Hydroelectric Planning and Optimization System



The optimisation of electricity production in watersheds is a highly complex problem due not only to the number of variables involved but also to a multitude of both technical and regulatory constraints that must be respected. The objective function is different if we are in a regulated electricity system (in which case we will try to maximize production) to whether we are in a liberalized system. In the latter case we will optimise the economic benefit, taking care of the different regulatory frameworks (such as remuneration for secondary or tertiary regulation, or special arrangements for mini-stations) market variables (price forecast, specific markets for regulation, etc.) and criteria arising from the marketing strategy that must be carried out to perform.

Moreover, the underlying optimisation problem must bear many technical aspects in mind: the coupling between the reservoirs in the same watershed, non-linear dependence of the power produced by each unit with respect to the flow and elevation, restrictions of stop / start units, flow rates and minimum and maximum volumes to respect, particularly casuistry pumping stations, and that of flowing plants. It is a non-linear optimisation problem with mixed continuous and discrete variables, along with a number of stiff constraints.




AIA has developed a unique technique to deal with this problem, based on a newer modelling output curve for the whole generating substation, which preserves the essential nonlinearity of the problem and allows application over Network Flow and Convex Optimisation mathematical techniques.

This technique has been successfully applied to several watersheds with coupled reservoirs, including pumping or central flowing stations. Optimisation can be calculated using annual, weekly, or intra-day time horizons.




  • Enables global optimisation of production in coupled watersheds, with the criteria of maximum electricity production or maximum market profit.
  • The innovative modelling of the behaviour of a whole generation plant provides high accuracy in results.
  • Calculates ideal scheduling for various horizons: yearly, weekly, and daily.
  • Integrates all present restrictions on the real problem, both technical and regulatory.
  • Integrates special cases for flowing or pumping stations.
  • Contemplates possible incentives to the availability of resources, regularization, or the existence of a market in itself.

Success Cases


AIA has successfully applied these methods of electricity market analysis in various stages:

  • Implementation of the SOPHIA System for optimising hydropower production, for one of the largest producers in the Spanish market.
  • Implementation of the SOPHIA system with another of the major Spanish market producers, for the optimisation of economic benefit in the management of hydropower production. Includes stratification help to market supply at different output levels available at each moment.