734 research outputs found
Stochastic Optimal Power Flow Based on Data-Driven Distributionally Robust Optimization
We propose a data-driven method to solve a stochastic optimal power flow
(OPF) problem based on limited information about forecast error distributions.
The objective is to determine power schedules for controllable devices in a
power network to balance operation cost and conditional value-at-risk (CVaR) of
device and network constraint violations. These decisions include scheduled
power output adjustments 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 assume the distributions are only
observable through a finite training dataset. By utilizing the Wasserstein
metric to quantify differences between the empirical data-based distribution
and the real data-generating distribution, we formulate a distributionally
robust optimization OPF problem to search for power schedules and reserve
policies that are robust to sampling errors inherent in the dataset. A simple
numerical example illustrates inherent tradeoffs between operation cost and
risk of constraint violation, and we show how our proposed method offers a
data-driven framework to balance these objectives
Data Valuation from Data-Driven Optimization
With the ongoing investment in data collection and communication technology
in power systems, data-driven optimization has been established as a powerful
tool for system operators to handle stochastic system states caused by weather-
and behavior-dependent resources. However, most methods are ignorant to data
quality, which may differ based on measurement and underlying
privacy-protection mechanisms. This paper addresses this shortcoming by (i)
proposing a practical data quality metric based on Wasserstein distance, (ii)
leveraging a novel modification of distributionally robust optimization using
information from multiple data sets with heterogeneous quality to valuate data,
(iii) applying the proposed optimization framework to an optimal power flow
problem, and (iv) showing a direct method to valuate data from the optimal
solution. We conduct numerical experiments to analyze and illustrate the
proposed model and publish the implementation open-source
Data-Driven Chance Constrained Optimization under Wasserstein Ambiguity Sets
We present a data-driven approach for distributionally robust chance
constrained optimization problems (DRCCPs). We consider the case where the
decision maker has access to a finite number of samples or realizations of the
uncertainty. The chance constraint is then required to hold for all
distributions that are close to the empirical distribution constructed from the
samples (where the distance between two distributions is defined via the
Wasserstein metric). We first reformulate DRCCPs under data-driven Wasserstein
ambiguity sets and a general class of constraint functions. When the
feasibility set of the chance constraint program is replaced by its convex
inner approximation, we present a convex reformulation of the program and show
its tractability when the constraint function is affine in both the decision
variable and the uncertainty. For constraint functions concave in the
uncertainty, we show that a cutting-surface algorithm converges to an
approximate solution of the convex inner approximation of DRCCPs. Finally, for
constraint functions convex in the uncertainty, we compare the feasibility set
with other sample-based approaches for chance constrained programs.Comment: A shorter version is submitted to the American Control Conference,
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