# A Methodology for the Design of RTC Strategies for Combined Sewer Networks

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- Identification of overflow locations
- Identification of control locations and
- Control algorithm design.

#### 2.1. Case Study Catchment Characteristics

#### 2.2. RTC Strategy Design

#### 2.2.1. Identification of Controllable Subbasins

#### Overflow Locations

#### Control Locations

- Using only existing control locations
**(E)**such as PS or existing sluice gates. In the literature, this is frequently the case for studies investigating the control of PS [30,39,40,41,42] and other existing control locations, such as sluice gates [20]. In practical implementation, this might require the installation of new actuators, as existing gates might not be configured to handle frequent control actions. - Considering network links based on the individual flow capacity of these links
**(Q)**, assuming that links with significantly lower capacity than their upstream (US) and downstream (DS) neighbors form suitable locations for the installation of actuators [4]. Studies applying simplified models (e.g., [24,43,44,45,46]) often inherently use this approach, as they use ‘throttle devices’ as control locations, e.g., as outflow of storage basins. This approach can thus be seen as the one most frequently documented in literature. It relies on the assumption that existing flow limiters have been designed to activate a significant amount of storage volume. The control locations can be identified by comparing the flow capacities of all links US of a node vs all links DS of a node, as illustrated in Figure 2a. As control will most likely be active when the system is below its maximum capacity but water levels significantly exceed dry weather conditions, the influence of the energy gradient can be assumed to be negligible. Conduits can then be represented by their cross-section for this comparison; conduit slopes are ignored (see Figure 2a, case (3)). - Selecting locations in a trunk sewer based on the in-sewer volume that can be activated in the collector upstream of the control location
**(V)**[2]. This method is here extended to also take all side branches of the network into consideration. This appears to be of high relevance, as it has been shown in a case study [47] that the zone of backwater influence caused by actuators can be considerable, and indeed, may extend far into side branches. A further potential extension could include steady states for partially closed actuators, as suggested by [27]. As actuators in this study cannot be assumed to remain partially open, this extension is omitted here. As opposed to [27,28], the volume activated by a potential control location is not limited by bifurcations if these are drained towards the same potential control location as the sewer branch under consideration (see Figure 2b). This, again, is determined using the drainage levels discussed above. New locations are placed such that they are not influenced by backwater from downstream control locations.

#### 2.2.2. Control Algorithm Design

- the mean of filling degrees over all subbasin (EQ glo), or
- the filling degree of the DS subbasin (DS loc), or
- the filling degree of the most DS subbasin (DS glo).

- aiming at filling the DS subbasin storage capacity up to a predefined maximum value (cs, see [22]) or
- using a desired discharge (qw) to the downstream basin as a means of negotiating a discharge that allows quickly emptying the upstream subbasin while considering downstream constraints and local boundaries for actuator flows and CSO activity (see [21]).

#### 2.3. Scenario Analyses

#### 2.3.1. Evaluated Criteria

#### 2.3.2. RTC Effectiveness and Parameter Sensitivity

_{abs}) representing the mean of all absolute values of the relative sensitivities per parameter is here used as measure of parameter sensitivity. Convergence of the Morris screening, as defined by [54], was assumed to be reached when the variability of neither total CSO nor flood volume exceeded 5%.

#### 2.3.3. Evaluation Period and Rainfall Data

## 3. Results

#### 3.1. Storage Potential

#### 3.2. RTC Effectiveness and Sensitivities

^{3}may require more in-depth investigations using a more accurate modelling approach (possibly 2D surface modelling) and more detailed rain data in order to ensure that a finally chosen RTC strategy will not result in an increased flood risk for this catchment. The potential for increased flooding could also indicate that there is no further potential for improvement of CSO volume performance for these scenarios.

_{min}was shown to be influential, and good tuning of these values is required for optimal performance. This is unexpected, as scenarios ‘pos’ (using simple two-point-control) show equally good overall results. For qw scenarios, almost all tested cases show high sensitivity to q

_{min}. Elementary effects for parameters FD

_{max}and T, which have a physical meaning, are less prominent. This indicates that a sensible choice of default values for these parameters can be expected to lead to good performance for most cases. Calibration efforts should then focus on PID-controlled setpoint tracking and Q

_{min}.

#### 3.3. Long-Term Simulations

## 4. Discussion

## 5. Conclusions

- The automated implementation of RTC strategies has led to good results for all five tested case studies.
- No single best control algorithm outperforming other algorithms could be found in terms of CSO volume or flooding.
- Both RBC and MPC are able to lead to considerable CSO volume reduction compared to the uncontrolled scenario.
- In comparison to the achieved system performance, screening methods for the ‘control-worthiness’ of a system can give a good indication whether or not the implementation of RTC can lead to performance improvements for all tested cases; a detailed ranking should, however, be refrained from.
- The selection of control locations plays a major role for the success of an RTC strategy. Scenarios using volume-based control location selection clearly outperform other tested selection strategies.
- Next to control algorithm development, the identification of suitable control locations in sewer systems can constitute a promising research topic in the future.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Algorithm for the identification of overflow locations. (

**a**) main algorithm calculating minimum node drainage levels based on constant link data c. (

**b**) determination of constant link invert data c for different link types depending on direction (USDS: from upstream to downstream, DSUS: from downstream to upstream node). (

**c**) Example graph for n links from node A to B (c

_{AB1}to c

_{ABn}) and from B to A (c

_{BA1}to c

_{BAn}).

## Appendix B

**Figure A2.**Morris screening results; (

**a**): mean elementary effect µ

_{abs}on CSO volume vs subbasin location; (

**b**) mean elementary effect µ

_{abs}on CSO volume vs subbasin storage capacity; (

**c**): mean elementary effect µ

_{abs}on CSO volume vs cumulated relative storage capacity; (

**d**) mean elementary effect µ

_{abs}on CSO volume vs downstream cumulated relative storage capacity.

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**Figure 2.**Identification of potential control locations: (

**a**) based on flow capacity (case 1, 2: potential control location, case 3: no control location); (

**b**) based on activated storage volume; dark blue: potentially activated storage volume.

**Figure 3.**Storage activation potential by different selection strategies for control locations (E: existing locations, Q: flow-based, V: volume-based). (

**a**) Controlled volumes and number of control locations; (

**b**) distribution of controlled volume per control location.

**Figure 4.**Morris screening results: Effect of parameter variation on total CSO volume and total flood volume with respect to the uncontrolled system for 24 chosen events for all control scenarios and control location identification procedures for Arendonk (

**a**,

**b**), Beerse (

**c**,

**d**), Geel (

**e**,

**f**), Retie (

**g**,

**h**) and Wolfsdonk (

**i**,

**j**).

**♢**: initial scenario with default parameterization.

**Figure 5.**Morris screening results; (

**a**): mean absolute elementary effect µ

_{abs}on CSO volume per control algorithm parameter, for all control locations of all catchments; (

**b**) mean absolute elementary effect µ

_{abs}on CSO volume vs relative downstream basin volume for all control locations of all catchments.

**Figure 6.**Effect on total CSO volume and total flood volume with respect to the uncontrolled system per event for all events of the 13-year rainfall series for all control scenarios and control location identification procedures for Arendonk (

**a**,

**b**), Beerse (

**c**,

**d**), Geel (

**e**,

**f**), Retie (

**g**,

**h**), and Wolfsdonk (

**i**,

**j**).

**Figure 7.**Comparison of the effect on CSO volume per rain event for existing (E), flow- (Q) and volume- (V) based control selection choice; catchments Arendonk (

**a**) and Retie (

**b**); control algorithm: proportionally controlled global equal filling degree (pid EQ glo).

Arendonk | Beerse | Geel | Retie | Wolfsdonk | |
---|---|---|---|---|---|

Total contributing area in ha | 479 | 650 | 1227 | 618 | 877 |

Reduced contributing area in ha | 113 | 139 | 251 | 64 | 25 |

Population equivalents | 15,100 | 12,780 | 20,080 | 5380 | 4210 |

Total pipe length in km | 69.8 | 106.6 | 156.2 | 74.9 | 66.9 |

Number of nodes | 1513 | 1386 | 1428 | 708 | 570 |

Number of PS ^{1} | 7 | 12 | 13 ^{2} | 8 | 13 |

RTC potential based on [33] | Medium | High | Very high | Medium | Low |

^{1}including WWTP influent works;

^{2}two hydraulically independent influent works at the WWTP.

Short Name | Control Algorithm Description |
---|---|

pos DS loc | 2-point-controlled actuator based on local downstream filling degree |

pos DS glo | 2-point-controlled actuator based on global downstream filling degree |

pos EQ glo | 2-point-controlled actuator based on global equal filling degree [4] |

pid DS loc | Proportionally controlled actuator based on local downstream filling degree |

pid DS glo | Proportionally controlled actuator based on global downstream filling degree |

pid EQ glo | Proportionally controlled actuator based on global equal filling degree |

cs DS loc | Capacity splitting controlled actuator based on local downstream filling degree [22] |

qw DS loc | Q_{wish}-negotiated actuator control based on local downstream filling degree [21] |

MPC | Model predictive control optimizing for minimization of total CSO volume using DORA2 [6]; model Arendonk only |

Setpoint Tracking Scenario | Parameter Name | Default Value | Lower Boundary | Upper Boundary | Parameter Description |
---|---|---|---|---|---|

pos | FD_{max} | 1 | 0.90 | 1.05 | Filling degree at which 100% filling of the subbasin is assumed (CSO becomes active) |

pid | FD_{max} | 1 | 0.90 | 1.05 | See above |

p | 1 | 0.5 | 1.5 | Proportional gain of the PID controller for local setpoint tracking of sluices | |

cs | FD_{max} | 0.95 | 0.90 | 1.05 | See above |

T | 300 s | 60 s | 500 s | Period over which the downstream subbasin may be filled up to its setpoint (see [22]) | |

qw | FD_{max} | 0.95 | 0.90 | 1.05 | See above |

T | 300 s | 60 s | 500 s | See above | |

Q_{min} ^{1} | Max. DWF | −100% | +100% | Minimum allowed flow capacity of the control location (see [21]) |

^{1}: Boundaries relative to default value.

**Table 4.**Parameter ranges relative to the default value for network parameters of the uncontrolled scenario.

Parameter Name | Default Value | Lower Boundary | Upper Boundary |
---|---|---|---|

Runoff coefficient | 0.8 | −10% | +10% |

CSO crest level | Measured value | −10 cm | +10 cm |

Weir discharge coefficient | 0.66 | −20% | +20% |

**Table 5.**Number of control locations and resulting total volume that can be controlled by the application of different control location identification algorithms (E: existing; Q: flow-based; V: volume-based).

Number of Control Locations | Total Controlled Volume in m³ | |||||
---|---|---|---|---|---|---|

Control Location Scenario | E | Q | V | E | Q | V |

Arendonk | 9 | 14 | 17 | 6163 | 10,261 | 12,278 |

Beerse | 17 | 18 | 20 | 6125 | 6190 | 9920 |

Geel | 16 | 23 | 24 | 9920 | 29,362 | 35,115 |

Retie | 12 | 13 | 15 | 5116 | 5766 | 8487 |

Wolfsdonk | 14 | 15 | 13 | 8194 | 8122 | 8162 |

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**MDPI and ACS Style**

Kroll, S.; Weemaes, M.; Van Impe, J.; Willems, P.
A Methodology for the Design of RTC Strategies for Combined Sewer Networks. *Water* **2018**, *10*, 1675.
https://doi.org/10.3390/w10111675

**AMA Style**

Kroll S, Weemaes M, Van Impe J, Willems P.
A Methodology for the Design of RTC Strategies for Combined Sewer Networks. *Water*. 2018; 10(11):1675.
https://doi.org/10.3390/w10111675

**Chicago/Turabian Style**

Kroll, Stefan, Marjoleine Weemaes, Jan Van Impe, and Patrick Willems.
2018. "A Methodology for the Design of RTC Strategies for Combined Sewer Networks" *Water* 10, no. 11: 1675.
https://doi.org/10.3390/w10111675