Ratio error estimation of the voltage transformers plays an important role in modern power delivery systems. Existing ratio error estimation methods mainly focus on periodical calibration but ignore the time-varying property. Consequently, it is difficult to efficiently estimate the state of the voltage transformers in real time. To address this issue, we formulate a time-varying ratio error estimation (TREE) problem into a large-scale multiobjective optimization problem, where the multiple objectives and inequality constraints are formulated by statistical and physical rules extracted from the power delivery systems. Furthermore, a set of TREE problems from different substations are systematically formulated into a benchmark test suite for characterizing their different properties. The formulation of these TREE problems not only transfers an expensive ratio error estimation task to a relatively cheaper optimization problem, but also promotes the research in large-scale multiobjective optimization by providing a real-world benchmark test suite with complex variable interactions and correlations to different objectives. To the best of our knowledge, this is the first time to formulate a real-world problem into a benchmark test suite for large-scale multiobjective optimization, and it is also the first work proposing to solve TREE problems via evolutionary multiobjective optimization.

In this paper, a measuring system based on Print Circuit Board (PCB) Rogowski coils is introduced for high current measurement with multi-conductor structure. A high current up to 300 kA is split into sixteen branches to fulfill engineering requirements. This high current and multi-split structure bring about many problems into measurement. Traditional Current Transformers (TCTs) are not suitable for this situation since they are saturated by these high currents. A series of PCB-based Rogowski coils is used in the presented system, which can measure this high current easily with high accuracy (<0.5% at Hz). To ensure high accuracy, the measuring system needs to have high uniformity and strong anti-interference ability. Uniformity is analyzed and relevant formula is proposed to calculate it. Anti-interference ability is mainly related to Adjacent Coil’s Mutual Inductance (ACMI), which is analyzed carefully to find variables affect it. Uniformity analysis and anti-interference ability analysis provide a theoretical basis for parameter design. This paper elaborates on parameter design and gives the basis for selecting each parameter, which could be used as a reference for peers. Besides, supporting circuits and frequency analysis are also given to guarantee the integrity of the measuring system. Finally, experiments are carried out to prove high uniformity and anti-interference ability of the measuring system, thus ensuring high measurement accuracy. Tests show that the measurement error can be repressed under 0.5%.

The non-contact accurate measurement of weak direct current (dc) is very important for various fields, such as the online insulation monitoring of power cables. Compared with other dc current sensors, the magnetic modulator is more suitable for dc measurement with its high sensitivity, low noise, and stable working. Most magnetic modulators adopt the closed-loop structure to achieve accurate measurement of large current. And the magnetic modulator only realized the accurate measurement of mA current in the filed of weak dc current, which is difficult to meet the μA current measurement requirements of the online insulation monitoring. Therefore, this paper proposes a new structure of open-loop digital magnetic modulator for precision measurement of μA dc current. It adopts an annular shielding layer to weaken the zero offset and stray magnetic field. And a low-frequency excitation source, which can be adjusted with the ambient temperature, is used to improve the temperature stability. Instead of the traditional analog demodulation method, a digital demodulation algorithm is designed to reduce the measurement error caused by the zero offset and excitation source fluctuation. Measurement results show that the new sensor with the absolute error of 0.5 μA can measure 5-1000 μA dc current with a relative error of 0.05% in the full scale. And the sensor can effectively suppress the measurement error caused by the fluctuation of the excitation source and the ambient temperature to less than 0.5%.

The deterioration of cable insulation is a widely acknowledged problem, and detection lays the foundation for maintenance and overhaul. The measurement of Tangent delta (tan $\boldsymbol {\delta }$ ) at very low frequency (VLF) works well on cable insulation detection, nevertheless the conventional method could only be conducted offline, where the power outage is usually required, interrupting the normal operation. To break thus a limitation, an advanced online method is proposed, and tan $\boldsymbol {\delta }$ would be calculated based on the measurement of an artificially injected VLF voltage and that of the VLF leakage current through cable insulation. To coordinate with this method, an injecting source, with the comprehensive self-protection and the by-pass channel for power-frequency signals, is developed to safely inject a VLF voltage to the power system, and a monitoring system, with an accuracy better than $\pm 0.3~\boldsymbol {\mu }\text{A}$ , is established to obtain the injected voltage’s and leakage current’s waveforms, which would be used to further calculate tan $\boldsymbol {\delta }$ with the cross-correlation algorithm. In addition, this method, as well as developed devices, is applied on several cables in China Electric Power Research Institute, and the measuring results keep consistent with the actual conditions, which verifies the validity.

With the rising popularity of computationally expensive multiobjective optimization problems (EMOPs) in real-world applications, many surrogate-assisted evolutionary algorithms (SAEAs) have been proposed in the recent decade. Nevertheless, high-dimensional EMOPs remain challenging for existing SAEAs attributed to their requirement in massive fitness evaluations and complex models. We propose an SAEA with a supervised reconstruction strategy, namely SR-SAEA, for solving high-dimensional EMOPs. In SR-SAEA, we first select several well-converged reference solutions to form a set of reference vectors in the decision space. Then each candidate solution is projected onto these reference vectors, reflecting the closeness between the candidate solution and those reference solutions. Each candidate solution is then projected onto these reference vectors, generating a projection vector that reflects its proximity to the reference solutions. This allows the optimization of the high-dimensional decision vector to be approximated by optimizing the low-dimensional projection vector. Subsequently, a supervised autoencoder is employed to reconstruct the optimized low-dimensional projection vector back to the original decision space. Notably, the latency vector of the autoencoder is replaced with the projection vector for supervised reconstruction. An ablation study confirms the effectiveness of the proposed supervised reconstruction strategy. The superiority of SR-SAEA, compared with six state-of-the-art SAEAs, is validated on benchmark problems with up to 200 decision variables.