, and efficiently. Currently, researchers attach great importance to voltage monitoring methods with optical elements or electro-optical materials. They have good electromagnetic shielding capability, large bandwidth, light weight, and small size. Generally, the optical voltage sensors based on Pockels effect using electro-optic crystals including lithium niobate or lithium titanate [ 1 ] have been researched extensively. However, the properties of electro-optic crystals, especially its birefringence, are susceptible to mechanical and optical instability due to vibration and temperature variation [ 2 , 3 ], which need to be compensated using complicated methods including films-coating on the z-faces of LiNbO 3 crystal [ 1 ] and annealing process on the crystal [ 4 ]. Besides, for the high electric field measurement, the Pockels effect-based methods are usually composed of discrete optical components such as polarizer (Pol), lenses, and polarizing filters, which make the system unstable and costly.
Another approach for optical voltage measurement is based on the piezoelectric ceramic (PZT) in conjunction with the optical fiber elements such as fiber Bragg grating (FBG). The change of the voltage will cause the deformation of the piezoelectric materials, leading to the deformation of the FBG bonded on the PZT. Therefore, the electric field/voltage can be measured by observing the wavelength shift of the FBG using an optical spectrum analyzer (OSA). Y.Yao et al . [ 5 ] fixed the FBG on the surface of the PZT-5 to measure the DC voltage and Ribeiro et al . [ 6 ] proposed a double-layered aluminum structure to accommodate the piezoelectric ceramic multilayer stack (PZT-Stack) with FBG to measure the DC voltage. Both of them used an OSA for voltage demodulation. However, due to the low resolution and slow interrogation speed of OSA, this kind of demodulation method has the problems with low resolution and slow interrogation speed. The demodulation method using Bragg meter [ 7 ] can improve the modulation resolution, but the response speed is still too slow. In order to achieve the high-speed demodulation, several demodulation techniques for PZT-based optical voltage schemes using Fabry-Perot tunable filter [ 8 , 9 ], the edge filter [ 10 , 11 ] or twin-grating configurations [ 12 , 13 ] are proposed, which can increase the interrogation speed with the limited sensing resolution.
With the development of microwave photonic technology [ 14 ], the sensing and measurement schemes using optoelectronic oscillator (OEO) technique have been intensely studied in recent years. The principle of the OEO-based sensing is to establish the relationship between the quantities to be measured and the oscillating frequency of microwave signal generated by OEO, which can be directly detected by an electrical spectrum analyzer (ESA) or a digital signal processor (DSP). In this case, the measurand can be mapped to the oscillating frequency in the microwave domain instead of the wavelength in the optical domain, thus the interrogation speed and resolution of sensing scheme are significantly increased. Recently, various OEO-based sensing schemes with high-performance have been proposed for different including temperature [ 15 ], strain [ 16 ], refractive index [ 17 ], angular velocity [ 18 ] and magnetic field [ 19 ]. For voltage measurement, a voltage sensor based on OEO with Equivalent Phase-Shifted Fiber Bragg (EPS-FBG) and PZT-Stack [ 20 ] has been proposed, which has a high sensitivity of 0.55?GHz/V with a very small range of 0-15?V. The main limitation of this voltage sensor is that the microwave frequency is directly determined by the wavelength spacing between the wavelength of the tunable laser source and the notch of the EPS-FBG. In this method, the wavelength drift of the laser used in the scheme may affect the stability of the system. In addition, a small change in voltage will lead to a large drift of the microwave frequency, making it impossible to accomplish large-range voltage measurements due to the frequency measurement limitation of ESA. Therefore, the voltage sensing with high performance as well as the large sensing range are strongly desired.
In this paper, we propose a voltage sensor with high resolution and large voltage sensing range based on the OEO combined with a Mach–Zehnder interferometer (MZI). In the OEO loop, the broadband optical source (BOS), the unbalanced MZI, the dispersion compensating fiber (DCF) and the photodetector (PD) jointly act as a finite impulse response (FIR)-microwave photonic filter (MPF) to select the oscillating frequency of the OEO. The center frequency of the FIR-MPF, which is consistent with the oscillation frequency of OEO, is related to the free spectrum range (FSR) of the MZI. The MZI consists of two 1 ${\times} $ 2 optical couplers (OC) and two unbalanced arms. An infinite impulse response (IIR)-MPF composed of an OC and a section of single mode fiber (SMF) is embedded into the OEO to ensure the single mode of the microwave signal. The relationship between the voltage variations and the oscillation frequency shift of OEO has been investigated in this paper. By monitoring the change of the oscillating frequency in the microwave domain, the voltage sensing can be achieved. With the repeated experiments, a total range of 1700V voltage measurement from – 200?V to 1500?V is accomplished, with the voltage sensitivity of 0.25?GHz/100?V and the resolution of 0.3?V. In the temperature experiments, adjusting the proportion of SMF length between the two branches of the MZI reduces voltage error caused by temperature changes from 108?V/°C to a drift of 0.55?V over a temperature range of 10°C.
2. Principle of the proposed sensor .
A schematic diagram of the proposed voltage sensing system is illustrated in Fig.? 1 . The sinusoidal broadband optical signal emitted from a BOS is polarized by a polarizer and then coupled into an MZI consisting of two 3-dB 1?×?2 couplers and two unbalanced arms. In the lower arm, a cylindrical PZT wrapped by optical fibers serves as the voltage sensing head, which will generate radial deformation under the voltage applied due to the inverse piezoelectric effect of PZT. The red dashed inset of Fig.? 1 shows the real wrapped cylindrical PZT used in the experiment. In addition, the lower arm has a polarization controller (PC) and a phase modulator (PM). The upper arm of MZI consists of a PC, a variable time delay line (VTDL), and a section of optical fiber. After transmission through the MZI, the optical signal is sent to the DCF acted as an optical dispersion element and amplified by an erbium-doped fiber amplifier (EDFA). Then, the signal is coupled into a fiber ring resonator and sent to a PD to perform optical-electrical conversion. Finally, the microwave signal is divided into two paths by a power divider, one path is amplified by an electrical amplifier (EA) and fed back to the PM to form the OEO, and the other path is sent to an ESA to monitor the microwave signal. Here, the BOS, MZI, DCF and PD jointly form the FIR-MPF which is free from the carrier suppression effect (CSE) to select the oscillating frequency of the OEO.
? Fig. 1. The schematic of the voltage sensor based on OEO using an unbalanced Mach–Zehnder interferometer. Inset: Zoomed-in physical image of the sensing head.
Download Full Size PDF
In the following, the operation of the OEO is discussed. Fig.? 2 (a) and (b) illustrate the propagation state of light waves passing through the MZI and DCF for one optical signal frequency. Suppose that the frequency domain expression for the electric field at the output of the Pol is E (Ω). Then, the light wave is divided into two branches after passing through OC1. When light waves enter the lower arm, the phase-modulated signal is generated at the output of PM. Assume that the PM works under small signal modulation conditions, the higher-order harmonic terms are ignored. The electrical field of the lower arm can be written as
(1) $${E_{down}}(\Omega ) \propto {J_0}(\gamma )E(\Omega ) + j{J_1}(\gamma )E(\Omega + {\omega _e}) - j{J_1}(\gamma )E(\Omega - {\omega _e})$$
where γ ?=? πV e / V π is the modulation index, V π is the half-wave voltage of the PM, J (·) denotes the n th-order Bessel function of the first kind. V e and $\omega $ e are the amplitude and angular frequency of the RF signal. ? Fig. 2. The principle of the operation of the MPF. Orange lines: the optical signal after phase modulating. Green lines: the optical signal delayed by VTDL. (a) The example of the spectrum evolution for one frequency after MZI. (b) The example of the spectrum evolution for one frequency after DCF. (c) The frequency response of the FIR-MPF and IIR-MPF. (d)?The response frequency of final MPF.
Download Full Size PDF
In the upper arm of the MZI, a section of SMF is used to roughly balance the length of the two branches of the MZI to ensure that the optical path difference of the MZI is within the interference range. The VTDL is used to adjust the fine differences between the two branches and the original FSR of the MZI. The electrical field delayed by VTDL can be written as
(2) $${E_{up}}(\Omega ) \propto E(\Omega )\exp ( - j\Omega \Delta \tau )$$
where $\Delta \tau $ is the light travelling time difference between the upper and lower branches determined by the initial arm length difference and the VTDL. Then, the light waves in the two branches combine via OC2, as shown in Fig.? 2 (a). Moreover, two PCs are embedded in the two arms, which can make the polarization in the both arms identical for the interference. After the OC2, the electrical field can be expressed as (3) $${E_c}(\Omega ) = {E_{down}}(\Omega ) + {E_{up}}(\Omega )$$
Subsequently, the light waves are sent to a DCF, which will introduce an optical-frequency-dependent time delay illustrated in Fig.? 2 (b). Assuming that all losses of this dispersion medium are omitted, the transfer function of the DCF can be expressed as
(4) $$\Phi (\Omega ) = \exp [{{ - j\beta {{(\Omega - {\Omega _0})}^2}} / 2}]$$
where $\beta $ is the total dispersion at Ω 0 , and Ω 0 is the central frequency of the optical spectral. After the DCF, the signal can be expressed as E out (Ω)?=? E c (Ω)Φ(Ω). Finally, the PD converts the optical signal to an electrical signal, and the electrical signal at the output of the PD can be expressed as (5) $$\begin{aligned} I(\omega ) &= \frac{\Re }{{2\pi }}\left\langle {\int {{E_{out}}(\Omega )E_{out}^ \ast } (\Omega - \omega )d\Omega } \right\rangle \\ &= \frac{\Re }{{2\pi }}\int {\left\langle {{E_c}(\Omega )E_c^ \ast (\Omega - \omega )} \right\rangle } \Phi (\Omega )\Phi _{}^ \ast (\Omega - \omega )d\Omega \end{aligned}$$
where $\mathrm{\Re }$ is the responsivity of the PD. Considering the frequency-domain representation of the input RF signal is πV e [ δ ( ω - ω e )?+? δ ( ω+ω e )], then the MPF’s transfer function can be written as [ 21 ]
(6) $$H(\omega ) = \frac{{I(\omega )}}{{\pi {V_e}[\delta (\omega - {\omega _e}) + \delta (\omega + {\omega _e})]}} = {H_0}(\omega ) + {H_1}(\omega )$$
(7) $$\begin{aligned} {H_0}(\omega ) &= \frac{{2\Re {J_0}(\gamma ){J_1}(\gamma )}}{{\pi {V_e}}}\exp ( - j\omega {\tau _0})\sin (\frac{{\beta {\omega ^2}}}{2}){H_b}(\omega )\\ {H_1}(\omega ) &= \frac{{\Re {J_1}(\gamma )}}{{\pi {V_e}}}\exp (\frac{{j\pi }}{2} - \omega {\tau _0} - \frac{{\beta {\omega ^2}}}{2} + \Delta \tau {\Omega _0}){H_b}(\omega - \frac{{\Delta \tau }}{\beta })\\ &\quad + \frac{{\Re {J_1}(\gamma )}}{{\pi {V_e}}}\exp (\frac{{ - j\pi }}{2} - \omega {\tau _0} + \frac{{\beta {\omega ^2}}}{2} - \Delta \tau {\Omega _0}){H_b}(\omega + \frac{{\Delta \tau }}{\beta }) \end{aligned}$$
where H b ( ω )=∫ N (Ω)exp [ $- $ jωβ (Ω-Ω 0 )]dΩ indicates the baseband response. N (Ω) is the power spectral density. Thus, according to Eq.?( 7 ), H 0 ( ω ) is eliminated by the CSE, and the MPF only have one passband H 1 ( ω ) whose amplitude response can be considered as the center frequency of ω?=? Δ τ / β , as shown in lower one of Fig.? 2 (c). By adjusting the time delay introduced by the cylindrical PZT or VTDL, the center frequency of each passband can be independently tuned. There, the central frequency of the single passband MPF can be written as (8) $${f_0} = \frac{{\Delta \tau }}{{2\pi \beta }} = \frac{{n\Delta {L_0}}}{{2\pi c{L_{DCF}}\beta }} = \frac{1}{{D \cdot {L_{DCF}} \cdot \Delta \lambda _{FSR}^0}}$$
where D is the total dispersion. β and D have the relationship of D? =? $- $ 2 πcβ / λ 2 , c is the light speed in vacuum, and L DCF is the fiber length of the DCF. Δ $\lambda _{FSR}^0\; $ = λ 2 / n Δ L 0 is the original FSR of the MZI without the influence of the voltage and temperature variations, where $\lambda $ is the wavelength of the incident light, n is the effective refractive index of the fiber, and Δ L 0 is the original length difference between the two arms of the MZI. Obviously, the center frequency of the FIR-MPF is determined by the FSR of the MZI and the chromatic dispersion of the DCF. To ensure single frequency operation of the OEO and enhance the measurement accuracy, the fiber ring composed of a 2?×?2 90:10 optical coupler and a length of optical fiber is cascaded with FIR-MPF. The fiber ring introduces an additional IIR-MPF with a periodic response and narrow bandwidth characteristics for each peak, as shown in upper one of Fig.? 2 (c). The FSR of IIR-MPF is determined by the length of fiber ring, which can be expressed as
(9) $$FS{R_{IIR}} = \frac{c}{{n \cdot {L_{IIR}}}}$$
where L IIR is the length of the fiber ring. Thus, the oscillation frequency generated by OEO is determined not only by the FIR-MPF, but also by the IIR-MPF with narrow bandwidth formed by the fiber ring. The final MPF is displayed in Fig.? 2 (d). As illustrated in Fig.? 1 , the purple dashed box represents the sensing probe of the system. The upper arm of the sensing probe is a section of optical fiber (fiber length: L 3 ) without any special processing, and the lower arm consists of a section of fiber wrapped around a cylindrical PZT (fiber length: L 1 ) and an untreated fiber at each end (fiber length: L 2 ), as shown in Fig.? 3 (a). Because of the inverse piezoelectric effect associated with the PZT, the deformation of the PZT will produce radial extension when the voltage is applied to the two electrodes of the inner and outer diameters that are self-contained on the PZT, so that only the fibers wrapped around the PZT will be affected by the voltage. In addition, all fibers in the upper and lower arms will be affected by temperature and have different temperature coefficients. Therefore, when the voltage or temperature changes, the change in the effective refractive index and length of each fiber region can be expressed as:
(10) $$\begin{array}{l} \left\{ {\begin{array}{{c}} {{n_1} = {n_2} = n{}_3 = n}\\ {\Delta {n_1} = n \cdot \xi \cdot \Delta T - n \cdot {\rho_e}[K\Delta U + ({\alpha_P} - {\alpha_F})\Delta T]}\\ {\Delta {n_2} = \Delta n_3^{} = n \cdot \xi \cdot \Delta T} \end{array}} \right.\\ \left\{ {\begin{array}{{c}} {\Delta {L_1} = [{\alpha_F} + ({\alpha_P} - {\alpha_F})]\Delta T \cdot {L_1} + K\Delta U \cdot {L_1}}\\ {\Delta {L_2} = {\alpha_F} \cdot \Delta T \cdot {L_2}}\\ {\Delta {L_2} = {\alpha_F} \cdot \Delta T \cdot {L_3}} \end{array}} \right. \end{array}$$
where Δ U is the driving voltage applied to the PZT, Δ T is the variation of the temperature, K is a constant associated to the PZT performance, ρ e (≈ 0.22) is the effective elastic-optic coefficient of the fiber, ξ (≈ 7 ${\times} 10$ -6 °C) is the thermo-optic coefficients, α F (≈ 0.5 ${\times} 10$ -6 °C) and α P are the thermal expansion coefficients of the fiber and cylindrical PZT, Δ n i and Δ L i are the refractive index and length changes of each part of the fiber, respectively. Therefore, the varied FSR of the MZI induced by temperature and voltage can be written as (11) $$\Delta {\lambda _{FSR}} = \frac{{{\lambda ^2}}}{{{n\Delta {L_0} + (\Delta {n_1}{L_1} + n\Delta {L_1} + \Delta {n_2}{L_2} + n\Delta {L_2}) - (\Delta {n_3}{L_3} + n\Delta {L_3})} }}$$
? Fig. 3. (a) Schematic diagram of the different regions of the fiber of MZI. (b) Zoom-in view of the cylindrical PZT.
Download Full Size PDF
If only the influence of temperature on the proposed sensor is considered, Eq.?( 11 ) can be rewritten as
(12) $$\Delta {\lambda _{FSR}} = \frac{{{\lambda ^2}}}{{{n\Delta {L_0} + \{ (\xi + {\alpha_F})({L_2} - {L_3}) + [\xi + {\alpha_P} - {\rho_e}({\alpha_P} - {\alpha_F})] \cdot {L_1}\} \cdot n \cdot \Delta T} }}$$
It can be seen that once the length of the fiber wound on the cylindrical PZT is fixed, theoretically, the temperature insensitivity of the proposed sensor can be achieved by selecting appropriate values of L 2 and L 3 to make the coefficient term of Δ T in the denominator equal to zero. In this case, when the temperature varies, the FSR of the MZI can keep constant. Therefore, the influence of temperature on the proposed sensor can be ignored by selecting appropriate values of L 2 and L 3 .
Then, the frequency shift of the microwave signal generated by OEO due to voltage change is analyzed in detail as follows. The varied FSR of the MZI induced by voltage can be written as
(13) $$\Delta \lambda _{FSR}^1 = \frac{{{\lambda ^2}}}{{n\Delta {L_0} + \Delta n{L_1} + n\Delta {L_1}}} = \frac{{{\lambda ^2}}}{{n\Delta {L_0} + (1 - {\rho _e}) \cdot n \cdot {L_1} \cdot K \cdot \Delta U}}$$
Thus, the frequency shift of the microwave signal generated by OEO induced by voltage can be derived as
(14) $$\Delta f = \left{\frac{1}{{D \cdot {L_{DCF}}\Delta \lambda_{FSR}^1}} - \frac{1}{{D \cdot {L_{DCF}}\Delta \lambda_{FSR}^0}}} \right= \frac{1}{{D \cdot {L_{DCF}}{\lambda ^2}}}(1 - {\rho _e})K \cdot \Delta U \cdot n \cdot {L_1}$$
According to Eq.?( 14 ), the mapping relationship between voltage and microwave frequency has been established. If K is a constant, the shift of the microwave frequency is linearly proportional to the change of the voltage. Therefore, the voltage variation can be measured by simply monitoring the oscillation frequency shift. Meanwhile, according to Eq.?( 12 ), the effect of temperature on frequency variation can be eliminated theoretically by adjusting the SMF length of the two arms exposed to the temperature variation.
3. Experiment setup and results .
An experiment is carried out according to the setup presented in Fig.? 1 . The homemade erbium-doped fiber amplifier is used to provide a sinusoidal broadband optical signal with a full bandwidth of 40?nm. The PM (EOSPACE, half-wave voltage: 5?V) has a 3-dB bandwidth of 10?GHz. The length of DCF is 2.4?km with a total dispersion of $- $ 334ps/nm. The optical light is detected by a PD with a 3-dB bandwidth of 10?GHz to do an optical-to-electrical conversion. The gain and 3-dB bandwidth of EA (SHWLNA-00101200-G28) are 28?dB and 12?GHz, respectively. The voltage sensing element is a high voltage resistant cylindrical PZT (HRBRZNX, Rps300/40?×?34/50) with the dimension of 40?mm ${\times} $ 34 mm ${\times} $ 50 mm and a section of 50 meters optical fiber, as shown in Fig.? 3 (b). We have wrapped approximately 20 meters, equivalent to 159 turns, of optical fibers around the PZT, reserving 15 meters of fiber on each side for convenient connection to the lower arm of the MZI. In order to keep the difference between the two arms within the interference range, a section of 50 meters optical fiber is connected to the upper arm. Meanwhile, to obtain the desired initial frequency of the oscillation signal, the VTDL (General Photonics, 0-350ps) is adjusted.
Figure? 4 (a) illustrates the optical spectrum of MZI measured at the output of the DCF using an OSA (YOKOGAWA, AD6370D) and the inset illustrates the zoom-in view of the sinusoidal broadband optical signal with a FSR of 0.98?nm. The joint operation of sinusoidal broadband optical signal, MZI, DCF, and PD leads to a single-passband FIR-MPF, and the frequency responses described in Fig.? 4 (b) is measured by a vector network analyzer (VNA). Correspondingly, as displayed in Fig.? 4 (c), the frequency of the microwave signal is 3.02?GHz measured by an ESA (Agilent N9010A), which agrees well with the theoretical value calculated based on Eq.?( 8 ). In addition, the mode spacing of the OEO is 74.5kHz determined by the total length of the OEO. Thanks to filtering effect of the IIR-MPF, the side mode suppression ratio of the generated signal can reach 44?dB.
? Fig. 4. (a) Optical spectrum measured at the output of the DCF. Inset: a zoom-in view of the optical spectrum with span of 2?nm. (b) Frequency response of the FIR-MPF. (c) The zoomed-in view of the microwave signal (span?=?350kHz, resolution bandwidth =4.7 kHz).
Download Full Size PDF
In our experiment, a voltage range from – 200?V to 1500?V is applied to the PZT at the interval of 100?V by tuning the voltage supply (HSPY-1500-002). Figure? 5 displays that the oscillating frequency of OEO shifts to a higher frequency as the voltage increases in one test. A total of three repeated experiments are performed and analyzed. Figure? 6 illustrates the experimental data of three voltage increases and its error bar curve. The three voltage-increasing linear curves almost coincide in the entire measurement range, and their sensitivities are all 0.25?GHz/100?V. The slope of the error bar curve is also 0.25?GHz/100?V with correlation coefficients ( R 2 ) of 0.9843. It can be seen that the voltage-increasing curves will slightly bend upwards. The reason is that the cylindrical PZT has hysteresis characteristics like any other viscoelastic materials.
? Fig. 5. Superimposed electrical spectra of the generated microwave signal at different voltage from – 200?V to 1500 with a step of 100?V.
Download Full Size PDF
? Fig. 6. (a) Relationship between the voltage increase and the frequency of microwave signal. (b) The error bar of the voltage increases versus the average frequency of microwave signal.
Download Full Size PDF
The effect of temperature on the proposed scheme is also tested. Firstly, the fiber length of 50 meters in the upper arm of MZI ( L 3? =?50 meters) is placed into the temperature control container for temperature testing, as displayed in Fig.? 7 (a). Figure? 7 (b) demonstrates the oscillating frequency of the OEO shifts toward lower frequency with increasing temperature. Three repeated experiments verify the consistency of the temperature performance, as shown in Fig.? 7 (c). The relationship between the frequency shift and the temperature is linear with temperature sensitivity of $- $ 0.27?GHz/℃ and R 2 of 0.9973, as shown in Fig.? 7 (d). It indicates that the stretch length of the upper arm of the sensing probe is greater than that of the lower arm of the sensing probe, and the difference between the two arms of MZI decreases, resulting in a lower frequency of the microwave signal generated by the OEO. This may be attributed to the thermal instability of the UV adhesive that fixes the ends of the L 1 fiber, the pre-stretched L 1 fiber is no longer tightly wrapped around the cylindrical surface of the cylindrical PZT as the temperature increases, resulting in the contraction of the length of L 1 . At the same time, the SMF stretches axially with increasing temperature. Therefore, as the temperature increases, the difference between the two arms of MZI decreases, leading to a left shift of the oscillating frequency.
? Fig. 7. (a) The schematic of two branches in the temperature control container. (b)?Superimposed electrical spectra of the generated microwave signal at different temperatures from 30 °C to 50 °C. (c) Voltage data for 3 temperature rises. (d) Relationship between the temperature increase and the average frequency of microwave signal.
Download Full Size PDF
Form Fig.? 7 , it can be seen that small changes in temperature can introduce large frequency drifts and lead to serious voltage errors. Thus, we continuously adjust the SMF length of the upper arm of the sensing probe in the temperature control container to achieve temperature insensitivity of the system. With repeated experiments, the experimental results indicate that the frequency shift of the oscillating signal induced by temperature can be greatly reduced by placing approximately 36 meters of SMF of the upper arm in the temperature control container, as shown in Fig.? 7 (a). Figure? 8 (a) illustrates the superimposed spectrum at different temperatures. In three repeated experiments, when the temperature increases from 30 °C to 40 °C, the frequency shift is only 1.37?MHz, leading to the maximum voltage error of 0.55?V, as displayed in Fig.? 8 (b). Compared with temperature experimental results of a system without any processing, this method can reduce the voltage error caused by temperature by thousands of times.
? Fig. 8. (a) Relationship between the temperature and the frequency of oscillating signal. (b)?Frequency fluctuation of microwave signal measured at different temperatures from 30 °C to 40 °C.
Download Full Size PDF
Besides, the stability and the resolution of the proposed sensing scheme is evaluated. In order to evaluate stability, we set the ESA at “max hold” mode and record the frequency of the tracking signals for 5 minutes. As displayed in Fig.? 9 (a), the shift of the oscillation frequency is approximately 218kHz with a constant temperature and without the voltage applied to PZT, leading to a voltage accuracy of ±0.043?V. In addition, the IIR-MPF and the OEO modes show discrete characteristics, and the resolution of the proposed voltage senor is theoretically determined by the FSR of the IIR-MPF. Figure? 9 (b) illustrates the frequency response of the IIR measured by a VNA, which demonstrates the FSR of IIR-MPF of 765 kHz and a low rejection ratio of about 5?dB, leading to the resolution of 0.3?V. In OEO loop, FSR is determined by the loop time delay, which is expressed as FSR?=?1/τ. The fiber ring used in our scheme consists of a 2?×?2 90:10 OC and a length of 270 meters SMF. Thus, the FSR can be reduced by increasing the length of fiber loop, and then the sensing resolution can be further improved. Obviously, the frequency offset of the microwave signal is smaller than the FSR between the signals during the sensing experiments. Therefore, there is no frequency hopping for the generated OEO signal during our measurements. However, for long-term applications, the instability of the devices in the loop and the external environment may affect the frequency variation of the oscillating signal, leading to the frequency hopping of the generated signal in the OEO. In order to improve the stability of the system, the phase locked loop (PLL) [ 22 ] technology can be applied in the real applications to lock the frequency and enhance the performance of the sensing scheme.
? Fig. 9. (a) Frequency stability measurement for 5 minutes. (b) Frequency response of the IIR-MPF.
Download Full Size PDF
The sensing performance for PZT-based voltage sensor using different demodulation methods are summarized in Table? 1 . It can be seen that the traditional PZT-based voltage sensors using OSA [ 5 ], Bragg meters [ 7 ], and Fabry Perot tunable filter [ 8 ] for interrogation have relatively poor voltage resolution, approximately tens of volts. Wang Pengfei et al. [ 11 ] proposed a voltage sensing scheme using edge filter demodulation based on macrobending optical fiber and PZT-Stack with a high resolution of 0.5?V. Meanwhile, Wu. et al [ 20 ] proposed a high sensitivity voltage sensor based on OEO using EPS-FBG and PZT-Stack, which can realize the high-resolution and high-speed interrogation. Considering the 11.9?MHz FSR of the scheme proposed by Wu.et al, the sensing resolution is calculated to be 0.021?V. However, the use of tunable laser source (TLS) not only increase the system cost, but most importantly, small fluctuations of the TLS wavelength can lead to significant drifts of the oscillation frequency, resulting in serious measurement errors. Besides, this method has a relatively small voltage measurement range due to two aspects. Firstly, the wavelength separation between two adjacent notches of the EPS-FBG used in the Ref. [ 20 ] is extremely narrow, and the beating of the notch of the EPS-FBG and the carrier generated by TLS may exceed the range of the OEO oscillating bandwidth. Secondly, the voltage sensing scheme using the PZT-stack [ 11 , 20 ] can only withstand about one hundred voltages due to the characteristics of the PZT-Stack, which may limit their applications in smart grids. The cylindrical PZT used in our scheme is co-fired monolithic PZT that can withstand positive and negative several thousand voltages. In our experiment, the sensing range from – 200?V to 1500?V is demonstrated due to the limitation of the power supply for the voltage generation, which can be further enlarged in the real application by using a larger voltage power supply. Therefore, compared with the above scheme, our proposed voltage sensor has relatively high resolution and can achieve large voltage sensing range.
Table 1. Performance of optical voltage sensors based on PZT
View Table
4. Conclusion .
In summary, an OEO-based voltage sensor combined with MZI and a wrapped cylindrical PZT has been proposed and experimentally demonstrated. Thanks to the cascade of a FIR-MPF and an IIR-MPF, the single-mode oscillating frequency and the high resolution are accomplished. In the OEO loop, voltage measurement is realized by monitoring the frequency of the generated microwave signal using DSP or ESA, which can realize high-speed interrogation. The experiment results indicate a high resolution of 0.3?V with 0.25?GHz/100?V in the large voltage measurement range from – 200?V to 1500?V. In addition, the measurement errors induced by the temperature change and optical source wavelength drift can be eliminated, resulting in a great improvement of the sensing accuracy. The proposed sensing scheme features of high-resolution, large sensing range and high-speed interrogation, which make it possible for voltage controlling/monitoring in future smart grids applications.
Funding .
National Natural Science Foundation of China (U2006217, 62371035, 62335001, 61801017); National Key Research and Development Program of China (2021YFB2800900); Natural Science Foundation of Shandong Province (ZR2023MF071); Youth Innovation Team Project of High School in Shandong Province (2022KJ044).
Disclosures .
The authors declare no conflicts of interest.
Data availability .
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References .
1. H. Wang, R. Zeng, C. J. Zhuang, et al. , “Thermal variation of electric field sensor bias caused by anisotropy of LiNbO3,” Appl. Phys. Lett. 114 (14), 7 (2019). [ CrossRef ] ?
2. N. A. F. Jaeger and F. Rahmatian, “INTEGRATED-OPTICS POCKELS CELL HIGH-VOLTAGE SENSOR,” IEEE Trans. Power Delivery 10 (1), 127–134 (1995). [ CrossRef ] ?
3. C. S. Li, X. Cui, I. Yamaguchi, et al. , “Optical voltage sensor using a pulse-controlled electrooptic quarter waveplate,” IEEE Trans. Instrum. Meas. 54 (1), 273–277 (2005). [ CrossRef ] ?
4. K. S. Lee, “Electrooptic voltage sensor: birefringence effects and compensation methods,” Appl. Opt. 29 (30), 4453–4461 (1990). [ CrossRef ] ?
5. Y. Yao, “FBG based voltage measurement using PZT modulation,” in 2nd International Conference on Wireless Communications, Networking and Mobile Computing (IEEE, 2006), 613–616.
6. B. Ribeiro, “FBG-PZT sensor system for high voltage measurements,” in International Instrumentation and Measurement Technology Conference (IEEE, 2011), 978–983.
7. R. Allil and M. M. Werneck, “Optical High-Voltage Sensor Based on Fiber Bragg Grating and PZT Piezoelectric Ceramics,” IEEE Trans. Instrum. Meas. 60 (6), 2118–2125 (2011). [ CrossRef ] ?
8. B. D. Ribeiro, M. M. Werneck, J. L. da Silva-Neto, et al. , “Novel Optimization Algorithm to Demodulate a PZT-FBG Sensor in AC High Voltage Measurements,” IEEE Sensors J. 13 (4), 1259–1264 (2013). [ CrossRef ] ?
9. M. N. Gon?alves and M. M. Werneck, “A temperature-independent optical voltage transformer based on FBG-PZT for 13.8 kV distribution lines,” Measurement 147 , 106891 (2019). [ CrossRef ] ?
10. A. Dante, Rodrigo M. Bacurau, Cesar C. Carvalho, et al. , “Optical high-voltage sensor based on fiber Bragg gratings and stacked piezoelectric actuators for a.c. measurements,” Appl. Opt. 58 (30), 8322–8330 (2019). [ CrossRef ] ?
11. P. Wang, “A fiber-optic voltage sensor based on macrobending structure,” Opt. Laser Technol. 43 (5), 922–925 (2011). [ CrossRef ] ?
12. Y. He, Q. Yang, L. Y. Huang, et al. , “Frequency Optimization of PZT-FBG Voltage Sensor Based on Temperature-Independent Demodulation Method,” IEEE Sensors J. 21 (23), 26821–26829 (2021). [ CrossRef ] ?
13. Q. Yang, Y. X. He, S. P. Sun, et al. , “An optical fiber Bragg grating and piezoelectric ceramic voltage sensor,” Rev. Sci. Instrum. 88 (10), 10 (2017). [ CrossRef ] ?
14. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1 (6), 319–330 (2007). [ CrossRef ] ?
15. Y. P. Wang, J. J. Zhang, J. P. Yao, et al. , “An Optoelectronic Oscillator for High Sensitivity Temperature Sensing,” IEEE Photon. Technol. Lett. 28 (13), 1458–1461 (2016). [ CrossRef ] ?
16. O. Xu, J. J. Zhang, H. Deng, et al. , “Dual-frequency Optoelectronic Oscillator for Thermal-Insensitive Interrogation of a FBG Strain Sensor,” IEEE Photon. Technol. Lett. 29 (4), 357–360 (2017). [ CrossRef ] ?
17. Q. Y. Shi, Y. P. Wang, Y. F. Cui, et al. , “Resolution-Enhanced Fiber Grating Refractive Index Sensor Based on an Optoelectronic Oscillator,” IEEE Sensors J. 18 (23), 9562–9567 (2018). [ CrossRef ] ?
18. J. Zhang, M. G. Wang, Y. Tang, et al. , “High-sensitivity measurement of angular velocity based on an optoelectronic oscillator with an intra-loop Sagnac interferometer,” Opt. Lett. 43 (12), 2799–2802 (2018). [ CrossRef ] ?
19. B. L. Wu, M. G. Wang, Y. Dong, et al. , “Magnetic field sensor based on a dual-frequency optoelectronic oscillator using cascaded magnetostrictive alloy-fiber Bragg grating-Fabry Perot and fiber Bragg grating-Fabry Perot filters,” Opt. Express 26 (21), 27628–27638 (2018). [ CrossRef ] ?
20. B. L. Wu, H. Chen, S. Y. Xiao, et al. , “High-Sensitivity Fiber-Optic Voltage Sensor Based on an Optoelectronic Oscillator Using a PZT-Stack and an Equivalent Phase-Shifted Fiber Bragg Grating,” IEEE Sensors J. 23 (17), 19332–19338 (2023). [ CrossRef ] ?
21. L. Huang, D. L. Chen, and F. Z. Zhang, “Microwave photonic filter with multiple independently tunable passbands based on a broadband optical source,” Opt. Express 23 (20), 25539–25552 (2015). [ CrossRef ] ?
22. M. Shi, L. L. Yi, W. S. Hu, et al. , “High-Resolution Brillouin Optoelectronic Oscillator Using High-Order Sideband Injection-Locking,” IEEE Photon. Technol. Lett. 31 (7), 513–516 (2019). [ CrossRef ] ? .
|
|
From：
|
|
|
系统抽取主题
|
(1)
|
|
(1)
|
|
(1)
|
|
(1)
|
|
(1)
|
|
(1)
|
|
(1)
|
|
(1)
|
(1)
|
|