Network-based stability analysis of electric power systems

Abstract

Electric power systems are dynamical systems evolving on power networks. The ongoing revolution in electric power systems led by advanced renewable energy and communication technologies brings many new network-related stability problems. However, the traditional and mainstream approaches for power system stability analysis are much oriented to the modeling of node dynamics, while power network parameters are simply treated as coefficients in the dynamical equations.

In this thesis, we study several stability problems in power systems with concentration on the role of power network structures. We make contributions in five aspects. First, we establish some new results on graph theory including the conditions to check the definiteness of graph Laplacian matrices with the presence of negative-weighted edges and self-loops and the characterization of graph cutsets and cycles. These results are not only valuable to graph theory but also closely linked to power system stability.

Second, we develop network-based approaches for power system small-disturbance stability. We introduce the graph concepts into power systems that describe the features of equilibrium points in terms of the power network structure. We reveal that the Laplacian matrices, negative-weighted edges and self-loops directly correspond to some particular physical concepts in power networks that are critical to system stability. New stability criteria are established based on the new graph theory results, which concisely interpret the instability mechanism by the structural properties of the underlying power network.

Third, by exploiting the network structure information contained in the system dynamic Jacobian matrix, we design an efficient and versatile framework to evaluate and enhance the small-disturbance stability of microgrids that relies on a distributed communication structure.

Fourth, we develop network-based approaches for power system transient stability. By the new characterization of graph cutsets and cycles, we give a new explanation of a common phenomenon in transient stability that the loss of synchronism initiates from the angle separation across a critical cutset. This phenomenon is shown to be closely related to the power network structural properties, which has not been revealed before. Also, we propose an improved cutset index based on the new cutset properties, which has a better performance than the conventional index in vulnerable cutset identification and stability region estimation.

Fifth, we make breakthrough in static voltage stability of distribution systems. We introduce a new concept called the network-load admittance ratio that characterizes the system loading status from the interaction among the power network, loads and distributed generators. We establish a necessary and sufficient voltage stability condition with the network-load admittance ratio. This condition generalizes the well-known voltage stability criterion of the line-load admittance ratio that holds for the single-load infinite-bus systems only. Also, we propose a new voltage stability index in terms of the network-load admittance ratio that performs well in voltage stability margin estimation.

Overall, the obtained results in this thesis provide new insights into power system stability. They also motivate us that the network-based paradigm is a powerful way to not only rewrite and extend prior results but also study new issues.