Jonathan Lee and Mohini Bariya and Duncan Callaway

EECS Department, University of California, Berkeley

Technical Report No. UCB/EECS-2022-60

May 11, 2022

http://www2.eecs.berkeley.edu/Pubs/TechRpts/2022/EECS-2022-60.pdf

Estimating the coincident peak load of a group of loads is a critical task in power system planning and reliability analysis. Classical methods using coincidence and load factors have long been used, but leave a challenge for designers and modelers to determine appropriate factors to use and do not lend themselves to reliability analysis. This paper follows work that models peak load as a random variable, and contributes a parametric model that relates the probability distribution of peak load to average energy consumption using extreme value theory. This model allows designers to specify failure probabilities, and under some simple assumptions yields closed-form functions that can be used in planning models. The paper presents a procedure for fitting the model and discusses some modifications for tuning it to particular applications. Computational experiments on reference residential load data sets from Texas and London show the model predicts peak load with 2% median error on test data across a range of group size and failure probabilities. We find the performance degrades somewhat for small samples of more heterogenous loads, with a 13% median error on a set of 25 loads from New York with individual load factors as low as 0.02 and as high as 0.15.

Advisors: Claire Tomlin

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BibTeX citation:

@mastersthesis{Lee:EECS-2022-60,
    Author= {Lee, Jonathan and Bariya, Mohini and Callaway, Duncan},
    Title= {Peak Load Estimation with the Generalized Extreme Value Distribution},
    School= {EECS Department, University of California, Berkeley},
    Year= {2022},
    Month= {May},
    Url= {http://www2.eecs.berkeley.edu/Pubs/TechRpts/2022/EECS-2022-60.html},
    Number= {UCB/EECS-2022-60},
    Abstract= {Estimating the coincident peak load of a group of loads is a critical task in power system planning and reliability analysis. Classical methods using coincidence and load factors have long been used, but leave a challenge for designers and modelers to determine appropriate factors to use and do not lend themselves to reliability analysis. This paper follows work that models peak load as a random variable, and contributes a parametric model that relates the probability distribution of peak load to average energy consumption using extreme value theory. This model allows designers to specify failure probabilities, and under some simple assumptions yields closed-form functions that can be used in planning models. The paper presents a procedure for fitting the model and discusses some modifications for tuning it to particular applications. Computational experiments on reference residential load data sets from Texas and London show the model predicts peak load with 2% median error on test data across a range of group size and failure probabilities. We find the performance degrades somewhat for small samples of more heterogenous loads, with a 13% median error on a set of 25 loads from New York with individual load factors as low as 0.02 and as high as 0.15.},
}

EndNote citation:

%0 Thesis
%A Lee, Jonathan 
%A Bariya, Mohini 
%A Callaway, Duncan 
%T Peak Load Estimation with the Generalized Extreme Value Distribution
%I EECS Department, University of California, Berkeley
%D 2022
%8 May 11
%@ UCB/EECS-2022-60
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/2022/EECS-2022-60.html
%F Lee:EECS-2022-60