Liguo Wang

In order to improve the poor tested accuracy of the State of Charge (SOC) caused by the suddenly changed discharge voltage of zinc bromine flow battery (ZBFB), an algorithm used to estimate and correct the SOC is proposed in this paper. The core work is to derive a calculation procedure for identifying the SOC based on the limited sampled data of the discharging voltage and current at the inflection points based on gradient boosting decision tree (GBDT). Considering the coulombic efficiency varies with the discharge current, the optimized weak learner and learning rate are given by generating the regression forecasting tree. Then, the SOC has been corrected by searching the optimization splitting node of the adaptive tree path based on searching minimum square error. Moreover, an assistant limit cycle analysis is attached to determine the calling condition of GBDT, which can reduce computational cost and running time. A 10kWh ZBFB experiment validated that with the proposed approach, the SOC at the inflection point of discharge voltage has reached 4.10% from 13.41%. This work can enhance the accuracy and efficiency of computing SOC by real-time estimating and correcting the SOC with the sample error under the discharging voltage sag of ZBFB.

Nonlinear differential equations and systems play a crucial role in modeling systems where time-dependent factors exhibit nonlinear characteristics. Due to their nonlinear nature, solving such systems often presents significant difficulties and challenges. In this study, we propose a method utilizing Physics-Informed Neural Networks (PINNs) to solve the nonlinear energy supply–demand (ESD) system. We design a neural network with four outputs, where each output approximates a function that corresponds to one of the unknown functions in the nonlinear system of differential equations describing the four-dimensional ESD problem. The neural network model is then trained, and the parameters are identified and optimized to achieve a more accurate solution. The solutions obtained from the neural network for this problem are equivalent when we compare and evaluate them against the Runge–Kutta numerical method of order 5(4) (RK45). However, the method utilizing neural networks is considered a modern and promising approach, as it effectively exploits the superior computational power of advanced computer systems, especially in solving complex problems. Another advantage is that the neural network model, after being trained, can solve the nonlinear system of differential equations across a continuous domain. In other words, neural networks are not only trained to approximate the solution functions for the nonlinear ESD system but can also represent the complex dynamic relationships between the system’s components. However, this approach requires significant time and computational power due to the need for model training. Furthermore, as this method is evaluated based on experimental results, ensuring the stability and convergence speed of the model poses a significant challenge. The key factors influencing this include the manner in which the neural network architecture is designed, such as the selection of hyperparameters and appropriate optimization functions. This is a critical and highly complex task, requiring experimentation and fine-tuning, which demand substantial expertise and time.

The paper focuses on the stationary self-consistent problem of magnetic insulation for a vacuum diode with space-charge limitation, described by a singularly perturbed Vlasov-Maxwell system of dimension 1.5. The case of insulated diode when the electrons are deflected back towards the cathode at the point 𝑥* is considered. First, the initial VM system is reduced to the nonlinear singular limit system of ODEs for the potentials of electric and magnetic fields. The second step deals with the limit system’s reduction to the new nonlinear singular ODE equation for effective potential 𝜃(𝑥). The existence of non-negative solutions is proved for the last equation on the interval [0, 𝑥* ) where 𝜃(𝑥) > 0. The most interesting and unexplored case takes place if 𝜃(𝑥) < 0 on the interval (𝑥*, 1] and such case corresponds to the case of an insulated diode. For the first time, a numerical analysis of complex bifurcation of solutions in insulated diode is considered for 𝜃(𝑥) < 0 depending on parameters and boundary conditions. Bifurcation diagrams of the dependence of solution 𝜃(𝑥) on a free point (free boundary) 𝑥* were constructed. Insulated diode spacing is found. These results could lead to more efficient and effective magnetically insulated diodes in future power conversion systems.

The purpose of the study is to develop an approach based on online measurements and the theory of Ritta–Wu characteristic sets from the field of algebraic geometry and computer algebra to solve one of the main tasks of wind energy studies such “abandon wind” caused by wind gusts. The Ritt-Wu theory is effective in studying polynomial systems and their solutions. To obtain an equivalent double-fed induction generator, the following basic steps are used: build the characteristic sets by modeling a wind farm; establish the polynomial rings based on the real-time aggregation data; derive analytical expressions of a model of an equivalent double-fed induction generator; validate of the developed approach to modeling an double-fed induction generator using mathematical modeling in the PSCAD software environment and analysis of a combination of model data and telemetry data. A general solution procedure is used, which can be applied to obtain the analytical expressions of the inductance and impedance of an equivalent wind farm. The expediency and effectiveness of the developed approach is illustrated by the example of a real wind farm with a capacity of 50 MW with 34 double-fed induction generators. The simulation results demonstrate that the obtained parameters of an equivalent double-fed induction generator can accurately follow wind speed fluctuations with a lower error. Thus, this study presents a new effective method for estimating the exact equivalent parameters of a wind farm during wind gusts. The developed method is suitable for obtaining the analytical solutions of equivalent wind farm parameters in real time. Validation of the accuracy and speed of the author’s method has been carried out. Moreover, this study can be applied to any wind farms equipped with double-fed induction generators.