89,707 research outputs found
Stochastic Model for Power Grid Dynamics
We introduce a stochastic model that describes the quasi-static dynamics of
an electric transmission network under perturbations introduced by random load
fluctuations, random removing of system components from service, random repair
times for the failed components, and random response times to implement optimal
system corrections for removing line overloads in a damaged or stressed
transmission network. We use a linear approximation to the network flow
equations and apply linear programming techniques that optimize the dispatching
of generators and loads in order to eliminate the network overloads associated
with a damaged system. We also provide a simple model for the operator's
response to various contingency events that is not always optimal due to either
failure of the state estimation system or due to the incorrect subjective
assessment of the severity associated with these events. This further allows us
to use a game theoretic framework for casting the optimization of the
operator's response into the choice of the optimal strategy which minimizes the
operating cost. We use a simple strategy space which is the degree of tolerance
to line overloads and which is an automatic control (optimization) parameter
that can be adjusted to trade off automatic load shed without propagating
cascades versus reduced load shed and an increased risk of propagating
cascades. The tolerance parameter is chosen to describes a smooth transition
from a risk averse to a risk taken strategy...Comment: framework for a system-level analysis of the power grid from the
viewpoint of complex network
Optimization in task--completion networks
We discuss the collective behavior of a network of individuals that receive,
process and forward to each other tasks. Given costs they store those tasks in
buffers, choosing optimally the frequency at which to check and process the
buffer. The individual optimizing strategy of each node determines the
aggregate behavior of the network. We find that, under general assumptions, the
whole system exhibits coexistence of equilibria and hysteresis.Comment: 18 pages, 3 figures, submitted to JSTA
Optimal Ensemble Control of Loads in Distribution Grids with Network Constraints
Flexible loads, e.g. thermostatically controlled loads (TCLs), are
technically feasible to participate in demand response (DR) programs. On the
other hand, there is a number of challenges that need to be resolved before it
can be implemented in practice en masse. First, individual TCLs must be
aggregated and operated in sync to scale DR benefits. Second, the uncertainty
of TCLs needs to be accounted for. Third, exercising the flexibility of TCLs
needs to be coordinated with distribution system operations to avoid
unnecessary power losses and compliance with power flow and voltage limits.
This paper addresses these challenges. We propose a network-constrained,
open-loop, stochastic optimal control formulation. The first part of this
formulation represents ensembles of collocated TCLs modelled by an aggregated
Markov Process (MP), where each MP state is associated with a given power
consumption or production level. The second part extends MPs to a multi-period
distribution power flow optimization. In this optimization, the control of TCL
ensembles is regulated by transition probability matrices and physically
enabled by local active and reactive power controls at TCL locations. The
optimization is solved with a Spatio-Temporal Dual Decomposition (ST-D2)
algorithm. The performance of the proposed formulation and algorithm is
demonstrated on the IEEE 33-bus distribution model.Comment: 7 pages, 6 figures, accepted PSCC 201
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