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Estimation of Very Large Linearized Systems (VLLS)
Electric or gas load varies in complex patterns in response to weather,
population, business activity, time of day, and calendar events. Over the longer
term, it responds to economic and technological changes, as well as to adaptive
behavior.
To analyze and predict load in this complex environment, we use an extensive
data set to capture and isolate the multiple interacting factors involved. To
evaluate a large number of factors on a very large data set, we have found the
most effective process to be a linearized model specified in great detail. In
particular, extensive use of categorical variables and highly detailed piecewise
linear functions yield very precise estimations of non-linear response
functions, compared to imposing shape restrictions on the data.
For example, the response of electric load to temperature depends on other
weather factors, the time of day, day of the week, season of the year, and other
"calendar events" such as holidays. The geometry of this response does not
conform well to any simple mathematical formula, but is an irregular,
bowl-shaped function that changes shape and location over time. Rather than try
to force a functional form on the data, the VLLS method allows the response to
temperature, given time and circumstances, to be estimated separately for very
small increments over the entire observed range. The VLLS method is more
accurate, because it does not effectively discard information by imposing
functional form.
The VLLS process extends to capture all factors found to be relevant in
forecasting load. The multiple factors it explicitly incorporates, including
(among others)
- time of day,
- day of the week,
- calendar events,
- multiple weather measures,
- angle of the sun above the horizon
- demographic and economic considerations,
make it a "causal" model. It will therefore not only provide short-term
forecasts of great accuracy, but also permit both long-term analyses
incorporating economic and demographic projections and weather-based scenario
analyses.
The practical value of the VLLS process is that it allows a great number of
relevant facts to be brought to bear on the problem. The VLLS process does not
exclude use of time series techniques such as Box-Jenkins analysis or pattern
recognition tools. However, the TESLA model incorporates these forms as
supplements to the causal relationships.
Value of VLLS
The VLLS approach measures directly those factors relevant in analyzing
electric load. Because of the large number of variables explicitly considered,
measures of individual effects are controlled for most other influences.
The TESLA VLLS model will forecast over multiple time horizons, with the same
basic structure and set of causal factors covering multiple time periods.
Consequently, assessing the incremental effects of different specified events
(bad or good weather, the business cycle, etc) is significantly more accurate
than with alternative techniques.
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