Hveding’s Conjecture: On the Aggregation of a Hydroelectric Multiplant – Multireservoir System
The optimal solution of a system of hydroelectric plants with many reservoirs can be significantly simplified if production capacities and reservoir capacities can be aggregated to a system with a single plant reservoir. The purpose of the paper is to find conditions for aggregating a multiple-plant hydro system to a single plant – single reservoir system based on making a mathematical representation of the system model. Introducing constraints only on the reservoirs and assuming full manoeuvrability of plants a system of multiplant and multi reservoirs aggregating the system to a single plant with a single reservoir should give us the optimal solution for period prices and total production in each period. Adding realistic constraints on plant production levels aggregation becomes more difficult because each plant must avoid locking-in of water. Aggregation is still possible if there is system manoeuvrability.