Optimal Design of a Booster Station
- Function? Starting from the customer, who defines load scenarios as shown in Fig. 1, a set of six pumps is available from which any combination can be chosen. For three out of the six pumps, the rotation speed can be adjusted.
- Goal? In our example, the aim is to minimize the investment costs plus the energy consumption costs with predefined weighting.Ziel: In unserem Beispiel ist es Ziel sowohl Energieverbrauch als auch Investitionskosten mit vorgegebener Gewichtung zu minimieren.
- Playing field? The fluid machines can be identified by their head curves (cf. Fig. 2). In our example a maximum of five pumps may be selected due to space reasons. Thus, the planner’s task is to choose at most five pumps from the product line in such a way that of course all load demands can be fulfilled, and that additionally the sum of investment costs plus the expected energy costs in the recovery period are minimal. For this purpose it is allowed to assume a flexible connection between the pumps, which means that the topology can partially be changed during the operations.
- TOR finds the optimal system. The new and essential part is that during this step, the system design is performed by an algorithm! The number of possible system topologies is huge. Thus, human planners hardly stand a chance of surveying all these possibilities. This is similar to the fact that a medium chess player has almost no chance of beating a good chess program, today. The algorithmic idea is to examine discrete scenarios and to select the most suitable subgraph from the graph representing all possibilities for the system topology. In Fig. 3, the complete graph with two different highlighted subgraphs is shown. In Graph 1, pumps P3 and P4 are connected in series, while pump P5 operates in parallel. Another possible alignment is shown in Graph 2: Pumps P1 and P3 are connected in parallel and behind them, pump P4 is connected in series.Finden eines optimalen Systems
Although at first glance this relatively simple example may seem easy to handle, it has a surprisingly complex solution, which is illustrated in Fig. 4. It strikes that in this solution only four pumps are employed and that the connections between these pumps are depending on the load scenario. In the first scenario, only one pump is used. In the second and third scenario, pumps P1 and P3 work in parallel, both being connected in series with pump P4. In the fourth scenario on the other hand, pumps P3 and P5 operate in parallel, while P1 is not employed. What is the special feature of this solution? Being provided by our method, we can guarantee that there is no better solution. Better is no option!