Stochastic optimal power flow (SOPF) formulations provide a mechanism to handle these uncertainties by computing dispatch decisions and control policies that maintain feasibility under uncertainty.
We observe that for samples coming from a dynamical process far from equilibrium, the sample complexity reduces exponentially compared to a dynamical process that mixes quickly.
In addition, we also show a variant of NeurISE that can be used to learn a neural net representation for the full energy function of the true model.
This paper discusses statistical structure estimation in power grids in the "under-excited" regime, where a subset of internal nodes do not have external injection.
We identify a single condition related to model parametrization that leads to rigorous guarantees on the recovery of model structure and parameters in any error norm, and is readily verifiable for a large class of models.
Although the number of possible bases is exponential in the size of the system, we show that only a few of them are relevant to system operation.
Optimization and Control
What is the optimal number of independent observations from which a sparse Gaussian Graphical Model can be correctly recovered?
As renewable wind energy penetration rates continue to increase, one of the major challenges facing grid operators is the question of how to control transmission grids in a reliable and a cost-efficient manner.
Systems and Control
Reconstruction of structure and parameters of an Ising model from binary samples is a problem of practical importance in a variety of disciplines, ranging from statistical physics and computational biology to image processing and machine learning.
In this paper, we formulate the optimal power flow problem over tree networks as an inference problem over a tree-structured graphical model where the nodal variables are low-dimensional vectors.
We prove that with appropriate regularization, the estimator recovers the underlying graph using a number of samples that is logarithmic in the system size p and exponential in the maximum coupling-intensity and maximum node-degree.
We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past.