Here we outline three possible methods which can be used to achieve the objective of the project. One of these methods will be used in the final modelling application.

1) SDDP method
This method is based on formal optimisation. The overall situation is considered as a multi-step optimisation problem in which the value of stochastic variables for the current week are made known at the beginning of the week.

The SDDP method is considered "state of the art" internationally and is in widespread operational use. SINTEF Energy Research has considerable experience of the use of SDDP and owns the SDDP model "ProdRisk" which is used operationally by several market players in their local planning. As far as we are aware, no attempts have been made to solve the fundamental market problem inherent in applying SDDP in relation to the large number of reservoirs (>100) and the fine time resolution we are considering here.

The SDDP method is highly suitable for parallel processing but has severe constraints when it comes to stochastic modelling. In earlier projects at SINTEF Energy Research, research challenges have been identified in connection with the modelling of inflow in systems involving multiple inflow series covering a wide geographical area.

The project "Power System Analysis and Transmission Planning in a Changing Environment" resulted in the development of an SDDP-based prototype with detailed hydroelectric, wind generation and grid constraints. This prototype has been tested on small systems such as the Icelandic power system.

The computation time of the prototype is high, and its existing implementation is not optimally adapted to large-scale parallel processing. If the SDDP method is considered to be the most suitable for this project, it will be natural to use this prototype as a starting point.

2) Scenario tree method
This method is based on formal optimisation in which the overall problem is considered as a sequence of optimisation problems. A stochastic two-stage optimisation problem is solved for each week of each inflow year throughout the analysis period, with the first-stage decision being carried forward. The values of stochastic variables such as inflow, temperature, wind and power price are specified in the second decision stage in each optimisation problem. The sequential optimisation problems may contain all types of constraints, including detailed hydropower and power flow constraints. The method also allows representation of non-linear relations and binary variables in the first stage.

The method is well suited to parallel processing. Although it requires a good representation of the time-correlation of the stochastic variables, it places few constraints on stochastic modelling. The method enables the direct use of historical data and bears similarities with the way many power generating companies currently carry out seasonal planning. The probability distribution, and in particular the distribution of extreme values, is represented effectively.

A prototype based on this method was developed ass part of the project "Power System Analysis and Transmission Planning in a Changing Environment" and tested on a Scandinavian system with 13 areas with an aggregated description of the hydropower system [9]. The tests show that the prototype provides good results, but the computation time is high. If the scenario tree method is considered to be the most suitable for this project, it will be natural to use this experience as a starting point.

3) Scenario tree method with limited time-horizon
There is some uncertainty as to whether the scenario tree method as described above provides acceptable computation times for a complete northern European system, even if large-scale parallel processing is used. The computation time can be reduced significantly by defining a shorter time interval, for example 2-3 months, for each scenario tree. The determination of the end value setting, in the form of quasi-individual water values, must therefore be generated using logic from the Multi-area Power-market Simulator model (EMPS). The projects "Power System Analysis and Transmission Planning in a Changing Environment" and "The Value of Flexible Hydropower Generation" resulted in the development of a model called "ReOpt" [10]. ReOpt solves the market problem for the entire system by means of a detailed description of hydropower generation based on volume control over a short time span provided by the drawdown model in the EMPS. The programming code of ReOpt is a good starting point for model development based on the scenario tree method.