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Due to high computation complexity, traditional design methods for LLC converter usually consider limited kinds of performance, and the process for searching the optimal parameter scheme is discrete, which might cause the missing of real optimal solution. In order to solve these problems, a multi‐objectives optimization design method for the LLC converter is proposed in this paper. According to the numerical calculation method, a closed parameter space for resonant parameters is established under the constraints of operation mode, switching frequency, zero voltage switching (ZVS), and voltage stress of resonant capacitor. Besides, the root‐mean‐square (RMS) value of resonant current and secondary current, as well as the core loss of the transformer, are selected as the optimization objectives. Non‐dominated sorting genetic algorithm (NSGA‐II) is utilized to deal with these multi‐objective formulations. In order to reduce the computation complexity, a data‐driven method, called adaptive polynomial approximation (APA), is selected to obtain the explicit expressions of the parameter space and the optimization objectives. Then, by substituting this simplified surrogate model into the NSGA‐II algorithm, the optimal parameter scheme is obtained. The comprehensive comparison analysis is performed, and a 400 W/48 V experimental prototype was built to verify the theoretical analysis, which shows that the proposed method features the highest efficiency of 95%. [ABSTRACT FROM AUTHOR]

The loss of small signal stability under parameter variation (e.g., fluctuation of loads and wind powers) can be ascribed to local bifurcations, i.e., saddle-node, Hopf, singularity-induced, and limit-induced bifurcations. Classic bifurcation calculation methods like the direct method and continuation method can only provide a bifurcation point or two-parameter bifurcation curve. Based on Galerkin method and the implicit function theorem, this paper proposes accurate polynomial approximations of bifurcation hypersurfaces in the multi-dimensional parameter space of interest. The proposed method can ensure high accuracy in this parameter space, and thus is preferable to the existing Taylor expansion-based local approximation method, given the intrinsic large-variation characteristic of wind powers. Acquired bifurcation hypersurfaces are immediately used to construct the small signal stability region of the continuous system, and then compute the stability margin for the operating point subjected to uncertainty of wind generation. Besides, the validity scope of the proposed method is analyzed, and the handling of limit-triggered equation switching as well as its computational difficulty is discussed. Computational results on the two-parameter 11-bus two-area and six-parameter IEEE 145-bus test systems validate the high accuracy and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Surrogate models that predict the behaviors of solid oxide cells (SOCs) accurately at low computational cost are crucial to the control and optimization of SOC plants. Lumped physical models of SOCs, while widely used in such applications, lack accuracy because of neglected physical details. Data-driven models are the other options of surrogate models, which are proved to be more accurate because these models are identified directly from experiments or numerical simulations. However, due to the time cost of experiments and numerical simulations of SOCs, it is hoped that data-driven models can be constructed from a minimum amount of data. Also, the trained data-driven models should be robust, in other words, insensitive to the data set as well as the initial settings. These requirements are hard to be achieved by existing data-driven models of SOCs, such as lookup tables and artificial neural networks (ANNs). Aiming to preserve robustness and reduce the required amount of data, this paper introduces an adaptive polynomial approximation (APA) method, which is derived from the latest findings of numerical computation science, to the surrogate modeling of SOCs. The obtained models by the APA method are validated by both experiments and simulations. By analyzing the models, the coupling relationship among operating parameters of SOCs is revealed. The physical interpretability makes the APA method distinctive from common data-driven modeling methods. Performance comparison shows that the APA method is more accurate and robust than the existing ones with similar sampling costs. Additionally, the APA method can control the accuracy of the model by setting an error criterion in the algorithm iteration, endowing the APA method with an error control ability as per different accuracy requirements for SOC modeling. • A data-driven method to construct surrogate models of SOC is introduced. • The models built by this method are validated by both experiments and simulations. • The models built by this method are physically interpretable. • The accuracy of this method is directly controlled by an error control parameter. • With similar time cost, this method is more robust and accurate than existing ones. [ABSTRACT FROM AUTHOR]

Parametric problems in the transient analysis refer to the investigations of the relationship between parameters and dynamic behavior. To solve parametric problems, we propose a Galerkin method-based polynomial approximation. The proposed method uses a series of polynomials combined with coefficients to approximately represent state variables with parameters, where the Galerkin method is introduced to determine the coefficients. Thereby, the relationship between parameters and dynamic behavior is established through the polynomial expressions. Because models in power system transient analysis are a set of complicated differential-algebraic equations, practical issues related to the non-polynomial model terms, parameterization of initial operation point are discussed in this paper. The proposed method is tested on a three-machine system and the IEEE 145-bus test system. The case studies show that compared to trajectory sensitivities, the proposed method can maintain high accuracy in cases of large parameter variations and strong non-linearity. We also illustrate that the validity of the proposed method for parametric problems like trajectory approximation, finding the critical parameter values and uncertainty quantification. [ABSTRACT FROM AUTHOR]

Power system static voltage stability region boundary (SVSRB) is a complicated hypersurface in parameter space. Due to inequality constraints such as generator reactive power limits, different critical points on the SVSRB may be related to different groups of active constraints and can be associated with different types of loadability limit, which makes it difficult to approximate the whole SVSRB at once or assemble many local approximations of the SVSRB. To overcome the difficulty, this paper proposes an approach for globally approximating the whole SVSRB considering generator reactive power limits at one go. First, a parametric optimization model incorporating all inequality constraints is formulated to describe the SVSRB, where the optimal solutions are the critical points on the SVSRB. The optimality condition, i.e., parametric Karush–Kuhn–Tucker conditions (KKT conditions), is also derived. Then, by applying the Galerkin method to the parametric KKT conditions in an interior-point-method-like manner, the whole SVSRB is approximated and represented using a single polynomial expression. Case studies in a 10-bus system and IEEE 300-bus system verify the effectiveness and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

A novel method for globally approximating the static voltage stability region boundaries (SVSRBs) of power systems is proposed by applying parametric polynomial approximation to the criterion equation which defines the SVSRB. Known as the Galerkin method, the implicit function portraying the SVSRB is described as a linear combination of basis polynomial functions, and the coefficients of the basis functions are obtained by projecting the SVSRB criterion onto each basis function. The approximation guarantees high precision globally in the whole domain of the parameter of interest rather than only in the neighborhood of a point, and the error can be controlled by the degree of polynomial basis functions. In the meantime, analytical expression of the left or right eigenvector of the system's Jacobian matrix corresponding to the zero eigenvalue is obtained in the form of polynomial, which provides valuable information for online voltage stability control or monitoring. Case studies in a 10-bus test system and IEEE 118-bus test system verifies the validity, accuracy, and flexibility of the proposed method. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) multiphysics models are powerful tools for investigating the distributions of physical quantities such as temperature inside solid oxide cell (SOC) stacks, but their high computational cost remains an obstacle to their application in simulating industrial-scale stacks with tens of cells. To accelerate the simulation for the 3D model of a novel flat-chip SOC (FCSOC) stack, this study proposes a simplification method that replaces part of the governing equations with data-driven surrogate cell submodels. The submodels, built with the adaptive polynomial approximation (APA) method, take the form of polynomials and are easy to integrate into commercial CFD software such as COMSOL. Simulation shows that the simplified stack model can predict the temperatures and voltages accurately compared with the original stack model. At the same time, the time and memory required for computation are reduced by approximately 60% for a short stack model containing seven cells, owing to the simplified fuel-side mass transfer and charge transfer processes. For a large stack model with 21 cells, the reduction in computation time can even exceed 70%. The reduced computational cost makes it possible to simulate the models of industrial-scale FCSOC stacks with up to 61 cells. • A novel 3D flat-chip SOC stack model is built and verified with experimental data. • The stack model simulation is accelerated by embedding data-driven cell submodels. • The computation time for industrial-scale stack models can be reduced by over 70%. • The proposed method can be implemented easily with commercial CFD software. [ABSTRACT FROM AUTHOR]