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Stochastic optimisation model of interconnected power systems in Germany and Nordic countries with wind power production forecasts as an input parameter

The model analyses power markets based on a description of generation, demand and transmission between reasonably defined model regions and derives electricity market prices from marginal system operation costs. The model is a stochastic linear programming model with wind power production as the stochastic input parameter. It optimises the unit commitment taking into account trading activities of different actors on different energy markets. Four electricity markets and one market for heat are included in the planning model:

1. A day-ahead market for the planned delivery of electricity.
2. An intra-day market for handling deviations between expected production and consumption agreed upon the day-ahead market and the realised values of production and consumption in the actual operation hour.
3. A day-ahead market for automatically activated reserve power (frequency activated or load-flow activated). The demand for these ancillary services is determined exogenously to the model.
4. A intra-day market for secondary reserve (regulating power). The demand for these ancillary services is determined exogenously to the model and covers the demand due to outages and due to large wind power production forecast errors.
5. Due to the interactions of CHP plants with the day-ahead and intra-day market, markets for district heating and process heat is included.

The objective function maximises the social surplus (the sum of consumer and producer surplus), which corresponds to minimising the operation costs in the whole system in the case of fixed electricity demands. It considers the operation and start-up costs of condensing and CHP plants and the operation costs of heat boilers, heat storages and electricity storages including pumped hydro. Power production costs of hydro reservoir plants are modelled through water values, which are calculated with the help of a long-term model optimising the use of water over a yearlong optimisation horizon using water inflow as a stochastic input parameter.

The inclusion of uncertainty about the wind power production in the optimisation model is considered by using a scenario tree. As it is not possible to cover the whole simulated time period with only one single scenario tree, the model is formulated by introducing a multi-stage recursion using rolling planning. In the model there exist two types of decisions: "root" decisions, i.e. the amounts bought and sold on the day-ahead market, that have to be taken before the realised wind power production is known and hence must be robust towards the different possible wind power forecasts, and "recourse decisions", i.e. down or up regulation of power plants, that are done after the actual wind power production becomes known.

In general, new information arrives on a continuous basis thus an hourly basis for updating information would be most adequate. However, it is necessary to simplify the information arrival and decision structure in the stochastic model due to calculation time considerations. In the current version of the model a three-stage model is implemented. The model steps forward in time using rolling planning with a 3-hour step. For each planning period a three-stage, stochastic optimisation problem is solved having a deterministic first stage covering 3 hours, a stochastic second stage with five scenarios covering 3 hours, and a stochastic third stage with 10 scenarios covering a variable number of hours according to the rolling planning period in question. In the planning period 1 the amount of power sold or bought from the day-ahead market for the next day is determined. In the subsequent re-planning periods the variables for the amounts of power sold or bought on the day-ahead market are fixed to the values found in planning period 1, such that the obligations on the day-ahead market are taken into account when the optimisation of the intra-day trading takes place.

To our knowledge the model is the first large-scale power market model that handles the uncertainty in wind power production forecasts endogenously, i.e. makes unit commitment decisions that are robust towards the uncertain wind power production predictions. This also includes being the first model to handle both a day-ahead market and an intra-day market for regulating power in the same model. The model is implemented in GAMS ( and requires licensing of GAMS and of a linear solver such as CPLEX. It is publicly available from model is suitable for analysing power system with a large share of fluctuating wind power production. It is suitable for analysing the fuel savings due to introducing more wind power in a power system, analysing the performance of wind power integration measures such as extension of transmission lines and building of heat pumps, and analysing the price response due to more wind power both on the day-ahead market and on the market for regulating power (intraday market).

Related information

Reported by

Risoe National Laboratory, System Analysis Department
P.O. Box 49
4000 Roskilde
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