LATEST RESEARCH
Ellipsoidal approximation of feasible region in physical systems​​
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In this project, I use relatively easy geometries to approximate the feasible region (a compact set) in a complex physical system operation. One property of the feasible region is that given a particular operating point , it is relatively efficient to verify its feasibility while it is relatively hard to depict the true boundary of the set. I use an ellipsoid to approximate this unknown boundary and more specifically an active sampling strategy is proposed. It can be shown that active sampling improves the query complexity by logarithmic steps, therefore efficiently improves computational time to make decisions in system operation.
A data-drive approach to solve stochastic programming problems in power distribution network
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Voltage control plays an important role in the operation of electricity distribution networks, especially with high penetration of distributed energy resources. These resources introduce significant and fast varying uncertainties. In this project, I focus on reactive power compensation to control voltage in the presence of uncertainties. I adopt a chance constraint approach that accounts for arbitrary correlations between renewable resources at each of the buses. It can be shown that the problem can be solved efficiently using historical samples via a stochastic quasi gradient method. In addition, this optimization problem is convex for a wide variety of probabilistic distributions. Compared to conventional per-bus chance constraints, this formulation is more robust to uncertainty and more computationally tractable.
A two-stage investment game in decentralized electricity market
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In this project, I study the capacity investment and pricing problem, where multiple renewable producers compete in a decentralized market. It is known that most deterministic capacity games tend to result in very inefficient equilibria, even when there are a large number of similar players. In contrast, I show that due to the inherent randomness of renewable resources, the equilibria in our capacity game becomes efficient as the number of players grows and coincides with the centralized decision from the social planner's problem. This result provides a new perspective on how to look at the positive influence of randomness in a game framework as well as its contribution to resource planning, scheduling, and bidding.
Model-free scenario generation for renewable energy resources
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In this project, I focus on methods to generate renewable scenarios using Bayesian probabilities by implementing the Bayesian generative adversarial network~(Bayesian GAN), which is a variant of generative adversarial networks based on two interconnected deep neural networks. By using a Bayesian formulation, generators can be constructed and trained to produce scenarios that capture different salient modes in the data, allowing for better diversity and more accurate representation of the underlying physical process. Compared to conventional statistical models that are often hard to scale or sample from, this method is model-free and can generate samples extremely efficiently.
Online convex optimization in designing incentives in system operation
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In this project I investigate the online algorithm to learn the unknown consumer utility while achieving optimized profits for the operator. The utility parameter can be learned through the dual formulation and is updated in an online fassion. The consumer and the operator are modeled through both cooperative game and nonoperative game depending on their perspective objective.
Causal Inference and online optimal experiment design in demand response
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In this project, I explore the performance of a signal impact using both randomized experiment design and targeted experiment design. When the least information is exposed, random design yields consistent estimator and is very efficient. I therefore propose three different linear estimators and discuss their performances based in variance.
However, in a high dimensional setting, random design leads to inefficient estimator and tailored design will dominate. To deal with this problem, I propose an combinatorial optimization problem and relax it into a dense graph partition problem. I then propose a constant performance ratio on the approximated solution when some conditions are met.
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Individual Consumption Prediction
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​In this project, I use sparse coding to recover the recurrent pattern in consumption behavior and predict based on historical data of single households. Granger causality and covariance test in LASSO are also applied to form pairs of users to enhance prediction accuracy.
Our model is shown to outperform both PCA and SVM. IAltough more complicated ensemble techniques yield a slightly better prediction, the cost is then model complexity and interpretability. It is hard to tune the hyperparameters in these models and is less intuitive than the proposed method in this work.
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