Published)
3.3 Case Study and Experimental Methods
3.3.1 System Configuration
The case study used to demonstrate the proposed approach is an inner-city urban catchment in Adelaide, South Australia (Figure 3.5). The catchment has a history of urban infill development, resulting in local flooding. In response, costly major pipe upgrades have been proposed. An alternative and potentially more cost-effective approach to addressing the flooding issues is to use the approach introduced in Section 3.2. This includes the use of optimised distributed storages and their optimal RTC to reduce peak system outflows.
The total catchment area for this case study is around 36 ha, and the land use is mostly medium-density residential. The topography of the catchment is shown in Figure 3.5 using 5 m contour lines. The catchment generally falls from southeast to northwest, with the stormwater flow path gradient ranging from 0.5% to 2%. The location where flooding problems occur is marked as the
‘system outfall’. Eight potential locations for the stormwater storages were
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determined in consultation with local government engineers dealing with the flooding issues and are shown in Figure 3.5.
Figure 3.5 Case study Information. Including location (GoogleMap 2020), catchment map with sub-catchments (5m counter lines) and eight potential
storage locations 3.3.2 Computational Experiments
In order to test the effectiveness of the proposed ‘distributed storage with optimised layout’ (Step 1) and the ‘distributed storage with optimised layout and control’ (Step 2) approaches, three computational experiments are conducted, as summarised in Figure 3.6. For experiment 1, the optimal trade- off between storage volume and peak flow is determined for an ‘end-of-system
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storage’ (EoS) as a benchmark against which the relative effectiveness of the two-step approach (Section 3.2) introduced in this paper is assessed. In Experiment 2, the benefit of using distributed storage with optimised layout (Step 1) is assessed by identifying optimal trade-offs between system storage volume and peak flow and comparing it to the ‘end-of-system storage’
(Experiment 1). Experiment 3 assesses the additional benefit achieved by adding optimal RTC to selected optimised layouts (Step 2) by comparing the results to the optimal trade-off curve from Experiment 2.
Figure 3.6 Experiment configurations for all three experiments in this study (Note: AEP = Annual Exceedance Probability)
3.3.2.1 Rainfall and Peak Flow Characteristics Common to all Experiments
An AEP of 10% is used to determine the design rainfall from Australian Rainfall and Runoff 2019 (ARR 2019 (Ball et al., 2019)) for all experiments (Figure 3.6), as the minor stormwater system (pipe and kerb flow) at the case study site is required to have the capacity to convey runoff for this storm frequency. In addition, all experiments are conducted using the ten recommended storm temporal patterns in ARR 2019, as storm temporal patterns can significantly influence peak flow. In order to assess the effectiveness of the different approaches to reducing peak flow tested in the three experiments, the average peak flows resulting from the ten storm patterns were used, as recommended in ARR 2019 (Ball et al., 2019). Consequently, for the remainder
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of this paper, ‘peak flows’ refers to the average peak flows of ten temporal storm patterns. It should be noted that a zero initial loss is assumed for the storm events, which ensures that all peak flows can be compared directly.
3.3.2.2 Experiment 1: End of System Storage
In order to determine the critical storm duration of the catchment (which is the duration that produces the biggest peak flow) and how this varies with the addition of storage, three storm durations (20, 25 and 45 min) were tested for the ‘end-of-system’ EoS storage.
The decision variables for the EoS storage optimisation runs include the storage volume and outlet orifice diameter. The largest possible outlet diameter is set to 525mm, which is equal to the connected pipe diameter. The EoS storage is placed at location 8 at the end of the stormwater system (Figure 3.5). The objectives of the EoS storage optimisation are to minimise: i) stormwater system peak flows and ii) volume of EoS storage.
Hypervolume convergence was used as the stopping criterion, as part of which the optimisation run stops when the hypervolume (Beume et al., 2007) of the solutions that provide the optimal trade-off between the two objectives (i.e. the Pareto front, (Van Veldhuizen and Lamont, 1998)) does not change by more than 0.01 for ten successive generations.
Based on the results of the optimisation runs, the single critical duration that provided the highest peak flow is determined and used for Experiments 2 and 3 (Figure 3.6).
3.3.2.3 Experiment 2: Distributed Storage with Optimised Layout (Step 1)
This experiment uses the single critical duration determined from Experiment 1. As discussed in Section 3.2.2, the decision variables for the distributed storage layout optimisation include storage locations and volumes. Eight potential locations for the storages (Figure 3.5) are considered, and the maximum volume for each of these is set to 1,000 m3 based on site constraints.
The storages are modelled as street-scale in-line storages, which are connected to the existing stormwater pipelines, with the underground in-line storage height set at 1.2 metres. It should be noted that the largest possible orifice sizes
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are the same as the diameter of the pipes to which they are connected (either 450 mm or 525 mm). Similar to Experiment 1, hypervolume convergence was used as the stopping criterion for the optimisation runs. The output from this experiment is the trade-off curve between system storage volume and peak flow.
3.3.2.4 Experiment 3: Distributed Storage with Optimised Layout and Control (Step 2)
The aim of this experiment is to determine the additional benefits of optimising the RTC of distributed storages for a range of selected optimised layouts. This experiment uses the single critical duration determined from Experiment 1 and selected optimal layouts from Experiment 2, which corresponded to different system storage volumes ranging from 100m3 to 1000m3 in 100 m3 increments (i.e., 100m3, 200 m3, …., 900 m3, 1000 m3).
The decision variables for the optimisation of the RTC include the percentage opening of the storage outlet orifices and the time step at which such changes will be made. The available percentage openings included 0% (fully closed), 5%, 10%, …, and 100% (fully open) and the control time step was 5-minutes.
As there was only a single objective (i.e., to minimise peak flow), objective function convergence was used as the stopping criterion, where the optimisation run stops when the peak flow does not change by more than 0.01L/s over ten successive generations of the EA.