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When the Dog Shivers
Modeling variables improves daily estimates of gas demand.
On October 14, 2004, the Columbus Dispatch quoted Jack Partridge, president of Columbia Gas of Ohio, “I’m proud to say that my furnace has not been turned on yet.” Living in a household with five others, Partridge said, “I cave in when the dog starts shivering.”
Dogs differ. At what daily temperature do customers turn on their furnaces? Or more realistically, given individual behavior, over what range of temperatures do they turn on their furnaces? What is the impact of model error on the daily balancing requirement? How does the seasonal variation in ground temperature affect gas demand? Given that wind speed affects daily gas demand in the winter but not the summer, over what range of temperatures does wind speed begin to have an impact? How many cold days cause customers to “cave in”?
The National Oceanic and Atmospheric Administration (NOAA) “measures heating energy demand” from a base of 65 degrees F. Customer conservation and building thermal efficiency have reduced this base for Columbia Gas of Ohio customers. To estimate the current base for its customers, Columbia used daily demand and temperature data for the three-year period from April 2005 through March 2008 (see Figure 1) . Columbia included all customers with annual demand less than 15,000 MCF/year. This group includes all residential customers and the smaller commercial customers.
Columbia Gas of Ohio’s winter demand of about 2 million dekatherms (Dth) at 0 degrees F exceeds the summer daily demand of about 100,000 Dth by a factor of 20. The bend in the curve is gradual because customers don’t turn on their furnaces in unison. Columbia approximated this gradual bend by modeling three portions to the fitted curve, portions when none, half, and all of the customers have their furnaces turned on. If the temperature range with only half of the furnaces operating is Base ± Tran, then heating degree days (HDD) is defined as: HDD = max (0, 0.5 * (Base + Tran – Temp), Base – Temp), where Temp is the average of the high and low temperatures for the day. Regression yields best fit values: Base = 59 degrees F and Tran = ±6 degrees F, so that as an approximation, half of the customers have their furnaces turned on the temperature range from 53 degrees F to 65 degrees F.
Figure 2 shows the model errors or “residuals,” the daily difference of actual less fitted demand. Residuals on a few days have magnitude greater than 200,000 Dth/day. The root mean square error (RMSE) is 61,843 Dth/day. By contrast, the model using NOAA’s Base = 65°F and no transition range has RMSE = 75,835 Dth/day.
Columbia uses storage injections and withdrawals to balance the difference between daily gas supply and the demand of its customers. CHOICE marketers, who serve about 45 percent of Columbia customers, deliver gas as a function of temperature according to