Small area forecasting with load growth curve

Small area load forecasting predicts the load of small zones (a feeder area, a grid cell of a few hectares) so that the location and timing of new substations, transformers and feeders can be planned.

The load of a small area follows an S-shaped growth curve (Gompertz-type), unlike the smooth growth of a large area:

 Load
  ^                       ___________  saturation
  |                    _/
  |                  _/
  |                 /    rapid growth
  |               _/
  |             _/
  |  __________/   dormant
  +-----------------------------------> Years
     |   I    |    II     |    III

1. Dormant period (I): the land is vacant or farmland; load is almost zero for many years.
2. Rapid growth (II): once development starts (new roads, housing, shops), load rises very fast, often over 5–10 years. The timing of this start is hard to predict.
3. Saturation (III): the area is fully developed; load grows slowly, only through higher consumption per consumer.

Forecasting using the curve:

• Each small area is located on its S-curve. Areas in the growth phase are forecast by fitting a Gompertz curve, $P(t) = a\,e^{-b e^{-ct}}$, to recent data, with the saturation level $a$ taken from land area × load density of the planned land use.
• Areas in the dormant phase cannot be trended; their start of growth is predicted by the simulation (land-use) method using zoning plans and infrastructure development.
• The sum of small-area forecasts is checked against the large-area (system) forecast.

The curve shows why trending alone fails for small areas and why spatial land-use information is required.