148 research outputs found
On the Economic Value and Price-Responsiveness of Ramp-Constrained Storage
The primary concerns of this paper are twofold: to understand the economic
value of storage in the presence of ramp constraints and exogenous electricity
prices, and to understand the implications of the associated optimal storage
management policy on qualitative and quantitative characteristics of storage
response to real-time prices. We present an analytic characterization of the
optimal policy, along with the associated finite-horizon time-averaged value of
storage. We also derive an analytical upperbound on the infinite-horizon
time-averaged value of storage. This bound is valid for any achievable
realization of prices when the support of the distribution is fixed, and
highlights the dependence of the value of storage on ramp constraints and
storage capacity. While the value of storage is a non-decreasing function of
price volatility, due to the finite ramp rate, the value of storage saturates
quickly as the capacity increases, regardless of volatility. To study the
implications of the optimal policy, we first present computational experiments
that suggest that optimal utilization of storage can, in expectation, induce a
considerable amount of price elasticity near the average price, but little or
no elasticity far from it. We then present a computational framework for
understanding the behavior of storage as a function of price and the amount of
stored energy, and for characterization of the buy/sell phase transition region
in the price-state plane. Finally, we study the impact of market-based
operation of storage on the required reserves, and show that the reserves may
need to be expanded to accommodate market-based storage
Resilience of Locally Routed Network Flows: More Capacity is Not Always Better
In this paper, we are concerned with the resilience of locally routed network
flows with finite link capacities. In this setting, an external inflow is
injected to the so-called origin nodes. The total inflow arriving at each node
is routed locally such that none of the outgoing links are overloaded unless
the node receives an inflow greater than its total outgoing capacity. A link
irreversibly fails if it is overloaded or if there is no operational link in
its immediate downstream to carry its flow. For such systems, resilience is
defined as the minimum amount of reduction in the link capacities that would
result in the failure of all the outgoing links of an origin node. We show that
such networks do not necessarily become more resilient as additional capacity
is built in the network. Moreover, when the external inflow does not exceed the
network capacity, selective reductions of capacity at certain links can
actually help averting the cascading failures, without requiring any change in
the local routing policies. This is an attractive feature as it is often easier
in practice to reduce the available capacity of some critical links than to add
physical capacity or to alter routing policies, e.g., when such policies are
determined by social behavior, as in the case of road traffic networks. The
results can thus be used for real-time monitoring of distance-to-failure in
such networks and devising a feasible course of actions to avert systemic
failures.Comment: Accepted to the IEEE Conference on Decision and Control (CDC), 201
Battery Capacity of Deferrable Energy Demand
We investigate the ability of a homogeneous collection of deferrable energy
loads to behave as a battery; that is, to absorb and release energy in a
controllable fashion up to fixed and predetermined limits on volume, charge
rate and discharge rate. We derive bounds on the battery capacity that can be
realized and show that there are fundamental trade-offs between battery
parameters. By characterizing the state trajectories under scheduling policies
that emulate two illustrative batteries, we show that the trade-offs occur
because the states that allow the loads to absorb and release energy at high
aggregate rates are conflicting
Robust Network Routing under Cascading Failures
We propose a dynamical model for cascading failures in single-commodity
network flows. In the proposed model, the network state consists of flows and
activation status of the links. Network dynamics is determined by a, possibly
state-dependent and adversarial, disturbance process that reduces flow capacity
on the links, and routing policies at the nodes that have access to the network
state, but are oblivious to the presence of disturbance. Under the proposed
dynamics, a link becomes irreversibly inactive either due to overload condition
on itself or on all of its immediate downstream links. The coupling between
link activation and flow dynamics implies that links to become inactive
successively are not necessarily adjacent to each other, and hence the pattern
of cascading failure under our model is qualitatively different than standard
cascade models. The magnitude of a disturbance process is defined as the sum of
cumulative capacity reductions across time and links of the network, and the
margin of resilience of the network is defined as the infimum over the
magnitude of all disturbance processes under which the links at the origin node
become inactive. We propose an algorithm to compute an upper bound on the
margin of resilience for the setting where the routing policy only has access
to information about the local state of the network. For the limiting case when
the routing policies update their action as fast as network dynamics, we
identify sufficient conditions on network parameters under which the upper
bound is tight under an appropriate routing policy. Our analysis relies on
making connections between network parameters and monotonicity in network state
evolution under proposed dynamics
Global analysis of piecewise linear systems using impact maps and surface Lyapunov functions
This paper presents an entirely new constructive global analysis methodology for a class of hybrid systems known as piecewise linear systems (PLS). This methodology infers global properties of PLS solely by studying the behavior at switching surfaces associated with PLS. The main idea is to analyze impact maps, i.e., maps from one switching surface to the next switching surface. Such maps are known to be "unfriendly" maps in the sense that they are highly nonlinear, multivalued, and not continuous. We found, however, that an impact map induced by an linear time-invariant flow between two switching surfaces can be represented as a linear transformation analytically parametrized by a scalar function of the state. This representation of impact maps allows the search for surface Lyapunov functions (SuLF) to be done by simply solving a semidefinite program, allowing global asymptotic stability, robustness, and performance of limit cycles and equilibrium points of PLS to be efficiently checked. This new analysis methodology has been applied to relay feedback, on/off and saturation systems, where it has shown to be very successful in globally analyzing a large number of examples. In fact, it is still an open problem whether there exists an example with a globally stable limit cycle or equilibrium point that cannot be successfully analyzed with this new methodology. Examples analyzed include systems of relative degree larger than one and of high dimension, for which no other analysis methodology could be applied. This success in globally analyzing certain classes of PLS has shown the power of this new methodology, and suggests its potential toward the analysis of larger and more complex PLS
Towards an Algebra for Cascade Effects
We introduce a new class of (dynamical) systems that inherently capture
cascading effects (viewed as consequential effects) and are naturally amenable
to combinations. We develop an axiomatic general theory around those systems,
and guide the endeavor towards an understanding of cascading failure. The
theory evolves as an interplay of lattices and fixed points, and its results
may be instantiated to commonly studied models of cascade effects.
We characterize the systems through their fixed points, and equip them with
two operators. We uncover properties of the operators, and express global
systems through combinations of local systems. We enhance the theory with a
notion of failure, and understand the class of shocks inducing a system to
failure. We develop a notion of mu-rank to capture the energy of a system, and
understand the minimal amount of effort required to fail a system, termed
resilience. We deduce a dual notion of fragility and show that the combination
of systems sets a limit on the amount of fragility inherited.Comment: 31 page
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