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When the Dog Shivers

Modeling variables improves daily estimates of gas demand.

Fortnightly Magazine - July 2009

demand curves provided by Columbia. By reducing model error in those demand curves, Columbia reduces the daily balancing requirement and the required storage capacity. The demand curves have both the historical model error discussed here plus forecast uncertainty: Price changes and other factors may cause future customer load patterns to differ from the historical pattern.

Model Error and Daily Balancing

Columbia uses several variables to reduce model error. First is ground temperature. Water companies in Ohio bury the pipes to residences about 3-feet deep to avoid freezing. Colder ground temperature in the winter increases the energy per gallon to heat water. Colder ground temperature also increases the heat loss through basement walls, increasing the load on the furnace.

Ground temperature varies sinusoidally. In a 1976 article, Williams and Gold wrote, “The temperature of the ground surface remains almost in phase with that of the air. Below the surface, however, the maximum or minimum occurs later than the corresponding values at the surface….” 1 At the 3-foot depth of water pipes, the coldest temperature occurs in February, generally a month after the coldest air temperature.

Columbia added sine and cosine terms to its model to measure the effect of ground temperature. According to the regression, the combined sine/cosine curve has amplitude 51,611 Dth/day and peaks in February, the month of coldest ground temperature. Ground temperature increases daily demand by 51,611 Dth in February, and decreases demand by the same volume six months later, in August (see Figure 3) .

The second variable is wind speed (see Figure 4) . According to a Penn State study, after cold outside temperature, “wind is the second greatest source of heat loss (from buildings) during the winter…. In fact, up to one-third of the annual residential heating energy goes to heat … infiltration air many times each winter day.” 2 But wind has negligible effect on summer gas usage, largely water heating. Over some range of temperatures, wind begins to have an effect. Columbia used a logistic curve to model this increasing effect (see Figs. 5 and 6) . Adding wind to the model reduces the RMSE to 45,571 Dth/day.

The third variable is the number of cold days. Successive cold days tend to cause increasing daily demand because the cold builds up in the dwelling structure. And psychologically, residents tire of the cold, cave in, and crank up the thermostat.

To measure this impact, Columbia added HDD from prior days to its model. Columbia tried periods of 1, 5, and 10 prior days. For the 5- and 10-day periods, Columbia assigned half the weight to HDD on the first prior day, and assigned the remainder to the earlier days, with each earlier day getting less weight (see Figure 7) . Adding prior day HDD to the model reduces the RMSE (see Figure 8) .

Continuing on to 15 prior days provided diminishing returns: RMSE reduced only slightly to 30,426 Dth/day. Columbia’s results use the 10-day lag period.

The fourth demand variable is the effect of holidays and weekends. Large industrial customers have large demand reductions on