7,722 research outputs found
Topology Estimation using Graphical Models in Multi-Phase Power Distribution Grids
Distribution grid is the medium and low voltage part of a large power system.
Structurally, the majority of distribution networks operate radially, such that
energized lines form a collection of trees, i.e. forest, with a substation
being at the root of any tree. The operational topology/forest may change from
time to time, however tracking these changes, even though important for the
distribution grid operation and control, is hindered by limited real-time
monitoring. This paper develops a learning framework to reconstruct radial
operational structure of the distribution grid from synchronized voltage
measurements in the grid subject to the exogenous fluctuations in nodal power
consumption. To detect operational lines our learning algorithm uses
conditional independence tests for continuous random variables that is
applicable to a wide class of probability distributions of the nodal
consumption and Gaussian injections in particular. Moreover, our algorithm
applies to the practical case of unbalanced three-phase power flow. Algorithm
performance is validated on AC power flow simulations over IEEE distribution
grid test cases.Comment: 12 pages 9 figure
Graphical Models in Meshed Distribution Grids: Topology estimation, change detection and limitations
Graphical models are a succinct way to represent the structure in probability
distributions. This article analyzes the graphical model of nodal voltages in
non-radial power distribution grids. Using algebraic and structural properties
of graphical models, algorithms exactly determining topology and detecting line
changes for distribution grids are presented along with their theoretical
limitations. We show that if distribution grids have cycles/loops of size
greater than three, then nodal voltages are sufficient for efficient topology
estimation without additional assumptions on system parameters. In contrast,
line failure or change detection using nodal voltages does not require any
structural assumption. Under noisy measurements, we provide the first
non-trivial bounds on the maximum noise that the system can tolerate for
asymptotically correct topology recovery. The performance of the designed
algorithms is validated with nonlinear AC power flow samples generated by
Matpower on test grids, including scenarios with injection correlations and
system noise.Comment: 12 pages, 9 figures, IEEE Transactions on Smart Gri
Topology Estimation in Bulk Power Grids: Guarantees on Exact Recovery
The topology of a power grid affects its dynamic operation and settlement in
the electricity market. Real-time topology identification can enable faster
control action following an emergency scenario like failure of a line. This
article discusses a graphical model framework for topology estimation in bulk
power grids (both loopy transmission and radial distribution) using
measurements of voltage collected from the grid nodes. The graphical model for
the probability distribution of nodal voltages in linear power flow models is
shown to include additional edges along with the operational edges in the true
grid. Our proposed estimation algorithms first learn the graphical model and
subsequently extract the operational edges using either thresholding or a
neighborhood counting scheme. For grid topologies containing no three-node
cycles (two buses do not share a common neighbor), we prove that an exact
extraction of the operational topology is theoretically guaranteed. This
includes a majority of distribution grids that have radial topologies. For
grids that include cycles of length three, we provide sufficient conditions
that ensure existence of algorithms for exact reconstruction. In particular,
for grids with constant impedance per unit length and uniform injection
covariances, this observation leads to conditions on geographical placement of
the buses. The performance of algorithms is demonstrated in test case
simulations.Comment: 10 pages, 8 figures. A version of this paper will appear in IREP 201
Unbalanced Multi-Phase Distribution Grid Topology Estimation and Bus Phase Identification
There is an increasing need for monitoring and controlling uncertainties
brought by distributed energy resources in distribution grids. For such goal,
accurate multi-phase topology is the basis for correlating measurements in
unbalanced distribution networks. Unfortunately, such topology knowledge is
often unavailable due to limited investment, especially for \revv{low-voltage}
distribution grids. Also, the bus phase labeling information is inaccurate due
to human errors or outdated records. For this challenge, this paper utilizes
smart meter data for an information-theoretic approach to learn the topology of
distribution grids. Specifically, multi-phase unbalanced systems are converted
into symmetrical components, namely positive, negative, and zero sequences.
Then, this paper proves that the Chow-Liu algorithm finds the topology by
utilizing power flow equations and the conditional independence relationships
implied by the radial multi-phase structure of distribution grids with the
presence of incorrect bus phase labels. At last, by utilizing Carson's
equation, this paper proves that the bus phase connection can be correctly
identified using voltage measurements. For validation, IEEE systems are
simulated using three real data sets. The simulation results demonstrate that
the algorithm is highly accurate for finding multi-phase topology even with
strong load unbalancing condition and DERs. This ensures close monitoring and
controlling DERs in distribution grids.Comment: 17 pages, 18 figure
Learning with End-Users in Distribution Grids: Topology and Parameter Estimation
Efficient operation of distribution grids in the smart-grid era is hindered
by the limited presence of real-time nodal and line meters. In particular, this
prevents the easy estimation of grid topology and associated line parameters
that are necessary for control and optimization efforts in the grid. This paper
studies the problems of topology and parameter estimation in radial balanced
distribution grids where measurements are restricted to only the leaf nodes and
all intermediate nodes are unobserved/hidden. To this end, we propose two exact
learning algorithms that use balanced voltage and injection measured only at
the end-users. The first algorithm requires time-stamped voltage samples,
statistics of nodal power injections and permissible line impedances to recover
the true topology. The second and improved algorithm requires only time-stamped
voltage and complex power samples to recover both the true topology and
impedances without any additional input (e.g., number of grid nodes, statistics
of injections at hidden nodes, permissible line impedances). We prove the
correctness of both learning algorithms for grids where unobserved buses/nodes
have a degree greater than three and discuss extensions to regimes where that
assumption doesn't hold. Further, we present computational and, more
importantly, the sample complexity of our proposed algorithm for joint topology
and impedance estimation. We illustrate the performance of the designed
algorithms through numerical experiments on the IEEE and custom power
distribution models
A Survey on State Estimation Techniques and Challenges in Smart Distribution Systems
This paper presents a review of the literature on State Estimation (SE) in
power systems. While covering some works related to SE in transmission systems,
the main focus of this paper is Distribution System State Estimation (DSSE).
The paper discusses a few critical topics of DSSE, including mathematical
problem formulation, application of pseudo-measurements, metering instrument
placement, network topology issues, impacts of renewable penetration, and
cyber-security. Both conventional and modern data-driven and probabilistic
techniques have been reviewed. This paper can provide researchers and utility
engineers with insights into the technical achievements, barriers, and future
research directions of DSSE
Joint Estimation of Topology and Injection Statistics in Distribution Grids with Missing Nodes
Optimal operation of distribution grid resources relies on accurate
estimation of its state and topology. Practical estimation of such quantities
is complicated by the limited presence of real-time meters. This paper
discusses a theoretical framework to jointly estimate the operational topology
and statistics of injections in radial distribution grids under limited
availability of nodal voltage measurements. In particular we show that our
proposed algorithms are able to provably learn the exact grid topology and
injection statistics at all unobserved nodes as long as they are not adjacent.
The algorithm design is based on novel ordered trends in voltage magnitude
fluctuations at node groups, that are independently of interest for radial
physical flow networks. The complexity of the designed algorithms is
theoretically analyzed and their performance validated using both linearized
and non-linear AC power flow samples in test distribution grids.Comment: 12 pages, 13 figure
Robust Hidden Topology Identification in Distribution Systems
With more distributed energy resources (DERs) connected to distribution
grids, better monitoring and control are needed, where identifying the topology
accurately is the prerequisite. However, due to frequent re-configurations,
operators usually cannot know a complete structure in distribution grids.
Luckily, the growing data from smart sensors, restricted by Ohm law, provides
the possibility of topology inference. In this paper, we show how line
parameters of Ohm equation can be estimated for topology identification even
when there are hidden nodes. Specifically, the introduced learning method
recursively conducts hidden-node detection and impedance calculation. However,
the assumptions on uncorrelated data, availability of phasor measurements, and
a balanced system, are not met in practices, causing large errors. To resolve
these problems, we employ Cholesky whitening first with a proof for measurement
decorrelations. For increasing robustness further, we show how to handle
practical scenarios when only measurement magnitudes are available or when the
grid is three-phase unbalanced. Numerical performance is verified on multi-size
distribution grids with both simulation and real-world data.Comment: 11 pages, 15 figures, journa
Tractable learning in under-excited power grids
Estimating the structure of physical flow networks such as power grids is
critical to secure delivery of energy. 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. Prior estimation
algorithms based on nodal potentials or voltages fail in the under-excited
regime. We propose a novel topology learning algorithm for learning
underexcited general (non-radial) networks based on physics-informed
conservation laws. We prove the asymptotic correctness of our algorithm for
grids with non-adjacent under-excited internal nodes. More importantly, we
theoretically analyze our algorithm's efficacy under noisy measurements, and
determine bounds on maximum noise under which asymptotically correct recovery
is guaranteed. Our approach is validated through simulations with non-linear
voltage samples generated on test grids with real injection dataComment: 10 pages, 8 figure
Physics Informed Topology Learning in Networks of Linear Dynamical Systems
Learning influence pathways of a network of dynamically related processes
from observations is of considerable importance in many disciplines. In this
article, influence networks of agents which interact dynamically via linear
dependencies are considered. An algorithm for the reconstruction of the
topology of interaction based on multivariate Wiener filtering is analyzed. It
is shown that for a vast and important class of interactions, that respect flow
conservation, the topology of the interactions can be exactly recovered. The
class of problems where reconstruction is guaranteed to be exact includes power
distribution networks, dynamic thermal networks and consensus networks. The
efficacy of the approach is illustrated through simulation and experiments on
consensus networks, IEEE power distribution networks and thermal dynamics of
buildings.Comment: 14 pages, 10 figure
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