Day-ahead scheduling of electricity generation or unit commitment is an important and challenging optimization problem in power systems. Variability in net load arising from the increasing penetration of renewable tec...
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We consider distributionally robust two-stage stochastic convex programming problems, in which the recourse problem is linear. Other than analyzing these new models case by case for different ambiguity sets, we adopt ...
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We consider distributionally robust two-stage stochastic convex programming problems, in which the recourse problem is linear. Other than analyzing these new models case by case for different ambiguity sets, we adopt a unified form of ambiguity sets proposed by Wiesemann, Kuhn and Sim, and extend their analysis from a single stochastic constraint to the two-stage stochastic programming setting. It is shown that under a standard set of regularity conditions, this class of problems can be converted to a conic optimization problem. Numerical results are presented to show the efficiency of the distributionally robust approach. (C) 2017 Elsevier Inc. All rights reserved.
In this paper a methodology is developed to solve a nonlinear interval optimization problem by transforming this to a general optimization problem which is free from interval uncertainty. To address the interval uncer...
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In this paper a methodology is developed to solve a nonlinear interval optimization problem by transforming this to a general optimization problem which is free from interval uncertainty. To address the interval uncertainty, relation between an interval and a random variable is established according to the 3 sigma-rule. Using this relation an interval function is associated with a function of random variables and an interval inequality is associated with a chance constraint. The interval optimization problem is then transformed into a nonlinear stochastic programming problem. Further, the existence of a preferable solution of the original problem is established using Chance Constrained programming technique.
The performance of many of the technologies used in physical protection systems that guard high-value assets are heavily influenced by weather and visibility conditions as well as intruder capabilities. This complicat...
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ISBN:
(纸本)9780998133102
The performance of many of the technologies used in physical protection systems that guard high-value assets are heavily influenced by weather and visibility conditions as well as intruder capabilities. This complicates the already difficult problem of optimizing the design of multi-layered physical protection systems. This paper develops an optimization model for the automatic design of these systems with explicit consideration of the impact of weather and visibility conditions as well as intruder capabilities on system performance. An illustrative case study is provided.
The traditional power grid is confronted with great challenges brought by the integration of renewable power sources (such as solar and wind) for their uncertain, volatile, and intermittent characteristics. This paper...
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ISBN:
(纸本)9781538635247
The traditional power grid is confronted with great challenges brought by the integration of renewable power sources (such as solar and wind) for their uncertain, volatile, and intermittent characteristics. This paper investigates the unit commitment problem with stochastic solar power integration and makes the following major contributions. First, the scheduling problem is formulated as a two-stage stochastic programming. In the first stage the unit commitment, economic dispatch, and solar power scheduling decisions are made based on the day ahead solar power prediction and in the second stage the solar power is rescheduled with real-time solar power generation as each decision instant approaching. Second, in the rescheduling, cost for buying reserve and penalty for curtailing solar power are considered for higher penetration and better utilization of solar power. Third, the problem is reformulated as a stochastic mix-integer linear programming to facilitate computation and the influences of spinning reserve price, penalty for curtailing solar power, and solar power uncertainty are analyzed and discussed. The performance of the proposed method is compared with a deterministic programming, a robust programming, and a stochastic programming through a modified six-bus system and the results demonstrate that the proposed method can better accommodate the fluctuation of solar power.
In this paper we analyze the effect of two modelling approaches for supply planning problems under uncertainty: two-stage stochastic programming (SP) and robust optimization (RO). The comparison between the two approa...
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In this paper we analyze the effect of two modelling approaches for supply planning problems under uncertainty: two-stage stochastic programming (SP) and robust optimization (RO). The comparison between the two approaches is performed through a scenario-based framework methodology, which can be applied to any optimization problem affected by uncertainty. For SP we compute the minimum expected cost based on the specific probability distribution of the uncertain parameters related to a set of scenarios. For RO we consider static approaches where random parameters belong to box or ellipsoidal uncertainty sets in compliance with the data used to generate SP scenarios. Dynamic approaches for RO, via the concept of adjustable robust counterpart, are also considered. The efficiency of the methodology has been illustrated for a supply planning problem to optimize vehicle-renting and procurement transportation activities involving uncertainty on demands and on buying costs for extra-vehicles. Numerical experiments through the scenario-based framework allow a fair comparison in real case instances. Advantages and disadvantages of RO and SP are discussed.
This paper addresses the generation of scenario trees to solve stochastic programming problems that have a large number of possible values for the random parameters (possibly infinitely many). For the sake of the comp...
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This paper addresses the generation of scenario trees to solve stochastic programming problems that have a large number of possible values for the random parameters (possibly infinitely many). For the sake of the computational efficiency, the scenario trees must include only a finite (rather small) number of scenarios, therefore, they provide decisions only for some values of the random parameters. To overcome the resulting loss of information, we propose to introduce an extension procedure. It is a systematic approach to interpolate and extrapolate the scenario-tree decisions to obtain a decision policy that can be implemented for any value of the random parameters at little computational cost. To assess the quality of the scenario-tree generation method and the extension procedure (STGM-EP), we introduce three generic quality parameters that focus on the quality of the decisions. We use these quality parameters to develop a framework that will help the decision-maker to select the most suitable STGM-EP for a given stochastic programming problem. We perform numerical experiments on two case studies. The quality parameters are used to compare three scenario-tree generation methods and three extension procedures (hence nine couples STGM-EP). We show that it is possible to single out the best couple in both problems, which provides decisions close to optimality at little computational cost.
In this paper we present a method of pricing catastrophe bonds (cat bonds) using stochastic programming. stochastic programming is a method ubiquitous in operations research when decision problems involve uncertainty....
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In this paper we present a method of pricing catastrophe bonds (cat bonds) using stochastic programming. stochastic programming is a method ubiquitous in operations research when decision problems involve uncertainty. We demonstrate the method for pricing cat bonds which bypasses the need to define the equivalent martingale measure or estimate the market price of risk. The price of the cat bond is simply the coupon that needs to be paid that attains a specified return on investment given a set of constraints that define the payoffs.
We address the problem of enhancing Quality-of-Service (QoS) in power constrained, mobile relay beamforming networks, by controlling the motion of the relaying nodes. We consider a time slotted system, where the relay...
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ISBN:
(纸本)9781509041176
We address the problem of enhancing Quality-of-Service (QoS) in power constrained, mobile relay beamforming networks, by controlling the motion of the relaying nodes. We consider a time slotted system, where the relays update their positions before the beginning of each time slot. Adopting a spatiotemporal stochastic field model of the wireless channel, we propose a novel 2-stage stochastic programming formulation for specifying the relay positions at each time slot, such that the QoS of the network is maximized on average, based on causal Channel State Information (CSI) and under a total relay transmit power budget. Via the Method of Statistical Differentials, the motion control problem considered is shown to be approximately equivalent to a set of simple subproblems, which are solved in a distributed fashion, one at each relay. Numerical simulations are also presented, corroborating the efficacy of the proposed approach.
A more realistic management of electric vehicle (EV) charging points requires to cope with stochastic behavior on vehicle staying patterns. This paper presents a stochastic programming model to achieve optimal managem...
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A more realistic management of electric vehicle (EV) charging points requires to cope with stochastic behavior on vehicle staying patterns. This paper presents a stochastic programming model to achieve optimal management taking into account price variation in day-ahead and intraday electricity markets, together with regulating reserve margins. In this model, first-stage decisions determine day-ahead energy purchases and sales and the upward and downward reserve margins committed. Second-stage decisions correspond to intraday markets and deal with reserve requirements and several possible scenarios for vehicle staying pattern. The design of the objective function prioritizes supplying energy to EV batteries while minimizing the net expected energy cost at the EV charging point. A case study describing a parking for 50 EVs is analyzed. The case includes household, commercial and mixed EV staying patterns with several intraday arrival and departure scenarios. Pure and hybrid EVs are included, taking into account their respective energy characteristics. Sensitivity analysis is used to show the potential energy cost savings and the impact of different non-supply penalizations. The case study considers several vehicle staying patterns, energy price profiles and discharge allowances. The model achieves energy cost reductions between 1% and 15% depending on the specific case. A model validation by simulation has been done.
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