Uncertainty of Complex Systems by Monte Carlo Simulation

Basil, M.; Jamieson, Andrew

doi:10.1177/002029409903200104

Cited by 22 publications

(14 citation statements)

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“…MCS is a simulation approach that is found on using random numbers and probability density function (PDF) of uncertain parameters in order to solve the problems. Very often, it is used when the model is complicated or nonlinear or involves several uncertain parameters [3]. Although the MCS is able to reach the accurate results, it is really time-consuming; therefore, it is not as attractive in online applications or where other approaches work satisfactorily.…”

Section: Plf Methodsmentioning

confidence: 99%

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Probabilistic Load Flow in Correlated Uncertain Environment Using Unscented Transformation

Aien

Fotuhi-Firuzabad

Aminifar

2012

IEEE Trans. Power Syst.

173

101

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As a matter of course, the unprecedented ascending penetration of distributed energy resources, mainly harvesting renewable energies, is a direct consequence of environmental concerns. This type of energy resource brings about more uncertainties in power system operation and planning; consequently, it necessitates probabilistic analyses of the system performance. This paper develops a new approach for probabilistic load flow (PLF) evaluation using the unscented transformation (UT) method. The UT method is recognized as a powerful approach in assessing stochastic problems with/without correlated uncertain variables. The capability of the UT method in modeling correlated uncertain variables is very appealing in the power system context, in which noticeable inherent correlation exists. The salient features of the UT method in probabilistic applications have been well proven in other engineering aspects. Following adaptation of the UT method for the PLF problem, three dimensionally different case studies are examined in order to inspect the performance of the proposed methodology. The obtained results are then compared with those of the Monte Carlo simulation as well as two-point estimation method with regards to both accuracy and execution time criteria.

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Section: Plf Methodsmentioning

confidence: 99%

“…In [2], MCS was used to perform the PLF study of a system with the wind integration. MCS is widely recognized as a system-dimension independent approach; however, its execution might be rather time-consuming [3].…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Load Flow in Correlated Uncertain Environment Using Unscented Transformation

Aien

Fotuhi-Firuzabad

Aminifar

2012

IEEE Trans. Power Syst.

173

101

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“…MCS provides more accurate results but its execution might be extremely time-consuming. MCS is commonly recognized as a system-dimension independent approach [21]. In order to reduce the computational effort, the analytical methods such as Gram-Charlier method [22][23][24] , fast Fourier transformation (FFT) [25], point estimation method (PEM) [26,27], and Unscented transformation (UT) method [28] were proposed.…”

Section: Nomenclaturementioning

confidence: 99%

“…It iteratively solves a given problem using sets of random numbers as inputs. This method is often used when the model is complicated, nonlinear, or involves many uncertain parameters [21]. Although the MCS is able to provide accurate results, its execution might be really timedemanding; therefore, it is not so attractive in real time applications especially when the problem under study is itself a complicated, time demanding problem such as UC.…”

Section: Amentioning

confidence: 99%

A probabilistic framework for unit commitment problem in deregulated markets with high penetration of wind and solar power

Aien

Khajeh

Mohammadi

et al. 2014

2014 22nd Iranian Conference on Electrical Engineering (ICEE)

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As a matter of fact, the soaring penetration of distributed energy resources (DERs), mainly those harvesting renewable energies (REs) such as wind and solar, is concomitant with environmentally friendly concerns. This type of energy resources are innately uncertain and bring about more uncertainties in the power system context, consequently, necessitates probabilistic analysis of the system performance. Unit commitment (UC) is a challenging optimization task which plays a crucial role in the daily operation of power systems, especially in deregulated power markets. The deterministic UC solution is used by the independent system operator (ISO) to run the system at its optimal operation point while on the contrary, the system parameters such as the load, wind and solar power are not fixed and vary ceaselessly, due to their inherent uncertainties. Therefore, the uncertainty analysis of the UC problem is an interesting issue. The two point estimation method (2PEM) is recognized as an appropriate probabilistic method to tackle with problems having uncertainties in their inputs. This paper develops a new methodology for probabilistic unit commitment (PUC) using the 2PEM to stochastically investigate on the UC problem. In order to justify the effectiveness of the proposed method, two case studies are examined using the suggested method.

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“…There have been a number of methods developed to characterize, quantify, or propagate uncertainties including probabilistic methods, such as classical or frequentist inference and Bayesian inference (Omlin and Reichert, 1999), sampling methods such as Monte Carlo (Basil and Jamieson, 1998) and bootstrapping (Efron, 1979), and response surface methods (intrusive methods) such as polynomial chaos expansions (Xiu and Karniadakis, 2003) and Kriging approach (Yuan et al, 2008). Among these different methods, Bayesian inference offers several advantages over other methods as it does not require modification to the model and provides a comprehensive treatment of parametric and model uncertainties without any simplifying assumptions about their distributions (Omlin and Reichert, 1999;Alfaro et al, 2003).…”

Section: Introductionmentioning

confidence: 99%

Bayesian estimation of parametric uncertainties, quantification and reduction using optimal design of experiments for CO2 adsorption on amine sorbents

Kalyanaraman

Fan

Labreche

et al. 2015

Computers & Chemical Engineering

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Please cite this article in press as: Kalyanaraman J, et al. Bayesian estimation of parametric uncertainties, quantification and reduction using optimal design of experiments for CO 2 adsorption on amine sorbents. Computers and Chemical Engineering (2015), http://dx. a b s t r a c tUncertainty quantification plays a significant role in establishing reliability of mathematical models, while applying to process optimization or technology feasibility studies. Uncertainties, in general, could occur either in mathematical model or in model parameters. In this work, process of CO 2 adsorption on amine sorbents, which are loaded in hollow fibers is studied to quantify the impact of uncertainties in the adsorption isotherm parameters on the model prediction. The process design variable that is most closely related to the process economics is the CO 2 sorption capacity, whose uncertainty is investigated. We apply Bayesian analysis and determine a utility function surface corresponding to the value of information gained by the respective experimental design point. It is demonstrated that performing an experiment at a condition with a higher utility has a higher reduction of design variable prediction uncertainty compared to choosing a design point at a lower utility.

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Uncertainty of Complex Systems by Monte Carlo Simulation

Cited by 22 publications

References 0 publications

Probabilistic Load Flow in Correlated Uncertain Environment Using Unscented Transformation

Probabilistic Load Flow in Correlated Uncertain Environment Using Unscented Transformation

A probabilistic framework for unit commitment problem in deregulated markets with high penetration of wind and solar power

Bayesian estimation of parametric uncertainties, quantification and reduction using optimal design of experiments for CO2 adsorption on amine sorbents

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