Structural Optimization With Storages

Use Case of a Structural Optimization With Storages

If the energy system contains storage components, these are coupled to each other via the storage level of successive time steps in MILP (mixed-integer linear programming). The storage level \(U\) is calculated from the added heat \(Q\) and the simulation time \(t\) using the equation

\(U_n=U_{n-1}+Q_{n-1}\cdot(t_n-t_{n-1})\).

The resulting typical time steps have no temporal relationship. This means that in the original time series, successive time steps no longer follow one another in the compressed time series. Therefore the time series compression cannot be used with independent time steps. This applies to all structural optimization models with storages – regardless of whether the storage itself is optimized in its size or not.

Time Series Compression With Typical Days

If there are storages in the model, typical days are generated as clusters during automatic time series compression due to the problems described above. The time series data are first sorted by days, and then similar days are grouped together. This is the Time Series Typical Day Compression procedure.

The number and resolution of the type days depend on the Compression level selected in the Simulation ribbon. They are displayed in a message from the Simulator, such as:

The time series have been compressed for structural optimization to 4 type days with 2 time steps each.

Time Step Coupling in the Structural Optimization Model

The compressed typical days are not consecutive because a single typical day can represent many different days in the year. In order to calculate the storage level realistically and to avoid that the storage is always empty at the end of the day, the level at the first time of the typical day is calculated from the level at the last time of the same typical day. So the following applies

\(U_0 = U_N\),

where \(N\) is the number of time steps per typical day.

Maximum and Minimum Values

In typical-day-compressed time series, the minimum and maximum values are not initially taken into account because meaningful peak loads for energy systems cannot simply be derived from the highest values, but it must also be taken into account how long the peak values occur. A “maximum day” is not determined by the compression method.

Instead, during compression after the typical days have been generated, the maximum and minimum are automatically added to the time series as individual time points with a duration of only one time step (usually one hour). The methodology of the coupling condition (see section 2.1.) prohibits the use of a storage to cover the demands of the additionally inserted maximum or minimum. The following figure shows the maximum heat demand inserted in the last time step.

Storage System Optimization for Peak Load Coverage

However, there are two alternative approaches to design an energy system in such a way that the storage system covers the peak loads: firstly, temporally high-resolution structural optimization and secondly, the allocation of additional costs to the peak load.

Temporally High-Resolution Structural Optimization

To include a storage device to cover the peak load of an energy system, compression possibly may dispensed with. In this way, the problems caused by compression during peak load design are avoided. The compression is switched off in the Simulation ribbon with No compression/exactly.
If you select No compression/exactly as the compression level and deactivate Use your own compressed time series, set a Look-ahead in the size of the entire simulation period. The structural optimization is then not executed before, but together with the operational optimization.

It is hardly possible to view an hourly resolved time series of one year (8760 h). Detailed information about this can be found in the section Automatic Time Series Compression. Depending on the complexity of the energy system, available solver, and computing capacity, representative days or a representative week can be used. In the case of a representative week, the design is only optimal for the week under consideration.

Extra Costs for Peak Load

The second approach to integrate a storage facility for peak load coverage is to perform structural optimization with compression and to allocate very high costs by an alternative supplier to the peak load which can be covered by the storage facility. Actual costs (through a tariff, as in the example below) or virtual costs (through a Programmable control or the manipulation of the target function in the PML) can be estimated.