Case Study and Performance Assessment .1 Case Study Configuration

6.3 Case Study and Computational Experiments

6.3.1 Case Study and Performance Assessment .1 Case Study Configuration

Three realistic multi-storage case studies are selected to test the effectiveness of the TFCS approach, with details summarised in Table 6.1. These case studies are selected due to their high complexity, realism, and diversity, which makes them representative of real storage systems. The storage layouts of the case studies are shown in Figure 6.4.

Case Study 1 (Gamma) is an example stormwater system inspired by an urban watershed in Ann Arbor, Michigan, USA. This case study utilizes a total of 11 stormwater storages to control the runoff from 400 hectares of an urbanized catchment (Figure 6.5a). Four of these storages, which are in series, are controlled using 1m² controllable gate valves. The objectives are to keep the outflow from storages 1, 2, 3 and 4 below a threshold of 0.14m³/s, (Mullapudi et al., 2020b) and to keep the storage levels at each of the storages below their maximum. Runoff is driven by a 25-year, 6-hour storm event, and uniform rainfall is used as this case study has a small catchment area (Rimer et al., 2021, Mullapudi et al., 2020b). The stormwater management model (SWMM) for this case study is provided in previous studies (Rimer et al., 2021).

Case Study 2 (Astlingen) is a benchmark urban stormwater network developed by the German Water Association (DWA). The Astlingen network consists of a combination of combined and separate stormwater systems to reflect realistic conditions in Central Europe. This case study utilizes six storages with a total volume of 5,900 m³ to control flows in a catchment with an area of 177 hectares (Figure 6.5b). Four of the storages (storages 2, 3, 4 and 6) are controlled, including three storages in parallel (storages 2, 3, and 4) and two storages in series (storages 3 and 6). The objective is to minimize the total overflow volume

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from the storage tanks and overflow structures. Spatially variable rainfall information is provided by the four rain gauges located in the Astlingen catchment. Continuous historical rainfall data of 1 year with 5min resolution is provided for continuous simulation.

Case Study 3 (Delta – M) is a slightly modified version of the Delta case study introduced by Rimer et al. (2021). The Delta case study consists of a combined urban stormwater network with six storages that are located in a residential neighbourhood in order to control flows in a catchment with an area of 250 hectares (Figure 6.5c). Five of the six storages are controlled, including four storages in series (storage N3, N2, N1, and C) and two storages in parallel (storage C and S). The objective of this case study is to maintain storage levels within upper and lower thresholds for water quality and aesthetic objectives.

Runoff is driven by a 48hr observed storm event with an approximate return period of 2 months that is spatially distributed uniformly across the catchment.

The modifications made to the Delta case study in this paper are to move the location of some of the controllers so that they are directly downstream of the outlets of the active storages, resulting in the Delta-M case study.

Table 6.1 Case Study Characteristics Case

Study

Name Catchment Area

Controlled Storage Number

Storages in Series

Storages in Parallel

Rainfall Information

Objective

Case Study 1

Gamma 400 ha 4 4 0 6hr 1 in 25-

year rainfall event

Keep flow below a threshold Case

Study 2

Astlingen 177 ha 4 2 3 1 year of

continuous rainfall

Minimize total overflow

volume Case

Study 3

Delta - M 250 ha 5 4 2 48hr

observed storm event

(approx.

return period of 2

months)

Keep the storage level

within the operational

boundary

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Figure 6.5 Storage Network Topology and Sizes for the Selected Case Studies: (a) Gamma, (b) Astlingen and (c) Delta – M

6.3.1.2 Quantitative Performance Assessment

As the objectives of the three selected case studies are different (see Table 6.1), different metrics are used as measures for assessing the performance of the TFCS approach and the benchmark control approaches (see Table 6.2). For case study 1, the percentage of time each storage exceeds the threshold is used, which corresponds to the sum of time that the threshold for all storages in the system are exceeded ( ∑ 𝑇^𝑁_{1 𝑒𝑥𝑐𝑒𝑒𝑑,𝑖}) compared to the total time ( ∑ 𝑇^𝑁_{1 𝑖} ).

Reduction of total overflow volume is used as the metric for case study 2, which corresponds to the difference in total overflow volume (i.e., the overflow volume of all storage in the system for the entire time period, ∑ (∑ 𝑉^𝑇₁ ^𝑁_{1 𝑖,𝑡}) ) compared to the ‘No Control’ baseline scenario (𝑉_{𝐵𝑎𝑠𝑙𝑖𝑛𝑒}). Case Study 3 (Delta – M) requires two metrics to assess the ability to keep storage levels within their required upper and lower bounds: (i) the percentage of time outside of the operational boundary, which corresponds to the sum of time outside of the boundary for all storages in the system( ∑ 𝑇^𝑁_{1 𝑒𝑥𝑐𝑒𝑒𝑑,𝑖}) compared to the total time ( ∑ 𝑇^𝑁_{1 𝑖}) and (ii) total deviation of storage level, which corresponds to the sum of differences between the storage level (𝐻_𝑖) and operational boundaries (upper

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level: 𝐻_{𝑢𝑝𝑝𝑒𝑟} and lower level: 𝐻_{𝑙𝑜𝑤𝑒𝑟}, see Table 6.2 Metric d) summed over all storages.

Table 6.2 Summary of Metrics

Case Study Objective Metric

Case Study 1 (Gamma)

Keep Flow Below the Threshold

a. Percentage of Time Exceeds Threshold:

𝑇𝑖𝑚𝑒 (%) = ∑ 𝑇

^𝑁_{1 𝑒𝑥𝑐𝑒𝑒𝑑,𝑖}

∑ 𝑇

^𝑁_{1 𝑖}

× 100%

Case Study 2 (Astlingen)

Minimize Overflow Volume

b. Percentage reduction of Total Overflow Volume:

Reduction (%) = (1 −

^{∑ (∑ 𝑉𝑇1 𝑁1 𝑖,𝑡)}

𝑉_{𝐵𝑎𝑠𝑙𝑖𝑛𝑒}

) × 100%

Case Study 3 (Delta - M)

Keep Storage

Level Within Upper and

Lower Threshold

c. Percentage of Time Outside of the Boundary:

𝑇𝑖𝑚𝑒 (%) =

^{∑ 𝑇𝑁1}_{∑ 𝑇}^{𝑒𝑥𝑐𝑒𝑒𝑑,𝑖}

𝑁 𝑖

1

× 100 %

d. Total Deviation of Storage Level from Operational Boundary:

𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 (𝑚) = ∑ (∑ (𝑓(𝐻

_𝑖,𝑡

))

𝑁 1

)

𝑇

where: 1

𝑓(𝐻

_𝑖,𝑡

)

= {

𝐻

_𝑖,𝑡

− 𝐻

_{𝑢𝑝𝑝𝑒𝑟}

, 𝐻

_𝑖,𝑡

> 𝐻

_{𝑢𝑝𝑝𝑒𝑟}

0, 𝐻

_{𝑙𝑜𝑤𝑒𝑟}

≤ 𝐻

_𝑖,𝑡

≤ 𝐻

_{𝑢𝑝𝑝𝑒𝑟}

𝐻

_{𝑙𝑜𝑤𝑒𝑟}

− 𝐻

_𝑖,𝑡

, 𝐻

_𝑖,𝑡

< 𝐻

_{𝑙𝑜𝑤𝑒𝑟}