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Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.


Papers
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Journal ArticleDOI
TL;DR: A stochastic programming framework for conducting optimal 24-h scheduling of CHP-based MGs consisting of wind turbine, fuel cell, boiler, a typical power-only unit, and energy storage devices is presented.
Abstract: Microgrids (MGs) are considered as a key solution for integrating renewable and distributed energy resources, combined heat and power (CHP) systems, as well as distributed energy-storage systems This paper presents a stochastic programming framework for conducting optimal 24-h scheduling of CHP-based MGs consisting of wind turbine, fuel cell, boiler, a typical power-only unit, and energy storage devices The objective of scheduling is to find the optimal set points of energy resources for profit maximization considering demand response programs and uncertainties The impact of the wind speed, market, and MG load uncertainties on the MG scheduling problem is characterized through a stochastic programming formulation This paper studies three cases to confirm the performance of the proposed model The effect of CHP-based MG scheduling in the islanded and grid-connected modes, as well as the effectiveness of applying the proposed DR program is investigated in the case studies

247 citations

Journal ArticleDOI
TL;DR: Under the assumption that the stochastic parameters are independently distributed, it is shown that two-stage Stochastic programming problems are ♯P-hard and certain multi-stage Stochastic Programming problems are PSPACE-hard.
Abstract: Stochastic programming is the subfield of mathematical programming that considers optimization in the presence of uncertainty. During the last four decades a vast quantity of literature on the subject has appeared. Developments in the theory of computational complexity allow us to establish the theoretical complexity of a variety of stochastic programming problems studied in this literature. Under the assumption that the stochastic parameters are independently distributed, we show that two-stage stochastic programming problems are ?P-hard. Under the same assumption we show that certain multi-stage stochastic programming problems are PSPACE-hard. The problems we consider are non-standard in that distributions of stochastic parameters in later stages depend on decisions made in earlier stages.

245 citations

Book
27 Sep 2012
TL;DR: In this paper, the authors propose a method for solving control problems by verification, which is based on the Viscosity Solution Equation (VSP) in the sense of VVS.
Abstract: Preface.- 1. Conditional Expectation and Linear Parabolic PDEs.- 2. Stochastic Control and Dynamic Programming.- 3. Optimal Stopping and Dynamic Programming.- 4. Solving Control Problems by Verification.- 5. Introduction to Viscosity Solutions.- 6. Dynamic Programming Equation in the Viscosity Sense.- 7. Stochastic Target Problems.- 8. Second Order Stochastic Target Problems.- 9. Backward SDEs and Stochastic Control.- 10. Quadratic Backward SDEs.- 11. Probabilistic Numerical Methods for Nonlinear PDEs.- 12. Introduction to Finite Differences Methods.- References.

244 citations

Journal ArticleDOI
TL;DR: In this article, a methodology for expansion planning of power systems under uncertainty in factors such as demand growth, fuel cost, delay in project completion, and financial constraints is described, and case studies within the Brazilian system are presented.
Abstract: A methodology is described for expansion planning of power systems under uncertainty in factors such as demand growth, fuel cost, delay in project completion, and financial constraints The approach draws upon three classes of techniques: decomposition and stochastic optimization provide the basic framework, and allow an implicit representation of alternative investment strategies; decision analysis is used to represent the dynamic aspects of decision-making as uncertainties are resolved over time; and hedging objectives from tradeoff analysis help select flexible and resilient expansion strategies. Case studies within the Brazilian system are presented and discussed. >

244 citations

Journal ArticleDOI
TL;DR: A probabilistic framework to design an N-1 secure day-ahead dispatch and determine the minimum cost reserves for power systems with wind power generation is proposed and a reserve strategy according to which the reserves are deployed in real-time operation is identified.
Abstract: We propose a probabilistic framework to design an N-1 secure day-ahead dispatch and determine the minimum cost reserves for power systems with wind power generation. We also identify a reserve strategy according to which we deploy the reserves in real-time operation, which serves as a corrective control action. To achieve this, we formulate a stochastic optimization program with chance constraints, which encode the probability of satisfying the transmission capacity constraints of the lines and the generation limits. To incorporate a reserve decision scheme, we take into account the steady-state behavior of the secondary frequency controller and, hence, consider the deployed reserves to be a linear function of the total generation-load mismatch. The overall problem results in a chance constrained bilinear program. To achieve tractability, we propose a convex reformulation and a heuristic algorithm, whereas to deal with the chance constraint we use a scenario-based-approach and an approach that considers only the quantiles of the stationary distribution of the wind power error. To quantify the effectiveness of the proposed methodologies and compare them in terms of cost and performance, we use the IEEE 30-bus network and carry out Monte Carlo simulations, corresponding to different wind power realizations generated by a Markov chain-based model.

244 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532