1. Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems Operation

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The evolutionary integral dynamical models of storage systems are addressed. Such models are based on systems of weakly regular nonlinear Volterra integral equations with piecewise smooth kernels. These equations can have non-unique solutions that depend on free parameters. The objective of this paper was two-fold. First, the iterative numerical method based on the modified Newton–Kantorovich iterative process is proposed for a solution of the nonlinear systems of such weakly regular Volterra equations. Second, the proposed numerical method was tested both on synthetic examples and real world problems related to the dynamic analysis of microgrids with energy storage systems.

本文研究储能系统的进化积分动力学模型，该模型基于具有分段平滑核的弱正则非线性Volterra积分方程组，这些方程存在依赖于自由参数的非唯一解。本文的目的有两方面，首先，提出了一种基于改进的Newton–Kantorovich迭代过程的迭代数值方法，用于求解这类弱正则Volterra方程组的非线性系统；其次，所提数值方法在关于含储能系统的微电网动态分析的合成案例及真实问题两方面进行了验证。

2. Mode Identification of Broad-band Oscillation Signal Based on Improved VMD Method

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Oscillation is one of the most important factors that affect the safety and stability of power system. In a power system, there may be multiple types of oscillation signal occurring at the same time. In this paper, a method based on improved variational modal decomposition (VMD) algorithm is proposed to identify the mode of broad-band oscillation signal. First, different types of oscillation are separated from broad-band oscillation signal by band pass filter. And then the modal signals are extracted from the filtered signals by improved VMD method. Finally, the parameters of the modal signals are identified by prony algorithm. The simulation shows that the method can extract the modal signals from broad-band signal and identify the parameters accurately

振荡是影响电力系统安全稳定运行的重要因素之一。在电力系统中，可能出现多种类型的振荡信号同时存在的情况。本文提出了一种基于改进变分模态分解算法（VMD）的宽频带振荡信号辨识方法。首先，通过带通滤波器，从宽频带振荡信号中分离出不同类型的振荡信号。然后，利用改进的VMD方法从滤波后的信号中提取得到模态信号。最后，利用Prony算法对模态信号进行参数辨识。仿真结果表明，该方法能够有效地从宽频带振荡信号中提取得到模态信号，并且能准确地辨识模态参数。

3. Toward Zero-Emission Hybrid AC/DC Power Systems with Renewable Energy Sources and Storages: A Case Study from Lake Baikal Region

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Tourism development in ecologically vulnerable areas like the lake Baikal region in Eastern Siberia is a challenging problem. To this end, the dynamical models of AC/DC hybrid isolated power system consisting of four power grids with renewable generation units and energy storage systems are proposed using the advanced methods based on deep reinforcement learning and integral equations. First, the wind and solar irradiance potential of several sites on the lake Baikal’s banks is analyzed as well as the electric load as a function of the climatic conditions. The optimal selection of the energy storage system components is supported in online mode. The approach is justified using the retrospective meteorological datasets. Such a formulation will allow us to develop a number of valuable recommendations related to the optimal control of several autonomous AC/DC hybrid power systems with different structures, equipment composition and kind of AC or DC current. Developed approach provides the valuable information at different stages of AC/DC hybrid power systems projects development with stand-alone hybrid solar-wind power generation systems.

生态脆弱地区（如西伯利亚东部的贝加尔湖地区）的旅游发展是一个具有挑战性的问题。为此，采用基于深度强化学习和积分方程的先进方法，建立了由4个具有可再生能源发电单元和储能系统的电网组成的AC/DC混合孤岛电力系统的动力学模型。首先，分析了贝加尔湖沿岸几个站点的风能和太阳能辐射潜力，把电力负荷作为气候条件的函数。在线模式下支持储能系统组件的优化选择。该方法使用历史气象数据集是可行的。该理论使我们能够针对含不同结构、设备元件和交流或直流类型的多个自主AC/DC混合电力系统的最优控制提出一系列有价值的建议。所提方法可在由独立的风-光混合发电系统构成的AC/DC混合电力系统的不同阶段提供有价值的信息。

4. Recurrent Neural Networks Application to Forecasting with Two Cases: Load and Pollution

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Forecasting problems exist widely in our life. Its purpose is to enable decision makers to make effective responses to future changes. The traditional prediction methods based on probability and statistics cannot guarantee the accuracy of multivariable dynamic prediction under the background of high randomness and big data. In recent years, with the improvement of hardware computing ability and the large-scale increase of training data, deep learning has been widely applied in the field of forecasting. This paper focuses on the analysis of the application of recurrent neural networks (RNN), an advanced algorithm in deep learning, in the forecasting task. The forecasting models based on long short-term memory (LSTM) and gated recurrent unit (GRU) were established respectively, and the real data of power load and air pollution were verified. Compared with traditional machine learning algorithms, the simulation proves the superiority of the forecasting model based on RNN.

预测问题广泛存在于现实中，其目的是辅助决策者对未来的变化做出有效的响应。传统基于概率统计的预测方法不能保证高随机性、大数据背景下多变量动态预测的预测精度。近年来，随着硬件计算能力的改进和大尺度训练数据的增加，深度学习在预测领域得到广泛应用。本文着重分析了循环神经网络（RNN）在预测任务中的应用，分别建立了基于长短期记忆网络（LSTM）和门控循环单元（GRU）的预测模型，并在电力负荷和空气污染两个真实数据集上进行了验证。与传统的机器学习算法相比，实验证明了基于RNN的预测模型的优越性。

5. Solvability and Bifurcation of Solutions of Nonlinear Equations with Fredholm Operator

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The necessary and sufficient conditions of existence of the nonlinear operator equations’ branches of solutions in the neighbourhood of branching points are derived. The approach is based on the reduction of the nonlinear operator equations to finite-dimensional problems. Methods of nonlinear functional analysis, integral equations, spectral theory based on index of Kronecker-Poincaré, Morse-Conley index, power geometry and other methods are employed. Proposed methodology enables justification of the theorems on existence of bifurcation points and bifurcation sets in the nonstandard models. Formulated theorems are constructive. For a certain smoothness of the nonlinear operator, the asymptotic behaviour of the solutions is analysed in the neighbourhood of the branch points and uniformly converging iterative schemes with a choice of the uniformization parameter enables the comprehensive analysis of the problems details. General theorems and effectiveness of the proposed methods are illustrated on the nonlinear integral equations.

6. Machine Learning for Energy Systems

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The objective of this editorial is to overview the content of the special issue “Machine Learning for Energy Systems”. This special issue collects innovative contributions addressing the top challenges in energy systems development, including electric power systems, heating and cooling systems, and gas transportation systems. The special attention is paid to the non-standard mathematical methods integrating data-driven black box dynamical models with classic mathematical and mechanical models. The general motivation of this special issue is driven by the considerable interest in the rethinking and improvement of energy systems due to the progress in heterogeneous data acquisition, data fusion, numerical methods, machine learning, and high-performance computing. The editor of this special issue has made an attempt to publish a book containing original contributions addressing theory and various applications of machine learning in energy systems’ operation, monitoring, and design. The response to our call had 27 submissions from 11 countries (Brazil, Canada, China, Denmark, Germany, Russia, Saudi Arabia, South Korea, Taiwan, UK, and USA), of which 12 were accepted and 15 were rejected. This issue contains 11 technical articles, one review, and one editorial. It covers a broad range of topics including reliability of power systems analysis, power quality issues in railway electrification systems, test systems of transformer oil, industrial control problems in metallurgy, power control for wind turbine fatigue balancing, advanced methods for forecasting of PV output power as well as wind speed and power, control of the AC/DC hybrid power systems with renewables and storage systems, electric-gas energy systems’ risk assessment, battery’s degradation status prediction, insulators fault forecasting, and autonomous energy coordination using blockchain-based negotiation model. In addition, review of the blockchain technology for information security of the energy internet is given. We believe that this special issue will be of interest not only to academics and researchers, but also to all the engineers who are seriously concerned about the unsolved problems in contemporary power engineering, multi-energy microgrids modeling.

7. Control of accuracy on Taylor-collocation method to solve the weakly regular Volterra integral equations of the first kind by using the CESTAC method

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Finding the optimal parameters and functions of iterative methods is among the main problems of the Numerical Analysis. For this aim, a technique of the stochastic arithmetic (SA) is used to control of accuracy on Taylor-collocation method for solving first kind weakly regular integral equations (IEs). Thus, the CESTAC method is applied and instead of usual mathematical software the CADNA library is used. Also, the convergence theorem of presented method is illustrated. In order to apply the CESTAC method we will prove a theorem that it will be our licence to use the new termination criterion instead of traditional absolute error. By using this theorem we can show that number of common significant digits (NCSDs) between two successive approximations are almost equal to NCSDs between exact and numerical solution. Finally, some examples are solved by using the Taylor-collocation method based on the CESTAC method. Several tables of numerical solutions based on the both arithmetics are presented. Comparison between number of iterations are demonstrated by using the floating point arithmetic (FPA) for different values of epsilon.

8. Machine Learning for Energy Systems

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This volume collects innovative contributions addressing the top challenges in energy systems development, including electric power systems, heating and cooling systems, and gas transportation systems. The special attention is paid to the non-standard mathematical methods integrating data-driven black box dynamical models with classic mathematical and mechanical models. The general motivation of this volume is driven by the considerable interest in the rethinking and improvement of energy systems due to the progress in heterogeneous data acquisition, data fusion, numerical methods, machine learning, and high-performance computing. This volume covers a broad range of topics including reliability of power systems analysis, power quality issues in railway electrification systems, test systems of transformer oil, industrial control problems in metallurgy, power control for wind turbine fatigue balancing, advanced methods for forecasting of PV output power as well as wind speed and power, control of the AC/DC hybrid power systems with renewables and storage systems, electric-gas energy systems’ risk assessment, battery’s degradation status prediction, insulators fault forecasting, and autonomous energy coordination using blockchain-based negotiation model. In addition, review of the blockchain technology for information security of the energy internet is given. We believe that this book will be of interest not only to academics and researchers, but also to all the engineers who are seriously concerned about the unsolved problems in contemporary power engineering, multi-energy microgrids modeling.

本书收集了解决能源系统发展中重要挑战的创新成果，包括电力系统、加热和冷却系统以及天然气运输系统，重点关注数据驱动的黑箱动力学模型与经典数学和力学模型相结合的非标准数学方法。随着异构数据采集、数据融合、数值方法、机器学习和高性能计算方面的进展，人们对能源系统的重新思考和改进产生了相当大的兴趣，这也是本书的总体动机。本书涵盖了广泛的主题，包括电力系统可靠性分析、铁路电气化系统电能质量问题、变压器油的测试系统、冶金工业控制问题、风机疲劳平衡的功率控制、光伏及风速、风电功率先进预测方法、含新能源发电与储能的AC/DC混合电力系统控制、电-气能源系统风险评估、电池退化状态预测、绝缘体故障预测及基于区块链协商模型的自主能源协调等。此外，还对用于能源互联网信息安全的区块链技术进行了综述。我们相信，这本书不仅会引起学者和研究人员的兴趣，也会吸引所有关注当代电力工程、多能源微电网建模领域待解决难题的工程师。

9. Volterra Model of Energy Storage with Nonlinear Efficiency in Integrated Power Systems

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The article deals with integrated power systems with renewable sources of generation in the settlements of Lake Baikal. The analysis of natural and climatic features in relation to the wind potential of the specified area is carried out. The construction of wind forecast using machine learning algorithms is considered. Global NWP forecast and machine learning model to achieve acceptable accuracy are combined. This forecast is used in the Volterra model to determine the operating parameters of energy storage units, in which the efficiency is a nonlinear function of the charge level, age and external operating conditions, i.e. the process of charging and discharging energy storage systems is described using Volterra integral equations. Such formulation of the problem will allow for the design of power systems to use a number of valuable recommendations regarding the optimal management of energy storage systems with several integrated power systems. The numerical solution of the proposed Volterra integral model was obtained using the spline collocation method.

本文讨论的是贝加尔湖居民区的可再生能源发电综合电力系统。分析了指定区域与风能有关的自然和气候特征，考虑了基于机器学习算法的风电预测。将全球NWP预报与机器学习模型相结合以达到可观的精度。预测用到Volterra模型中确定储能机组的运行参数，其中功效是充电水平、寿命和外部运行条件的非线性函数，即利用Volterra积分方程描述储能系统的充放电过程。该问题的这种规划将使电力系统的设计能够采用若干有关储能系统与若干综合电力系统优化管理的有价值的建议。利用样条配点法得到了所提Volterra积分模型的数值解。