Date of Award
Doctor of Philosophy
Kai Sun, Fangxing (Fran) Li, Kevin Tomsovic, Xueping Li
This work proposes a novel approach for efficient and robust power system simulation based on differential transformation (DT).
First, this work introduces the DT to study power systems as high-dimensional nonlinear dynamical systems for the first time. This work designs a DT-based high-order semi-analytical simulation scheme that allows significantly prolonged time steps to reduce simulation time compared to a traditional numerical approach. The numerical stability, accuracy, and time performance of the proposed approach are compared with widely used numerical methods on the IEEE 39-bus system and Polish 2383-bus system.
Second, this work proposes a novel non-iterative method to solve power system differential-algebraic equations (DAEs) using the DT. The non-state variables (e.g. current injections and bus voltages), nonlinearly coupled in network equations, are conventionally solved by numerical methods with time-consuming iterations, but their DTs are proved to satisfy formally linear equations in this work. Thus, a non-iterative algorithm is designed to analytically solve all variables of a power system DAE model. From test results on a Polish 2383-bus system, the proposed method demonstrates fast and reliable time performance compared to traditional numerical approaches.
Third, this work proposes a novel dynamized power flow (DPF) method for solving and tracing power flow solutions. Different from the conventional continuation power flow (CPF) method, the proposed method extends the power flow model into a fictitious dynamic system by adding a differential equation on the loading parameter. A non-iterative algorithm based on DT is proposed to analytically solve the dynamized model in form of power series of time. Case studies on several test systems including a 2383-bus system show the merits of the proposed method.
Fourth, this work integrates the DT into Parareal, a Parallel in time framework, as the first step towards industrial applications. The case studies on large systems demonstrate that the combination of DT and Parareal provide a promising direction towards faster-than-real-time simulation.
Besides, this work also employs the DT for adaptive frequency control of wind turbines and further generalizes the DT method for general nonlinear DAEs.
Liu, Yang, "Power System Simulation Using a Differential Transformation Method. " PhD diss., University of Tennessee, 2022.