33 research outputs found
Inexact Convex Relaxations for AC Optimal Power Flow: Towards AC Feasibility
Convex relaxations of AC optimal power flow (AC-OPF) problems have attracted
significant interest as in several instances they provably yield the global
optimum to the original non-convex problem. If, however, the relaxation is
inexact, the obtained solution is not AC-feasible. The quality of the obtained
solution is essential for several practical applications of AC-OPF, but
detailed analyses are lacking in existing literature. This paper aims to cover
this gap. We provide an in-depth investigation of the solution characteristics
when convex relaxations are inexact, we assess the most promising AC
feasibility recovery methods for large-scale systems, and we propose two new
metrics that lead to a better understanding of the quality of the identified
solutions. We perform a comprehensive assessment on 96 different test cases,
ranging from 14 to 3120 buses, and we show the following: (i) Despite an
optimality gap of less than 1%, several test cases still exhibit substantial
distances to both AC feasibility and local optimality and the newly proposed
metrics characterize these deviations. (ii) Penalization methods fail to
recover an AC-feasible solution in 15 out of 45 cases, and using the proposed
metrics, we show that most failed test instances exhibit substantial distances
to both AC-feasibility and local optimality. For failed test instances with
small distances, we show how our proposed metrics inform a fine-tuning of
penalty weights to obtain AC-feasible solutions. (iii) The computational
benefits of warm-starting non-convex solvers have significant variation, but a
computational speedup exists in over 75% of the cases
Efficient Database Generation for Data-driven Security Assessment of Power Systems
Power system security assessment methods require large datasets of operating
points to train or test their performance. As historical data often contain
limited number of abnormal situations, simulation data are necessary to
accurately determine the security boundary. Generating such a database is an
extremely demanding task, which becomes intractable even for small system
sizes. This paper proposes a modular and highly scalable algorithm for
computationally efficient database generation. Using convex relaxation
techniques and complex network theory, we discard large infeasible regions and
drastically reduce the search space. We explore the remaining space by a highly
parallelizable algorithm and substantially decrease computation time. Our
method accommodates numerous definitions of power system security. Here we
focus on the combination of N-k security and small-signal stability.
Demonstrating our algorithm on IEEE 14-bus and NESTA 162-bus systems, we show
how it outperforms existing approaches requiring less than 10% of the time
other methods require.Comment: Database publicly available at:
https://github.com/johnnyDEDK/OPs_Nesta162Bus - Paper accepted for
publication at IEEE Transactions on Power System
Verification of Neural Network Behaviour: Formal Guarantees for Power System Applications
This paper presents for the first time, to our knowledge, a framework for
verifying neural network behavior in power system applications. Up to this
moment, neural networks have been applied in power systems as a black-box; this
has presented a major barrier for their adoption in practice. Developing a
rigorous framework based on mixed integer linear programming, our methods can
determine the range of inputs that neural networks classify as safe or unsafe,
and are able to systematically identify adversarial examples. Such methods have
the potential to build the missing trust of power system operators on neural
networks, and unlock a series of new applications in power systems. This paper
presents the framework, methods to assess and improve neural network robustness
in power systems, and addresses concerns related to scalability and accuracy.
We demonstrate our methods on the IEEE 9-bus, 14-bus, and 162-bus systems,
treating both N-1 security and small-signal stability.Comment: published in IEEE Transactions on Smart Grid
(https://ieeexplore.ieee.org/abstract/document/9141308
Convex Relaxations of Probabilistic AC Optimal Power Flow for Interconnected AC and HVDC Grids
High Voltage Direct Current (HVDC) systems interconnect AC grids to increase
reliability, connect offshore wind generation, and enable coupling of
electricity markets. Considering the growing uncertainty in power infeed and
the complexity introduced by additional controls, robust decision support tools
are necessary. This paper proposes a chance constrained AC-OPF for AC and HVDC
grids, which considers wind uncertainty, fully utilizes HVDC control
capabilities, and uses the semidefinite relaxation of the AC-OPF. We consider a
joint chance constraint for both AC and HVDC systems, we introduce a piecewise
affine approximation to achieve tractability of the chance constraint, and we
allow corrective control policies for HVDC converters and generators to be
determined. An active loss penalty term in the objective function and a
systematic procedure to choose the penalty weights allow us to obtain
AC-feasible solutions. We introduce Benders decomposition to maintain
scalability. Using realistic forecast data, we demonstrate our approach on a
53-bus and a 214-bus AC-DC system, obtaining tight near-global optimality
guarantees. With a Monte Carlo analysis, we show that a chance constrained
DC-OPF leads to violations, whereas our proposed approach complies with the
joint chance constraint
Chance-Constrained AC Optimal Power Flow Integrating HVDC Lines and Controllability
The integration of large-scale renewable generation has major implications on
the operation of power systems, two of which we address in this work. First,
system operators have to deal with higher degrees of uncertainty due to
forecast errors and variability in renewable energy production. Second, with
abundant potential of renewable generation in remote locations, there is an
increasing interest in the use of High Voltage Direct Current lines (HVDC) to
increase transmission capacity. These HVDC transmission lines and the
flexibility and controllability they offer must be incorporated effectively and
safely into the system. In this work, we introduce an optimization tool that
addresses both challenges by incorporating the full AC power flow equations,
chance constraints to address the uncertainty of renewable infeed, modelling of
point-to-point HVDC lines, and optimized corrective control policies to model
the generator and HVDC response to uncertainty. The main contributions are
twofold. First, we introduce a HVDC line model and the corresponding HVDC
participation factors in a chance-constrained AC-OPF framework. Second, we
modify an existing algorithm for solving the chance-constrained AC-OPF to allow
for optimization of the generation and HVDC participation factors. Using
realistic wind forecast data, for 10 and IEEE 39 bus systems with HVDC lines
and wind farms, we show that our proposed OPF formulation achieves good in- and
out-of-sample performance whereas not considering uncertainty leads to high
constraint violation probabilities. In addition, we find that optimizing the
participation factors reduces the cost of uncertainty significantly
Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networks
This paper introduces for the first time a framework to obtain provable worst-case guarantees for neural network performance, using learning for optimal power flow (OPF) problems as a guiding example. Neural networks have the potential to substantially reduce the computing time of OPF solutions. However, the lack of guarantees for their worst-case performance remains a major barrier for their adoption in practice. This work aims to remove this barrier. We formulate mixed-integer linear programs to obtain worst-case guarantees for neural network predictions related to (i) maximum constraint violations, (ii) maximum distances between predicted and optimal decision variables, and (iii) maximum sub-optimality. We demonstrate our methods on a range of PGLib-OPF networks up to 300 buses. We show that the worst-case guarantees can be up to one order of magnitude larger than the empirical lower bounds calculated with conventional methods. More importantly, we show that the worst-case predictions appear at the boundaries of the training input domain, and we demonstrate how we can systematically reduce the worst-case guarantees by training on a larger input domain than the domain they are evaluated on
Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networks
This paper introduces for the first time a framework to obtain provable
worst-case guarantees for neural network performance, using learning for
optimal power flow (OPF) problems as a guiding example. Neural networks have
the potential to substantially reduce the computing time of OPF solutions.
However, the lack of guarantees for their worst-case performance remains a
major barrier for their adoption in practice. This work aims to remove this
barrier. We formulate mixed-integer linear programs to obtain worst-case
guarantees for neural network predictions related to (i) maximum constraint
violations, (ii) maximum distances between predicted and optimal decision
variables, and (iii) maximum sub-optimality. We demonstrate our methods on a
range of PGLib-OPF networks up to 300 buses. We show that the worst-case
guarantees can be up to one order of magnitude larger than the empirical lower
bounds calculated with conventional methods. More importantly, we show that the
worst-case predictions appear at the boundaries of the training input domain,
and we demonstrate how we can systematically reduce the worst-case guarantees
by training on a larger input domain than the domain they are evaluated on.Comment: The code to reproduce the simulation results is available
https://doi.org/10.5281/zenodo.387175