79 research outputs found
Construction of power flow feasibility sets
We develop a new approach for construction of convex analytically simple
regions where the AC power flow equations are guaranteed to have a feasible
solutions. Construction of these regions is based on efficient semidefinite
programming techniques accelerated via sparsity exploiting algorithms.
Resulting regions have a simple geometric shape in the space of power
injections (polytope or ellipsoid) and can be efficiently used for assessment
of system security in the presence of uncertainty. Efficiency and tightness of
the approach is validated on a number of test networks
A differential analysis of the power flow equations
The AC power flow equations are fundamental in all aspects of power systems
planning and operations. They are routinely solved using Newton-Raphson like
methods. However, there is little theoretical understanding of when these
algorithms are guaranteed to find a solution of the power flow equations or how
long they may take to converge. Further, it is known that in general these
equations have multiple solutions and can exhibit chaotic behavior. In this
paper, we show that the power flow equations can be solved efficiently provided
that the solution lies in a certain set. We introduce a family of convex
domains, characterized by Linear Matrix Inequalities, in the space of voltages
such that there is at most one power flow solution in each of these domains.
Further, if a solution exists in one of these domains, it can be found
efficiently, and if one does not exist, a certificate of non-existence can also
be obtained efficiently. The approach is based on the theory of monotone
operators and related algorithms for solving variational inequalities involving
monotone operators. We validate our approach on IEEE test networks and show
that practical power flow solutions lie within an appropriately chosen convex
domain.Comment: arXiv admin note: text overlap with arXiv:1506.0847
Storage Sizing and Placement through Operational and Uncertainty-Aware Simulations
As the penetration level of transmission-scale time-intermittent renewable
generation resources increases, control of flexible resources will become
important to mitigating the fluctuations due to these new renewable resources.
Flexible resources may include new or existing synchronous generators as well
as new energy storage devices. Optimal placement and sizing of energy storage
to minimize costs of integrating renewable resources is a difficult
optimization problem. Further,optimal planning procedures typically do not
consider the effect of the time dependence of operations and may lead to
unsatisfactory results. Here, we use an optimal energy storage control
algorithm to develop a heuristic procedure for energy storage placement and
sizing. We perform operational simulation under various time profiles of
intermittent generation, loads and interchanges (artificially generated or from
historical data) and accumulate statistics of the usage of storage at each node
under the optimal dispatch. We develop a greedy heuristic based on the
accumulated statistics to obtain a minimal set of nodes for storage placement.
The quality of the heuristic is explored by comparing our results to the
obvious heuristic of placing storage at the renewables for IEEE benchmarks and
real-world network topologies.Comment: To Appear in proceedings of Hawaii International Conference on System
Sciences (HICSS-2014
Universal Convexification via Risk-Aversion
We develop a framework for convexifying a fairly general class of
optimization problems. Under additional assumptions, we analyze the
suboptimality of the solution to the convexified problem relative to the
original nonconvex problem and prove additive approximation guarantees. We then
develop algorithms based on stochastic gradient methods to solve the resulting
optimization problems and show bounds on convergence rates. %We show a simple
application of this framework to supervised learning, where one can perform
integration explicitly and can use standard (non-stochastic) optimization
algorithms with better convergence guarantees. We then extend this framework to
apply to a general class of discrete-time dynamical systems. In this context,
our convexification approach falls under the well-studied paradigm of
risk-sensitive Markov Decision Processes. We derive the first known model-based
and model-free policy gradient optimization algorithms with guaranteed
convergence to the optimal solution. Finally, we present numerical results
validating our formulation in different applications
- …