1 Impact of Sample Estimate Rounding on Accuracy ERCOT Load Profiling Department May 22, 2007

2 Overview Objective is to assess the impact of rounding on the accuracy of sample estimates and on load profile accuracy Monte Carlo simulation of sample results Settlement in a test environment

3 Simulation Methodology Monte Carlo simulations of repeated sampling to analyze the impact of various levels of rounding on the precision of the resulting sample estimates Use SAS random number generator functions RANUNI … random numbers from a uniform distribution to generate test population means RANNOR … random numbers from a normal distribution to generate sample estimates based on a population mean and standard deviation

4 Simulation Methodology (continued) Simulation steps Generate a randomized population mean Simulate a sample result based on Sampling from a population having that mean Based on a sample design with a selected statistical accuracy (at 90% confidence level) Round the sample estimate to the hundredths, thousandths and ten-thousandths place Calculate the difference between the rounded estimate and the population mean Replicate 10,000 times at each precision level

5 Simulation Results

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10 Simulation Findings If the precision is ±10% or worse, and the population mean is > 0.3, MAPEs for 2-digit rounding and 3-digit rounding are virtually identical If the precision is better than ±10%, and the population mean is < 0.3, MAPEs for 3-digit rounding are somewhat better If the population mean is ≥ 1, 3-digit rounding is likely to do more harm than good regardless of the sample precision

11 Test Settlement Data Aggregation ran a test settlement using profiles with three digit rounding for January 27, 2006 Compared UFE for original 2-digit profiles with results for 3-digit profiles Compared total aggregated residential load for the same day

12 January 27, 2006 UFE Comparison

13 January 27, 2006 Residential Load Comparison Red = 3 decimals Blue = 2 decimals

14 Test Settlement Result 3-digit profile rounding produced virtually no difference in settlement for the selected day