Understanding the cascading failures in Indian power grids with complex networks theory

Two huge blackouts, occurred separately on 30 and 31 July 2012 in India, spread over half the country when three of its five regional grids collapsed, leaving hundreds of millions of people without government-supplied electricity and ringing once again alarm bells with security problems in electric power grid systems. The first investigation reveals that the outage of the second (backup) 400 kV Bina–Gwalior–Agra line on 29 July 2012 led to the cascading failure through the grid, which can be simulated and explained from the perspective of the complex networks theory. In this paper, a new model of a power grid involving the active and reactive power loads is proposed and then used to analyze the cascading behavior of power grids, which is also used to explain the reason of the blackout happening in India. Furthermore, some strategic advices are given for improving the stability and security of power grids, especially Indian power grids.     

Models for the modern power grid

This article reviews different kinds of models for the electric power grid that can be used to understand the modern power system, the smart grid. From the physical network to abstract energy markets, we identify in the literature different aspects that co-determine the spatio-temporal multilayer dynamics of power system. We start our review by showing how the generation, transmission and distribution characteristics of the traditional power grids are already subject to complex behaviour appearing as a result of the the interplay between dynamics of the nodes and topology, namely synchronisation and cascade effects. When dealing with smart grids, the system complexity increases even more: on top of the physical network of power lines and controllable sources of electricity, the modernisation brings information networks, renewable intermittent generation, market liberalisation, prosumers, among other aspects. In this case, we forecast a dynamical co-evolution of the smart grid and other kind of networked systems that cannot be understood isolated. This review compiles recent results that model electric power grids as complex systems, going beyond pure technological aspects. From this perspective, we then indicate possible ways to incorporate the diverse co-evolving systems into the smart grid model using, for example, network theory and multi-agent simulation.     

An IOT based smart grid system for advanced cooperative transmission and communication

In the Internet of Things (IoT) ecosystem, devices will predominate, using it in a manner similar to how people used it. Devices will cooperating in a multicast network to collect, share, and forward information way while interacting with one another autonomously and without centralised supervision. The building of an intelligent environment the capability of real-time collection of data, which is crucial for maximising the value of the IoT, will make this possible. A typical electric grid is made up of many power plants that use various power generating units, such as coal-based units, gas-based units, hydro units, etc. The majority of the infrastructure and wires that make up the conventional electricity grid have been in existence for a long time, it should be mentioned. They require significant investments, so providing them could take years. As a result, many grid components are outmoded and must be maintained and monitored on a regular basis to keep power flowing. A sophisticated technology is the smart grid (SG) system that makes it easier to integrate green technology and environmental considerations. The SG cyber–physical system was implemented thanks to the advancement and use of communication technologies in the conventional power system. The Internet of Things (IoT) and essential devices are both present in the complicated architecture of the SG systems. The traditional electric grids are been transformed into smart and efficient grid known as “Smart grid”. The Internet of Things’ smart grid allows for two-way communications among connected devices and technology that can recognise and respond to human needs. The cost and reliability of a smart grid are superior to that of conventional power infrastructure. Through use and data maintenance, smart grid technology will assist in reducing energy use and costs. One of the primary contributions made to grids is the integration of IoT with producing facilities using sustainable energy at various levels. To enhance the smart grid for bidirectional information exchange, improve power quality, and increase reliability Internet of Things (IOT) devices are becoming an important part of smart electric grid. IOT Infrastructure (IOTI) provide a flexible, efficient and secure platform providing strategic management for monitoring and controlling of different operations under different working conditions. This paper discusses cyber security on IOT based infrastructure for electric power systems. A comprehensive study is highlighted which includes type of IOTs, architecture used for smart grid, and future challenges.     

News and Views: Nuclear Power in Brazil

No energy, whether renewable, clean or known by any other name can possibly be relied upon as the only solution for ensuring a supply of electricity compatible with a nation’s economic and social development. Brazilian consumption and installed capacity of electric power generation per capita indices are still inadequate and below the world average—this crucial fact must be considered. It obliges Brazil to take the most advantage of all resources available to increase its electricity generation capacity as rapidly as possible, thereby enabling consumption to reach levels compatible with the quality of life the Brazilian population aspires to. Planning of a country’s electric system requires efficient management of a diversified portfolio of energy sources. In Brazil, hydroelectricity will continue for many years yet to be the main component of its portfolio of electric power generation sources, but it must be supplemented by thermal sources—uranium, coal, biomass, natural gas, and oil by-products derived from petroleum—in this order of importance, keeping in mind aspects related to local availability, cost, environmental impacts, and use in other applications.     

Non-monotonic increase of robustness with capacity tolerance in power grids

The robustness of different scale power grids is analyzed based on complex network theory in terms of electrical betweenness and weighted efficiency. The robustness of a power grid does not always increase monotonically with the capacity. This property is different from the results obtained in previous studies, which have indicated that the robustness increases monotonically with capacity. To understand the non-monotonic phenomenon, the cascading failure is divided into several sub-stages, and we analyze the number of overloaded nodes and the average remaining load in each sub-stage. The results indicate that the increasing capacity is barely able to reduce the number of overloaded nodes at the beginning of malfunction, which may lead to more nodes being removed subsequently, including certain nodes with many connections or large load. More loads remain in the power grid such that certain nodes cannot take the load. This eventually causes overloading of more nodes and a decline in the robustness of the power grid. The conclusion may be useful for power grid planners seeking to design grids with cost-effective capacity.     

基于复杂网络的电网结构健壮性及Braess悖论现象研究

应用复杂网络理论,建立电力系统的改进导纳模型,结合电网拓扑特性和电气特性对电网的级联故障进行研究。通过随机移除传输线引发电网级联故障,研究网络的节点数、平均度、发电站数量以及发电站的分布状况对系统健壮性的影响,并对小世界电网级联故障过程中的布雷斯(Braess)悖论现象进行分析。研究表明：网络的健壮性与其拓扑结构密切相关,平均度较大时,最近邻耦合网络和小世界网络健壮性曲线存在多个分叉点;在小世界结构电网中,一般平均度和节点数越大,发电站的数量越多,电网健壮性越好;发电站分散分布比发电站集中分布的电网健壮性更好。对网络容量增加导致健壮性降低的布雷斯现象进行解释。     

Random matrix theory models of electric grid topology

The random matrix theory is useful in the study of large systems such as electric grids. These transmission systems can be modeled as complex networks, with high-voltage lines the edges that connect nodes representing power plants and substations. We draw upon established literature of complex systems theory and introduce methods from nuclear and statistical physics to identify new characteristics of these networks. We show that most grids can be characterized by the Gaussian Orthogonal Ensemble, an indicator of chaos in many complex systems. Under certain circumstances, however, grids may be described by Poisson statistics, an indicator of regularity. We use the random matrix formalism to describe the interconnection of multiple grids and construct a simple model of a distributed grid.     

一种新型电力网络局域世界演化模型

现实世界中的许多系统都可以用复杂网络来描述,电力系统是人类创造的最为复杂的网络系统之一.当前经典的网络模型与实际电力网络存在较大差异.从电力网络本身的演化机理入手,提出并研究了一种可以模拟电力网络演化规律的新型局域世界网络演化模型.理论分析表明该模型的度分布具有幂尾特性,且幂律指数在3—∞之间可调.最后通过对中国北方电网和美国西部电网的仿真以及和无标度网络、随机网络的对比,验证了该模型可以很好地反映电力网络的演化规律,并且进一步证实了电力网络既不是无标度网络,也不是完全的随机网络. 关键词： 电力网络 演化模型 局域世界 幂律分布     

Interdisciplinary challenges in the study of power grid resilience and stability and their relation to extreme weather events

This topical issue collects contributions to the interdisciplinary study of power grid stability in face of increasing volatility of energy production and consumption due to increasing renewable energy infeed and changing climatic conditions. The individual papers focus on different aspects of this field and bring together modern achievements from various disciplines, in particular complex systems science, nonlinear data analysis, control theory, electrical engineering, and climatology. Main topics considered here are prediction and volatility of renewable infeed, modelling and theoretical analysis of power grid topology, dynamics and stability, relationships between stability and complex network topology, and improvements via topological changes or control. Impacts for the design of smart power grids are discussed in detail.     

Dynamic properties of three-dimensional piezoelectric Kagome grids

Piezoelectric Kagome grids can be considered as a kind of functional material because they have vibration isolation performance and can transform mechanical energy to electric energy. In this study, the dynamic properties of three-dimensional (3D) piezoelectric Kagome grids without and with material defects are studied based on the frequency-domain responses. The spectral element method (SEM) is adopted to solve a 3D piezoelectric beam which contains bending components in two planes, tensional components, and torsional components. The dynamic stiffness matrix of a spectral piezoelectric beam is derived. Highly accurate solutions in the frequency-domain are obtained by solving the equation of motion of the whole structure. Compared with the results from the FEM and those in the existing literature, it can be seen that the SEM can be effectively used to study the 3D piezoelectric Kagome grids. The band-gap properties of Kagome grid and defect state properties of Kagome grid with material defects are analyzed. The effect of the piezoelectric parameter on the band-gap property is investigated further.     

An electrical betweenness approach for vulnerability assessment of power grids considering the capacity of generators and load

Most existing research on the vulnerability of power grids based on complex networks ignores the electrical characteristics and the capacity of generators and load. In this paper, the electrical betweenness is defined by considering the maximal demand of load and the capacity of generators in power grids. The loss of load, which reflects the ability of power grids to provide sufficient power to customers, is introduced to measure the vulnerability together with the size of the largest cluster. The simulation results of the IEEE-118 bus system and the Central China Power Grid show that the cumulative distributions of node electrical betweenness follow a power-law and that the nodes with high electrical betweenness play critical roles in both topological structure and power transmission of power grids. The results prove that the model proposed in this paper is effective for analyzing the vulnerability of power grids.     

八叉树网格到非结构混合网格的转换

在数值模拟中, 非结构网格的优势是可以采用相同的数值格式统一处理任意复杂的计算区域, 但在网格生成过程中难度大, 并且不容易控制网格质量。树结构网格可以认为是介于结构网格和非结构网格之间的一种网格, 目前已经有相对成熟的方法快速在复杂区域内生成二维四叉树网格和三维八叉树网格。在实际应用中, 数值方法往往需要在连接协调的非结构网格上做离散, 树结构网格中不同尺寸的网格之间连接不是协调的, 在应用上会受到很多限制。文章实现了树结构网格到非结构混合网格的转换, 这种转换在二维情况下就是将四叉树网格转换为非结构三角形和四边形的混合网格, 三维情况下则将八叉树网格转换为非结构混合网格。这一转换过程的难点在于需要考虑数千种不同的八叉树单元, 并给出能实现连接协调的非结构混合网格划分。可以出现的网格单元包括六面体、三棱柱、金字塔和四面体这4种不同情况。通过特别的分类, 实现了程序的自动生成, 这种程序自动生成技术一方面可以避免人工编写大量程序时的失误, 另一方面也使得对数以千计的不同情况的处理成为可能。通过对几个简单网格的测试, 对网格数据转换方法做了初步的验证。      

Self-organized synchronization and voltage stability in networks of synchronous machines

The integration of renewable energy sources in the course of the energy transition is accompanied by grid decentralization and fluctuating power feed-in characteristics. This development raises novel challenges for power system stability and design. We investigate power system stability from the viewpoint of self-organized synchronization aspects. In this approach, the power grid is represented by a network of synchronous machines. We supplement the classical Kuramoto-like network model, which assumes constant voltages, with dynamical voltage equations, and thus obtain an extended model, that incorporates the coupled categories voltage stability and rotor angle synchronization. We compare disturbance scenarios in small systems simulated on the basis of both classical and extended model and we discuss resultant implications and possible applications to complex modern power grids.     

A Linear programming formulation for routing asynchronous power systems of the Digital Grid

In recent years, practical research related to distributed power generation and networked distribution grids has been increasing. This research uses a relatively abstract model for the cost reduction in the Digital Grid Power Network. In the Digital Grid, the traditional wide-area synchronous grid is divided into smaller segmented grids which are connected asynchronously. In this paper, we demonstrate how to formulate the minimized cost of power generation by using linear programming methods, while considering the cost of electric transmission and distribution and using asynchronous power interchange among separate grids.     

云计算技术在未来智能电网信息处理平台中的应用

未来的电网将会是一个高度自动化、智能化的电网,如此一个庞大、复杂的系统从发电、输电一直到变、配、用电的过程时刻都会生成海量的电能信息及设备运行状态数据,这就需要一个强有力的信息处理平台作为支撑,且这个平台应具有对海量数据的可靠存储、准确分析、实时同步更新及共享的功能,尤其是音视频等异构数据的分析与处理.云计算技术在大数据处理中具有得天独厚的优势,本文将云计算技术引入到未来智能电网的信息处理平台的建设中,针对未来智能电网信息处理平台的各项功能需求,对比目前电网信息处理平台的诸多瓶颈进行深层次的探讨,证明了将云计算技术应用到未来智能电网信息处理平台中的可行性。     

用分层求解的方法快速形成二维数值网格

讨论了用分层求解的思想来快速构造二维数值网格。把以往文献中针对于外场区域的解抛物型方程的方法推广到封闭的二维区域,并把分层求解的思想应用于更为复杂的用椭圆型方程构造网格的数值求解中,给出了一些闭域的网格构造图。     

分布式发电优化配置研究

随着分布式发电与大电网联接的研究,使运行成本较高的分布式发电的经济利用成为可能.本文通过分析与大电网联接的可控分布式发电与大电网的供电年费用,建立了与大电网联接的可控分布式发电经济性判断模型和最优备用容量模型,在合理利用经济判断的基础上,对分布式发电的备用容量进行了优化.案例计算表明,模型正确可行,具有较强的适用性.本文的研究为可控分布式发电的合理利用提供了技术支持,为分布式发电与大电网联接、分布式发电的合理配置,降低供电成本做出了贡献.     

Provably stable overset grid methods for computational aeroacoustics

The simulation of sound generating flows in complex geometries requires accurate numerical methods that are non-dissipative and stable, and well-posed boundary conditions. A structured mesh approach is often desired for a higher-order discretization that better uses the provided grids, but at the expense of complex geometry capabilities relative to techniques for unstructured grids. One solution is to use an overset mesh-based discretization where locally structured meshes are globally assembled in an unstructured manner. This article discusses recent advancements in overset methods, also called Chimera methods, concerning boundary conditions, parallel methods for overset grid management, and stable and accurate interpolation between the grids. Several examples are given, some of which include moving grids.     

用非结构网格与欧拉方程计算复杂区域的二维流动

提出用Delaunay三角化方法生成非结构网格的一种过程。所生成的网格可用于复杂多连通域内的可压流计算。采用Euler方程和格心有限体积法,研制出程序,给出了算例。     

一种三柱式超导电抗器的概念设计

无功平衡对提高电网的经济效益和改善供电质量至关重要。目前用于电网无功补偿的传统电抗器难以实现无级调节,容量较小,或装置控制复杂,有较严重的谐波,难以在高电压等级的电网中大规模应用。为了解决高压电网的无功缺额问题,研究了一种三柱式的超导电抗器。文章介绍了该超导电抗器的工作原理,阐述了超导电抗器的设计方法。按照设计方法,对35kV电压等级的超导电抗器进行设计;在理论设计的基础上,采用有限元方法对理论设计进行优化,完成概念设计。仿真结果表明,该三柱式超导电抗器有较好的无功调节性能;该概念设计为高压大容量超导电抗器的研制提供了一定的参考依据。