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The presence of dc offsets results in fundamental frequency oscillations in the frequency estimation and it is a challenging problem in single-phase grids. In this article, a four consecutive samples (4CSs) based method is proposed to estimate grid frequency with strong dc offset rejection capability. In details, a 4CS model is established based on the relationship among the fundamental grid voltage, dc offsets, and their consecutive sample signals. Different from the traditional 3CS model, the proposed 4CS model can reject the negative effects of dc offsets completely. Based on the obtained model, a frequency estimation is proposed and stability analysis is provided according to the adaptive control theory. Unlike the traditional 3CSs relying on prefilters, the proposed method is filter-free and it still has strong suppression capability against dc offsets. The theoretical sound and experimental results indicate that the proposed method achieves accurate frequency estimation with good dc offset rejection capability.

Due to the short distance between stations in DC mass transit systems, the trains accelerate and decelerate frequently with high traction current. If numerous trains are accelerating simultaneously, an extremely high traction current peak occurs. This current will have a great impact on the power supply system, and cause elevated rail potential in reflow system. This study presents an optimal model on traction current by adjusting the train's dwell time, reducing the coincidence degree when multi-train accelerate. Niche improved particle swarm algorithms for traction current optimisation is constructed. Optimised calculation results from the simulation of actual line show that the optimisation can significantly reduce the total maximum traction current value.

Instantaneous frequency (IF) of shaft rotation is pivotal for bearing fault diagnosis under variable speed operations. However, shaft IF cannot always be measured as tachometers are not allowed to be installed in every case due to design reasons and cost concerns. Extracting the shaft IF ridge from time frequency representation (TFR) of vibration signals, therefore, becomes an alternative. Linear transform (LT), such as short time Fourier transform (STFT), has been widely adopted for such a purpose. Nevertheless, the accuracy of extracted IF ridges relies on the readability of TFR. Unfortunately, readability of TFR from STFT is often impaired by the smearing effect caused by non-synchronous frequencies between bases and signal components and limited time frequency resolution capability, which in turn adversely influences the accuracy of IF ridge extraction. To accurately extract IF ridges from vibration signals, this paper focuses on the first factor, which causes the smearing problem, and proposes a method named frequency matching linear transform (FMLT) to enhance the TFR, where transforming bases with frequencies varying with the shaft IF are constructed to alleviate the smearing effects. To construct the transforming bases with frequencies synchronous with shaft IF, a fast path optimization (FPO) algorithm, which generates all possible optimization paths among amplitude peaks and thereby ensures the continuity of extracted IF ridges, is adopted for IF pre-estimation. The TFR with improved readability can be subsequently obtained via FMLT, paving the way for accurate IF ridge extraction. Then, multiple IF ridges can be iteratively extracted using the FPO algorithm. The accuracy of extracted IF ridges before and after TFR enhancement is compared, indicating that the proposed FMLT can enhance the readability of TFR and lead to more accurate IF ridge extraction for bearing condition monitoring.