Optimal peak shaving capacity and control for a known load curve: application to irrigated agriculture

Efficiency at low flow rates, and ease of use, make electric pumps the preferred means of providing irrigation water in regions with weakening aquifers. In predominantly agricultural areas with large numbers of irrigators the resulting summer demand peak may be two or more times higher than the average yearly load. Meeting these peaks is expensive for the rural electric cooperatives that serve these areas. This paper considers the optimal control of small, distributed, generator sets in order to reduce these operating costs. Once the optimal control is established, methods are provided to determine how many of these units to purchase or lease. Because the rate structure-and hence the optimal control-is discontinuous, care is taken to show continuity and convexity of the cost function. An example is given using averaged load curve data for a cooperative in the Texas High Plains. The major simplifying assumption is that the load curve is known. This is appropriate for planning purposes, but extensions will be necessary for operations