A cryogenic air separation unit produces large volumes of high-purity oxygen, nitrogen, and argon through distillation. Such a complex process with a heat-coupling design, a high purity requirement, and a large-scale feature is difficult to analyze and optimize. In this study, a complete equation-oriented (EO) model, which includes a unit model and a thermodynamic model, is developed for cryogenic air separation involving a low-pressure column, a high-pressure column, and an argon side arm column. The EO approach is then applied to deal with the following three issues in air separation: thermodynamic parameter estimation, process analysis with heat-coupling design, and process optimization with varying load demands. The proposed EO method is superior to traditional sequential modular based commercial software in terms of convergence performance.

The single-phase phase-locked loop (PLL) is essential for the stable operation and control of single-phase grid-connected converters. However, in practical applications, the grid voltage is usually affected by harmonics and dc offset, which will cause errors in the output of the PLL. Therefore, using sliding discrete Fourier transform filter (SDFT) as a prefilter, this paper proposes an improved single-phase synchronous reference frame PLL with a fixed sampling frequency, which can accurately and quickly obtain the grid parameters under distorted grid conditions. Most importantly, the paper theoretically analyzes phase and amplitude errors generated by SDFT for the first time and a quantitative compensation method is proposed, which is straightforward to be used by a reader. Finally, the proposed PLL is compared with other PLLs through simulation and experiments. The experimental results show the effectiveness and practicability of the proposed method.INDEX TERMS Sliding discrete Fourier transform filter (SDFT), phase-locked loop (PLL), dc offset, harmonic.

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