Homotopy-continuation Methods In Large-scale Power System Analysis: Algorithms And Applications

Recent years have witnessed a growing trend towards the development and deploy-ment of distributed generation (DG). This trend in combination with new distributiongeneration technologies have profoundly changed the traditional analysis, design, con-trol paradigm of distribution networks. It is hence important to develop comprehensiveanalysis tools for assessing the impacts of large integration of distributed generations ondistribution networks, and then to mitigate the adverse consequences of distributed re-sources integration.Homotopy-continuation methods are powerful and robust methods and have beensuccessfully applied to solve a wide variety problems arising from physical and engi-neering. Typically, they can be used to overcome the local convergence of typical iter-ative methods such as the Newton-Raphson method. In this dissertation, an extendablehomotopy-continuation algorithm library is developed for improving the robustness andconvergence of existing tools based on a three-stage homotopy-enhanced framework. Ahomotopy-enhanced distribution newton power flow method and a homotopy-enhancedtransmission power flow method for large-scale systems are presented in this dissertation,the construction of their corresponding easy problems are also proposed; they not onlytake advantage of the quadratic convergence of the Newton-Raphson method, but alsoovercome the divergence due to poor starting values, ill-condition or singular.The complexity of nonlinear behaviors of the distribution networks increases as largeintegration of distributed generation, especially renewables on distribution networks. Ex-cept for the traditional local bifurcation, the saddle node bifurcation, a peculiar bifurca-tion, the structure-induced bifurcation can occurs in large distribution networks due tothe integration of distributed generators introducing P-V buses in three phase power flowequations. The theories of these two types of local bifurcations are studied in this disser-tation, and the numerical methods for computing them are also presented.Continuation method is efective method for tracing solution curve due to one ormore parameters varies. In this dissertation, a comprehensive tool, termed CDFLOW(Continuation Distribution Power Flow) is presented and evaluated. CDFLOW can reli-ably compute the solution curve and accurate bifurcation points due to parameter varia-tion; hence it allows operators to exploit the potential of existing distribution networks todelivery more renewable energy resources to loads.The trend of integrating a wide variety of distributed resources into distribution net- works imposes great operational challenges; in particular, large-scale wind/solar powerpenetration may cause overloading occurring in distribution lines and transformers, volt-age violation and stability problems. In this disseration, the task of accurate determinationof available delivery capability (ADC) subject to voltage limits, thermal limits and volt-age stability limit is formulated. A rigorous numerical method to calculate the ADC oflarge-scale distribution networks with renewables is presented. The deterministic avail-able delivery capability assessment ignores uncertainties in the distribution systems, e.g.the variations of renewables and load demands. In this dissertation, a scenario generationmethod based on the distribution of forecasting error considering the diferences betweendiferent time scales is proposed. Instead of a single value, the look-ahead and day-aheadstochastic ADC yields the confidence interval of ADC to voltage violation, thermal limitsand voltage collapse and identifys the weak buses and branches in the network.