To ensure low failure and high reliability of fiber optic current transducers (FOCTs), it is urgent to study methods of condition monitoring and fault diagnosis in FOCT. Faults in FOCT have statistical characteristics. With the analyzing of time domain and frequency domain features in fiber optic current transformers’ measurement data, we establish correspondence between the physical characteristics of key components in transformer and data features and then build diagnostic analysis model based on Allan variance. According to the Allan variance calculation results, we can diagnose fiber optic current transformer’s health state and realize faults location. Experiment results show that diagnostic methods based on Allan variance are accurate and effective to identify fault features.
Fiber optic current transducers (FOCTs) are achieving increased acceptance and application in high voltage substations due to their superior accuracy, bandwidth, dynamic range, and inherent isolation. FOCTs are influenced by various factors such as electricity, heat, machinery, and environment in operation [
According to the information about measured values by condition monitoring and their processing results, fault diagnosis of FOCT reasons, judges, finds out fault’s types, location, and severity, and then puts forward proposals on equipment repair processing. Condition monitoring is the collection process of characteristic quantity [
As a complement to the frequency domain analysis, Allan variance is a time domain analysis technique originally developed to study the frequency stability of oscillators [
In this paper, we analyze the principle of Allan variance, evaluate types of random noise error, identify the statistical properties of various types of random errors, and locate noise error source. In the application of condition monitoring and fault diagnosis, we establish relational models between the noise characteristics and fault source with analysis of noise characteristics in time and frequency domain, respectively, according to the characteristics and trend of relevant parameters in FOCT. The model can monitor the health status of FOCT, judge fault position in fault state, provide the alarm when necessary, and finally provide the basis for further steps.
FOCT is a kind of optical sensor based on Faraday magneto optical effects and optical interference theory [
According to the structure of fiber optic sensor head, FOCTs are divided into reflective FOCT and Sagnac FOCT [
Structure of reflective FOCT with reflection mirror.
Structure of Sagnac FOCT with fiber loop.
Propagation process of light waves in reflective FOCT can be described as follows. The waves generated by the light source are polarized to linear polarized waves by polarizer after passing through the coupler. The linear polarized waves enter the polarization-maintaining fiber at 45°, transferring evenly into the polarization axis
Propagation process of light waves in Sagnac FOCT can be described as follows. The waves generated by the light source enter the integrated optical chip through the coupler and are polarized to linear polarized waves through the polarizer. The polarized waves are split into two parts at the beam splitter in the integrated optical chip, entering the wave plate, respectively, at plus or minus 45° (clockwise light is 45° and counterclockwise light is 45°). Prior to entering a low birefringence polarization-maintaining fiber optic sensor head in opposite directions, respectively, the polarized waves are converted into left and right circular polarized waves by 1/4
Although Sagnac FOCT and reflection FOCT are different in structure, they have the similar light waves sensing principle and signal processing steps. That means they all build digital closed-loop feedback system using high speed signal processing unit and electrooptic phase modulator in order to measure the information of nonreciprocal phase caused by Faraday magnetic field effect in real time and finally acquire the information of external current. Influenced by environmental factors and inherent factors, FOCTs reflect the same noise characteristics, which are mainly divided as the following categories [
Bias instability (BI) noises reflect the bias low-frequency fluctuation of FOCT. BI noises originate from discharge assembly in FOCTs, plasma discharge, circuit noises, environmental noises, and many other components which can generate random flashing. It is useful to inhibit BI by reliability design of FOCTs and taking corresponding filtering method. Angle random walk (ARW) noises show the ultimate precision of FOCTs and are an important indicator to measure the IFOG noise level. Photon shot noises of photoelectric detector (PIN) in FOCT result in the uncertainty of Faraday phase shift measurement, which cause a limit of current measurement. Shot noises also cause current random fluctuation of current-voltage feedback impedance in PIN preamplifier, resulting in pseudo-Faraday phase shift. The phase shift influences IFOG minimum bias stability and decides FOCT’s precision. ARW noises are the result of integrated broadband rate power spectral density, originating mainly from photodetector shot noises, amplifier noises, electronic device thermal noises, and some high frequency noises whose relevant time is shorter than sampling time. High frequency noises whose relevant time is shorter than sampling time can be eliminated. It is also efficient to inhibit ARW noises by using high-qualified light source and photoelectric detector and improving the stability of environmental temperature. Rate ramp (RR) is in essence a definite error, rather than a random error. The strength of light source in FOCT changes monotonously and very slowly and lasts for a long time, which causes RR noises. It is useful to reduce RR noises by ensuring the long-term stability of optoelectronic devices and working environment of FOCTs and determining the error compensation in the method of establishing the mathematical model. Rate random walk (RRW) noises reflect index correlated noises of long correlation time in limit condition. RRW noises are the integral result of phase value power spectral density, associated with long term effects of resonator. They are generated after white noises pass the integrator. RRW can be inhibited by reducing the aging effect of crystal oscillator. Sinusoidal noise (SN) is a kind of systematic error whose power spectral density is presented by several different frequencies. High frequency noises are generated by laser plasma oscillations in the discharge process; low frequency noises are caused by environmental periodic change. When the sinusoidal noises have sinusoidal waveform with multipeak, it is easier to show SN by the plot of power spectral density. Quantization noises (QN) reflect the minimum resolution of current’s information of FOCTs. Sampling values of interference signals in FOCT are converted to digital quantities by A/D and are sent into signal processor. In the measurement of time interval, measurement phase induced by current electromagnetic field is not integer times of quantified step size, while the amplitude of signals gets quantified over time, which causes quantization error. In the application environment with requirement of high sampling rate, large QN is caused, which can be reduced by improving the accuracy of acquisition system and shortening the initial sampling time.
Supposing that the current data with
The Allan variance can be expressed as follows:
The Allan variance obtained by performing the prescribed operations is related to the PSD of the noise terms in the original data set. The relationship between Allan variance and the two-sided PSD
Equation (
Equation (
For angle random walk, the associated rate PSD is represented by the following equation:
The following equation is obtained by performing integration:
For bias instability, the associated rate PSD is represented by the following equation:
For rate random walk, the associated rate PSD is represented by the following equation:
For quantization noise, the associated rate PSD is represented by the following equation:
Different error terms of random noises in FOCT appear in different correlation time domain. It is different in the power spectral density and the function relationship with correlation time
In (
Allan variance analysis method and the modeling technology can effectively separate and identify several main types of random noises which influence FOCT’s precision. By analyzing the curve, the corresponding noise error values can be estimated, making a comprehensive evaluation of overall performance of FOCT. In addition, error source of FOCT’s noise error can be located by analyzing different types of noise values. It is not only effective to improve the performance of FOCT, but also convenient to identify and locate fault in FOCT.
Combining FOCT state parameters and available information, we can build an intelligent diagnosis system based on some algorithms, to determine the status of the device with theoretical derivation and realize fault detection and diagnosis [
Structure of fault diagnosis system in FOCT.
Flow chart of fault diagnosis in FOCT.
To verify the performance and fault diagnosis methods of fiber optic current transducer, we built a current transformer test system, as shown in Figure
Experimental environment of current transducer test system.
Principle block of current transducer test system.
We test fault characteristics of several fiber optic current transformers, respectively. Figure
Current measurements data in FOCT.
Allan variance curve of first FOCT.
Allan variance curve of second FOCT.
Allan variance can be used to analyze the time domain characteristics of the underlying random processes in FOCT. It helps to identify the source of a given noise term present in the data, whether it is inherently in FOCT or in the absence of any plausible mechanism within FOCT. In this paper, we verified the validity of the Allan variance methods in soft fault diagnosis through theoretical analysis and fault simulation experiments. Allan variance is suitable for evaluation and diagnosis of soft fault in FOCT, which can avoid potential failures, such as performance fault induced by temperature, light source, and other factors. For abrupt-changing fault, we can compare and judge the fault characteristics with feature model by using wavelet transform methods and then decide whether the fault is from FOCT or grid failure.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The project is supported by the following funds. Fundamental Research Funds for the Central Universities (2242013R30016), Natural Science Foundation of Jiangsu Province (BK2012326, BK20130099), National Natural Science Foundation of China (61203192), Research Fund of China Ship 8 Industry (13J3.8.4), and Foundation of Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education (201103).