4,008 research outputs found
Learning Graphs from Linear Measurements: Fundamental Trade-offs and Applications
We consider a specific graph learning task: reconstructing a symmetric matrix that represents an underlying graph using linear measurements. We present a sparsity characterization for distributions of random graphs (that are allowed to contain high-degree nodes), based on which we study fundamental trade-offs between the number of measurements, the complexity of the graph class, and the probability of error. We first derive a necessary condition on the number of measurements. Then, by considering a three-stage recovery scheme, we give a sufficient condition for recovery. Furthermore, assuming the measurements are Gaussian IID, we prove upper and lower bounds on the (worst-case) sample complexity for both noisy and noiseless recovery. In the special cases of the uniform distribution on trees with n nodes and the Erdős-Rényi (n,p) class, the fundamental trade-offs are tight up to multiplicative factors with noiseless measurements. In addition, for practical applications, we design and implement a polynomial-time (in n ) algorithm based on the three-stage recovery scheme. Experiments show that the heuristic algorithm outperforms basis pursuit on star graphs. We apply the heuristic algorithm to learn admittance matrices in electric grids. Simulations for several canonical graph classes and IEEE power system test cases demonstrate the effectiveness and robustness of the proposed algorithm for parameter reconstruction
Exact Topology and Parameter Estimation in Distribution Grids with Minimal Observability
Limited presence of nodal and line meters in distribution grids hinders their
optimal operation and participation in real-time markets. In particular lack of
real-time information on the grid topology and infrequently calibrated line
parameters (impedances) adversely affect the accuracy of any operational power
flow control. This paper suggests a novel algorithm for learning the topology
of distribution grid and estimating impedances of the operational lines with
minimal observational requirements - it provably reconstructs topology and
impedances using voltage and injection measured only at the terminal (end-user)
nodes of the distribution grid. All other (intermediate) nodes in the network
may be unobserved/hidden. Furthermore no additional input (e.g., number of grid
nodes, historical information on injections at hidden nodes) is needed for the
learning to succeed. Performance of the algorithm is illustrated in numerical
experiments on the IEEE and custom power distribution models
Modeling and performance evaluation of stealthy false data injection attacks on smart grid in the presence of corrupted measurements
The false data injection (FDI) attack cannot be detected by the traditional
anomaly detection techniques used in the energy system state estimators. In
this paper, we demonstrate how FDI attacks can be constructed blindly, i.e.,
without system knowledge, including topological connectivity and line reactance
information. Our analysis reveals that existing FDI attacks become detectable
(consequently unsuccessful) by the state estimator if the data contains grossly
corrupted measurements such as device malfunction and communication errors. The
proposed sparse optimization based stealthy attacks construction strategy
overcomes this limitation by separating the gross errors from the measurement
matrix. Extensive theoretical modeling and experimental evaluation show that
the proposed technique performs more stealthily (has less relative error) and
efficiently (fast enough to maintain time requirement) compared to other
methods on IEEE benchmark test systems.Comment: Keywords: Smart grid, False data injection, Blind attack, Principal
component analysis (PCA), Journal of Computer and System Sciences, Elsevier,
201
Sparsity-Based Error Detection in DC Power Flow State Estimation
This paper presents a new approach for identifying the measurement error in
the DC power flow state estimation problem. The proposed algorithm exploits the
singularity of the impedance matrix and the sparsity of the error vector by
posing the DC power flow problem as a sparse vector recovery problem that
leverages the structure of the power system and uses -norm minimization
for state estimation. This approach can provably compute the measurement errors
exactly, and its performance is robust to the arbitrary magnitudes of the
measurement errors. Hence, the proposed approach can detect the noisy elements
if the measurements are contaminated with additive white Gaussian noise plus
sparse noise with large magnitude. The effectiveness of the proposed
sparsity-based decomposition-DC power flow approach is demonstrated on the IEEE
118-bus and 300-bus test systems
A Holistic Approach to Forecasting Wholesale Energy Market Prices
Electricity market price predictions enable energy market participants to
shape their consumption or supply while meeting their economic and
environmental objectives. By utilizing the basic properties of the
supply-demand matching process performed by grid operators, known as Optimal
Power Flow (OPF), we develop a methodology to recover energy market's structure
and predict the resulting nodal prices by using only publicly available data,
specifically grid-wide generation type mix, system load, and historical prices.
Our methodology uses the latest advancements in statistical learning to cope
with high dimensional and sparse real power grid topologies, as well as scarce,
public market data, while exploiting structural characteristics of the
underlying OPF mechanism. Rigorous validations using the Southwest Power Pool
(SPP) market data reveal a strong correlation between the grid level mix and
corresponding market prices, resulting in accurate day-ahead predictions of
real time prices. The proposed approach demonstrates remarkable proximity to
the state-of-the-art industry benchmark while assuming a fully decentralized,
market-participant perspective. Finally, we recognize the limitations of the
proposed and other evaluated methodologies in predicting large price spike
values.Comment: 14 pages, 14 figures. Accepted for publication in IEEE Transactions
on Power System
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