Small-Signal Stability Constrained Optimal Power Flow Based On Eigenvalue Optimization

The interconnections of large regional power network bring more challenges for the security of modern power system. Due to small-signal instability, low frequency oscillations pose a lethal threat to power system. Although the damping controllers can enhance the small signal stability effectively, it cannot guarantee that no oscillations occur. Therefore, it requires dispatchers to schedule the system generation not only based on economic object with the aid of the powerful tool Optimal Power Flow (OPF), but also ensuring a security margin with respect to small signal stability. In this context, it has been proposed to include small signal stability constraints into the optimal power flow model, thus creating Small-Signal Stability Constrained OPF (SSSC-OPF) techniques. They have aroused more and more interest recently.For the implicit and non-Lipschitz property of spectral abscissa of system state matrix, it is a big challenge to model the SSSC-OPF directly. In general, SSSC-OPF is an eigenvalue optimization problem naturally. This theory had not made much progress for a long time, until the dramatic breakthrough in the interior point methods for the semi-definite programming (SDP). Nowadays, the therory has been introduced to many fields, having a number of successful applications.Based on the eigenvalue optimization, this dissertation presents a nonlinear semi-definite programming (NLSDP) model and algorithm for SSSC-OPF. The research has made important contribution to theory and practicality as well as a good attempt for enhancing small-signal stability using eigenvalue optimization. The main research achievements are as follows:1. A nonlinear semi-definite programming (NLSDP) model for SSSC-OPF is proposed. According to the Lyapunov theorem, positive definite constraints are introduced to describe the small signal stability through an accurate equivalent expression. Thus, the SSSC-OPF will not spend more economic cost to meet the small-signal stability constraints. Furthermore, by transforming the eigenvalue optimization of a nonsymmetric matrix to SDP model over a symmetric matrix, the oscillation of the iterations of sensitivity-based algorithm because of the non-Lipschitz of spectral abscissa will not be suffered.2. A transforming method which can formulate the positive definite constraints into smooth concave and nonlinear ones is proposed. Then the NLSDP model is transformed into a nonlinear programming (NLP), one which can be solved by the modern interior point method.3. By choosing the controller parameters as variables, a NLSDP model for coordinated tuning of damping controller is proposed. It can coordinate the parameters of PSS and FACTS devices simultaneously or respectively. Besides, it can consider a wide range of operating conditions leading to a robust design.There are six chapters in this dissertation. The main contents of the dissertation are arranged as follows:In chapter1, the background of small-signal stability constrained OPF problem is introduced at first. The literature of the problem is also reviewed and the advantages and disadvantages of the reviewed methods are pointed out. Besides, the motivations of proposing an accurate model of SSSC-OPF based on eigenvalue optimization are analyzed in this chapter as well.The conventional optimal power flow model and the modern interior point method are presented respectively in chapter2. Furthermore, multi-machine dynamic models and the small-signal stability analysis model are introduced. The relationships between the OPF problem and small-signal stability analysis are discussed. Meanwhile, the difficulty of SSSC-OPF is analyzed. This chapter is the foundation for the discussions of the coming chapters.In chapter3, the eigenvalue optimization is introduced in details including its history, linear semi-definite programming model, nonlinear semi-definite programming model and their algorithm. This chapter provides the theoretical preparation for the coming chapters.The small-signal stability constrained OPF problems are discussed in Chapter4, and the nonlinear semidefinite programming model of SSSC-OPF is proposed as well. By using the model transformation method, the NLSDP model is formulated to a NLP model accurately, and then solved by the modern interior point method. Extensive numerical simulations on WSCC3machine9bus system, Kundur4machine10bus system and IEEE5machine14bus system have shown that effectiveness of the model and correctness and robustness of the algorithm.The chapter5extends the SSSC-OPF model in chapter and proposes a nonlinear semidefinite programming model for co-ordination of stabilizer parameter settings. It is solved by the same model transformation method. The feasibility is validated by the simulations of two systems.The conclusions and remained questions worthy to be studied further are given in chapter6.