Model concept

The model is a linear optimization model that minimizes the total operational sys-tem costs. All technical restrictions in the syssys-tem operation like capacity limits are thereby considered by constraints. The calculated optimum can be interpreted in two ways. It can be interpreted as an operation that is planned by a hypothetical single system operator that is responsible for the total power system, so the power plant operation and the power transmission. The result can also be interpreted as the solution that is realized by an ideal electricity market with pure competition that respects the transmission restrictions. In the concept of pure competition, market distortions like market power or irrational behaviour of the market partic-ipants are neglected. The model only optimizes the operational system costs and investment costs or renewable feed-in tariffs are not considered. The model has an hourly resolution.

Table 3.1 shows the input and output of the model. The power plant portfolio is defined by the generation capacities in the model regions. For CHP and storage plants, the maximal heat or pumping capacity is also needed. The power plants are also defined by parameters that describe their technical operation like their efficiency or maximal storage content. Flexibility is described by parameters as minimal operation times, start up costs and others. The technical capability to provide primary, secondary or tertiary reserve is another characteristic of a power plant. The fuel prices and CO2 prices are required. No other taxes than the CO2 price are considered in the model. The transmission between the model regions is restricted by the thermal capacities and susceptances of the connecting lines. For each model region the reserve requirements are indicated. The heat and power demand as well as the generation from fluctuating renewable sources are given in an hourly resolution. In the case of wind power, not only the generation but also forecasts of the wind power generation are required for each optimization. The wind power generation and forecasts are simulated as described in Chapter 4. The simulation has its own input parameters that are for example related to forecast quality.

The results of the optimization model can be analyzed in different ways. Some examples are given in Table 3.1. The two basic results are the system costs (the value of the objective function) and the operation of the power plants (the vari-ables in the optimization). Other values can be deduced as the curtailment or the emissions. The transmission between the model regions is another result. The marginal values of the balance equations are interpreted as market prices. The op-timization model in combination with the simulation in Chapter 4 therefore allows to analyze the effects of high wind power shares on the power system operation

Table 3.1.: Input and output of the optimization model Input data Output examples

• Installed capacities

(power, heat, pumping)

• Plant parameters (efficiency, operation costs, emissions, flexibility, storage, CHP, reserve)

• Prices (fuel prices, CO₂ tax)

• Transmission (capacities, susceptances)

• Demand (power, heat)

• Reserve requirements

• Wind power (generation, forecasts)

• Other fluctuating power gen-eration

• Generation and curtailment

• Operational costs

• Storage operation

• Fuel usage

• Emissions

• Transmission

• Market prices

for different system configurations.

The wind power forecasts are considered by a stochastic rolling planning ap-proach. Power plant operators have to decide on the plant operation before the precise wind power production is known.¹ As wind power forecasts are not per-fect, recourse actions are necessary when the delivery period is in the nearer future and the wind power forecasts become more accurate. Hence, there is a continuous alternation of first decisions based on first forecasts and re-dispatch actions at a later date based on updated forecast information. Differences between former forecasts and updated forecasts are balanced by changes in the power plant oper-ation. The rescheduling of the plant operation can be interpreted as the result of intraday trading. The intraday optimizations therefore update the results of the day-ahead optimization and precedent intraday optimizations.

There are two ways how wind power forecasts can be considered in the intra-day optimizations of the model. In the first mode, deterministic optimizations are executed that only consider the actual predicted wind power production (ex-pected value forecast). This decision structure is illustrated in Figure 3.1-(a). The

1Next to wind forecasts, there are other uncertainties in the system as described in Sec-tion 2.2.2. It was shown that, for day-ahead forecasts, load forecast errors are negligible com-pared to wind forecast errors. Load forecast errors and uncertainties resulting from unplanned power plant outages are considered in the calculation of tertiary reserve requirements.

rolling planning is thereby based on an intraday optimizations taking place every 3 hours.² The optimizations cover the hours until the end of the next day and, in each optimization, the forecast for the first two hours is assumed to be perfect.

The forecast errors related to forecast horizons with one or two hours are only considered in the calculation of the tertiary reserve capacities.

(a) Deterministic optimizations (b) Stochastic optimizations

Figure 3.1.: Two modes of rolling planning

In the second model mode, not only the expected value forecast but also possible forecast errors are considered in the intraday optimizations. This allows to hedge possible forecast errors. In these stochastic optimizations, the random variable

“forecast error” is represented by several discrete scenarios (or scenario paths as more than one forecast hour is considered). Each scenario is weighted by its proba-bility in the objective function and the constraints are respected for all scenarios.

Thus, an optimal solution is found that also considers possible forecast errors.

This approach is illustrated in Figure 3.1-(b). The number of considered scenarios is a trade-off between calculation time and a good statistical representation of the forecast error. Calculation time is above all critical due to the rolling planning.

The calculation of one year for example demands 2920 successive optimizations (one every three hours). The generation of the error scenarios and their statistical characteristics are presented in Chapter 4.

Concluding, the model is defined by (stochastic) optimizations of the power plant operation under uncertain wind power forecasts, [92, 93], combined with a

2The intraday trading at the EEX takes place every hour but the wind power forecasts are updated only every four hours [91].

rolling planning approach, [94], where the recourse decisions of former optimiza-tions become continuously the root decisions of the following ones.