Quantifying uncertainty in wholesale electricity price projections using Bayesian emulation of a generation investment model

Abstract Policy-makers need to be confident that decisions based on the outputs of energy system models will be robust in the real-world. To make robust decisions it is critical that the consequences of uncertainty in model outputs are assessed. This paper presents statistical methodology for quantifying uncertainty associated with the output of a computer model of the long-term GB electricity supply. The output of the computer model studied is the projection of wholesale electricity prices from 2016 to 2030. The effect on wholesale prices of both uncertainty in input parameters and structural discrepancy is modelled. A probability distribution is used to model uncertainty over four inputs of the model: gas price, demand, EU ETS price and future offshore deployment. Estimates of the structural discrepancy introduced by the use of smoothed gas price projections and assuming that coal prices out to 2030 are known are obtained from experimentation with the computer model. A statistical model, known as an emulator, is fitted to a set of computer model evaluations and used to model uncertainty in the output of the computer model at inputs that have not been tested. The emulator is combined with the probability distribution over the inputs and the estimate of structural discrepancy to make an assessment of the overall uncertainty in the wholesale electricity price projections. A sensitivity analysis is also performed to investigate the effect of each of the four inputs on the trajectory of wholesale electricity prices.

[1]  A. O'Hagan,et al.  Bayesian inference for the uncertainty distribution of computer model outputs , 2002 .

[2]  David W. Coit,et al.  Multi-period multi-objective electricity generation expansion planning problem with Monte-Carlo simulation , 2010 .

[3]  Michael E. Tipping,et al.  Probabilistic Principal Component Analysis , 1999 .

[4]  M. Shahidehpour,et al.  Market-Based Generation and Transmission Planning With Uncertainties , 2009, IEEE Transactions on Power Systems.

[5]  G. Strbac,et al.  Valuation of Flexible Transmission Investment Options Under Uncertainty , 2015, IEEE Transactions on Power Systems.

[6]  Evelina Trutnevyte,et al.  UKERC Energy Systems Theme Reflecting on Scenarios , 2014 .

[7]  Marc C. Kennedy,et al.  Case studies in Gaussian process modelling of computer codes , 2006, Reliab. Eng. Syst. Saf..

[8]  James Price,et al.  Modelling to generate alternatives: A technique to explore uncertainty in energy-environment-economy models , 2017 .

[9]  Michael Grubb,et al.  Induced Technological Change: Exploring its Implications for the Economics of Atmospheric Stabilization: Synthesis Report from the innovation Modeling Comparison Project , 2006 .

[10]  Dirk Eddelbuettel,et al.  Rcpp: Seamless R and C++ Integration , 2011 .

[11]  A. O'Hagan,et al.  Bayesian emulation of complex multi-output and dynamic computer models , 2010 .

[12]  Meng Xu,et al.  Calibration and sensitivity analysis of long-term generation investment models using Bayesian emulation , 2016 .

[13]  Heng Tao Shen,et al.  Principal Component Analysis , 2009, Encyclopedia of Biometrics.

[14]  Ian Vernon,et al.  Galaxy formation : a Bayesian uncertainty analysis. , 2010 .

[15]  B. F. Hobbs,et al.  Dynamic Modeling of Thermal Generation Capacity Investment: Application to Markets With High Wind Penetration , 2012, IEEE Transactions on Power Systems.

[16]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[17]  B. Hobbs,et al.  The economics of planning electricity transmission to accommodate renewables: Using two-stage optimisation to evaluate flexibility and the cost of disregarding uncertainty , 2012 .

[18]  Ming-Che Hu,et al.  A Dynamic Analysis of a Demand Curve-Based Capacity Market Proposal: The PJM Reliability Pricing Model , 2007, IEEE Transactions on Power Systems.

[19]  Michael C. Georgiadis,et al.  An integrated stochastic multi-regional long-term energy planning model incorporating autonomous power systems and demand response , 2015 .

[20]  N. Strachan,et al.  Critical mid-term uncertainties in long-term decarbonisation pathways , 2012 .

[21]  William C. Horrace,et al.  Some results on the multivariate truncated normal distribution , 2005 .

[22]  Michael Goldstein,et al.  Bayesian framework for power network planning under uncertainty , 2016 .

[23]  Michael Goldstein,et al.  Small Sample Bayesian Designs for Complex High-Dimensional Models Based on Information Gained Using Fast Approximations , 2009, Technometrics.

[24]  L. Wasserman,et al.  The Selection of Prior Distributions by Formal Rules , 1996 .

[25]  A. OHagan,et al.  Bayesian analysis of computer code outputs: A tutorial , 2006, Reliab. Eng. Syst. Saf..

[26]  Conrad Sanderson,et al.  RcppArmadillo: Accelerating R with high-performance C++ linear algebra , 2014, Comput. Stat. Data Anal..

[27]  D. Higdon,et al.  Computer Model Calibration Using High-Dimensional Output , 2008 .

[28]  Will Usher,et al.  An expert elicitation of climate, energy and economic uncertainties , 2013 .

[29]  Stefan Wilhelm,et al.  tmvtnorm: A Package for the Truncated Multivariate Normal Distribution , 2010, R J..

[30]  David Wooff,et al.  Bayes Linear Statistics: Theory and Methods , 2007 .

[31]  A. Seheult,et al.  Pressure Matching for Hydrocarbon Reservoirs: A Case Study in the Use of Bayes Linear Strategies for Large Computer Experiments , 1997 .

[32]  B. Hobbs,et al.  Analysis of multi-pollutant policies for the U.S. power sector under technology and policy uncertainty using MARKAL , 2010 .

[33]  Michael Goldstein,et al.  Bayes linear uncertainty analysis for oil reservoirs based on multiscale computer experiments. , 2010 .

[34]  David Wooff,et al.  Bayes Linear Statistics , 2007 .

[35]  Alastair R. Buckley,et al.  A review of energy systems models in the UK: Prevalent usage and categorisation , 2016 .