18,440 research outputs found
Data-driven Chance-constrained Regulation Capacity Offering for Distributed Energy Resources
This paper studies the behavior of a strategic aggregator offering regulation
capacity on behalf of a group of distributed energy resources (DERs, e.g.
plug-in electric vehicles) in a power market. Our objective is to maximize the
aggregator's revenue while controlling the risk of penalties due to poor
service delivery. To achieve this goal, we propose data-driven risk-averse
strategies to effectively handle uncertainties in: 1) The DER parameters (e.g.,
load demands and flexibilities) and 2) sub-hourly regulation signals (to the
accuracy of every few seconds). We design both the day-ahead and the hour-ahead
strategies. In the day-ahead model, we develop a two-stage stochastic program
to roughly model the above uncertainties, which achieves computational
efficiency by leveraging novel aggregate models of both DER parameters and
sub-hourly regulation signals. In the hour-ahead model, we formulate a
data-driven distributionally robust chance-constrained program to explicitly
model the aforementioned uncertainties. This program can effectively control
the quality of regulation service based on the aggregator's risk aversion.
Furthermore, it learns the distributions of the uncertain parameters from
empirical data so that it outperforms existing techniques, (e.g. robust
optimization or traditional chance-constrained programming) in both modelling
accuracy and cost of robustness. Finally, we derive a conic safe approximation
for it which can be efficiently solved by commercial solvers. Numerical
experiments are conducted to validate the proposed method
Optimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming
This paper reviews recent advances in the field of optimization under
uncertainty via a modern data lens, highlights key research challenges and
promise of data-driven optimization that organically integrates machine
learning and mathematical programming for decision-making under uncertainty,
and identifies potential research opportunities. A brief review of classical
mathematical programming techniques for hedging against uncertainty is first
presented, along with their wide spectrum of applications in Process Systems
Engineering. A comprehensive review and classification of the relevant
publications on data-driven distributionally robust optimization, data-driven
chance constrained program, data-driven robust optimization, and data-driven
scenario-based optimization is then presented. This paper also identifies
fertile avenues for future research that focuses on a closed-loop data-driven
optimization framework, which allows the feedback from mathematical programming
to machine learning, as well as scenario-based optimization leveraging the
power of deep learning techniques. Perspectives on online learning-based
data-driven multistage optimization with a learning-while-optimizing scheme is
presented
Distributionally Robust Chance Constrained Programming with Generative Adversarial Networks (GANs)
This paper presents a novel deep learning based data-driven optimization
method. A novel generative adversarial network (GAN) based data-driven
distributionally robust chance constrained programming framework is proposed.
GAN is applied to fully extract distributional information from historical data
in a nonparametric and unsupervised way without a priori approximation or
assumption. Since GAN utilizes deep neural networks, complicated data
distributions and modes can be learned, and it can model uncertainty
efficiently and accurately. Distributionally robust chance constrained
programming takes into consideration ambiguous probability distributions of
uncertain parameters. To tackle the computational challenges, sample average
approximation method is adopted, and the required data samples are generated by
GAN in an end-to-end way through the differentiable networks. The proposed
framework is then applied to supply chain optimization under demand
uncertainty. The applicability of the proposed approach is illustrated through
a county-level case study of a spatially explicit biofuel supply chain in
Illinois
Data-driven Decision Making with Probabilistic Guarantees (Part 2): Applications of Chance-constrained Optimization in Power Systems
Uncertainties from deepening penetration of renewable energy resources have
posed critical challenges to the secure and reliable operations of future
electric grids. Among various approaches for decision making in uncertain
environments, this paper focuses on chance-constrained optimization, which
provides explicit probabilistic guarantees on the feasibility of optimal
solutions. Although quite a few methods have been proposed to solve
chance-constrained optimization problems, there is a lack of comprehensive
review and comparative analysis of the proposed methods. Part I of this
two-part paper reviews three categories of existing methods to
chance-constrained optimization: (1) scenario approach; (2) sample average
approximation; and (3) robust optimization based methods. Data-driven methods,
which are not constrained by any particular distributions of the underlying
uncertainties, are of particular interest. Part II of this two-part paper
provides a literature review on the applications of chance-constrained
optimization in power systems. Part II also provides a critical comparison of
existing methods based on numerical simulations, which are conducted on
standard power system test cases.Comment: (under review) to be update
Data-based Distributionally Robust Stochastic Optimal Power Flow, Part I: Methodologies
We propose a data-based method to solve a multi-stage stochastic optimal
power flow (OPF) problem based on limited information about forecast error
distributions. The framework explicitly combines multi-stage feedback policies
with any forecasting method and historical forecast error data. The objective
is to determine power scheduling policies for controllable devices in a power
network to balance operational cost and conditional value-at-risk (CVaR) of
device and network constraint violations. These decisions include both nominal
power schedules and reserve policies, which specify planned reactions to
forecast errors in order to accommodate fluctuating renewable energy sources.
Instead of assuming the uncertainties across the networks follow prescribed
probability distributions, we consider ambiguity sets of distributions centered
around a finite training dataset. By utilizing the Wasserstein metric to
quantify differences between the empirical data-based distribution and the real
unknown data-generating distribution, we formulate a multi-stage
distributionally robust OPF problem to compute optimal control policies that
are robust to both forecast errors and sampling errors inherent in the dataset.
Two specific data-based distributionally robust stochastic OPF problems are
proposed for distribution networks and transmission systems.Comment: arXiv admin note: text overlap with arXiv:1706.0426
A data-driven robust optimization approach to scenario-based stochastic model predictive control
Stochastic model predictive control (SMPC) has been a promising solution to
complex control problems under uncertain disturbances. However, traditional
SMPC approaches either require exact knowledge of probabilistic distributions,
or rely on massive scenarios that are generated to represent uncertainties. In
this paper, a novel scenario-based SMPC approach is proposed by actively
learning a data-driven uncertainty set from available data with machine
learning techniques. A systematical procedure is then proposed to further
calibrate the uncertainty set, which gives appropriate probabilistic guarantee.
The resulting data-driven uncertainty set is more compact than traditional
norm-based sets, and can help reducing conservatism of control actions.
Meanwhile, the proposed method requires less data samples than traditional
scenario-based SMPC approaches, thereby enhancing the practicability of SMPC.
Finally the optimal control problem is cast as a single-stage robust
optimization problem, which can be solved efficiently by deriving the robust
counterpart problem. The feasibility and stability issue is also discussed in
detail. The efficacy of the proposed approach is demonstrated through a
two-mass-spring system and a building energy control problem under uncertain
disturbances
Optimal corrective dispatch of uncertain virtual energy storage systems
High penetrations of intermittent renewable energy resources in the power
system require large balancing reserves for reliable operations. Aggregated and
coordinated behind-the-meter loads can provide these fast reserves, but
represent energy-constrained and uncertain reserves (in their energy state and
capacity). To optimally dispatch uncertain, energy-constrained reserves,
optimization-based techniques allow one to develop an appropriate trade-off
between closed-loop performance and robustness of the dispatch. Therefore, this
paper investigates the uncertainty associated with energy-constrained
aggregations of flexible, behind-the-meter distributed energy resources (DERs).
The uncertainty studied herein is associated with estimating the state of
charge and the capacity of an aggregation of DERs (i.e., a virtual energy
storage system or VESS). To that effect, a risk-based chance-constrained
control strategy is developed that optimizes the operational risk of
unexpectedly saturating the VESS against deviating generators from their
scheduled set-points. The controller coordinates energy-constrained VESSs to
minimize unscheduled participation of and overcome ramp-rate limited generators
for balancing variability from renewable generation, while taking into account
grid conditions. To illustrate the effectiveness of the proposed method,
simulation-based analysis is carried out on an augmented IEEE RTS-96 network
with uncertain energy resources and temperature-based dynamic line ratings
Distributionally Robust Chance Constrained Optimal Power Flow Assuming Unimodal Distributions with Misspecified Modes
Chance constrained optimal power flow (CC-OPF) formulations have been
proposed to minimize operational costs while controlling the risk arising from
uncertainties like renewable generation and load consumption. To solve CC-OPF,
we often need access to the (true) joint probability distribution of all
uncertainties, which is rarely known in practice. A solution based on a biased
estimate of the distribution can result in poor reliability. To overcome this
challenge, recent work has explored distributionally robust chance constraints,
in which the chance constraints are satisfied over a family of distributions
called the ambiguity set. Commonly, ambiguity sets are only based on moment
information (e.g., mean and covariance) of the random variables; however,
specifying additional characteristics of the random variables reduces
conservatism and cost. Here, we consider ambiguity sets that additionally
incorporate unimodality information. In practice, it is difficult to estimate
the mode location from the data and so we allow it to be potentially
misspecified. We formulate the problem and derive a separation-based algorithm
to efficiently solve it. Finally, we evaluate the performance of the proposed
approach on a modified IEEE-30 bus network with wind uncertainty and compare
with other distributionally robust approaches. We find that a misspecified mode
significantly affects the reliability of the solution and the proposed model
demonstrates a good trade-off between cost and reliability
A Data-Driven Distributionally Robust Bound on the Expected Optimal Value of Uncertain Mixed 0-1 Linear Programming
This paper studies the expected optimal value of a mixed 0-1 programming
problem with uncertain objective coefficients following a joint distribution.
We assume that the true distribution is not known exactly, but a set of
independent samples can be observed. Using the Wasserstein metric, we construct
an ambiguity set centered at the empirical distribution from the observed
samples and containing the true distribution with a high statistical guarantee.
The problem of interest is to investigate the bound on the expected optimal
value over the Wasserstein ambiguity set. Under standard assumptions, we
reformulate the problem into a copositive program, which naturally leads to a
tractable semidefinite-based approximation. We compare our approach with a
moment-based approach from the literature on three applications. Numerical
results illustrate the effectiveness of our approach.Comment: 29 pages, 8 figures, and 3 table
Optimal Power Flow: An Introduction to Predictive, Distributed and Stochastic Control Challenges
The Energiewende is a paradigm change that can be witnessed at latest since
the political decision to step out of nuclear energy. Moreover, despite common
roots in Electrical Engineering, the control community and the power systems
community face a lack of common vocabulary. In this context, this paper aims at
providing a systems-and-control specific introduction to optimal power flow
problems which are pivotal in the operation of energy systems. Based on a
concise problem statement, we introduce a common description of optimal power
flow variants including multi-stage-problems and predictive control, stochastic
uncertainties, and issues of distributed optimization. Moreover, we sketch open
questions that might be of interest for the systems and control community
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