Probabilistic Approaches to Energy Systems

It has been predicted that electric vehicles will play a crucial role in incorporating a large renewable component in the energy sector. If electric vehicles are integrated in a naive way, they may exacerbate issues related to peak demand and transmission capacity limits while not reducing polluting emissions. Optimizing the charging of electric vehicles is paramount for their successful integration. This paper presents a model to describe the driving patterns of electric vehicles, in order to provide primary input information to any mathematical programming model for optimal charging. Specifically, an inhomogeneous Markov model that captures the diurnal variation in the use of a vehicle is presented. The model is defined by the time-varying probabilities of starting and ending a trip and is justified due to the uncertainty associated with the use of the vehicle. The model is fitted to data collected from the actual utilization of a vehicle. Inhomogeneous Markov models imply a large number of parameters. The number of parameters in the proposed model is reduced using B-splines.

[1]  Ramteen Sioshansi,et al.  OR Forum - Modeling the Impacts of Electricity Tariffs on Plug-In Hybrid Electric Vehicle Charging, Costs, and Emissions , 2012, Oper. Res..

[2]  M O'Malley,et al.  Impact of optimal charging of electric vehicles on future generation portfolios , 2009, 2009 IEEE PES/IAS Conference on Sustainable Alternative Energy (SAE).

[3]  A. Lawson,et al.  Review of methods for space–time disease surveillance , 2010, Spatial and Spatio-temporal Epidemiology.

[4]  S. Richardson,et al.  Bayesian Models for Sparse Regression Analysis of High Dimensional Data , 2012 .

[5]  Willett Kempton,et al.  ELECTRIC VEHICLES AS A NEW POWER SOURCE FOR ELECTRIC UTILITIES , 1997 .

[6]  Dorota Kurowicka,et al.  From transportation patterns to power demand: Stochastic modeling of uncontrolled domestic charging of electric vehicles , 2011, 2011 IEEE Power and Energy Society General Meeting.

[7]  Ilan Momber,et al.  PEV fleet scheduling with electricity market and grid signals Charging schedules with capacity pricing based on DSO's long run marginal cost , 2013, 2013 10th International Conference on the European Energy Market (EEM).

[8]  X.-m. Xu,et al.  Modelling Plant Disease Epidemics , 2003, European Journal of Plant Pathology.

[9]  Robert C. Green,et al.  The impact of plug-in hybrid electric vehicles on distribution networks: a review and outlook , 2010, PES 2010.

[10]  Henrik Madsen,et al.  Inhomogeneous Markov Models for Describing Driving Patterns , 2017, IEEE Transactions on Smart Grid.

[11]  Henrik Madsen,et al.  Space-time scenarios of wind power generation produced using a Gaussian copula with parametrized precision matrix , 2013 .

[12]  D. Sherrington.  Stochastic Processes in Physics and Chemistry , 1983 .

[13]  Juha Kiviluoma,et al.  Influence of wind power, plug-in electric vehicles, and heat storages on power system investments , 2010 .

[14]  G. Grimmett,et al.  Probability and random processes , 2002 .

[15]  A. Sterl,et al.  The ERA‐40 re‐analysis , 2005 .

[16]  M. Ilic,et al.  Optimal Charge Control of Plug-In Hybrid Electric Vehicles in Deregulated Electricity Markets , 2011, IEEE Transactions on Power Systems.

[17]  E. Süli,et al.  Numerical Solution of Partial Differential Equations , 2014 .

[18]  Henrik Madsen,et al.  Introduction to General and Generalized Linear Models , 2010 .

[19]  Claire Weiller,et al.  Plug-in hybrid electric vehicle impacts on hourly electricity demand in the United States , 2011 .

[20]  Pierre Pinson,et al.  Wind Energy: Forecasting Challenges for Its Operational Management , 2013, 1312.6471.

[21]  Manuel A. Matos,et al.  Economic and technical management of an aggregation agent for electric vehicles: a literature survey , 2012 .

[22]  W. Stahel,et al.  Stochastic partial differential equation based modelling of large space–time data sets , 2012, 1204.6118.

[23]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[24]  Saifur Rahman,et al.  Grid Integration of Electric Vehicles and Demand Response With Customer Choice , 2012, IEEE Transactions on Smart Grid.

[25]  Ke Xu,et al.  A Kernel-Based Spatio-Temporal Dynamical Model for Nowcasting Weather Radar Reflectivities , 2005 .

[26]  P. Versini.  Use of radar rainfall estimates and forecasts to prevent flash flood in real time by using a road inundation warning system , 2012 .

[27]  D. Ruppert.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction , 2004 .

[28]  Bradley P. Carlin,et al.  Hierarchical Spatio-Temporal Mapping of Disease Rates , 1997 .

[29]  Le Xie,et al.  Multitime-Scale Data-Driven Spatio-Temporal Forecast of Photovoltaic Generation , 2015, IEEE Transactions on Sustainable Energy.

[30]  Ufuk Topcu,et al.  Optimal decentralized protocol for electric vehicle charging , 2011, IEEE Transactions on Power Systems.

[31]  Karsten Emil Capion,et al.  Optimal charging of electric drive vehicles in a market environment , 2011 .

[32]  W. Zucchini,et al.  Hidden Markov Models for Time Series: An Introduction Using R , 2009 .

[33]  Damian Flynn,et al.  Local Versus Centralized Charging Strategies for Electric Vehicles in Low Voltage Distribution Systems , 2012, IEEE Transactions on Smart Grid.

[34]  Willett Kempton,et al.  Vehicle-to-grid power fundamentals: Calculating capacity and net revenue , 2005 .