Published)
Chapter 4 Calibration-free Approach to Reactive Real-time Control of Stormwater
4.2 Methodology
4.2.1 Proposed Target Flow Control Approach
The urban flooding problem addressed is the exceedance of the capacity of a stormwater conveyance system at a point of interest, such that the peak flow in the system at that location (Qpeak) is greater than its flow capacity (Qcapacity, Qpeak>
Qcapacity). The concept underpinning the proposed Target Flow Control (TFC) approach is to temporarily detain any excess flow with the aid of storage and to control the outflow of this storage in real-time during a storm event to maintain the peak of the controlled storage outflow (Qout,t) at the capacity of the
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stormwater system (Qpeak = Qcapacity) for as long as possible. By doing this, the storage outflow can be maximized and, thereby, the storage volume utilized effectively. Consequently, the flow target of the TFC approach is set as the stormwater conveyance system capacity (Qtarget = Qcapacity).
The controlled storage outflow (Qout,t) is a function of the orifice opening percentage (Ot) and the storage level at time t (Ht). The maximum storage outflow (Qmax,t) is the uncontrolled storage outflow with the orifice fully open and is a function of the storage level at time t (Ht). Based on the maximum storage outflow (Qmax,t), the proposed control strategy adjusts the controlled storage outflow at time t (Qout,t) such that it satisfies the following conditions:
• If Qmax,t> Qtarget, then Qout,t = Qtarget
• If Qmax,t ≤ Qtarget, then Qout,t = Qmax,t
To ensure the controlled storage outflow equals the system flow target (Qout,t = Qtarget) when the maximum storage outflow is larger than the system flow target (Qmax,t > Qtarget), the TFC approach uses the following equation, which is a re- arranged version of the orifice equation (Reader-Harris and Sattary, 1990, Reader-Harris et al., 1995), to adjust the opening percentage of the storage outlet orifice at time t (Ot) based on the storage level at time t (Ht) as follows (also see Figure 4.1):
𝑂𝑡= 𝑄𝑡𝑎𝑟𝑔𝑒𝑡
𝑐𝑑𝐴𝑜𝑟𝑖𝑓𝑖𝑐𝑒√2𝑔𝐻𝑡 (4.1)
Where 𝑐𝑑 is the orifice discharge coefficient, 𝐴𝑜𝑟𝑖𝑓𝑖𝑐𝑒 is the area of the orifice (i.e., the storage outlet), 𝑔 is the gravitational constant, and 𝐻𝑡 is the storage level at time t.
As storage levels can be measured in real-time during a rainfall event very easily by using low-cost pressure sensors, the orifice opening can be adjusted accordingly, and thus the TFC approach does not require calibration.
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Figure 4.1 The conceptual approach of the proposed TFC
Figure 4.2 illustrates how the TFC approach is able to maintain storage outflows at the target flow (Qtarget) for rainfall events with various temporal patterns. As can be seen, the storage outflow is controlled during the rainfall event based on storage level with the aid of Equation 4.1, and the outflow is always maintained at or below the target flow (stormwater conveyance system capacity, red line, Figures 4.2g&h). The orifice is kept fully open when the maximum outflow does not exceed the target flow (Qtarget), but once the maximum outflow exceeds the target flow (Qtarget), the orifice is adjusted to be partially open based on real- time storage level information (green lines, Figures 4.2c&d). By doing this, regardless of the rainfall event, the TFC approach is able to ensure storage outflows are maintained at or below the target flow (green lines, Figures 4.2g&h), provided the tank volume is sufficiently large, therefore utilizing the maximum capacity of the existing stormwater conveyance system.
With the help of the TFC approach, storage outflows are maintained at the stormwater conveyance system capacity for as long as possible, which eliminates unnecessary usage of storage volume (for example, the retention
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storage volume is used before the capacity is exceeded), and as a result, the required storage volume can be minimized.
Figure 4.2 Conceptual performance of the proposed TFC approach 4.2.2 Implementation of the TFC Approach
To test the effectiveness of the proposed Target Flow Control (TFC) approach, it is implemented using the simulation approach shown in Figure 4.3. As part of this approach, the target flow (Qtarget) is derived from the stormwater conveyance system capacity, and the control time step (Δt) is pre-determined before the application of the TFC approach, which would be based on the capabilities of the selected control infrastructure (e.g., hardware and software) in practice.
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For the first time step (t = control time step (Δt)), the storage level (Ht) is measured and retrieved in real-time with the aid of sensors in the storage. Next, the maximum outflow (Qmax,t) is calculated with the aid of the orifice equation based on the real-time storage level (Ht) information and a 100% open orifice opening percentage (fully open). If the maximum outflow (Qmax,t) is larger than the target flow (Qtarget), the orifice opening percentage (Ot) is calculated and updated using the real-time storage level (Ht) and the target flow (Qtarget) using Equation 4.1. If the maximum storage outflow (Qmax,t) is less than or equal to the pre-determined target flow (Qtarget), the orifice opening percentage (Ot) is set to 100% open (fully open) to achieve the maximum storage outflow (Qmax,t).
For the next time step (t = t + Δt), the orifice opening percentage (Ot) is determined using the same procedure, and this cycle continues until the end of the rainfall event. By applying this approach, the storage outflow (Qout,t) can have the best chance of being maintained at or below the pre-determined target flow (Qtarget), which is the stormwater conveyance system capacity.
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Figure 4.3 Framework for implementing the proposed TFC approach 4.3 Case Study and Computational Experiments
As mentioned previously, the second objective of this paper is to test the effectiveness of the proposed TFC approach in a simulated environment. This is done with the aid of a case study, details of which are given in Section 4.3.1.
The simulation environment used is detailed in Section 4.3.2, with information on the computational experiments provided in Section 4.3.3 and details of the metric used to assess the performance of the TFC approach given in Section 4.3.4.