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“Power Grid Complexity” introduces the complex system theory known as self-organized criticality (SOC) theory and complex network theory, and their applications to power systems. It studies the network characteristics of power systems, such as their small-world properties, structural vulnerability, decomposition and coordination strategies, and simplification and equivalence methods. The book also establishes four blackout models based on SOC theory through which the SOC of power systems is studied at both the macroscopic and microscopic levels. Additionally, applications of complex system theory in power system planning and emergency management platforms are also discussed in depth. This book can serve as a useful reference for engineers and researchers working with power systems.

Shengwei Mei is a Professor at the Department of Electrical Engineering at Tsinghua University, China. Xuemin Zhang is a Lecturer at the Department of Electrical Engineering at Tsinghua University, China. Ming Cao is an Assistant Professor at the Faculty of Mathematics and Natural Sciences at the University of Groningen, the Netherlands.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
This chapter gives an overview about power system blackouts and self-organized criticality (SOC) using tools from complexity science. It also discusses briefly, based on the existing blackout models, how to apply SOC to reveal the mechanism for cascading failures in power systems. We summarize the related background information and the organization of the book in the end.
Shengwei Mei, Xuemin Zhang, Ming Cao

Chapter 2. SOC and Complex Networks

Abstract
The main thread of this chapter is the power law distribution, which is the most common mathematical description of SOC. We first introduce some important concepts related to SOC, such as the scale-free distribution, fluctuation and long-range correlation. We then discuss the mathematical description of the mechanism of phase transitions and extreme events in complex systems. We also review some key definitions in complex networks, such as the node degree distribution, average path length, clustering coefficient and betweenness centrality. Special attention is paid to the small-world networks and scale-free networks, which are the most popular models used for complex networks. Finally, topics of community structures, central node identification, structural vulnerability and network synchronization are covered in order to investigate the relationship between a network’s topology and its functionalities.
Shengwei Mei, Xuemin Zhang, Ming Cao

Chapter 3. Foundation of SOC in Power Systems

Abstract
This chapter first introduces the notions of organization and self-organization and then discusses the general principles of SOC based on cybernetics. In addition, we construct the mathematical model describing the power system evolution mechanisms, and discuss the SOC phenomena in large-scale power grids. Further analysis is carried out using statistical data about the blackouts in the Chinese power systems. Finally, two categories of risk evaluation indices, VaR and CVaR, are discussed.
Shengwei Mei, Xuemin Zhang, Ming Cao

Chapter 4. Power Grid Growth and Evolution

Abstract
This chapter models and analyzes in detail the slow dynamics in power grids. The driving forces for power grid evolutions are identified and then utilized to construct the general evolution model for complex power grids. In addition, the evolution principles are delineated for the growth of power grids. We develop a small-world power grid evolution model to analyze how the topology of a power grid evolves when the grid itself grows dynamically. We consider various factors that affect power grids’ evolutions, such as the energy resource distributions, load growth patterns and power gird parameters.
Shengwei Mei, Xuemin Zhang, Ming Cao

Chapter 5. Complex Small-World Power Grids

Abstract
The electric features of small-world power grids are the focus of this chapter. The DC power flow model is utilized to analyze the power flow characteristics and the synchronization capabilities of small-world power grids. We then perform the assessment of the grid’s structural vulnerability when examining the key buses of power plants, substations and important tie lines.
Shengwei Mei, Xuemin Zhang, Ming Cao

Chapter 6. Decomposition and Coordination of Static Power Grids

Abstract
This chapter proposes a new algorithm to realize the control-oriented reactive power partitioning and key-bus selection. The first step is to decompose a network into several communities in order to decouple partitioning from control. By using the centrality degree index, the second step is to compare nodes’ capabilities to affect the whole system’s operation. Such a comparison provides information about how effective it will be to control the system at each node and hence helps us to simplify the control strategy to be running the key buses at their target operation modes. The effectiveness of the proposed algorithm is validated through simulations at the end of this chapter.
Shengwei Mei, Xuemin Zhang, Ming Cao

Chapter 7. Vulnerability Assessment of Static Power Grids

Abstract
This chapter develops a vulnerability evaluation method for transmission lines in static power grids using vulnerability theory. It first proposes an integrated vulnerability index considering both average electric transmission distances of active powers over the entire network and local balances of reactive powers. Then it assesses the vulnerability of transmission lines, which examines, from both the active and reactive power aspects, the system’s stability after a line fault based on the vulnerability index.
Shengwei Mei, Xuemin Zhang, Ming Cao

Chapter 8. Simplification, Equivalence, and Synchronization Control of Dynamic Power Grids

Abstract
This chapter studies the dynamic performances of power systems. It introduces the simplification and equivalence methods for dynamic power systems. In the proposed simplification method, the Laplacian matrix of a dynamic power system is used to evaluate the synchronization capacities among generators, and is utilized as the main tool for the coherence equivalence analysis. It also discusses the synchronization problem for complex power grids. The synchronization control method discussed in this chapter chooses the optimal tripping locations using a linear model of power networks. After a tripping strategy is determined, the effectiveness of the strategy is checked using a nonlinear model.
Shengwei Mei, Xuemin Zhang, Ming Cao

Chapter 9. Blackout Model Based on DC Power Flow

Abstract
This chapter first reviews briefly how to compute DC power flows. Then the blackouts and SOC phenomena in the Northeast Power Grid of China are discussed so that one can apply the blackout model to this power grid based on DC power flows. Consequently, we are able to identify the relationship between certain power system parameters and the blackouts and find the probability distribution of faults. At the same time, indices for blackout risks are defined and computed.
Shengwei Mei, Xuemin Zhang, Ming Cao

Chapter 10. Blackout Model Based on AC Power Flow

Abstract
Cascading blackout models based on optimal AC power flows are constructed in this chapter. Since these models are developed using SOC theory and incorporate the Manchester model, they can be utilized to describe the fast dynamics in cascading failures as well as the slow dynamics during the evolution of power grids. The advantage of this approach is that at both the macroscopic and microscopic levels, one can reveal and then study in depth the SOC characteristics in power grids.
Shengwei Mei, Xuemin Zhang, Ming Cao

Chapter 11. Blackout Model Considering Reactive Power/Voltage Characteristics

Abstract
This chapter embeds two types of voltage stability analysis modules based on the blackout model developed in the previous chapters. The aim is to construct blackout models that take into account the reactive power/voltage characteristics. Improvements can then be made to simulate more faithfully the fast and slow dynamics in power systems. In the meanwhile, the change of voltage stability levels can be tracked more precisely, and the SOC characteristics become more obvious.
Shengwei Mei, Xuemin Zhang, Ming Cao

Chapter 12. Blackout Model Based on the OTS

Abstract
The blackout models discussed in this chapter present transient dynamics, power flows and power system planning on three time scales. The main tools used in building these models are the index of transient stability margin and the optimal power flow with transient stability constraints (OTS). The advantage of using the models constructed in this chapter is that they are close to the physical realities of the cause and the evolution of cascading failures. Most importantly they incorporate preventive and emergency control actions, so we can use them to evaluate operators’ roles during blackouts. Furthermore, weak links in the system can be identified in the mean time, which, for the purpose of preventing large-scale blackouts, can be critical for decision making in secure operations.
Shengwei Mei, Xuemin Zhang, Ming Cao

Chapter 13. Applications to Generation Expansion Planning and Power Network Planning

Abstract
This chapter utilizes the OTS model to construct a general method to identify critical lines and buses in power grids. This leads to plannings for generation expansion and power network development. Since parameters of the OTS model may affect cascading failures and large-scale blackouts, we discuss the rules to set the line capacity growth rate as well as the probability for tripping overloaded lines.
Shengwei Mei, Xuemin Zhang, Ming Cao

Chapter 14. Applications in Electric Power Emergency Management Platform

Abstract
In this chapter, to discuss the electric power emergency management platform, we begin with a brief introduction about its background information and the overall structure. Correspondingly, the fundamental principles of the decision support system are also discussed. We use the improved OPA algorithm to design catastrophe evolution models in this chapter since it converges fast and is applicable to large-scale systems. Then the decision support system is constructed for the disaster assessment and disaster prevention evaluation. As case studies, we evaluate the operational risk of the Northeast Power Grid of China under several simulated disasters. The analysis of the affected areas are carried out, based on which disaster prevention plans are made. A power grid disaster forcasting and early-warning model based on AC power flow is also included in this chapter.
Shengwei Mei, Xuemin Zhang, Ming Cao

Backmatter

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