An Evolutionary Computational Approach for Designing Micro Hydro Power Plants
Abstract
:1. Introduction
1.1. Micro-Hydro Power Plants
1.2. Traditional Design Procedure of MHPPs in Rural Emplacements
- Measurement of available flow rate, Q.
- Measurement of available height, .
- Decision-making of dam and powerhouse location.
- Estimation of power generation, P.
- Sizing of the equipment.
Contributions
2. Related Work
3. Problem Statement
3.1. Model of the System
3.1.1. Generated Power
3.1.2. Cost Function
3.1.3. Model of the MHPP Layout
- Each represents the placement of an elbow in point .
- The minimal index i that makes represents the location of the powerhouse.
- The maximum index i that makes represents the location of the water intake (dam).
3.2. Problem Formulation
3.2.1. Power Constraint
3.2.2. Flow Constraint
3.2.3. Feasibility Constraints
- The pipe can be disposed at a certain height from the terrain (see points 4 and 5 in Figure 4), where the use of supports is assumed, only if this height remains under a maximum value, .
- The pipe can be disposed under a certain depth from the terrain (see points 8 and 9 in Figure 4), where excavations are assumed as part of the civil works, only if this depth remains under a maximum value, .
4. Evolutionary Computational Approach
4.1. Single-Objective Optimization Problem
Algorithm 1: GA mupluslambda. |
|
4.1.1. Individual Representation
4.1.2. Fitness Function
4.1.3. Genetic Operators
4.2. Multi-Objective Optimization Problem
Algorithm 2: GA based on NSGA-II. |
|
4.2.1. Individual Representation
4.2.2. Fitness Function
4.2.3. Genetic Operators
5. Simulation Results
5.1. Example Scenario Settings
5.2. Genetic Algorithm Settings
5.3. Case-Studies Proposal
- Case-study 1: Fixed diameter, without considering elbows. For this first case, a fixed pipe diameter is considered. The problem is formulated in the form of a cost-minimization problem in single-objective mode. The objective function is formulated as minimizing the length of the penstock, L.
- Case-study 2: Fixed diameter, considering an equivalent cost of the elbows. This second case consists in the problem proposed in case-study 1 with the additional consideration of an equivalent cost for the pipe elbows, . Thus, the objective function is formulated as minimizing the cost C.
- Case-study 3: Variable diameter, single-objective. In this third case, the problem in case 2 is extended by considering a range of available discrete values for the pipe diameter , this being considered as an additional optimization variable (see Figure 5a). The problem is then formulated in the form of a cost-minimization problem (single-objective mode), with the objective function formulated as minimizing the cost of the penstock, defined in terms of its length L, number of elbows and diameter .
- Case-study 4: Variable diameter, multi-objective. The last case is formulated on the same basis of case-study 2, but considering a multi-objective mode, where the cost of the plant is minimized and the generated power P is maximized.
5.4. Results
5.4.1. Case-Study 1: Fixed Diameter, without Considering Elbows
5.4.2. Case-Study 2: Fixed Diameter, Considering an Equivalent Cost of the Elbows
5.4.3. Case-Study 3: Variable Diameter, Single-Objective
5.4.4. Case-Study 4: Variable Diameter, Multi-Objective
5.4.5. Comparison with Other Algorithms
5.4.6. Application to a Real Scenario
5.5. Discussion of the Results
- An example scenario domain has been introduced first, in order to propose a total of four case-studies that have been addressed in order to validate the benefits of the GA to optimize an MHPP layout.
- When the objective function is assumed to be the minimization of the length of the penstock, the GA provides approximately the same solution than the BBA, with a slight improvement (about 0.055%) in the length, and reaching also a lower number of elbows, although it is not considered a design variable in the minimization function.
- The minimization of the equivalent cost leads to noticeabley better solutions, reaching an improvement of 11.78% in the cost, reducing both the length (about 0.05%) and the number of elbows (20%) of the penstock.
- The GA has been proven to be especially effective addressing the optimization problem when considering the penstock diameter as an optimization variable, leading to a cost reduction of 70.67%. Note that this problem can not be addressed by BBA-based due to its complexity, which implies nonlinearities in its formulation.
- In all the studied cases, the convergence is reached in the first 50 generations, with small improvements until the 100th generation.
- The problem has been addressed in a multi-objective mode, minimizing the cost and maximizing the generated power. The solutions have been used to determine the Pareto front, and, from this, the marginal rate of substitution, which allows for studying how variances in the cost can affect the performance of the plant.
- The problem has also been solved using Random Search and SA algorithms. Although the results of the random search algorithm and SA are poor and far from the optimal solutions obtained with the GA, the implementation of the proposed mutation scheme in the SA provides a noticeable improvement in its performance. Nevertheless, it reaches a reduction of 99.66% of the cost obtained with the SA. This noticeable difference is a consequence of the high number of elbows obtained by the SA algorithm (20 elbows obtained from SA facing five elbows obtained using GA), while the difference in length between the solutions is not that high (481.3 m using SA facing 175 m from GA).
- The GA has been successfully used to solve a real scenario problem, proving a good robustness when dealing with a low quality sampled domain.
6. Conclusions and Further Work
Author Contributions
Funding
Conflicts of Interest
Abbreviations
BBA | Branch and Bound Algorithm |
CCS | Carbon Capture and Storage |
GA | Genetic Algorithm |
GHG | Greenhouse Gas |
HBMO | Honey Bee Mating Optimization |
MHPP | Micro Hydro Power Plants |
RES | Renewable Energy Sources |
SA | Simulated Annealing |
References
- Nejat, P.; Jomehzadeh, F.; Taheri, M.M.; Gohari, M.; Majid, M.Z.A. A global review of energy consumption, CO2 emissions and policy in the residential sector (with an overview of the top ten CO2 emitting countries). Renew. Sustain. Energy Rev. 2015, 43, 843–862. [Google Scholar] [CrossRef]
- The World Bank. Access to Electricity. World Development Indicators. 2016. Available online: http://data.worldbank.org/indicator/EG.ELC.ACCS.UR.ZS (accessed on 2 December 2018).
- Pereira, M.G.; Sena, J.A.; Freitas, M.A.V.; Da Silva, N.F. Evaluation of the impact of access to electricity: A comparative analysis of South Africa, China, India and Brazil. Renew. Sustain. Energy Rev. 2011, 15, 1427–1441. [Google Scholar] [CrossRef]
- OECD. Linking Renewable Energy to Rural Development, OECD Green Growth Studies; OECD Publishing: Paris, France, 2016. [Google Scholar]
- Krewitt, W.; Simon, S.; Graus, W.; Teskec, S.; Zervos, A.; Schafer, O. The 2 degrees C scenario-A sustainable world energy perspective (vol 35, pg 4969, 2007). Energy Policy 2008, 36, 494. [Google Scholar] [CrossRef]
- Luderer, G.; Krey, V.; Calvin, K.; Merrick, J.; Mima, S.; Pietzcker, R.; Van Vliet, J.; Wada, K. The role of renewable energy in climate stabilization: Results from the EMF27 scenarios. Clim. Chang. 2014, 123, 427–441. [Google Scholar] [CrossRef]
- REN21 Renewables Global Status Report: 2009. Available online: http://www.unep.fr/shared/docs/publications/RE_GSR_2009_Update.pdf (accessed on 21 November 2018).
- Kanase-Patil, A.; Saini, R.; Sharma, M. Integrated renewable energy systems for off grid rural electrification of remote area. Renew. Energy 2010, 35, 1342–1349. [Google Scholar] [CrossRef]
- Bugaje, I. Renewable energy for sustainable development in Africa: A review. Renew. Sustain. Energy Rev. 2006, 10, 603–612. [Google Scholar] [CrossRef]
- Sahoo, S.K. Renew. Sustain. Energy Rev. solar photovoltaic energy progress in India: A review. Renew. Sustain. Energy Rev. 2016, 59, 927–939. [Google Scholar] [CrossRef]
- Saheb-Koussa, D.; Haddadi, M.; Belhamel, M. Economic and technical study of a hybrid system (wind–photovoltaic–diesel) for rural electrification in Algeria. Appl. Energy 2009, 86, 1024–1030. [Google Scholar] [CrossRef]
- Mohammed, Y.; Mokhtar, A.; Bashir, N.; Saidur, R. An overview of agricultural biomass for decentralized rural energy in Ghana. Renew. Sustain. Energy Rev. 2013, 20, 15–25. [Google Scholar] [CrossRef]
- Sachdev, H.S.; Akella, A.K.; Kumar, N. Analysis and evaluation of small hydropower plants: A bibliographical survey. Renew. Sustain. Energy Rev. 2015, 51, 1013–1022. [Google Scholar] [CrossRef]
- Gaglia, A.; Kaldellis, J.; Kavadias, K.; Konstantinidis, P.; Sigalas, J.; Vlachou, D. Integrated studies on renewable energy sources. The soft energy application laboratory, mechanical engineering department, TEI of Piraeus. In World Renewable Energy Congress VI; Elsevier: Amsterdam, The Netherlands, 2000; pp. 1588–1591. [Google Scholar]
- Al Irsyad, M.I.; Halog, A.; Nepal, R. Renewable energy projections for climate change mitigation: An analysis of uncertainty and errors. Renew. Energy 2019, 130, 536–546. [Google Scholar] [CrossRef]
- Jawahar, C.; Michael, P.A. A review on turbines for micro hydro power plant. Renew. Sustain. Energy Rev. 2017, 72, 882–887. [Google Scholar] [CrossRef]
- World Bank. Technical and Economic Assessment of Off Grid, Mini-Grid and Grid Electrification Technologies; Energy Sector Management Assistance Program (ESMAP) Technical Paper Series, ESM 212/07; World Bank: Washington, DC, USA, 2007. [Google Scholar]
- Khurana, S.; Kumar, A. Small hydro power—A review. Int. J. Therm. Technol. 2011, 1, 107–110. [Google Scholar]
- Mandelli, S.; Barbieri, J.; Mereu, R.; Colombo, E. Off-grid systems for rural electrification in developing countries: Definitions, classification and a comprehensive literature review. Renew. Sustain. Energy Rev. 2016, 58, 1621–1646. [Google Scholar] [CrossRef]
- Carravetta, A.; Derakhshan Houreh, S.; Ramos, H.M. Pumps as Turbines; Springer Tracts in Mechanical Engineering; Springer: Berlin/Heidelberg, Germany, 2018. [Google Scholar]
- Sangal, S.; Garg, A.; Kumar, D. Review of optimal selection of turbines for hydroelectric projects. Int. J. Emerg. Technol. Adv. Eng. 2013, 3, 424–430. [Google Scholar]
- Herschy, R.W. Chapter 10. Weirs and flumes. In Streamflow Measurement; CRC Press: Boca Raton, FL, USA, 2014; Volume 3. [Google Scholar]
- Thake, J. Micro-Hydro Pelton Turbine Manual: Design, Manufacture and Installation for Small-Scale Hydropower; Practical ACtion Publishing: Warwickshire, UK, 2000; pp. 136–142. [Google Scholar]
- Mishra, S.; Singal, S.; Khatod, D. Optimal installation of small hydropower plant—A review. Renew. Sustain. Energy Rev. 2011, 15, 3862–3869. [Google Scholar] [CrossRef]
- Elbatran, A.; Yaakob, O.; Ahmed, Y.M.; Shabara, H. 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]
- Bozorg Haddad, O.; Moradi-Jalal, M.; Marino, M.A. Design–operation optimisation of run-of-river power plants. In Proceedings of the Institution of Civil Engineers-Water Management; Thomas Telford Ltd.: London, UK, 2011; Volume 164, pp. 463–475. [Google Scholar]
- Anagnostopoulos, J.S.; Papantonis, D.E. Optimal sizing of a run-of-river small hydropower plant. Energy Convers. Manag. 2007, 48, 2663–2670. [Google Scholar] [CrossRef]
- Alexander, K.V.; Giddens, E.P. Optimum penstocks for low head microhydro schemes. Renew. Energy 2008, 33, 507–519. [Google Scholar] [CrossRef]
- Tapia, A.; Millán, P.; Gómez-Estern, F. Integer programming to optimize Micro-Hydro Power Plants for generic river profiles. Renew. Energy 2018, 126, 905–914. [Google Scholar] [CrossRef]
- Gingold, P. The optimum size of small run-of-river plants. Int. Water Power Dam Constr. 1981, 33, 2663–2670. [Google Scholar]
- Ehteram, M.; Karami, H.; Mousavi, S.F.; Farzin, S.; Kisi, O. Evaluation of contemporary evolutionary algorithms for optimization in reservoir operation and water supply. J. Water Supply Res. Technol.-Aqua 2018, 67, 54–67. [Google Scholar] [CrossRef]
- Aslan, Y.; Arslan, O.; Yasar, C. A sensitivity analysis for the design of small-scale hydropower plant: Kayabogazi case study. Renew. Energy 2008, 33, 791–801. [Google Scholar] [CrossRef]
- Williamson, S.; Stark, B.; Booker, J. Low head pico hydro turbine selection using a multi-criteria analysis. Renew. Energy 2014, 61, 43–50. [Google Scholar] [CrossRef]
- Singal, S.; Saini, R.; Raghuvanshi, C. Analysis for cost estimation of low head run-of-river small hydropower schemes. Energy Sustain. Dev. 2010, 14, 117–126. [Google Scholar] [CrossRef]
- Banos, R.; Manzano-Agugliaro, F.; Montoya, F.; Gil, C.; Alcayde, A.; Gómez, J. Optimization methods applied to renewable and sustainable energy: A review. Renew. Sustain. Energy Rev. 2011, 15, 1753–1766. [Google Scholar] [CrossRef]
- Iqbal, M.; Azam, M.; Naeem, M.; Khwaja, A.; Anpalagan, A. Optimization classification, algorithms and tools for renewable energy: A review. Renew. Sustain. Energy Rev. 2014, 39, 640–654. [Google Scholar] [CrossRef]
- Bozorg-Haddad, O.; Loáiciga, H.A. Honey-Bee Mating Optimization; John Wiley and Sons, Ltd.: Hoboken, NJ, USA, 2017; Chapter 12; pp. 145–161. [Google Scholar] [CrossRef]
- Basso, S.; Botter, G. Streamflow variability and optimal capacity of run-of-river hydropower plants. Water Resour. Res. 2012, 48. [Google Scholar] [CrossRef] [Green Version]
- Yoo, J.H. Maximization of hydropower generation through the application of a linear programming model. J. Hydrol. 2009, 376, 182–187. [Google Scholar] [CrossRef]
- Bragalli, C.; D’Ambrosio, C.; Lee, J.; Lodi, A.; Toth, P. On the optimal design of water distribution networks: A practical MINLP approach. Optim. Eng. 2012, 13, 219–246. [Google Scholar] [CrossRef]
- Fecarotta, O.; McNabola, A. Optimal location of pump as turbines (PATs) in water distribution networks to recover energy and reduce leakage. Water Resour. Res. 2017, 31, 5043–5059. [Google Scholar] [CrossRef]
- Fecarotta, O.; Carravetta, A.; Morani, M.; Padulano, R. Optimal Pump Scheduling for Urban Drainage under Variable Flow Conditions. Resources 2018, 7, 73. [Google Scholar] [CrossRef]
- Alexander, K.V.; Giddens, E.P. Microhydro: Cost-effective, modular systems for low heads. Renew. Energy 2008, 33, 1379–1391. [Google Scholar] [CrossRef]
- Leon, A.S.; Zhu, L. A dimensional analysis for determining optimal discharge and penstock diameter in impulse and reaction water turbines. Renew. Energy 2014, 71, 609–615. [Google Scholar] [CrossRef]
- Green, D.W. Perry’s Chemical Engineers’ Handbook, 8th ed.; McGraw-Hill: New York, NY, USA, 2008. [Google Scholar]
- Holland, J.H. Genetic Algorithms and Adaptation; Springer: Boston, MA, USA, 1984; pp. 317–333. [Google Scholar] [CrossRef]
- Reina, D.; Camp, T.; Munjal, A.; Toral, S. Evolutionary deployment and local search-based movements of 0th responders in disaster scenarios. Future Gener. Comput. Syst. 2018, 88, 61–78. [Google Scholar] [CrossRef]
- Arzamendia, M.; Gregor, D.; Reina, D.G.; Toral, S.L. An evolutionary approach to constrained path planning of an autonomous surface vehicle for maximizing the covered area of Ypacarai Lake. Soft Comput. 2017, 23, 1723–1734. [Google Scholar] [CrossRef]
- Gutiérrez-Reina, D.; Sharma, V.; You, I.; Toral, S. Dissimilarity Metric Based on Local Neighboring Information and Genetic Programming for Data Dissemination in Vehicular Ad Hoc Networks (VANETs). Sensors 2018, 18, 2320. [Google Scholar] [CrossRef] [PubMed]
- Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 2002, 6, 182–197. [Google Scholar] [CrossRef] [Green Version]
- Ter-Sarkisov, A.; Marsland, S. Convergence Properties of Two ({∖mu}+{∖lambda}) Evolutionary Algorithms On OneMax and Royal Roads Test Functions. arXiv, 2011; arXiv:1108.4080. [Google Scholar]
- Luke, S. Essentials of Metaheuristics; Lulu Raleigh: San Francisco, CA, USA, 2009; Volume 113. [Google Scholar]
- Gutierrez, D. Evolutionary MHPP. 2018. Available online: https://github.com/Dany503/Evolutionary-MHPP (accessed on 11 December 2018).
- Fortin, F.A.; Rainville, F.M.D.; Gardner, M.A.; Parizeau, M.; Gagné, C. DEAP: Evolutionary algorithms made easy. J. Mach. Learn. Res. 2012, 13, 2171–2175. [Google Scholar]
- G Reina, D.; Ciobanu, R.; Toral, S.; Dobre, C. A Multi-objective Optimization of Data Dissemination in Delay Tolerant Networks. Expert Syst. Appl. 2016, 57, 178–191. [Google Scholar] [CrossRef]
- Kirkpatrick, S.; Gelatt, C.D.; Vecchi, M.P. Optimization by Simulated Annealing. Science 1983, 220, 671–680. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Leitold, D.; Vathy-Fogarassy, A.; Abonyi, J. Network Distance-Based Simulated Annealing and Fuzzy Clustering for Sensor Placement Ensuring Observability and Minimal Relative Degree. Sensors 2018, 18, 3096. [Google Scholar] [CrossRef] [PubMed]
Parameter | Value | Unit |
---|---|---|
8 | kW | |
70 | L/s | |
0.5 | - | |
50 | m | |
1.5 | m | |
1.5 | m |
Parameter | Value |
---|---|
2000 | |
2000 | |
Individuals (multi-objective) | 2000 |
Generations | 100 |
Selection | Tournament size = 3 (single-objective) NSGA-II (multi-objective) |
Crossover | Two-point scheme |
Mutation | Modified bitflip , , |
Number of trials | 30 |
Case | Objective Function | Pipe Diameter |
---|---|---|
Case-study 1 | min L (13) | Fixed |
Case-study 2 | min C (9) | Fixed |
Case-study 3 | min C (9) | Variable |
Case-study 4 | min C (9), max P (8) | Variable |
Genetic Algorithm | BBA [29] | |||
---|---|---|---|---|
0.80 | 0.70 | 0.60 | ||
0.20 | 0.30 | 0.40 | ||
Gross height (m) | 66.648 | 66.648 | 66.648 | 66.648 |
Flow rate (L/s) | 13.718 | 13.718 | 13.718 | 13.718 |
Power (kW) | 8.064 | 8.064 | 8.064 | 8.064 |
Number of elbows | 4 | 4 | 4 | 7 |
Length (m) | 174.903 | 174.903 | 174.903 | 174.999 |
Genetic Algorithm | BBA [29] | |||
---|---|---|---|---|
0.80 | 0.70 | 0.60 | ||
0.20 | 0.30 | 0.40 | ||
Gross height (m) | 66.648 | 66.648 | 66.648 | 66.648 |
Flow rate (L/s) | 13.718 | 13.718 | 13.718 | 13.718 |
Power (kW) | 8.039 | 8.039 | 8.039 | 8.039 |
Length (m) | 174.9240 | 174.9240 | 174.9240 | 175.005 |
Number of elbows | 4 | 4 | 4 | 5 |
Cost (m) | 14.997 | 14.997 | 14.997 | 17.000 |
Genetic Algorithm | BBA [29] | |||
---|---|---|---|---|
0.80 | 0.70 | 0.60 | ||
0.20 | 0.30 | 0.40 | ||
Gross height (m) | 78.919 | 115.642 | 115.642 | 66.648 |
Flow rate (L/s) | 13.7863 | 13.7127 | 13.7128 | 13.718 |
Power (kW) | 8.160 | 8.030 | 8.030 | 8.039 |
Length (m) | 310.754 | 429.114 | 429.103 | 175.005 |
Number of elbows | 5 | 7 | 7 | 5 |
Pipe diameter (cm) | 10 | 8 | 8 | 20 |
Cost (c.u.) | 5.608 | 4.986 | 4.986 | 17.000 |
Random Search | Simulated Annealing | Reference [29] | ||
---|---|---|---|---|
Bit Flip | Custom Mutation | |||
Gross height (m) | 226.192 | 216.005 | 123.513 | 66.648 |
Flow rate (L/s) | 14.601 | 14.491 | 13.819 | 13.718 |
Power (kW) | 9.695 | 9.477 | 8.217 | 8.039 |
Length (m) | 1159.8 | 1106.8 | 481.3 | 175.005 |
Number of elbows | 99 | 63 | 20 | 5 |
Pipe diameter (cm) | 8 | 8 | 8 | 20 |
Cost (c.u.) | 6109.8 | 4256.8 | 1481.3 | 17.000 |
Parameter | Value | Unit |
---|---|---|
8 | kW | |
50 | L/s | |
0.5 | - | |
50 | m | |
1.5 | m | |
1.5 | m |
Genetic Algorithm | |||
---|---|---|---|
0.80 | 0.70 | 0.60 | |
0.20 | 0.30 | 0.40 | |
Gross height (m) | 86.664 | 77.756 | 77.756 |
Flow rate (L/s) | 15.445 | 14.654 | 14.654 |
Power (kW) | 11.473 | 9.800 | 9.800 |
Length (m) | 536.247 | 471.740 | 471.740 |
Number of elbows | 8 | 5 | 5 |
Pipe diameter (cm) | 16 | 16 | 16 |
Cost (c.u.) | 23.968 | 18.4765 | 18.4765 |
© 2019 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 (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Tapia Córdoba, A.; Gutiérrez Reina, D.; Millán Gata, P. An Evolutionary Computational Approach for Designing Micro Hydro Power Plants. Energies 2019, 12, 878. https://doi.org/10.3390/en12050878
Tapia Córdoba A, Gutiérrez Reina D, Millán Gata P. An Evolutionary Computational Approach for Designing Micro Hydro Power Plants. Energies. 2019; 12(5):878. https://doi.org/10.3390/en12050878
Chicago/Turabian StyleTapia Córdoba, Alejandro, Daniel Gutiérrez Reina, and Pablo Millán Gata. 2019. "An Evolutionary Computational Approach for Designing Micro Hydro Power Plants" Energies 12, no. 5: 878. https://doi.org/10.3390/en12050878