1,721,031 research outputs found
A steady-state optimal coordination strategy for DERs systems with guaranteed probabilistic performance
Full text linkWe consider the problem of coordinating multiple Distributed Energy Resources (DERs) so as to supply energy to the grid while minimizing its variability around a reference profile that must also be optimized. We focus on the case when each DER is equipped with solar panels and a battery storage device, and jointly design the disturbance compensation strategies for charging and discharging the batteries on a one-day time horizon. To this purpose, we linearly parameterize the strategies and search for a solution minimizing the fluctuations of the energy exchange with the grid in steady-state, with a bound on their extent that holds in probability given the stochastic nature of the solar energy. Interestingly, the probability measure of the resulting chance-constrained optimization problem depends on the parameters of the disturbance compensation strategies, which makes the application of the scenario approach not standard. The proposed scenario-based solution is feasible for the original steady-state chance-constrained optimization problem and proves effective in numerical simulations
Vehicle-to-Grid and ancillary services: a profitability analysis under uncertainty*
Full text linkThe rapid and massive diffusion of electric vehicles poses new challenges to the electric system, which must be able to supply these new loads, but at the same time opens up new opportunities thanks to the possible provision of ancillary services. Indeed, in the so-called Vehicle-to-Grid (V2G) set-up, the charging power can be modulated throughout the day so that a fleet of vehicles can absorb an excess of power from the grid or provide extra power during a shortage. To this end, many works in the literature focus on the optimization of each vehicle daily charging profiles to offer the requested ancillary services while guaranteeing a charged battery for each vehicle at the end of the day. However, the size of the economic benefits related to the provision of ancillary services varies significantly with the modeling approaches, different assumptions, and considered scenarios. In this paper we propose a profitability analysis with reference to a recently proposed framework for V2G optimal operation in presence of uncertainty. We provide necessary and sufficient conditions for profitability in a simplified case and we show via simulation that they also hold for the general case
Probabilistic feasibility in data-driven multi-agent non-convex optimization
No full textIn this paper, we focus on the optimal operation of a multi-agent system affected by uncertainty. In particular, we consider a cooperative setting where agents jointly optimize a performance index compatibly with individual constraints on their discrete and continuous decision variables and with coupling global constraints. We assume that individual constraints are affected by uncertainty, which is known to each agent via a private set of data that cannot be shared with others. Exploiting tools from statistical learning theory, we provide data-based probabilistic feasibility guarantees for a (possibly sub-optimal) solution of the multi-agent problem that is obtained via a decentralized/distributed scheme that preserves the privacy of the local information. The generalization properties of the data-based solution are shown to depend on the size of each local dataset and on the complexity of the uncertain individual constraint sets. Explicit bounds are derived in the case of linear individual constraints. A comparative analysis with the cases of a common dataset and of local uncertainties that are independent is performed
A randomized algorithm for nonlinear model structure selection
Full text linkThe identification of polynomial Nonlinear Autoregressive [Moving Average] models with eXogenous variables (NAR[MA]X) is typically carried out with incremental model building techniques that progressively select the terms to include in the model. The Model Structure Selection (MSS) turns out to be the hardest task of the identification process due to the difficulty of correctly evaluating the importance of a generic term. As a result, classical MSS methods sometimes yield unsatisfactory models, that are unreliable over long-range prediction horizons. The MSS problem is here recast into a probabilistic framework based on which a randomized algorithm for MSS is derived, denoted RaMSS. The method introduces a tentative probability distribution over models and progressively updates it by extracting useful information on the importance of each term from sampled model structures. The proposed method is validated over models with different characteristics by means of Monte Carlo simulations, which show its advantages over classical and competitor probabilistic MSS methods in terms of both reliability and computational efficiency
A novel decentralized approach to large-scale multi-agent MILPs
Full text linkWe address the optimal operation of a large-scale multi-agent system where agents have to set their own continuous and/or discrete decision variables so as to jointly minimize the sum of local linear performance indices while satisfying local and global linear constraints. When the number of discrete decision variables is large, solving the resulting Mixed Integer Linear Program becomes computationally demanding, and often impossible in practice. Inspired by some recent methods in the literature, we propose a decentralized iterative scheme that recovers computational tractability by decomposing the dual of the MILP problem into lower-dimensional MILPs, one per agent, and obtains feasibility of the recovered primal solution by introducing a fictitious tightening of the global constraints. The tightening is updated in an adaptive fashion according to an heuristic strategy which allows it to both increase and decrease throughout the iterations, depending on the mismatch between the recovered mixed-integer primal solution and the solution to the relaxed linear problem associated with the current tightening. The procedure is shown to be effective and to outperform state-of-the-art alternative resolution schemes in a benchmark example on optimal charging of a fleet of electric vehicles
DualBi: A dual bisection algorithm for non-convex problems with a scalar complicating constraint
No full textThis paper addresses non-convex constrained optimization problems that are characterized by a scalar
complicating constraint. We propose an iterative bisection method for the dual problem (DualBi
Algorithm) that recovers a feasible primal solution, with a performance that progressively improves
throughout iterations. Application to multi-agent problems with a scalar coupling constraint results in a
decentralized resolution scheme where a central unit is in charge of updating the (scalar) dual variable
while agents compute their local primal variables. In the case of multi-agent MILPs, simulations
showcase the performance of the proposed method compared with state-of-the-art duality-based
approache
A Dual Bisection Approach to Economic Dispatch of Generators with Prohibited Operating Zones
Full text linkWe address economic dispatch of power generators with prohibited operating zones. The problem can be formulated as an optimization program with a quadratic cost, non-convex local operating constraints, and a scalar quadratic coupling constraint accounting for load demand and power losses. A duality-based resolution approach integrating a bisection iterative scheme is proposed to reduce computational complexity while guaranteeing finite time feasibility of the primal iterates and a cost improvement throughout iterations. Extensive simulations show that the approach outperforms state-of-the-art competitors and consistently computes feasible primal solutions with a close-to-zero optimality gap at a low computational cost
An Iterative Scheme for the Approximate Linear Programming Solution to the Optimal Control of a Markov Decision Process
Full text linkThis paper addresses the computational issues involved in the solution to an infinite-horizon optimal control problem for a Markov Decision Process (MDP) with a continuous state component and a discrete control input. The optimal Markov policy for the MDP can be determined based on the fixed point solution to the Bellman equation, which can be rephrased as a constrained Linear Program (LP) with an infinite number of constraints and an infinite dimensional optimization variable (the optimal value function). To compute an (approximate) solution to the LP, an iterative randomized scheme is proposed where the optimization variable is expressed as a linear combination of basis functions in a given class: at each iteration, the resulting semi-infinite LP is solved via constraint sampling, whereas the number of basis functions is progressively increased through the iterations so as to meet some performance goal. The effectiveness of the proposed scheme is shown on a multi-room heating system example
A Randomized Approach to Probabilistic Footprint Estimation of a Space Debris Uncontrolled Reentry
Full text linkThis paper studies the problem of characterizing the region of the airspace that will be occupied by a space debris during an uncontrolled reentry (footprint), with the final goal of supporting the air traffic controllers in their task of guiding aircraft safely from their origin to their destination. Given the various sources of uncertainty affecting the debris dynamics, the reentry process is characterized probabilistically and the problem of determining the footprint is formulated in terms of a chance-constrained optimization program, which is solved via a simulation-based method. When observations of the debris initial position and radar measurements of the aircraft prior to the reentry event are available, nonlinear filtering techniques can be adopted and the posterior probability distribution of the debris position as well as of the wind field affecting the reentry process can be integrated in the chance-constraint formulation so as to obtain an enhanced estimate of the footprint. Simulation results show the efficacy of the approach
A Randomized Approach to Space Debris Footprint Characterization
Full text linkThis paper studies the problem of characterizing the 4D (space cross time) region of the airspace that will be occupied by a space debris during an uncontrolled reentry, with the final goal of supporting the air traffic controllers in re-routing the air traffic when such an event occurs. The problem is formulated in terms of a chance-constrained optimization program, which is solved via a simulation-based method. The approach is comparatively evaluated against the so-called covariance propagation method recently proposed in the literature, emphasizing how some of the limitations of the latter method are overcome
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