The Model

How does MaxHydro work?

MaxHydro uses dynamic programming (DP) to solve optimization problems defined as sequential decision processes. DP is not restricted by any requirement of linearity, convexity or even continuity, making it specially suitable for hydropower optimization. The feasible reservoir space is divided in a number of discretization points. The algorithm evaluates the objective function for each point and selects the reservoir level that maximize/minimize the objective function or optimization criteria, as the optimal for that period.

Iterations

In order to improve the accuracy of the model results a two step seamless process is adopted. The first step produces a near optimal solution. In the second step the previous operating policy is further refined, until the optimal one that maximizes / minimizes the objective function, is obtained.

Constraints

Numerous constraints can be specified and applied during the optimization process:
Variable minimum or maximum station releases
Minimum or maximum ramping rates, big changes of reservoir storage from time step to time step
Evaporation losses
Smoothing functions
Generating unit start-up costs

Implementation process

The hydropower system historical operation and production is analysed and baseline methodology of the historical operation is established and documented. This methodology includes the entire hydropower system or only a portion to which MaxHydro will be implemented.

From the historical (3-5 years) flows series, reservoir levels, tail water levels, hydraulic losses, efficiencies and other relevant historical data, we will estimate the relationship between the river flows, reservoir levels and energy generation for the baseline calculation. This will be done through regression and other methodologies taking into account suggestions from the hydropower system owners and operators. After this baseline methodology is established and agreed upon by both parties, it will be easy to determine how much benefits or additional energy is produced by the implementation of MaxHydro.

21 different system layouts

By combining the reservoirs in series or parallel, a number of different layouts can be optimized and by varying other system parameters, the number of possible system configuration is practically unlimited.

Version 3.0 of MaxHydro can accommodate up to nine (9) cascading reservoirs and associated power stations. This is achieved by combination of optimization and simulation. The smaller reservoirs are simplified and are operated by pre-defined operating rules and the station efficiency is defined as a function of the station release on a constant reservoir level. Up to 2 additional reservoirs can be included downstream of the main reservoirs. The energy-benefits obtained from the additional reservoirs are included in the overall objective function. In this way global optimum of the system is calculated. The end user can easily switch between different system layouts by a click of a button. The 21 possible system layouts for which MaxHydro can calculate the optimal solution are shown on the right. Follow the reservoir icon, dotted line, reservoir icon to abtain the possible layout that can be optimized. The colored areas on the figure represent two of the 21 possible system layouts.

In order to improve the accuracy of the model results a two step seamless process is adopted. The first step produces a near optimal solution. In the second step the previous operating policy is further refined, until the optimal one that maximizes / minimizes the objective function, is obtained.