In both operating modes scenarios, the initial flow released through the turbines is 20m3/s.
Pairs of gains from the tuning criterion. This article was most recently revised and updated by, https://www.britannica.com/technology/spillway-engineering. In this case, these boundary conditions are given by the head at both ends of the conduit. where is the number of -shaped elements the pipe is divided in. Each step has the area of two Canadian football fields! Although in more recent works advanced control techniques have been applied [22], the interest for robust PID controllers is still active [23].
Tidal Energy Pros, Cons & Costs | How is Tidal Energy Used? Water flowing down a spillway can travel at very high speedsabout 160 km (100 miles) per hour in the case of a dam 100 metres (330 feet) highand form a standing wave where it enters the riverbed; it proceeds downstream at lower mean velocity but in a highly turbulent state. ):Headrace conduit losses (p.u. In the case of water level control in [8], it is found that with a PI controller a good response may be obtained; the derivative component could be affected by the noise transmitted with the sensor signal. What is geothermal energy? Learn the definition of hydroelectric power and see examples. The overall project consists of replacing the existing overflow spillway and small gates with six large Tainter gates and also a downstream stilling basin which will helps reduce the risk of eroding the riverbed at the dam. Surge Tank. In these cases [9, 31], a static model is used to include the turbine dynamics (5). PlantSolar Lounge The following linearized expressions are obtained. For example, in [34] some strategies for obtaining an appropriate response were proposed but in the context of load-frequency control. ), reflected in the parameter (13), affect the stability of the plant, as can be seen in Figure 7. /Size 286 /Prev 1416906 Serious consequences can follow if a dam is overtopped. The power plant modeled is supposed to operate connected to a large network. The most frequently used control scheme in run-of-river plants is based on controlling the water level in the head pond [613]. % Contact our creative partners at. ):Proportional gain of PI controller:Proportional gain of PI controller (p.u. The plant consists of a head pond with a spillway for excess of flow during flood periods, long headrace conduit of more than 5 kilometers, surge tank, penstock, and two Francis turbines. 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See our User Agreement and Privacy Policy. Water stored in large dams passes through penstocks and makes the turbine rotor to rotate and in turn the turbine rotates the alternator to produce electrical energy. Advantages of Hydropower | What is Hydroelectric Energy? The following expression (18) gives its value as a function of the plant design parameters: ):Headrace loss coefficient:Headrace conduit length (m):Crest spillway length (m):Penstock length (m):Turbine rotational speed (p.u. In this paper, the stability of a run-of-river diversion hydropower plant with a spillway in the head pond that evacuates a portion of the river flow is analyzed. Our editors will review what youve submitted and determine whether to revise the article. 257 0 obj The characteristic polynomial (13) of the linearized system has, in general, four conjugate complex roots: >> A scheme of the model can be seen in Figure 3. In addition, analytical expressions, based on a heuristic criterion, have been obtained for both the proportional and integral gains in flood operation conditions. Hello! The results obtained in the case study highlight the importance of carrying out a stability analysis similar to the one presented here in the design phase of a run-of-river diversion power plant. Third, the rate of floodwater discharge should not increase much above that experienced before the construction of the dam. @J0@"OH R^ 4"v j QHo@D@5$&d$&k0. The coefficients and , acquired from the hill curves, and the initial per unit headrace conduit flow variable, , used to obtain these figures, correspond to the initial operating point; the per unit initial flow and head losses in the conduit have been assumed to be equal to 1 and 0.08p.u., respectively; for the water inertia time constant, , the value 12.09s has been used, as in the case study. where the coefficients are Figures 9 and 10 include the relation between and (spillway dimension) with the and parameters obtained using (22). They may lead over the dam or a portion of it or along a channel around the dam or a conduit through it, and the erosive energy of the water at the foot of the spillway is dissipated away from the foundation. In the three figures, the area under the curves determines the stable region, that is, the combination of and that guarantees a stable operation of the level control system. It is equal to zero in normal operation. We dont have enough spillway capacity here so if we got a big flood here we wouldnt be able to pass it and certainly if youve watched around the country youve seen episodes where dams have been over inundated by flood flow.. ):Turbine flow (p.u. Different algorithms for controlling the water levels in three or more cascade hydro plants are presented in [7, 12]. High head hydropower plants also benefit from the utilization of Obermeyer spillway gates. Free access to premium services like Tuneln, Mubi and more. APIdays Paris 2019 - Innovation @ scale, APIs as Digital Factories' New Machi Mammalian Brain Chemistry Explains Everything. Fourth, floodwater discharged over the height of a dam can be destructive to the dam structure itself and to the riverbed unless its energy is controlled and dissipated in harmless turbulence. A PI controller is used for maintaining a constant water level in the head pond; the effects of a surge tank have been considered. PID regulator has been extensively used in turbine governors of conventional hydro plants. Enjoy access to millions of ebooks, audiobooks, magazines, and more from Scribd. As it can be seen in these figures, the magnitude of the controller gains is large. From Figure 11, it can be deduced that the pair of gains for flood operation (G) can cause instabilities if used during normal operation. The plant response has been obtained by means of simulations. As expected, the response for adjustment at point F results unstable. There is an increasing need to develop clean energy technologies to cope with the problems relating to climate change, sustainable development, and energy security. In flooding operating conditions, the excess flow is discharged through a spillway; in this case, the water level reference is changed in order to allow controlling the spilled flow as in [14]. Jos Ignacio Sarasa, Paz Elas, Guillermo Martnez-Lucas, Juan Ignacio Prez-Daz, Jos Romn Wilhelmi, Jos ngel Snchez, "Stability Analysis of a Run-of-River Diversion Hydropower Plant with Surge Tank and Spillway in the Head Pond", The Scientific World Journal, vol. In Section 3, a small perturbation stability analysis is discussed and in Section 4 the PI controller is tuned by using a heuristic criterion. For instance, in Ecuador, hydropower produced more than one half of the generated electrical energy in 2012 [2], and one of the objectives of the Plan Maestro de Electrificacin (Electrification Master Plan) 20122021 is that 90% of electric energy is to be generated from renewable sources, hydro and wind. According to Routh-Hurwitz criterion, the system (9) is asymptotically stable if the following conditions are satisfied. The control system proposed in [14] is aimed at maintaining a minimum environmental flow in the intermediate river reach between the intake and the tailrace. Disaster is likely in the case of an embankment dam not designed to permit uncontrolled Grand Coulee Dam is a hydroelectric power station on the Columbia River in Washington state. Also, it has been found that the level controller gains should be updated in real-time operation, not only as a function of the actual operating point (full or partial load) but also as a function of the actual operating mode (normal or flood conditions) in order to guarantee a stable and quality response of the water level control system.
Simond, and F. Avellan, Stability study of a complete hydroelectric production site by eigenvalues analysis method based on phase variables, in, X. Liu and C. Liu, Eigenanalysis of oscillatory instability of a hydropower plant including water conduit dynamics,, C. Nicolet, Y. Pannatier, B. Kawkabani, A. Schwery, F. Avellan, and J. Simond, Benefits of variable speed pumped storage units in mixed islanded power network during transient operation, in, J. I. Prez-Daz, J. I. Sarasa, and J. R. Wilhelmi, Contribution of a hydraulic short-circuit pumped-storage power plant to the load-frequency regulation of an isolated power system,, IEEE Working-Group on Prime Mover and Energy Supply Models for System Dynamic Studies, Hydraulic turbine and control models for system dynamic studies,, L. Fu, J. Yang, H. Bao, and J. Li, Effect of turbine characteristic on the response of hydroturbine governing system with surge tank, in, F. Collier and L. Wozniak, Control synthesis for an impulse turbine: the Bradley Lake project,, M. Vinatoru, C. Maican, and C. Vinatoru, Level control using a feed-forward structure, in. In practice, the first condition is always fulfilled, and the second condition may be shown to reduce to In addition, initial and operating costs are lower than those associated with other renewables sources, such as wind parks [, Penstock dynamics is not considered because the associated time constant is in most cases very small compared to the relatively slow dynamics of the other components [, The oscillations of water level in the head pond are much slower than pressure waves in the conduits. (i)Run-of-river hydro plants allow harnessing the energy associated with water flows for other uses, such as water supply or irrigation, or the environmental minimum flows. Equation (5) should be obtained from the turbine hill curves; in Figure 4, the efficiency hill of the turbine considered in the case study is shown. << /Linearized 1 /L 1418409 /H [ 1030 710 ] /O 261 /E 186765 /N 49 /T 1416905 >> Obermeyer Spillway Gates allow spillway flows to be directed in the most beneficial manner. Pairs of gains selected for carrying out simulations. 1. This phenomenal capacity corresponds to an exceptional flood likely to occur once every 10,000 years. Therefore, the design of the spillway should be taken into account if water level control is considered. Clipping is a handy way to collect important slides you want to go back to later. The main features of the plant are reflected in Table 1. The SlideShare family just got bigger. SlideShare uses cookies to improve functionality and performance, and to provide you with relevant advertising. The influence of the operating point in the dynamics response is studied, concluding that for better performance the controller gains should be adapted to the operation conditions. The instability observed for the pair of gains G confirms the results obtained from the linear model. (2)One of these pairs should have its imaginary part close to zero, thus avoiding the appearance of oscillations as far as possible.Analytical expressions (22) for the proportional gain in p.u.
Plant dimensions, parameters and base values. Arch dams possess greater resistance to failure after overtopping. are obtained from the rules formulated. By using independently controlled sections of Obermeyer Spillway Gate this can be easily accomplished. Learn about geothermal energy pros and cons and its different uses. As stated in [9], it is worthy to mention that these expressions are independent of each other.
In normal hydrologic conditions, the water level control system operates in a conventional way: the wicket gates position is changed, adapting the discharged flow to the inflow, in order to maintain the water level close to the reference value. GED Social Studies: Civics & Government, US History, Economics, Geography & World, Introduction to Human Geography: Help and Review, SAT Subject Test Chemistry: Practice and Study Guide, Political Science 102: American Government, CLEP Principles of Marketing: Study Guide & Test Prep, UExcel Anatomy & Physiology: Study Guide & Test Prep, CLEP Principles of Management: Study Guide & Test Prep, CLEP English Literature: Study Guide & Test Prep, CLEP American Literature: Study Guide & Test Prep, All Teacher Certification Test Prep Courses, Working Scholars Bringing Tuition-Free College to the Community. With arch dams it is convenient to construct gated openings in the shell structure at some distance below the crest of the dam, ensuring that the discharging jets fall well clear downstream. In Figure 5, the effect of varying the parameter is represented. The conduit that joins the surge tank and the turbine is modeled as the headrace tunnel using the lumped parameters approach. Finally in Section 6 the conclusions derived from this study are presented. The plant layout can be seen in Figure 1. All rights reserved. Moreover, as it can be seen in Figure 15, when the controller is tuned according to the criterion (gains H), the oscillation of the wicket gates position is almost eliminated, thus contributing to both increasing the equipment service life and reducing the settling time of the response.
In addition, initial and operating costs are lower than those associated with other renewables sources, such as wind parks [5].Run-of-river plants have limited regulation capacity and in general do not participate in power-frequency regulation. On the other hand, it has been found that the fulfillment of the well-known Thoma stability condition is not necessary in this case. In Table 2, it is indicated whether or not each pair of gains is located inside or outside the corresponding stability region. See our Privacy Policy and User Agreement for details. Then, the headrace tunnel dynamics is approximated by a rigid water column model (. The spillway at Mangla discharges 28,000 cubic metres (36,600 cubic yards) of water per second; the upper stilling basin has the dimensions of an Olympic Games stadium, including its grandstands. The characteristics of the spillway (length, spillway discharge coefficient, etc. This results in greatly increased power production when high flows are available and high tailwater elevations would otherwise reduce power production.
Pairs of gains from the tuning criterion. This article was most recently revised and updated by, https://www.britannica.com/technology/spillway-engineering. In this case, these boundary conditions are given by the head at both ends of the conduit. where is the number of -shaped elements the pipe is divided in. Each step has the area of two Canadian football fields! Although in more recent works advanced control techniques have been applied [22], the interest for robust PID controllers is still active [23].
Tidal Energy Pros, Cons & Costs | How is Tidal Energy Used? Water flowing down a spillway can travel at very high speedsabout 160 km (100 miles) per hour in the case of a dam 100 metres (330 feet) highand form a standing wave where it enters the riverbed; it proceeds downstream at lower mean velocity but in a highly turbulent state. ):Headrace conduit losses (p.u. In the case of water level control in [8], it is found that with a PI controller a good response may be obtained; the derivative component could be affected by the noise transmitted with the sensor signal. What is geothermal energy? Learn the definition of hydroelectric power and see examples. The overall project consists of replacing the existing overflow spillway and small gates with six large Tainter gates and also a downstream stilling basin which will helps reduce the risk of eroding the riverbed at the dam. Surge Tank. In these cases [9, 31], a static model is used to include the turbine dynamics (5). PlantSolar Lounge The following linearized expressions are obtained. For example, in [34] some strategies for obtaining an appropriate response were proposed but in the context of load-frequency control. ), reflected in the parameter (13), affect the stability of the plant, as can be seen in Figure 7. /Size 286 /Prev 1416906 Serious consequences can follow if a dam is overtopped. The power plant modeled is supposed to operate connected to a large network. The most frequently used control scheme in run-of-river plants is based on controlling the water level in the head pond [613]. % Contact our creative partners at. ):Proportional gain of PI controller:Proportional gain of PI controller (p.u. The plant consists of a head pond with a spillway for excess of flow during flood periods, long headrace conduit of more than 5 kilometers, surge tank, penstock, and two Francis turbines. AI and Machine Learning Demystified by Carol Smith at Midwest UX 2017, Pew Research Center's Internet & American Life Project, Harry Surden - Artificial Intelligence and Law Overview, Pinot: Realtime Distributed OLAP datastore, How to Become a Thought Leader in Your Niche, UX, ethnography and possibilities: for Libraries, Museums and Archives, Winners and Losers - All the (Russian) President's Men, No public clipboards found for this slide, Autonomy: The Quest to Build the Driverless CarAnd How It Will Reshape Our World, Bezonomics: How Amazon Is Changing Our Lives and What the World's Best Companies Are Learning from It, So You Want to Start a Podcast: Finding Your Voice, Telling Your Story, and Building a Community That Will Listen, The Future Is Faster Than You Think: How Converging Technologies Are Transforming Business, Industries, and Our Lives, SAM: One Robot, a Dozen Engineers, and the Race to Revolutionize the Way We Build, Talk to Me: How Voice Computing Will Transform the Way We Live, Work, and Think, Everybody Lies: Big Data, New Data, and What the Internet Can Tell Us About Who We Really Are, Life After Google: The Fall of Big Data and the Rise of the Blockchain Economy, Live Work Work Work Die: A Journey into the Savage Heart of Silicon Valley, Future Presence: How Virtual Reality Is Changing Human Connection, Intimacy, and the Limits of Ordinary Life, From Gutenberg to Google: The History of Our Future, Full Out: Lessons in Life and Leadership from America's Favorite Coach, We Should All Be Millionaires: A Womans Guide to Earning More, Building Wealth, and Gaining Economic Power, Authentic: A Memoir by the Founder of Vans, Believe IT: How to Go from Underestimated to Unstoppable, Second Nature: Scenes from a World Remade, Test Gods: Virgin Galactic and the Making of a Modern Astronaut, A Brief History of Motion: From the Wheel, to the Car, to What Comes Next, The Metaverse: And How It Will Revolutionize Everything, An Ugly Truth: Inside Facebooks Battle for Domination, System Error: Where Big Tech Went Wrong and How We Can Reboot, The Wires of War: Technology and the Global Struggle for Power, The Quiet Zone: Unraveling the Mystery of a Town Suspended in Silence. See our User Agreement and Privacy Policy. Water stored in large dams passes through penstocks and makes the turbine rotor to rotate and in turn the turbine rotates the alternator to produce electrical energy. Advantages of Hydropower | What is Hydroelectric Energy? The following expression (18) gives its value as a function of the plant design parameters: ):Headrace loss coefficient:Headrace conduit length (m):Crest spillway length (m):Penstock length (m):Turbine rotational speed (p.u. In this paper, the stability of a run-of-river diversion hydropower plant with a spillway in the head pond that evacuates a portion of the river flow is analyzed. Our editors will review what youve submitted and determine whether to revise the article. 257 0 obj The characteristic polynomial (13) of the linearized system has, in general, four conjugate complex roots: >> A scheme of the model can be seen in Figure 3. In addition, analytical expressions, based on a heuristic criterion, have been obtained for both the proportional and integral gains in flood operation conditions. Hello! The results obtained in the case study highlight the importance of carrying out a stability analysis similar to the one presented here in the design phase of a run-of-river diversion power plant. Third, the rate of floodwater discharge should not increase much above that experienced before the construction of the dam. @J0@"OH R^ 4"v j QHo@D@5$&d$&k0. The coefficients and , acquired from the hill curves, and the initial per unit headrace conduit flow variable, , used to obtain these figures, correspond to the initial operating point; the per unit initial flow and head losses in the conduit have been assumed to be equal to 1 and 0.08p.u., respectively; for the water inertia time constant, , the value 12.09s has been used, as in the case study. where the coefficients are Figures 9 and 10 include the relation between and (spillway dimension) with the and parameters obtained using (22). They may lead over the dam or a portion of it or along a channel around the dam or a conduit through it, and the erosive energy of the water at the foot of the spillway is dissipated away from the foundation. In the three figures, the area under the curves determines the stable region, that is, the combination of and that guarantees a stable operation of the level control system. It is equal to zero in normal operation. We dont have enough spillway capacity here so if we got a big flood here we wouldnt be able to pass it and certainly if youve watched around the country youve seen episodes where dams have been over inundated by flood flow.. ):Turbine flow (p.u. Different algorithms for controlling the water levels in three or more cascade hydro plants are presented in [7, 12]. High head hydropower plants also benefit from the utilization of Obermeyer spillway gates. Free access to premium services like Tuneln, Mubi and more. APIdays Paris 2019 - Innovation @ scale, APIs as Digital Factories' New Machi Mammalian Brain Chemistry Explains Everything. Fourth, floodwater discharged over the height of a dam can be destructive to the dam structure itself and to the riverbed unless its energy is controlled and dissipated in harmless turbulence. A PI controller is used for maintaining a constant water level in the head pond; the effects of a surge tank have been considered. PID regulator has been extensively used in turbine governors of conventional hydro plants. Enjoy access to millions of ebooks, audiobooks, magazines, and more from Scribd. As it can be seen in these figures, the magnitude of the controller gains is large. From Figure 11, it can be deduced that the pair of gains for flood operation (G) can cause instabilities if used during normal operation. The plant response has been obtained by means of simulations. As expected, the response for adjustment at point F results unstable. There is an increasing need to develop clean energy technologies to cope with the problems relating to climate change, sustainable development, and energy security. In flooding operating conditions, the excess flow is discharged through a spillway; in this case, the water level reference is changed in order to allow controlling the spilled flow as in [14]. Jos Ignacio Sarasa, Paz Elas, Guillermo Martnez-Lucas, Juan Ignacio Prez-Daz, Jos Romn Wilhelmi, Jos ngel Snchez, "Stability Analysis of a Run-of-River Diversion Hydropower Plant with Surge Tank and Spillway in the Head Pond", The Scientific World Journal, vol. In Section 3, a small perturbation stability analysis is discussed and in Section 4 the PI controller is tuned by using a heuristic criterion. For instance, in Ecuador, hydropower produced more than one half of the generated electrical energy in 2012 [2], and one of the objectives of the Plan Maestro de Electrificacin (Electrification Master Plan) 20122021 is that 90% of electric energy is to be generated from renewable sources, hydro and wind. According to Routh-Hurwitz criterion, the system (9) is asymptotically stable if the following conditions are satisfied. The control system proposed in [14] is aimed at maintaining a minimum environmental flow in the intermediate river reach between the intake and the tailrace. Disaster is likely in the case of an embankment dam not designed to permit uncontrolled Grand Coulee Dam is a hydroelectric power station on the Columbia River in Washington state. Also, it has been found that the level controller gains should be updated in real-time operation, not only as a function of the actual operating point (full or partial load) but also as a function of the actual operating mode (normal or flood conditions) in order to guarantee a stable and quality response of the water level control system. Simond, and F. Avellan, Stability study of a complete hydroelectric production site by eigenvalues analysis method based on phase variables, in, X. Liu and C. Liu, Eigenanalysis of oscillatory instability of a hydropower plant including water conduit dynamics,, C. Nicolet, Y. Pannatier, B. Kawkabani, A. Schwery, F. Avellan, and J. Simond, Benefits of variable speed pumped storage units in mixed islanded power network during transient operation, in, J. I. Prez-Daz, J. I. Sarasa, and J. R. Wilhelmi, Contribution of a hydraulic short-circuit pumped-storage power plant to the load-frequency regulation of an isolated power system,, IEEE Working-Group on Prime Mover and Energy Supply Models for System Dynamic Studies, Hydraulic turbine and control models for system dynamic studies,, L. Fu, J. Yang, H. Bao, and J. Li, Effect of turbine characteristic on the response of hydroturbine governing system with surge tank, in, F. Collier and L. Wozniak, Control synthesis for an impulse turbine: the Bradley Lake project,, M. Vinatoru, C. Maican, and C. Vinatoru, Level control using a feed-forward structure, in. In practice, the first condition is always fulfilled, and the second condition may be shown to reduce to In addition, initial and operating costs are lower than those associated with other renewables sources, such as wind parks [, Penstock dynamics is not considered because the associated time constant is in most cases very small compared to the relatively slow dynamics of the other components [, The oscillations of water level in the head pond are much slower than pressure waves in the conduits. (i)Run-of-river hydro plants allow harnessing the energy associated with water flows for other uses, such as water supply or irrigation, or the environmental minimum flows. Equation (5) should be obtained from the turbine hill curves; in Figure 4, the efficiency hill of the turbine considered in the case study is shown. << /Linearized 1 /L 1418409 /H [ 1030 710 ] /O 261 /E 186765 /N 49 /T 1416905 >> Obermeyer Spillway Gates allow spillway flows to be directed in the most beneficial manner. Pairs of gains selected for carrying out simulations. 1. This phenomenal capacity corresponds to an exceptional flood likely to occur once every 10,000 years. Therefore, the design of the spillway should be taken into account if water level control is considered. Clipping is a handy way to collect important slides you want to go back to later. The main features of the plant are reflected in Table 1. The SlideShare family just got bigger. SlideShare uses cookies to improve functionality and performance, and to provide you with relevant advertising. The influence of the operating point in the dynamics response is studied, concluding that for better performance the controller gains should be adapted to the operation conditions. The instability observed for the pair of gains G confirms the results obtained from the linear model. (2)One of these pairs should have its imaginary part close to zero, thus avoiding the appearance of oscillations as far as possible.Analytical expressions (22) for the proportional gain in p.u.
Plant dimensions, parameters and base values. Arch dams possess greater resistance to failure after overtopping. are obtained from the rules formulated. By using independently controlled sections of Obermeyer Spillway Gate this can be easily accomplished. Learn about geothermal energy pros and cons and its different uses. As stated in [9], it is worthy to mention that these expressions are independent of each other.
In normal hydrologic conditions, the water level control system operates in a conventional way: the wicket gates position is changed, adapting the discharged flow to the inflow, in order to maintain the water level close to the reference value. GED Social Studies: Civics & Government, US History, Economics, Geography & World, Introduction to Human Geography: Help and Review, SAT Subject Test Chemistry: Practice and Study Guide, Political Science 102: American Government, CLEP Principles of Marketing: Study Guide & Test Prep, UExcel Anatomy & Physiology: Study Guide & Test Prep, CLEP Principles of Management: Study Guide & Test Prep, CLEP English Literature: Study Guide & Test Prep, CLEP American Literature: Study Guide & Test Prep, All Teacher Certification Test Prep Courses, Working Scholars Bringing Tuition-Free College to the Community. With arch dams it is convenient to construct gated openings in the shell structure at some distance below the crest of the dam, ensuring that the discharging jets fall well clear downstream. In Figure 5, the effect of varying the parameter is represented. The conduit that joins the surge tank and the turbine is modeled as the headrace tunnel using the lumped parameters approach. Finally in Section 6 the conclusions derived from this study are presented. The plant layout can be seen in Figure 1. All rights reserved. Moreover, as it can be seen in Figure 15, when the controller is tuned according to the criterion (gains H), the oscillation of the wicket gates position is almost eliminated, thus contributing to both increasing the equipment service life and reducing the settling time of the response.
In addition, initial and operating costs are lower than those associated with other renewables sources, such as wind parks [5].Run-of-river plants have limited regulation capacity and in general do not participate in power-frequency regulation. On the other hand, it has been found that the fulfillment of the well-known Thoma stability condition is not necessary in this case. In Table 2, it is indicated whether or not each pair of gains is located inside or outside the corresponding stability region. See our Privacy Policy and User Agreement for details. Then, the headrace tunnel dynamics is approximated by a rigid water column model (. The spillway at Mangla discharges 28,000 cubic metres (36,600 cubic yards) of water per second; the upper stilling basin has the dimensions of an Olympic Games stadium, including its grandstands. The characteristics of the spillway (length, spillway discharge coefficient, etc. This results in greatly increased power production when high flows are available and high tailwater elevations would otherwise reduce power production.