# Optimizing Conduit Hydropower Potential by Determining Pareto-Optimal Trade-Off Curve

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- Dam releases, which feed into the bulk supply line/transfer scheme;
- Inline conduit hydropower, where excess pressure is available along the pipeline route;
- Break pressure tanks along the pipeline route;
- Water-treatment works (raw water),where excess energy needs to be dissipated before entering the treatment facility;
- Potable water at reservoirs (pressure-reducing valves (PRVs)), where excess energy is dissipated before entering the distribution/service reservoir; and
- Potable water at pressure-reducing stations (PRSs) in the supply network or at specific locations in the network.

## 2. The Optimization Problem in Water Distribution/Supply Networks

- A dynamic analysis of the pipe system to determine safe operational ranges (maximum velocity; pressure);
- A hydraulic assessment of the pipe system (pressure and flow measurements from which the pipe roughness can be back calculated);
- Definition of the acceptable reservoir levels (which could be based on the proposed location of the hydropower plant in relation to other storage facilities); and
- Analyses of the water source to determine the historical supply characteristics and physical constraints.

- Selection and thus survival and reproduction of the fittest members of the population;
- The maintenance of a population to have diverse members at all times;
- The inheritance of genetic information from parents i.e., combining fit solutions; and
- The occasional mutation of genes, resulting in incremental alteration of the present solution.

- $T$ is the operating period (for example, one week of operation)
- $\rho $ is the water density (kg/m
^{3}) and $g$ is the gravitational acceleration (m/s²) - ${H}_{t,j}$ is the average head of the j-th CHP within time period $t$ (m)
- ${Q}_{h,t,j}$ is the average water discharge of the j-th CHP within time period $t$ (m
^{3}/s) - ${\eta}_{t,j}$ is the average hydropower plant efficiency of the $j$-th CHP within time period $t$ (%)
- ${C}_{t,j}$ is the energy tariff within time period $t$ (unit cost/kW)

- Reservoir storage limits (Equation (2))$${V}_{t,j,min}\le {V}_{t,j}\le {V}_{t,j,max}$$
^{3}) and ${V}_{t,j,min}$ and ${V}_{t,j,max}$ are the minimum and maximum values allowed, respectively. - Pipe system discharge limits (Equation (3))$${Q}_{t,j,min}\le {Q}_{t,j}\le {Q}_{t,j,max}$$
^{3}/s). - Hydropower station power generation limits (Equation (4))$${N}_{j,min}\le \rho g{H}_{t,j}{Q}_{h,t,j}{\eta}_{t,j}\le {N}_{j,max}$$
- Hydropower station discharge limits (Equation (5))$${Q}_{h,t,j,min}+{Q}_{b,t,j,min}\le {Q}_{t,j}\le {Q}_{h,t,j,max}+{Q}_{b,t,j,max}$$
^{3}/s), whereas ${Q}_{b,t,j,min}$ and ${Q}_{b,t,j,max}$ are the minimum and maximum water discharge capacity of the bypass (m^{3}/s). - Water balance equation (Equation (6))$${V}_{t+1,j}={V}_{t,j}+\left({Q}_{h,t,j}+{Q}_{b,t,j}\right)\Delta t$$

- Define the scope/analysis objective;
- Provide a system description;
- Identify hazards and hazardous events; and
- Assess the risk (evaluating probabilities and consequences).

- Probability (fraction of time) that the supply cannot be met, due to a low reservoir level, for instance.
- Frequency of events resulting in failure to supply water due to, for instance, pipe bursts.
- Volume of water shortage due to demand exceeding supply and low reservoir levels.
- Time required after a failure such as a reservoir “run-dry” for re-filling of the pipeline or reservoir.
- Potential of dynamic pressures when operating above design capacity.

- ${P}_{t,i}$ is the risk probability [%]
- ${I}_{t,i}$ is the risk impact
- ${\alpha}_{t,i}=f\left({P}_{t,i}{I}_{t,i}\right)$ is a coefficient to incorporate variation in the operating risk at reservoirs (risk quantification), which ranges from 0 to 100. Indeed, the consequence of operating a reservoir at a certain water level is not static and is dependent on the time of day/demand pattern.
- ${\beta}_{t,i}=f\left({P}_{t,i}{I}_{t,i}\right)$ is a coefficient to incorporate variation in operating risk for the pipe system (risk quantification), which ranges from 0 to 100. Indeed, the consequence of operating the pipeline in a specific manner is not inert.

## 3. Multi-Objective Optimization Procedure

## 4. The Case Study

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

C_{t} | energy tariff at time period t (unit cost/kW) |

F | objective function (cost unit) |

g | gravitational acceleration (m/s²) |

H_{t} | average head at time period t (m) |

I_{i} | impact factor (consequence) |

N_{max} | maximum installed plant capacity (kW) |

N_{min} | hydro power minimum power generation constraint (kW) |

P_{i} | probability (%) |

R_{i} | risk value for each component in the pipeline system which could have an impact on the reliability and needs to be assessed |

Q_{t} | average water discharge in pipe system (m^{3}/s) |

Q_{h} | average water discharge through turbine (m^{3}/s) |

Q_{b} | average water discharge through bypass (m^{3}/s) |

Q_{t,max} | maximum water discharge capacity of pipe system (m^{3}/s) |

Q_{t,min} | minimum water discharge capacity of pipe system (m^{3}/s) |

Q_{h,t,max} | maximum water discharge capacity of hydropower plant (m^{3}/s) |

Q_{h,t,min} | minimum water discharge capacity of hydropower plant (m^{3}/s) |

Q_{b,t,max} | maximum water discharge capacity of bypass (m^{3}/s) |

Q_{b,t,min} | minimum water discharge capacity of bypass (m^{3}/s) |

T | total period count for a week, T = 672 (15 min time steps) |

V_{t} | volume of reservoir storage at the beginning of period t (m^{3}) |

V_{t,max} | maximum volume of reservoir storage (m^{3}) |

V_{t,min} | minimum volume of reservoir storage (m^{3}) |

α | coefficient to incorporate variation in operational risk at reservoirs (risk quantification) |

β | coefficient to incorporate variation in operational risk for pipe system (risk quantification) |

Δt | time step (s) |

ρ | density of water (kg/m^{3}) |

η_{t} | hydropower plant efficiency at time period t (%) |

## References

- Sari, M.A.; Badruzzaman, M.; Cherchi, C.; Swindle, M.; Ajami, N.; Jacangelo, J.G. Recent Innovations and Trends in In-conduit Hydropower Technologies and Their Applications in Water Distribution Systems. J. Environ. Manag.
**2018**, 228, 416–428. [Google Scholar] [CrossRef] [PubMed] - Pérez-Sánchez, M.; Sánchez-Romero, F.J.; Ramos, H.M.; López-Jiménez, P.A. Energy Recovery in Existing Water Networks: Towards Greater Sustainability. Water
**2017**, 9, 97. [Google Scholar] [CrossRef] [Green Version] - Van Dijk, M.; Niebuhr, C.M.; Bekker, A.; Kurtz, A.A. Inline Pressure Wheel—Pico hydropower development. In Proceedings of the HYDRO—2020 IWRA Online Conference Addressing Groundwater Resilience under Climate Change, Online, 26–28 October 2020. [Google Scholar]
- Loots, I.; Van Dijk, M.; van Vuuren, S.J.; Bhagwan, J.N.; Kurtz, A. Conduit-hydropower potential in the City of Tshwane water distribution system: A discussion of potential applications, financial and other benefits. J. South Afr. Inst. Civ. Eng.
**2014**, 56, 2–13. [Google Scholar] - White, J. Recovering energy from an existing conduit. Int. Water Power Dam Constr.
**2011**, 63, 18–20. Available online: https://www.waterpowermagazine.com/features/featurerecovering-energy-from-an-existing-conduit/ (accessed on 12 April 2022). - Lisk, B.; Greenberg, E.; Bloetscher, F. Implementing Renewable Energy at Water Utilities—Case Studies; Water Research Foundation: Denver, CO, USA, 2012. [Google Scholar]
- McNabola, A.; Coughlan, P.; Williams, A.P. Energy recovery in the water industry: An assessment of the potential of micro hydropower. Water Environ. J.
**2014**, 28, 294–304. [Google Scholar] [CrossRef] - Van Vuuren, S.J.; Van Dijk, M.; Loots, I.; Barta, B.; Scharfetter, B.G. Conduit Hydropower Development Guide; WRC Report No TT597/14; Water Research Commission: Pretoria, South Africa, 2014. [Google Scholar]
- Southern Nevada Water Authority (SNWA). Sustainability in Action. 2010. Available online: www.snwa.com/assets/pdf/reports-sustainability.pdf (accessed on 15 July 2021).
- Hennig, T.; Wang, W.; Feng, Y.; Ou, X.; He, D. Review of Yunnan’s hydropower development. Comparing small and large hydropower projects regarding their environmental implications and socio-economic consequences. Renew. Sustain. Energy Rev.
**2013**, 27, 585–595. [Google Scholar] [CrossRef] - Van Vuuren, S.J.; Van Dijk, M.; Loots, I. Conduit Hydropower Pilot Plants; WRC Report No TT596/14; Water Research Commission: Pretoria, South Africa, 2014. [Google Scholar]
- Colombo, A.F.; Karney, B.W. Energy and Costs of Leaky Pipes: Toward Comprehensive Picture. J. Water Resour. Plan. Manag.
**2002**, 128, 441–450. [Google Scholar] [CrossRef] [Green Version] - Ramos, H.; Borga, A. Pumps as turbines: An unconventional solution to energy production. Urban Water
**1999**, 1, 261–263. [Google Scholar] [CrossRef] - Fecarotta, O.; Aricò, C.; Carravetta, A.; Martino, R.; Ramos, H.M. Hydropower Potential in Water Distribution Networks: Pressure Control by PATs. Water Resour. Manag.
**2014**, 29, 699–714. [Google Scholar] [CrossRef] - Butera, I.; Balestra, R. Estimation of the hydropower potential of irrigation networks. Renew. Sustain. Energy Rev.
**2015**, 48, 140–151. [Google Scholar] [CrossRef] - Fontana, N.; Giugni, M.; Portolano, D. Losses Reduction and Energy Production in Water-Distribution Networks. J. Water Resour. Plan. Manag.
**2012**, 138, 237–244. [Google Scholar] [CrossRef] - Bonthuys, G.J.; Van Dijk, M.; Cavazzini, G. Energy Recovery and Leakage-Reduction Optimization of Water Distribution Systems Using Hydro Turbines. J. Water Resour. Plan. Manag.
**2020**, 146. [Google Scholar] [CrossRef] - Parra, S.; Krause, S. Pressure Management by Combining Pressure Reducing Valves and Pumps as Turbines for Water Loss Reduction and Energy Recovery. Int. J. Sustain. Dev. Plan.
**2017**, 12, 89–97. [Google Scholar] [CrossRef] - Patelis, M.; Kanakoudis, V.; Gonelas, K. Combining pressure management and energy recovery benefits in a water distribution system installing PATs. J. Water Supply Res. Technol.—AQUA
**2017**, 66, 520–527. [Google Scholar] [CrossRef] [Green Version] - Corcoran, L.; McNabola, A.; Coughlan, P. Optimization of Water Distribution Networks for Combined Hydropower Energy Recovery and Leakage Reduction. J. Water Resour. Plan. Manag.
**2015**, 142, 1–8. [Google Scholar] [CrossRef] - Caxaria, G.; Mesquita, D.; Ramos, H.M. Small Scale Hydropower: Generator Analysis and Optimization for Water Supply Systems. In Proceedings of the World Renewable Energy Congress, Linköping, Sweden, 8–13 May 2011; pp. 1386–1393. [Google Scholar]
- Ramos, H.M.; Mello, M.; De, P.K. Clean power in water supply systems as a sustainable solution: From planning to practical implementation. Water Sci. Technol. Water Supply-WSTWS
**2010**, 10, 39–49. [Google Scholar] [CrossRef] - Jafari, R.; Khanjani, M.J.; Esmaelian, H.R. Pressure Management and Electric Power Production using Pumps as Turbines. J. AWWA
**2015**, 107, E351–E363. [Google Scholar] [CrossRef] - Lydon, T.; Coughlan, P.; McNabola, A. Pump-as-Turbine: Characterization as an Energy Recovery Device for the Water Distribution Network. J. Hydraul. Eng.
**2015**, 143, 04017020. [Google Scholar] [CrossRef] - Elbatran, A.H.; Yaakob, O.B.; Ahmed, Y.M.; Shabara, H.M. Operation, performance and economic analysis of low head micro-hydropower turbines for rural and remote areas: A review. Renew. Sustain. Energy Rev.
**2015**, 43, 40–50. [Google Scholar] [CrossRef] - Simão, M.; Ramos, H.M. Hydrodynamic and performance of low power turbines: Conception, modelling and experimental tests. Int. J. Energy Environ.
**2010**, 1, 431–444. [Google Scholar] - Razan, J.I.; Islam, R.S.; Hasan, R.; Hasan, S.; Islam, F. A Comprehensive Study of Micro-Hydropower Plant and Its Potential in Bangladesh. Renew. Energy
**2012**, 2012, 635396. [Google Scholar] [CrossRef] [Green Version] - Senior, J.A.; Muller, G.; Wiemann, P. The development of the rotary hydraulic pressure machine. In Proceedings of the 2007 32nd IAHR World Congress, Venice, Italy, 1–6 July 2007. [Google Scholar]
- Senior, J.A.; Saenger, N.; Müller, G. New hydropower converters for very low-head differences. J. Hydraul. Res.
**2010**, 48, 703–714. [Google Scholar] [CrossRef] - Carravetta, A.; Del Giudice, G.; Oreste, F.; Ramos, H.M. PAT design strategy for energy recovery in water distribution networks by electrical regulation. Energies
**2013**, 6, 411–424. [Google Scholar] [CrossRef] [Green Version] - Arriaga, M. Pump as turbine-A pico-hydro alternative in Lao People's Democratic Republic. Renew. Energy
**2010**, 35, 1109–1115. [Google Scholar] [CrossRef] - Lima, G.M.; Luvizotto Junior, E.; Brentan, B.M. Selection and Location of Pumps as Turbines Substituting Pressure Reducing Valves. Renew. Energy
**2017**, 109, 392–405. [Google Scholar] [CrossRef] - Derakhshan, S.; Nourbakhsh, A. Experimental study of characteristic curves of centrifugal pumps working as turbines in different specific speeds. Exp. Therm. Fluid Sci.
**2008**, 32, 800–807. [Google Scholar] [CrossRef] - Nourbakhsh, A.; Jahangiri, G. Inexpensive small hydropower stations for small areas of developing countries. In Proceedings of the 1992 Conference on Advanced in Planning-Design and Management of Irrigation Systems as Related to Sustainable Land Use, Louvain, Belgium, 14–17 September 1992; pp. 313–319. [Google Scholar]
- Fecarotta, O.; Carravetta, A.; Ramos, H.M.; Martino, R. An improved affinity model to enhance variable operating strategy for pumps used as turbines. J. Hydraul. Res.
**2016**, 54, 332–341. [Google Scholar] [CrossRef] - Ramos, H.M.; Dadfar, A.; Besharat, M.; Adeyeye, K. Inline Pumped Storage Hydropower towards Smart and Flexible Energy Recovery in Water Networks. Water
**2020**, 12, 2224. [Google Scholar] [CrossRef] - Creaco, E.; Galuppini, G.; Campisano, A.; Ciaponi, C.; Pezzinga, G. A Bi-Objective Approach for Optimizing the Installation of PATs in Systems of Transmission Mains. Water
**2020**, 12, 330. [Google Scholar] [CrossRef] [Green Version] - Pérez-Sánchez MSánchez-Romero, F.J.; Ramos, H.M.; López-Jiménez, P.A. Improved Planning of Energy Recovery in Water Systems Using a New Analytic Approach to PAT Performance Curves. Water
**2020**, 12, 468. [Google Scholar] [CrossRef] [Green Version] - Pérez García, J.; Cortés Marco, A.; Nevado Santos, S. Use of Centrifugal Pumps Operating as Turbines for Energy Recovery in Water Distribution Networks. Two Case Study. AMR
**2010**, 107, 87–92. [Google Scholar] [CrossRef] - Carravetta, A.; Fecarotta, O.; Del Giudice, G.; Ramos, H.M. Energy Recovery in Water Systems by PATs: A Comparisons among the Different Installation Schemes. Procedia Eng.
**2014**, 70, 275–284. [Google Scholar] [CrossRef] [Green Version] - Vilanova, M.R.; Balestieri, J.A. Hydropower recovery in water supply systems: Models and case study. Energy Convers. Manag.
**2014**, 84, 414–426. [Google Scholar] [CrossRef] - Shapes. Energy Recovery in Existing Infrastructures with Small Hydropower Plants Multipurpose Schemes—Overview and Examples; FP6 Project Shapes (work package 5-WP5) 2010; European Directorate for Transport and Energy: Brussels, Belgium, 2010. [Google Scholar]
- Bonthuys, G.J.; Van Dijk, M.; Cavazzini, G. The Optimization of Energy Recovery Device Sizes and Locations in Municipal Water Distribution Systems during Extended-Period Simulation. Water
**2020**, 12, 2447. [Google Scholar] [CrossRef] - Bekker, A.; Van Dijk, M.; Bhagwan, J.N.; Niebuhr, C.M. Development of a framework to identify hydropower potential at pressure reducing stations in South African water supply and distribution systems. In Proceedings of the 2019 HYDRO Conference, Porto, Portugal, 14–16 October 2019. [Google Scholar]
- Bekker, A.; Van Dijk, M.; Bhagwan, J.N.; Niebuhr, C.M. Development of a tool to identify hydropower potential at pressure reducing stations in South African water distribution systems. In Proceedings of the HYDRO 2020 Conference, Online, 26–28 October 2020. [Google Scholar]
- Bekker, A.; Van Dijk, M.; Niebuhr, C.M.; Hansen, C.D. Framework Development for the Evaluation of Conduit Hydropower within Water Distribution Systems: A South African Case Study. J. Clean. Prod.
**2020**, 283, 1–15. [Google Scholar] [CrossRef] - Su, P.A.; Karney, B. Micro hydroelectric energy recovery in municipal water systems: A case study for Vancouver. Urban Water J.
**2015**, 12, 678–690. [Google Scholar] [CrossRef] - Venturini, M.; Stefano Alvisi, S.; Simani, S.; Manservigi, L. Energy Production by Means of Pumps as Turbines in Water Distribution Networks. Energies
**2017**, 10, 1666. [Google Scholar] [CrossRef] [Green Version] - Rodríguez-Pérez, A.M.; Pérez-Calañas, C.; Pulido-Calvo, I. Energy Recovery in Pressurized Hydraulic Networks. Water Resour. Manag.
**2021**, 35, 1977–1990. [Google Scholar] [CrossRef] - Choulot, A.; Denis, V.; Punys, P. Integration of Small Hydro Turbines into Existing Water Infrastructures. In Hydropower—Practice and Application; IntechOpen: London, UK. [CrossRef] [Green Version]
- California Energy Commission (CEC). San Gabriel Valley Water Company “Plug-and-Play” In-Conduit Hydropower Development Project. Report no CEC-500-2021-032; 2021. Available online: https://www.energy.ca.gov/sites/default/files/2021-05/CEC-500-2021-032.pdf (accessed on 10 January 2022).
- Asfar, A.; Jemaa, F.B.; Mariño, M.A. Optimization of Hydropower Plant Integration in Water Supply System. J. Water Resour. Plan. Manag.
**1990**, 116, 665–675. [Google Scholar] - Tarragó, E.F.; Ramos, H. Micro-Hydro Solutions in Alqueva Multipurpose Project (AMP) towards Water-Energy-Environmental Efficiency Improvements. Bachelor’s Thesis, Universidade de Lisboa, Lisboa, Portugal, 2015. [Google Scholar]
- Corcoran, L.; Coughlan, P.; McNabola, A. Energy Recovery Potential Using Micro Hydropower in Water Supply Networks in The UK and Ireland. Water Sci. Technol.-Water Supply
**2013**, 13, 552–560. [Google Scholar] [CrossRef] - Novara, D.; Stanek, W.; Ramos, H. Energy Harvesting from Municipal Water Management Systems: From Storage and Distribution to Wastewater Treatment. Master’s Thesis, Universidade de Lisboa, Lisboa, Portugal, 2016. [Google Scholar]
- Adhau, S.P.; Moharil, R.M.; Adhau, P.G. Mini-hydro power generation on existing irrigation projects: Case study of Indian sites. Renew. Sustain. Energy Rev.
**2012**, 16, 4785–4795. [Google Scholar] [CrossRef] - Sitzenfrei, R.; Von Leon, J. Long-time simulation of water distribution systems for the design of small hydropower systems. Renew. Energy
**2014**, 72, 182–187. [Google Scholar] [CrossRef] - Samora, I.; Franca, M.; Schleiss, A.; Ramos, H.M. Simulated Annealing in Optimization of Energy Production in a Water Supply Network. Water Resour. Manag.
**2016**, 30, 1533–1547. [Google Scholar] [CrossRef] - Samora, I.; Manso, P.; Franca, M.J.; Schleiss, A.J.; Ramos, H.M. Opportunity and Economic Feasibility of Inline Microhydropower Units in Water Supply Networks. J. Water Resour. Plan. Manag.
**2016**, 142, 04016052. [Google Scholar] [CrossRef] - Samora, I.; Manso, P.; Franca Mário Schleiss, A.; Ramos, H. Energy Recovery Using Micro-Hydropower Technology in Water Supply Systems: The Case Study of the City of Fribourg. Water
**2016**, 8, 344. [Google Scholar] [CrossRef] [Green Version] - Pérez-Sánchez, M.; Sánchez-Romero, F.; Ramos, H.; López-Jiménez, P. Modelling Irrigation Networks for the Quantification of Potential Energy Recovering: A Case Study. Water
**2016**, 8, 234. [Google Scholar] [CrossRef] [Green Version] - Cubides-Castro, E.D.; López-Aburto, C.S.; Iglesias-Rey, P.L.; Martínez-Solano, F.J.; Mora-Meliá, D.; Iglesias-Castelló, M. Methodology for Determining the Maximum Potentially Recoverable Energy in Water Distribution Networks. Water
**2021**, 13, 464. [Google Scholar] [CrossRef] - Carravetta, A.; Del Giudice, G.; Fecarotta, O.; Ramos, H. Pump as Turbine (PAT) Design in Water Distribution Network by System Effectiveness. Water
**2013**, 5, 1211–1225. [Google Scholar] [CrossRef] [Green Version] - Santolin, A.; Pavesi, G.; Cavazzini, G.; Ardizzon, G.; Perez-Diaz, J.I.; Van Dijk, M. Techno-economic feasibility analysis for energy production by variable speed Francis turbines in water distribution networks. In Proceedings of the 2017 HYDRO-Africa Conference, Marrakech, Morocco, 14–16 March 2017. [Google Scholar]
- California Energy Commission (CEC). California’s In-Conduit Hydropower Implementation Guidebook—A Compendium of Resources, Best Practices, and Tools. Report no CEC-500-2020-030. Available online: www.energy.ca.gov/sites/default/files/2021-05/CEC-500-2020-030.pdf (accessed on 15 July 2021).
- Kumar, D.; Katoch, S.S. Small hydropower development in western Himalayas: Strategy for faster implementation. Renew. Energy
**2015**, 77, 571–578. [Google Scholar] [CrossRef] - Tilmant, A.; Goor, Q.; Pinte, D. Agricultural-to-hydropower water transfers: Sharing water and benefits in hydropower-irrigation systems. Hydrol. Earth Syst. Sci.
**2009**, 13, 1091–1101. [Google Scholar] [CrossRef] [Green Version] - Alonso-Tristán, C.; González-Peña, D.; Díez-Mediavilla, M.; Rodríguez-Amigo, M.; García-Calderón, T. Small hydropower plants in Spain: A case study. Renew. Sustain. Energy Rev.
**2011**, 15, 2729–2735. [Google Scholar] [CrossRef] [Green Version] - Ohunakin, O.S.; Ojolo, S.J.; Ajayi, O.O. Small hydropower (SHP) development in Nigeria: An assessment. Renew. Sustain. Energy Rev.
**2011**, 15, 2006–2013. [Google Scholar] [CrossRef] - Vicente, S.; Bludszuweit, H. Flexible design of a pico-hydropower system for Laos communities. Renew. Energy
**2012**, 44, 406–413. [Google Scholar] [CrossRef] - Punys, P.; Dumbrauskas, A.; Kasiulis, E.; Vyciene, G.; Šilinis, L. Flow Regime Changes: From Impounding a Temperate Lowland River to Small Hydropower Operations. Energies
**2015**, 8, 7478–7501. [Google Scholar] [CrossRef] [Green Version] - Punys, P.; Dumbrauskas, A.; Kvaraciejus, A.; Vyciene, G. Tools for Small Hydropower Plant Resource Planning and Development: A Review of Technology and Applications. Energies
**2011**, 4, 1258–1277. [Google Scholar] [CrossRef] [Green Version] - Adeyeye, K.; Gallagher, J.; McNabola, A.; Ramos, H.M.; Coughlan, P. Socio-Technical Viability Framework for Micro Hydropower in Group Water-Energy Schemes. Energies
**2021**, 14, 4222. [Google Scholar] [CrossRef] - Van Dijk, M.; Van Vuuren, S.J.; Barta, B. Optimization of Energy Generation from Water Supply and Distribution Systems. In Proceedings of the 2012 HYDRO Conference, Bilbao, Spain, 29–31 October 2012. [Google Scholar]
- Frijns, J.; Cabrera, E.; Carriço, N.; Covas, D.; Monteiro, A.J.; Ramos, H.M.; Bolognesi, A.; Bragalli, C.; Baki, S.; Makropoulos, C. Management Tools for Hydro Energy Interventions in Water Supply Systems. Water Pract. Technol.
**2015**, 10, 214–228. [Google Scholar] [CrossRef] - Itani, Y.; Soliman, M.R.; Kahil, M. Recovering energy by hydro-turbines application in water transmission pipelines: A case study west of Saudi Arabia. Energy
**2020**, 211, 118613. [Google Scholar] [CrossRef] - Pasha, M.F.K.; Weathers, M.; Smith, B. Water-Energy Storage Configuration for Generating Energy in Water Distribution Systems. In Proceedings of the ASCE World Environmental and Water Resources Congress, Henderson, NV, USA, 17–21 May 2020; Available online: https://doi.org/10.1061/9780784482971.040 (accessed on 30 July 2017). [CrossRef]
- Delplanque, J.; Cooperman, A.; Mann, S. Technical Assessment of In-Conduit Small Hydro Power Technologies. University of California, Davis. California Energy Commission. Publication number: CEC-500-2017-007-APL. 2014. Available online: www.energy.ca.gov/2017publications/CEC-500-2017-007/CEC-500-2017-007-APL.pdf (accessed on 30 July 2017).
- Van Dijk, M.; Van Vuuren, S.J.; Van Zyl, J.E. Optimising Water Distribution Systems using a weighted penalty in a Genetic Algorithm. Water
**2008**, 3, 5. [Google Scholar] [CrossRef] [Green Version] - Wu, C.; Fang, G.; Liao, T.; Huang, X.; Qu, B. Integrated Software Development and Case Studies for Optimal Operation of Cascade Reservoir within the Environmental Flow Constraints. Sustainability
**2020**, 12, 4064. [Google Scholar] [CrossRef] - Ahmadi, M.H.; Ahmadi, M.A.; Mellit, A.; Pourfayaz, F.; Feidt, M. Thermodynamic analysis and multi objective optimization of performance of solar dish Stirling engine by the centrality of entransy and entropy generation. Int. J. Electr. Power Energy Syst.
**2016**, 78, 88–95. [Google Scholar] [CrossRef] - Beiranvand, A.; Ehyaei, M.A.; Ahmadi, A.; Silvaria, J.L. Energy, exergy, and economic analyses and optimization of solar organic Rankine cycle with multi-objective particle swarm algorithm. Renew. Energy Res. Appl.
**2020**, 2, 9–23. [Google Scholar] - Ghazvini, M.; Pourkiaei, S.M.; Pourfayaz, F. Thermo-economic assessment and optimization of actual heat engine performance by implementation of NSGA II. Renew. Energy Res. Appl.
**2020**, 1, 235–245. [Google Scholar] - Hounnou, A.H.J.; Dubas, F.; Fifatin, F.; Chamagne, D.; Vianou, A. Multi-Objective Optimization of Run-of-River Small-Hydropower Plants Considering Both Investment Cost and Annual Energy Generation. Int. J. Energy Power Eng.
**2019**, 13, 17–21. [Google Scholar] - Dong, J.; Yang, P.; Nie, S. Day-Ahead Scheduling Model of the Distributed Small Hydro-Wind-Energy Storage Power System Based on Two-Stage Stochastic Robust Optimization. Sustainability
**2019**, 11, 2829. [Google Scholar] [CrossRef] [Green Version] - Keedwell, E.; Khu, S.-T. A hybrid genetic algorithm for the design of water distribution networks. Eng. Appl. Artif. Intell.
**2005**, 18, 461–472. [Google Scholar] [CrossRef] - Harpman, D.A. Advanced Algorithms for Hydropower Optimization; Technical Report S&T—2011-486; U.S. Department of the Interior, Technical Service Center, Bureau of Reclamation: Denver, CO, USA, 2012. Available online: https://www.usbr.gov/research/projects/download_product.cfm?id=402 (accessed on 30 July 2017).
- Michalewicz, Z. Genetic Algorithms + Data Structures = Evolution Programs, 2nd ed.; Springer: Berlin/Heidelberg, Germany, 1994. [Google Scholar]
- Cheng, C.-T.; Wang, W.-C.; Xu, D.-M.; Chau, K.W. Optimizing hydropower reservoir operation using hybrid genetic algorithm and chaos. Water Resour. Manag.
**2008**, 22, 895–909. [Google Scholar] [CrossRef] [Green Version] - Chang, C.-C.; Van Zyl, J.E. Optimal reliability-based design of bulk water supply systems. J. Water Resour. Plan. Manag.
**2014**, 140, 1. [Google Scholar] [CrossRef] [Green Version] - Hokstad, P.; Røstum, J.; Sklet, S.; Rosén, L.; Pettersson, T.J.R.; Linde, A.; Sturm, S.; Beuken, R.; Kirchner, D.; Niewersch, C. Methods for Risk Analysis of Drinking Water Systems from Source to Tap—Guidance Report on Risk Analysis; Techneau Report D 4.2.4; Techneau: Marigny-le-Lozon, France, 2009. [Google Scholar]
- Gonzalez Perea, R.; Ballesteros, R.; Ortega, J.F.; Moreno, M.A. Water and energy demand forecasting in large-scale water distribution networks for irrigation using open data and machine learning algorithms. Comput. Electron. Agric.
**2021**, 188, 106327. [Google Scholar] [CrossRef] - Rossman, L.A.; Woo, H.; Tryby, M.; Shang, F.; Janke, R.; Haxton, T. EPANET 2.2 User Manual; EPA/600/R-20/133; United States Environmental Protection Agency: Cincinnati, OH, USA, 2020.
- Vieira, F.; Ramos, H.M. Optimization of operational planning for wind/hydro hybrid water supply systems. Renew. Energy
**2009**, 34, 928–936. [Google Scholar] [CrossRef] - Afshar, A.; Shafii, M.; Haddad, O.B. Optimizing multi-reservoir operation rules: An improved HBMO approach. J. Hydroinformatics
**2011**, 13, 121–139. [Google Scholar] [CrossRef] [Green Version] - Jamali, S.; Jamali, B. Cascade hydropower systems optimal operation: Implications for Iran’s Great Karun hydropower systems. Appl. Water Sci.
**2019**, 9, 66. [Google Scholar] [CrossRef] [Green Version] - Lin, N.M.; Tian, X.; Rutten, M.; Abraham, E.; Maestre, J.M.; Van de Giesen, N. Multi-Objective Model Predictive Control for Real-Time Operation of a Multi-Reservoir System. Water
**2020**, 12, 1898. [Google Scholar] [CrossRef] - Wu, J.; Liu, L.; Gao, J.; Wang, Q. Study on cascade hydropower alternative schemes based on multi-objective particle swarm optimization algorithm. Energy Reports. In Proceedings of the 6th International Conference on Power and Energy Systems Engineering (CPESE 2019), Okinawa, Japan, 20–23 September 2019; pp. 235–242. Available online: https://www.sciencedirect.com/science/article/pii/S2352484719309412?via%3Dihub (accessed on 30 July 2017).

**Figure 1.**Locations with energy generation potential (adapted from [3]).

**Figure 4.**Example of definition of an electricity tariff structure used to determine revenue (Megaflex) for every time period.

**Table 1.**Researched topics related to energy recovery from water supply and distribution networks (adapted from [2]).

Researched Topic | References |
---|---|

Reduction of leaks, decreasing the pressure in water supply systems and increasing the efficiency | [12,13,14,15,16,17,18,19,20] |

Proposal to use adapted machines (PATs and tubular propeller) in water supply systems to reduce the pressure | [21,22,23,24] |

Description and operation of a PAT with a review of available technologies | [25,26,27,28,29,30] |

Performance and modeling of a PAT | [26,31,32,33,34,35,36,37,38] |

Installation of energy recovery systems or devices in water supply networks | [1,4,9,11,15,17,39,40,41,42,43,44,45,46,47,48,49,50,51] |

Implementation of simulations to determine the theoretical recovered energy in water supply and irrigation systems | [52,53,54,55,56,57,58,59,60,61,62] |

Design of variable operating strategies to maximize the recovered energy | [12,14,40,63] |

Economic cost of implementing recovery systems in water supply and irrigation networks | [10,12,25,64,65] |

Environmental advantages | [22,66,67] |

Policies and analyses to help development | [31,68,69,70,71,72,73] |

Pilot plants built in water supply networks | [4,6,7,8,50,51] |

Optimization to maximize recovered energy in water supply systems | [58,62,74,75,76,77] |

**Table 2.**Types of optimization for water supply/distribution systems (adapted [79]).

Optimization Type | Objective | Possible Variables | Main Constraints |
---|---|---|---|

Design | Minimize cost | Pipe layout; pipe diameters; pipe rehabilitation | Min level of service; available diameters; rehabilitation options; available budget; LCC |

Operation | Minimize operational cost | Pump controls; reservoir levels; sources and capacity | Min level of service; number of pump switches; source capacity; pump capacity |

Calibration | Minimize difference between model and observed values | Valve settings; pipe roughness, diameter; leakage; demands | System layout; available data |

Level-of-service | Maximize level of service, e.g., pressure, water quality or reliability | All of the above | System configuration; budget |

Monitoring system design | Minimize cost of monitoring system | Number and position of monitoring points | System configuration; budget |

Conduit hydropower | Maximize energy generation potential | Turbine selection; reservoir levels; sources and capacity; operating scenarios | Acceptable operating risk levels; hydraulic operating range; pressure requirements; source capacity; turbine capacity; LCC |

**Table 3.**Example of risk matrix [91].

Severity of Consequences | |||||
---|---|---|---|---|---|

Likelihood | Insignificant | Minor | Moderate | Major | Catastrophic |

Almost certain | ❺ | ❻ | ❼ | ❽ | ❾ |

Likely | ❹ | ❺ | ❻ | ❼ | ❽ |

Moderately likely | ❸ | ❹ | ❺ | ❻ | ❼ |

Unlikely | ❷ | ❸ | ❹ | ❺ | ❻ |

Rare | ❶ | ❷ | ❸ | ❹ | ❺ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

van Dijk, M.; van Vuuren, S.J.; Cavazzini, G.; Niebuhr, C.M.; Santolin, A.
Optimizing Conduit Hydropower Potential by Determining Pareto-Optimal Trade-Off Curve. *Sustainability* **2022**, *14*, 7876.
https://doi.org/10.3390/su14137876

**AMA Style**

van Dijk M, van Vuuren SJ, Cavazzini G, Niebuhr CM, Santolin A.
Optimizing Conduit Hydropower Potential by Determining Pareto-Optimal Trade-Off Curve. *Sustainability*. 2022; 14(13):7876.
https://doi.org/10.3390/su14137876

**Chicago/Turabian Style**

van Dijk, Marco, Stefanus Johannes van Vuuren, Giovanna Cavazzini, Chantel Monica Niebuhr, and Alberto Santolin.
2022. "Optimizing Conduit Hydropower Potential by Determining Pareto-Optimal Trade-Off Curve" *Sustainability* 14, no. 13: 7876.
https://doi.org/10.3390/su14137876