Project Description: In the next generation electrical grid, or "smart grid", there will be many heterogeneous power generators, power storage devices and power consumers. This will include residential customers who traditionally are only part of the ecosystem as consumers, but will in the foreseeable future increasingly provide renewable energy generation through photovoltaics and wind energy and provide energy storage through plug-in hybrid vehicles. What makes this electrical grid "smart" is the capability to insert a vast number of sensors and actuators into the system. This allows a wide variety of information about all the constituents to be collected and various aspects of the electrical grid to be controlled via advanced electric meters, smart appliances, etc. Information gathered consists of e.g. amount of energy use, planned energy consumption, efficiency and status of equipment, energy generation costs, etc and this information is then used by all constituents to optimize certain objectives. This necessitates communication and information technology to transmit and process this information. The goal of this project is to focus on the optimization of local objectives in a smart grid. In particular, we study various centralized and decentralized optimization algorithms to determine the optimal matching and maintain stability between energy producers, energy storage, and energy consumers all connected in a complex and dynamic network. Technical prerequisites: scripting languages (Matlab, python), optimization, linear and nonlinear programming. Preferred but not necessary: graph theory, combinatorics, computer programming, experience with CPLEX, R.