Published)
Chapter 4 Calibration-free Approach to Reactive Real-time Control of Stormwater
4.4 Results
4.4.1 Overview of Results: Performance of the TFC Approach
Figure 4.4 summarises the performance of the TFC approach for the experiments described in section 4.3.3 (Table 4.2). In Figure 4.4, the quartiles of the target flows are shown by the coloured box and whisker plots using the scale on the left and the quartiles of the percentage errors are shown by the grey box and whisker plots using the scale on the right. As can be seen from Figure 4.4, for a wide range of rainfalls and corresponding target flows, the TFC approach performs well for all trials (<20% error), with 95% of the target flow errors being less than 10%.
The performance of the TFC approach improves when the duration of rainfall increases (Figure 4.4). For example, the mean target flow errors are reduced from around 8% for 30min rainfall in Adelaide to around 1% for 24hr rainfall in Adelaide with the2kL storage (Figure 4.4a). For the three selected cities, the target flows for Adelaide and Melbourne are similar, while the target flows for Sydney are much higher. However, the target flow errors are always generally small and have no significant differences between the selected cities. For
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example, the mean target flow of 1% AEP, 30min duration rainfall increases significantly from 6.9 L/S in Adelaide (blue box, Figure 4.4a) to 13.8 L/S in Sydney (blue box, Figure 4.4c) with the same 2kL storage, but the target flow errors are both around 10% (black box, Figures 4.4a & 4.4c).
It should be noted that although most target flow errors are less than 10%, there are still some relatively higher errors that are close to 20%. For example, the maximum 20% target flow error for all trials occurs for 1% AEP, 60min rainfall in Adelaide with 2kL storage (Figure 4.4a). However, when the storage volume is increased from 2kL to 10kL (and the target flow is reduced accordingly), the error is always less than 10% (Figures 4.4d, 4.4e & 4.4f).
The results suggest that the TFC approach, which only uses information on current tank water levels, is able to perform well for a wide range of rainfalls without requiring any calibration. This highlights that the proposed approach is able to overcome the shortcomings of existing calibrated reactive control schemes, as their performance would not be able to deal with changes in future rainfall patterns caused by climate change.
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Figure 4.4 Performance of the proposed TFC approach for a wide range of design rainfall events. Coloured box and whisker plots represent range of target flows, with scale on left y-axis and grey box and whisker plots represent range of target flow errors, with scale on right y-axis.
Box represents the upper and lower quartiles of the range, while whiskers represent 90% limits of this range
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This section examines two typical control strategies (simple and complex) resulting from the application of the TFC approach to maintaining storage outflow at the system target flows (Qtarget). As the operation of the TFC approach is based on real-time measurements of storage level (Ht), two examples are selected based on differences in the way storage levels change over time for the 2kL storage. For Example 1 (simple), the storage level simply rises to the maximum storage level and then falls to zero. For Example 2 (complex), the storage level rises and falls several times during the rainfall event. In order to clearly illustrate the impact of the control scheme, as well as how it works, plots of system inflow, orifice opening percentage, storage level and system outflow are provided and discussed.
Example 1 (Simple Variation in Storage Level)
For Example 1, the storage level first increases as the system inflow is larger than the target flow (Qtarget)(Figures 4.5a & e). From t = 18min, based on the required orifice opening percentage calculated by Equation 4.1, the actual orifice opening percentage is set to be partially open to achieve the system target flow (Figure 4.5c). From t = 18min to t =38min, the actual orifice opening percentage is adjusted gradually from 100% (fully open) to 40% open (Figure 4.5c). At t = 38 min, the inflow rate of the storage equals the target flow, resulting in the maximum storage level (Figure 4.5e). After that, the storage level falls from its maximum level to zero. Because of the decreasing storage level, the orifice opening percentage is adjusted gradually from 40% to 100%
(fully open, t = 60 min) (Figure 4.5c) in order to maintain the storage outflow at the target flow for as long as possible based on Equation 4.1 (Figure 4.5g).
This demonstrates the ability of the proposed TFC approach to perform as expected (Figures 4.2 c &d).
Example 2 (Complex Variation in Storage Level)
For Example 2, the storage level increases from t = 2h to 4h (Figure 4.5f) as the inflow is larger than the target flow, and as a result, the orifice opening percentage is gradually reduced from 100% open (fully open) to 36% open (Figure 4.5d) in accordance with Equation 4.1 to maintain the outflow at the
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target flow (Figure 4.5h). The storage level reaches its maximum at t = 4h (Figure 4.5f), and from t = 4h to 7h, the storage level decreases from its maximum level to a local minimum value (60% of the maximum level, Figure 4.5f). During this time period, the orifice opening percentage increases from 36%
open to 42% open in response to the changes in storage level. After that, between t = 7 h to 8h, the storage level rises again to a local maximum value (70% of the maximum level, Figure 4.5f), and the orifice opening percentage is decreased accordingly from 42% open to 39% open (Figure 4.5d). By following the same procedure and adjusting the orifice opening percentage based on the change of storage level between the local maximum and minimum values, the storage outflow is always maintained at or below the target flow, as desired.
Thus, the results indicate that the proposed TFC approach is able to achieve the target flow with the aid of Equation 4.1, irrespective of the complexity of the temporal variation of the incoming rainfall, without requiring any calibration to local conditions.
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Figure 4.5 Impact and operation of TFC approach for two typical rainfall patterns: 1) Example 1 (Simple) (Sydney: 1% AEP, 30 min duration, Temporal Pattern 9) and 2) Example 2 (Complex) (Sydney: 50% AEP, 24 hr
duration, Temporal Pattern 7) for 2kL storage 4.5 Discussion