677 research outputs found
Adaptive Robust Optimization with Dynamic Uncertainty Sets for Multi-Period Economic Dispatch under Significant Wind
The exceptional benefits of wind power as an environmentally responsible
renewable energy resource have led to an increasing penetration of wind energy
in today's power systems. This trend has started to reshape the paradigms of
power system operations, as dealing with uncertainty caused by the highly
intermittent and uncertain wind power becomes a significant issue. Motivated by
this, we present a new framework using adaptive robust optimization for the
economic dispatch of power systems with high level of wind penetration. In
particular, we propose an adaptive robust optimization model for multi-period
economic dispatch, and introduce the concept of dynamic uncertainty sets and
methods to construct such sets to model temporal and spatial correlations of
uncertainty. We also develop a simulation platform which combines the proposed
robust economic dispatch model with statistical prediction tools in a rolling
horizon framework. We have conducted extensive computational experiments on
this platform using real wind data. The results are promising and demonstrate
the benefits of our approach in terms of cost and reliability over existing
robust optimization models as well as recent look-ahead dispatch models.Comment: Accepted for publication at IEEE Transactions on Power System
New Formulation and Strong MISOCP Relaxations for AC Optimal Transmission Switching Problem
As the modern transmission control and relay technologies evolve,
transmission line switching has become an important option in power system
operators' toolkits to reduce operational cost and improve system reliability.
Most recent research has relied on the DC approximation of the power flow model
in the optimal transmission switching problem. However, it is known that DC
approximation may lead to inaccurate flow solutions and also overlook stability
issues. In this paper, we focus on the optimal transmission switching problem
with the full AC power flow model, abbreviated as AC OTS. We propose a new
exact formulation for AC OTS and its mixed-integer second-order conic
programming (MISOCP) relaxation. We improve this relaxation via several types
of strong valid inequalities inspired by the recent development for the closely
related AC Optimal Power Flow (AC OPF) problem. We also propose a practical
algorithm to obtain high quality feasible solutions for the AC OTS problem.
Extensive computational experiments show that the proposed formulation and
algorithms efficiently solve IEEE standard and congested instances and lead to
significant cost benefits with provably tight bounds
Dual Descent ALM and ADMM
Classical primal-dual algorithms attempt to solve by alternatively minimizing over the primal variable
through primal descent and maximizing the dual variable through dual
ascent. However, when is highly nonconvex with complex
constraints in , the minimization over may not achieve global
optimality, and hence the dual ascent step loses its valid intuition. This
observation motivates us to propose a new class of primal-dual algorithms for
nonconvex constrained optimization with the key feature to reverse dual ascent
to a conceptually new dual descent, in a sense, elevating the dual variable to
the same status as the primal variable. Surprisingly, this new dual scheme
achieves some best iteration complexities for solving nonconvex optimization
problems. In particular, when the dual descent step is scaled by a fractional
constant, we name it scaled dual descent (SDD), otherwise, unscaled dual
descent (UDD). For nonconvex multiblock optimization with nonlinear equality
constraints, we propose SDD-ADMM and show that it finds an
-stationary solution in iterations. The
complexity is further improved to and
under proper conditions. We also propose UDD-ALM,
combining UDD with ALM, for weakly convex minimization over affine constraints.
We show that UDD-ALM finds an -stationary solution in
iterations. These complexity bounds for both
algorithms either achieve or improve the best-known results in the ADMM and ALM
literature. Moreover, SDD-ADMM addresses a long-standing limitation of existing
ADMM frameworks
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