Overview

    My research revolves around the area of nonlinear optimization applications in power system. The majority of my work involves designing algorithms, and developing software to solve problems of the form

\(
\begin{equation}
\begin{aligned}
& \underset{\boldsymbol x}{\text{min}}
& & f(\boldsymbol x) \\
& \text{s.t.}
& & \boldsymbol h(\boldsymbol x) = 0 \\
& & & \underline{\boldsymbol g} \leq \boldsymbol g(\boldsymbol x) \leq \overline{\boldsymbol g},
\end{aligned}
\end{equation}
\)

where \(f:\mathbb{R}^n\to\mathbb{R}, h:\mathbb{R}^n\to\mathbb{R}^p, \text{and}\; g:\mathbb{R}^n\to\mathbb{R}^q\) are continuously differentiable, or at least locally Lipschitz over \(\mathbb{R}^n\) and continuously differentiable almost everywhere in \(\mathbb{R}^n\).

   Specific topics in which I am interested are listed below. Corresponding publications that relate to these and other categories are listed on my publications page.

• Optimal Power Flow

     A couple years ago my tutor Hua Wei, the pioneer who applied Interior Point Method (IPM) to OPF, inspired my interest in this amazing research field. Since he published his novel method to solve the OPF problem, the research of OPF has been made much progress. Based on this method, our research team, Institute of Power System Optimization, has developed several OPF offline and online applications using ANSI C language. Moreover these applications have been excellently performed in several dispatching centers around the world.

      Although the IPM is the workhorse to solve the OPF, there  still exists some challenges when developing realistic applications such as computation speed, global convergence, global optimality, and detecting infeasibility, etc. In fact, electric industry users care more about the algorithm’s robustness and stability than optimality. It is unacceptable for OPF to get a nonconvergence solution especially for online application. Additionally, IPM might be invalidated if the model has nonsmooth constraints or objective function.

      All in all, I hope I can take a step forward against OPF’s challenges.

• Optimization on Small-Signal Stability

      In Small-signal stability, the basic linearization technique is often used to obtain the system state matrix based on the classic Lyapunov theory. Then eigenvalues of the state matrix  are  found to analyze  the power system oscillations.  The system is proved stable if all the eigenvalues lie in the left of the complex plane.  With no much advance in this analysis framework over a long history, I plan to  work on this problem in an optimization view. It relates to a field called eigenvalue optimization in mathematics. Although this field is hard to understand and apply, I would like to throw myself into  it.

• Power System Resilience

     I focus on modeling the power system restoration and cascading outage in an optimization way. The protective relay scheme makes these models nonsmooth and nonconvex, which brings great challenges in this research field.