The capacitor energizing transient as a kind of typical disturbance is used in the studies of power quality, condition monitoring and other fields, and all studies heavily rely on transient characteristics. However, most characteristics are established based on the three-phase capacitor synchronous energizing (SE), and the effect of asynchronous energizing (AE) is neglected, which may affect the relevant studies. In this paper, the main characterizations of the capacitor AE transient, such as the oscillation frequency, time constant and transient magnitude, are analyzed considering the operation modes of the system and capacitor neutral points. The effect of the three-phase circuit asymmetry on the characterizations is investigated. The downstream voltage magnification phenomena in not only positive-sequence circuit but also zero-sequence circuit caused by the capacitor AE are also revealed. The theoretical analysis, computer simulation and lab experiment results have verified the effectiveness of the characteristics.

As a common incipient fault for a compensation capacitor, the internal capacitor element breakdown fault (CEBF) causes slight changes in the steady-state voltage and current, which are difficult to accurately capture under the influence of measurement error. Therefore, to meet the demand for intelligent equipment maintenance by a smart grid, transient disturbances induced by a CEBF are used in this study to acquire element breakdown information for online monitoring of capacitor health. A transient response analysis of the CEBF in the time and frequency domains is used to establish the typical transient characteristics. Then, a multiple-kernel support vector machine algorithm is adopted to identify the transient disturbances. A method for determining the faulty capacitor unit is proposed based on the position of the waveform monitor. Under the assumption and statistics of the number of failed elements in a series group, a scheme for assessing the health condition is investigated. The proposed method can effectively obtain breakdown information to assess capacitor health with little influence of measurement error and background noise. The results of a theoretical analysis, computer simulation, lab experiment and field monitoring verify the effectiveness of the proposed method.

A novel scheme is proposed to monitor the operation of capacitors scattered in MV distribution systems. It first codes each capacitor with a distinctive switching character by setting a unique combination of a three-phase switching order and time interval. As a result, the transient of the three-phase reactive power during capacitor switching will appear in a unique way. Then, the reactive power disturbances monitored in the substation are decoded to identify which capacitor is being switched on and off. A detailed decoding method is developed to realize this identification without being impacted by the switching interference of loads and other reactive power compensation devices. Moreover, the implementation of the proposed scheme in the field is elaborated, and the resultant three-phase voltage unbalance is analyzed in this paper. Compared with existing methods, this scheme only requires one power quality monitor (PQM) located at the substation to monitor the operations (energizing or de-energizing) of downstream distribution capacitors without extra communication devices. The operation information is valuable for tackling power quality problems caused by capacitor switching and optimizing the distribution grid operation.

To address the issues of quadrature component attenuation and signal-to-noise ratio (SNR) degradation caused by carrier phase delay in Phase-Generated Carrier (PGC) demodulation, this paper proposes a phase delay compensation method based on sampling-point shift pre-calibration. By establishing a discrete phase offset model, we derive the mathematical relationship between sampling point shift and carrier cycle duration, and introduce a compensation mechanism that adjusts the starting point of the sampling sequence to achieve carrier phase pre-alignment. Theoretical analysis demonstrates that this method restricts the residual phase error to within Δθ_max = πf₀/f_s, thereby fundamentally avoiding the denominator-zero problem inherent in traditional compensation algorithms when θ approaches 45°. Experimental validation using an Extrinsic Fabry–Perot Interferometric (EFPI) ultrasonic sensor shows that, at a sampling rate of 10 MS/s, the proposed pre-alignment algorithm improves the minimum demodulation SNR by 35 dB and reduces phase fluctuation error to 2% of that of conventional methods. Notably, in 1100 consecutive measurements, the proposed method eliminates demodulation failures at critical phase points (e.g., π/4, π/2), which are commonly problematic in traditional techniques. By performing phase pre-compensation at the signal acquisition level, this method significantly enhances the long-term measurement stability of interferometric fiber-optic sensors in complex environments while maintaining the existing PGC demodulation architecture.

In this study, a phase-generated carrier (PGC) demodulation algorithm combined with the extended Kalman filter (EKF) algorithm based on an electro-optic modulator (EOM) is proposed, which can achieve nonlinear distortion (such as modulation depth drift and carrier phase delay) suppression for high-frequency phase carrier modulation. The improved algorithm is implemented on a field-programmable gate array (FPGA) hardware platform. The experimental results by the PGC-EKF method show that total harmonic distortion (THD) decreases from −32.61 to −54.51 dB, and SINAD increases from 32.59 to 47.86 dB, compared to the traditional PGC-Arctan method. This indicates that the PGC-EKF demodulation algorithm proposed in this paper can be widely used in many important fields such as hydrophone, transformer, and ultrasound signal detection.