Brief Summary

My main expertise is in the broad area of control systems, networks, power systems, and optimization. In the past two years, my research has been focused on the optimization techniques specialized for energy systems with the aim of solving hard nonconvex problems, such as the 50-year-old optimal power flow problem. In the 4 previous years, my research was to apply control and optimization theory to related interdisciplinary applications in communications, circuits, networks, and computer science. Specific results include:

  • Convexification of the optimal power flow problem,

  • Smart antenna design for wireless communication

  • Optimal design of very large-scale circuits

  • Design of optimal transmission protocols for internetworks

  • Distributed averaging (consensus) under communication constraints

  • A variety of fundamental control problems such as decentralized control of interconnected systems and biologically motivated controller design

Current Research Direction

Smart Grid

Over the past few years, the idea of upgrading today's transmission grid into a Smart Grid has been seriously considered by the electric power industry, state and federal regulators, government agencies, and academics. At the high level, the goal is to modernize the electricity transmission and distribution system to maintain a reliable and secure electricity infrastructure that can meet future demand growth. In particular, a smart grid must have many properties, including:

  • Optimized efficiency, reliability, and flexibility

  • The ability to integrate distributed (renewable) resources and distributed generation

  • The capability to interact with plug-in hybrid electric vehicles. From the system point of view, the deign of a smart grid requires several tools and theories from various areas of mathematics and engineering.

All of the areas that I have worked on fit within a multi-faceted, interdisciplinary approach to the problem of designing a smart grid:

  • Optimization: According to a National Science Foundation report, one of the three important actions needed to be taken towards designing a smart grid is to create new optimization methods that can solve the existing nonconvex problems associated with power grids.

  • Control: The controllers used in the existing conventional grids are mainly based on the centralized control theory. However, a truly decentralized and robust controller is needed for a smart grid with extensive use of small distributed generators and active load control.

  • Communications: Meters, appliances, consumer devices and plug-in hybrid electric vehicles must be made ‘‘smart," meaning that they should be able to communicate with each other and with the grid. Wireless communication theory plays an important role in deciding what type of communication means suits the needs of a smart grid.

  • Networks: More generally, internetworking plays a fundamental role in devising a communication protocol (e.g. TCP/IP and extensions) that specifies how much information each smart device should exchange with the rest of the grid and how the required amount of information can be shared in the network while minimizing channel usage.

  • Computer Science: The signals transmitted to the local controllers of the grid by smart devices are noisy, lossy and asynchronous. To deal with this issue, ideas from computer science, such as consensus, need to complement those from control and optimization.

Projects by Area