Computing the aperiodic and oscillatory small signal stability boundaries in modern power grids

This paper is devoted to exploring the aperiodic and oscillatory small signal stability boundaries in the space of power system parameters. In practical terms, they restrict the domain where all power system operating points must be kept for stable operation. In the proposed technique, to trace these boundaries, the saddle node and Hopf bifurcation points are computed along a given ray (loading direction) in the parameter space. By rotation of the ray, the entire boundaries are revealed. The bifurcation expressed in a plane provide a clear geometrical view of the stability constraints when a number of power system parameters are treated as variables. In the paper, particular attention is given to finding the initial guesses of unknown variables in the first step of the proposed technique, and to reliable and accurate tracing the boundaries in its second step. The corresponding numerical techniques, as well as examples of their application, are given.link_to_subscribed_fulltex

Advanced Methods For Small Signal Stability Analysis And Control In Modern Power Systems

This thesis is aimed at exploring issues relating to power system security analysis particularly arising under an open access deregulated environment. Numerical methods and computation algorithms locating the critical security condition points and visualizing the security hyper-plane in the parameter space are proposed. The power industry is undergoing changes leading to restructuring and privatizing in many countries. This restructuring consists in changing the power industry from a regulated and vertically integrated form into regional, competitive and functionally separate entities. This is done with the prospect of increasing efficiency by better management and better usage of existing equipment and lower price of electricity to all types of customers while maintaining a reliable system. As a result of deregulation and restructuring, power suppliers will increasingly try to deliver more energy to customers using existing system facilities, thereby putting the system under heavy stress. Accordingly, many technical and economic issues have arisen, for example, all or some of transient instability, aperiodic and oscillatory instability, insufficient reactive power supply, and even voltage collapse problems may coexist. This situation introduces the requirement for comprehensive analytical tools to assess the system security conditions, as well as to provide optimal control strategies to overcome these problems. There are computational techniques for assessing the power system stability critical conditions in given loading directions, but it is not enough to just have a few critical points in the parameter space to formulate an optimal control to avoid insecurity. A boundary or hyper-plane containing all such critical and subcritical security condition points will provide a comprehensive understanding of the power system operational situation and therefore can be used to provide a global optimal control action to enhance the system security. With the security boundary or hyper-plane available, the system operators can place the power system inside the security boundaries, away from instability, and enhance its security in an optimal way. Based on proper power system modelling, a general method is proposed to locate the power system small signal stability characteristic points, which include load flow feasibility points, aperiodic and oscillatory stability points, minimum and maximum damping points. Numerical methods for tracing the power system bifurcation boundaries are proposed to overcome nonconvexity and provide an efficient parameter continuation approach to trace stability boundaries of interest. A Delta-plane method for visualizing the power system load flow feasibility and bifurcation boundaries is proposed. The optimization problem defined by assessing the minimal distance from an operating point to the boundaries is considered. In particular, emphasis is placed on computing all locally minimal and the global minimum distances. Due to the complexity of any power system, traditional optimization techniques sometimes fail to locate the global optimal solutions which are essential to power system security analysis. However, genetic algorithms, due to their robustness and loose problem pre-requisites, are shown to fulfill the task rather satisfactorily. Finally, a toolbox is described which incorporates all these proposed techniques, and is being developed for power system stability assessment and enhancement analysis