Greenhouse gases, Regulated Emissions, and Energy use in Transportation (GREET) excel model has been developed by Argonne National Labs [1], for estimating the full fuel-cycle energy and emission impacts of various transportation fuels and vehicle technologies. It calculates fuel-cycle energy use in Btu/mi and emissions in g/mi for various transportation fuels and vehicle technologies. For energy use, GREET includes total energy use (all energy sources), fossil energy use (petroleum, natural gas [NG], and coal), and petroleum use. For emissions, the model includes three major greenhouse gases (GHGs) (carbon dioxide [CO2], methane [CH4], and nitrous oxide [N2O]), and five criteria pollutants (volatile organic compound [VOC], carbon monoxide [CO], nitrogen oxides [NOX], particulate matter with a diameter of 10 micrometers or less [PM10], and sulfur oxides [SOX]) [2]. Since the parameters in GREET are uncertain, the resulting output variables consequently have to be represented by distributions. The GREET model incorporates large number of input parameters and a wide variety of output results. Many of the input parameter assumptions involve uncertainties, which require probability distributions to represent the trend of occurrence of the parameter over a specific range that define the uncertainty. For complicated and complex systems involving more decisions and much higher stakes, heuristics becomes obsolete and mathematical models are required to deal with uncertainty [3]. In situations involving uncertainties, a deterministic approach to solve the problem would produce results which might not be a true reflection of reality and in such cases stochastic simulations incorporating uncertainties need to be performed [4]. The steps in a stochastic simulation are the following:

1. Characterize and quantify the uncertainties in terms of probability distribution functions

2. Sample the distributions with a suitable sampling technique

3. Run the model and compute the output for each sample set

4. Statistically analyze each output variable

We have developed a stochastic simulation tool in order to simplify setting up and executing a stochastic simulation for any Excel model. The tool has been built as a Microsoft® Excel add-in file with Visual Basic macros which can be loaded whenever the user needs to perform a stochastic simulation within the model. This new tool automates the process of setting up a stochastic simulation to a great extent and guides the user in each step of the process through user-friendly graphical user interface (GUI) windows. It incorporates six sampling techniques including the new and efficient Hammersley Sequence Sampling (HSS) and Leaped HSS ( variant of HSS) [4] and an inbuilt bank of 11 input probability distribution functions for representing uncertain parameters. The tool has been applied to a case-study of the This tool facilitates representation of the uncertain parameters through PDFs with user-friendly GUI windows in which the changes in the shape and scale of the plot can be dynamicaly viewed based on changes in the distribution parameters. After completion of PDF assignment, the no. of samples and the sampling technique are specified. Upon completion of a simulation run, various statistical measures for the output variables like the percentiles, mean, standard deviation etc are presented to the user. We have applied this tool to the GREEt model and compared the performance of the 4 main sampling techniques for selected output variables with different number of samples.

Reference:

1.http://www.transportation.anl.gov/software/GREET/index.html

2.Wang, M.Q., ‘Well-to-Wheels Energy Use, Greenhouse Gas Emissions, and Criteria Pollutant Emissions - Hybrid Electric and Fuel-Cell Vehicles', Presented at the SAE Future Transportation Conference, Costa Mesa, CA, June 2003

3.Subramanyan, K., and Diwekar U.; ‘Characterization and quantification of uncertainty in solid oxide fuel cell hybrid power plants ', Journal of Power Sources, 142, 103-116, 2005.

4.Diwekar, U. M.; Introduction to Applied Optimization, Kluwer Academic Publishers, Dordrecht, 2003