Space charge observation under periodic stresses — Part 1: The simplest system and corresponding phase identification

The simplest space charge measurement system is introduced for the direct space charge observation under arbitrary periodic stresses. An essential component of the system is the frequency allocation strategy for periodic stress fa and detection source fp. This strategy is based on the modified automatic equal phase shift (AEPS) principle, in which the relationship between fa and fp can be an integral multiple and a non-integral multiple. The phase detection in the range of 0°-360° can be completed during Na cycles of periodic stress with Np detected excitation to realize phase resolution Δ' = 2π/Np. Two different allocation strategies, namely, Na = 1 for the integral multiple between fa and fp and Na > 1 for the non-integral multiple between fa and fp, can be used to realize a high-phase resolution with consideration of the available frequency range for the detected source. Phase monitoring can be realized with the discrete voltage Va(i) of periodic stress at the detection phase and with the peak voltage Vg(i) of the raw signal representing the space charge density of the ground electrode. Phase delay is also introduced between the monitoring signal and real phase to avoid phase errors, especially at a high frequency and electric field. The detection phase of the space charge can be accurately identified through the monitoring signal via the data fitting or the Hilbert transform using the base wave component acquired with the Fourier transform. However, the data processing is complex for both methods. Thus, a simple and fast identification method is presented on the basis of the characteristic sequence of the AEPS principle. Finally, the feasibility and accuracy of the proposed system are successfully verified through the direct detection of the space charge within low-density polyethylene under several practical periodic stresses, namely, AC wave at 0.01 Hz, square wave at 1 kHz, and harmonic wave at 10 kHz.