Xuemin Zhang

Foundation of SOC in Power Systems

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.

SOC and Complex Networks

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.

Complex Small-World Power Grids

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.

Applications in Electric Power Emergency Management Platform

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.

Applications to Generation Expansion Planning and Power Network Planning

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.

Simplification, Equivalence, and Synchronization Control of Dynamic Power Grids

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.

Decomposition and Coordination of Static Power Grids

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.

Power Grid Growth and Evolution

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.

Blackout Model Considering Reactive Power/Voltage Characteristics

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.

Vulnerability Assessment of Static Power Grids

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.