ResearchBig PictureThe landscape and word cloud visualization of my research thrusts and PhD thesis: Here are a number of research projects that I have been working on. Power System State Estimation
Research challenges: Contributions: We propose a convexification framework based on semidefinite programming (SDP) and secondorder cone programming (SOCP) relaxations to cope with inherent nonconvexity of power flow (PF) and power system state estimation (PSSE) problems. We study the performance of the proposed framework in the case where the set of measurements includes: (i) nodal voltage magnitudes, and (ii) branch active power flows over a spanning tree of the network. It is shown that the SDP and SOCP relaxations both recover the true PF solution as long as the voltage angle difference across each line of the network is not too large. By capitalizing on the result for the PF problem, penalized SDP and SOCP problems are designed to solve the PSSE. Strong theoretical results are derived to quantify the optimal solution of the penalized SDP problem, which is shown to possess a dominant rankone component formed by lifting the true voltage vector. An upper bound on the estimation error is also derived as a function of the noise power, which decreases exponentially fast as the number of measurements increases. Related paper:
Robust and Stochastic Energy Management with HighPenetration Renewables
Research challenges: Contributions: Due to its reduced communication overhead and robustness to failures, distributed energy management is of paramount importance in smart grids, especially in microgrids, which feature distributed generation (DG) and distributed storage (DS). To address the intrinsically stochastic availability of renewable energy sources (RES), a novel power scheduling approach is introduced. The approach involves the actual renewable energy as well as the energy traded with the main grid, so that the supply–demand balance is maintained. Leveraging the dual decomposition, the optimization problem formulated is solved in a distributed fashion by the local controllers of DG, DS, and dispatchable loads. Capitalizing on the conditional valueatrisk (CVaR), the novel dayahead stochastic market clearing model is able to mitigate the potentially high risk of the recourse actions to compensate wind forecast errors. The resulting convex optimization task is tackled via a distributionfree sample average based approximation to bypass the prohibitively complex highdimensional integration. Furthermore, to cope with possibly largescale dispatchable loads, a fast distributed solver is developed with guaranteed convergence using the alternating direction method of multipliers (ADMM). Related papers:
Energy Data Analytics
Research challenges: Contributions: The smart grid vision entails advanced information technology and data analytics to enhance the efficiency, sustainability, and economics of the power grid infrastructure. Aligned to this end, modern statistical learning tools are leveraged for electricity market inference. Dayahead price forecasting is cast as a lowrank kernel learning problem. Uniquely exploiting the market clearing process, congestion patterns are modeled as rankone components in the matrix of spatiotemporally varying prices. Through a novel nuclear normbased regularization, kernels across pricing nodes and hours can be systematically selected. Even though marketwide forecasting is beneficial from a learning perspective, it involves processing highdimensional market data. The latter becomes possible after devising a blockcoordinate descent algorithm for solving the nonconvex optimization problem involved. The algorithm utilizes results from blocksparse vector recovery and is guaranteed to converge to a stationary point. Related papers:
Big Data Sketching
Research challenges: Abstract: Data reduction for largescale linear regression is one of the most important tasks in this era of data deluge. Exact model information is however not often available for big data analytics. We propose a framework for big data sketching (i.e., a data reduction tool) that is robust to possible model mismatch. Such a sketching task is cast as a Boolean minmax optimization problem, and then equivalently reduced to a Boolean minimization program. Capitalizing on the block coordinate descent algorithm, a scalable solver is developed to yield an efficient sampler and a good estimate of the unknown regression coefficient. Related paper:
Optimal Resource Allocation for Green Communications and GeoDistributed Data Centers
Research challenges: Contributions: We develop dynamic energy management for smartgrid powered coordinated multipoint (CoMP) transmissions. To address the intrinsic variability of renewable energy sources, a novel energy transaction mechanism is introduced for gridconnected base stations that are also equipped with an energy storage unit. Aiming to minimize the expected energy transaction cost while guaranteeing the worstcase users’ quality of service, an infinitehorizon optimization problem is formulated to obtain the optimal downlink transmit beamformers that are robust to channel uncertainties. Capitalizing on the virtualqueue based relaxation technique and the stochastic dualsubgradient method, an efficient online algorithm is developed yielding a feasible and asymptotically optimal solution. A large number of geodistributed data centers begin to surge in the era of data deluge and information explosion. To meet the growing demand in massive data processing, the infrastructure of future data centers must be energyefficient and sustainable. Facing this challenge, a systematic framework is put forth to integrate renewable energy sources (RES), distributed storage units, cooling facilities, as well as dynamic pricing into the workload and energy management tasks of a data center network. To cope with RES uncertainty, the resource allocation task is formulated as a robust optimization problem minimizing the worstcase net cost. Related papers:
Optimal Transceiver Design for Wireless Communication Networks
Research challenges: Abstract: We optimize the design of transmit and receivebeamformers for ad hoc CR networks when CRtoCR channels are known, but CRtoPU channels cannot be estimated accurately. Capitalizing on a normbounded channel uncertainty model, the optimal beamforming design is formulated to minimize the overall meansquare error (MSE) from all data streams, while enforcing protection of the PU system when the CRtoPU channels are uncertain. Even though the resultant optimization problem is nonconvex, algorithms with provable convergence to stationary points are developed by resorting to block coordinate ascent iterations, along with suitable convex approximation techniques. Enticingly, the novel schemes also lend themselves naturally to distributed implementations. Related papers:
