Candidate for Doctor of Philosophy
Defense of PhD Dissertation

Faculty Advisor: Kai Sun

Title: 
Stability Analysis and Control of Nonlinear Power System Oscillations

Abstract:
This work investigates the nonlinear oscillation behaviors of multi-machine power systems via both model-based and measurement-based approaches. New stability monitoring approaches are proposed as well as new control designs.

A recently proposed model-based nonlinear oscillation analysis method, nonlinear modal decoupling (NMD), is investigated on its ability in capturing the stability information of the original system. NMD inversely constructs a set of 1-degree-of-freedom (DOF) nonlinear oscillators, referred to as decoupled system, from the original system model, with each representing an oscillation mode of the original system. It is shown that the truncation of higher order polynomial terms during the decoupling process leads to the inconsistency of the stability information between the original system and the decoupled system. For power system analysis, keeping the polynomial terms up to the 3rd-order during the decoupling is acceptable for stability analysis purpose. A transient stability analysis (TSA) approach is proposed to apply the NMD to the early warning of instability, which reduces the monitoring of the whole power systems to only a few critical modes. The most critical mode that could induce instability can also be identified. 

Then, a real-time damping estimation approach for nonlinear electromechanical oscillation is proposed for the situational awareness of potential angular instability in power systems. By identifying a nonlinear oscillator to fit a dominant mode, the proposed approach can utilize the complete post-disturbance data for robust damping estimation independent of the measuring window, while the traditional linear system theory based methods have to discard the first several swings that manifest obvious nonlinearity in measurements, and are sensitive to the length and starting point of the measuring window. Numerical studies on the IEEE 9-bus system and a 48-machine Northeast Power Coordinating Council system validating the proposed approach for providing accurate and robust estimation compared with the Prony’s method and recursive least square method. In addition, three factors that could influence the damping estimation in practical applications are also addressed, including measurement noises, limited coverage of PMU measurements, and existence of multiple dominant modes.

Finally, a direct damping feedback control method is proposed to eliminate the damping ratio deviation for a target mode by controlling the power converters based devices in the system. A PI controller based feedback control system is designed. The power system together with the damping estimation is approximated by a transfer function in the control system. This approximation is enabled by a) representing the target mode as a single oscillator model which is obtained from model reduction via the NMD method, and b) considering the parametric resonance of the single oscillator model. Then, the parameters of the PI controller are determined by considering the trade-off between robustness and control performance. Numerical studies on the 48-machine Northeast Power Coordinating Council system validate the effectiveness of the proposed damping control method.