# Hydraulic power and system

The network of hydroelectric power consist of reservoirs and hydro power plants, connections between and their behaviors. Reservoirs collect water through inflow or flowing from an upstream source, in the manner of a battery. Hydro power plants can spend saved water in order to produce power to cover the grid load. 

## Hydro power plant Power/Discharge curves

Each power plant will have an associated PQ-curve that describes the relationship between water discharged through the station and the power produced from said station. While the efficiency curve is continuous in reality, to simplify the PQ curves are made out of piece-wise linear segments. 

The segments are directly translated to discharge segments in the model. Each segment is part of the sum of total discharge. In order to ensure that each segment is used in order, the PQ curves need to be strictly concave, so that the first segment is the most efficient and then in turn become less and less efficient. It is allowed for a segment to be less efficient than the previous segment.

A preprocessing step is added to make each PQ curve concave. Each point of the curve is visited in turn and the slope of each line is checked. If the next slope is steeper than the current one, the point in the middle is removed and the new line now goes to the first to the third point.

#TODO [INSERT ILLUSTRATION HERE]

Each segment is translated into a discharge segment.