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• Published: 16 January 2023
• Hydroelectricity

The potential for sustainable hydropower

• Patrick Bogaart   ORCID: orcid.org/0000-0002-8612-1289 1  

Nature Water volume  1 ,  pages 22–23 ( 2023 ) Cite this article

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• Environmental impact

Development of the world’s hydropower is controversial because of its many documented environmental and societal implications. A global assessment of the unused profitable hydropower potential is performed with strict criteria to limit the environmental and social impact.

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Bogaart, P. The potential for sustainable hydropower. Nat Water 1 , 22–23 (2023). https://doi.org/10.1038/s44221-022-00018-9

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Published : 16 January 2023

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• Published: 15 February 2023

Design models for small run-of-river hydropower plants: a review

• David Tsuanyo   ORCID: orcid.org/0000-0001-7073-4980 1 ,
• Boris Amougou 1 , 2 ,
• Abdoul Aziz 1 ,
• Bernadette Nka Nnomo 3 ,
• Davide Fioriti 4 &
• Joseph Kenfack 2  

Sustainable Energy Research volume  10 , Article number:  3 ( 2023 ) Cite this article

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Hydropower plants are among the most efficient and reliable renewable energy systems in the world as far as electricity production is concerned. Run-of-river hydropower plants seem more attractive than conventional hydroelectric plants since they can be a cheaper and environmentally friendly alternative. However, their expected energy production pattern heavily depends on several construction variables that need an appropriate design using specific models. This paper analyzes several existing models used for the calculation of the diameter and thickness of a penstock, the optimal selection and implantation (admissible suction head) of a turbine, to estimate the energy produced and expected cost of small hydropower projects for grid-connected and off-grid/micro-grid applications. This review particularly brings out the specificities of each of the models to suggest the most appropriate model according to the context of study and proposes methods to use them more efficiently. This review can be used as a guide in the design and simulation of run-of-river hydropower plants, thus helping in the assessment of the economic feasibility of projects that usually requires a high level of experience and expertise.

A critical review focused particularly on run-of-river hydropower plant design models was carried out.

Several calculation models including diameter and thickness of a penstock, admissible suction head of a turbine, and cost and energy production estimation for grid-connected applications are collected and analyzed.

Hydropower models for design and generation profile prediction presented can be used to optimally come against the variability problem of run-of river plants.

The paper can be used as a guide in the design and simulation of run-of-river hydropower plants with appropriate models.

Introduction

Till date, more than 81% of the world's energy consumption comes from fossil sources despite the setbacks related, such as environmental impact and the gradual disappearance of the resource (Safarian et al., 2019 ). Global energy demand remains constantly growing, but the contribution of renewable energy sources is still estimated to be very low (13.7%) (Safarian et al., 2019 ; Yildiz & Vrugt, 2019 ). Renewable energy sources (wind, solar, geothermal, biomass and hydropower) are cleaner, sustainable and environmentally friendly sources, meaning they should be harnessed as much as possible.

Among all the renewable energy sources, hydropower, representing about 2.5% of the world energy resource and about 15.9% of the global electricity generation, is among the most efficient and reliable as far as electricity generation in the world is concerned (Bozorg Haddad et al., 2011 ; Hydropower status report, sector trends & insights, 2019 ; Jadoon et al., 2020 ; Safarian et al., 2019 ). A hydro-power plant harnesses the energy of moving water to drive a turbine, which in turn will run a generator for electricity production. This technology is well understood and has many advantages (Breeze, 2005 ), among which a relatively low-marginal-cost and low greenhouse gas emission (Stoll et al., 2017 ), with nearly constant prices over the years (Ghosh & Prelas, 2011 ; Sattouf, 2014 ).

Usually, a typical hydropower plant is made of a dam (which creates the reservoir), a trash rack (that prevents debris from entering the intake), a water tunnel, a penstock (to divert the water to the turbine), a speed governor (controlling wicket gates to permanently adapt water flow variations to the energy demand), a turbine and a generator (Fig.  1 a) (Acakpovi et al., 2014 ; Pagès et al., 2003 ; Singh & Chauhan, 2011 ). As for run-of-river hydropower plants, it is generally a weir which is responsible for diverting the water from the river toward the intake. The water usually gets to the turbine after crossing a desilting tank. Water can also be brought to a forebay by a canal, and then the penstock will convey it to the turbine (Vougioukli et al., 2017 ). Figure  1 b shows the components of run-of-river hydropower plants.

a Typical hydropower plant with reservoir; b Run-of-river hydropower plant

The main particularity of run-of-river projects is that they do not need large reservoirs, which leads to several benefits. First, their construction time is shorter and their overall cost is lower compared to storage plants projects of this same capacity (Ibrahim et al., 2019 ). Second, they pose less problems of inundation and sedimentation, have a less harmful impact on fish migration, and decrease the problem of high rehabilitation, the disorder at the level of navigation and the problem of people moving, aspects that usually go with large-scale hydropower projects (Kumar & Katoch, 2014 ). Another advantage of run-of-river hydropower projects is the fact that they drive generators with small turbines that can be easily manufactured locally, thus promoting job creation and economic development through local industry (Goodland, 1994 ). Because of these advantages mentioned above, it is easier to get public and government’s acceptance for run-of-river hydropower projects as compared to storage plant projects, which need large submergence areas (Kumar & Katoch, 2014 ).

In the work of Korkovelos et al. ( 2018 ), it was found that the small-scale (1–10 MW) hydropower potential in Sub-Saharan Africa is estimated at 21,800 MW, and run-of-river hydropower plants are generally categorized as small hydropower plants (Bozorg Haddad et al., 2011 ; Safdar et al., 2020 ; Vougioukli et al., 2017 ). An overview of the small hydropower potential of each of the 44 Sub-Saharan African countries can be seen in Appendix 1 (Korkovelos, et al., 2018 ). In view of this great potential, it emerges that the small-scale hydropower and consequently run-of-river systems can be a very suitable option for rural electrification in Africa (Okedu et al., 2020 ). Indeed, they have made a significant contribution to the sustainable development of rural and remote areas in various developing countries these last years (Malhan & Mittal, 2021 ). There is no internationally agreed definition of small hydropower plants. The level of development of a country makes it possible to classify hydropower plants as shown in the Appendix 2 (Bhat & Prakash, 2014 ; Elbatran et al., 2015 ; Mishra et al., 2012 ; Ohunakin et al., 2011 ).

Despite the fact that the use of run-of-river hydropower plants goes with many advantages (Casila et al., 2019 ; Yildiz & Vrugt, 2019 ), the intense variability of their resource can have a significant impact on the quality of electricity and on the balance of the grid. Many hydropower models for design and generation profile prediction are used to come against this variability problem. Each of the models has its singularity. It is for this reason that this review regroups them to present their particularities and to orientate their choices for more efficient use. Moreover, the prefeasibility study of small hydropower projects generally represents a significant proportion of overall project costs and requires a high level of experience and expertise (Punys et al., 2011 ). Hence, it is important to analyze existing models to provide the elements, which can facilitate optimal design and operation of run-of-river hydropower plants from the least possible data (average daily flow and gross head), and less expertise possible in a single document.

However, the recent literature is lacking extensive literature reviews on modeling run-of-river projects. In Kuriqi et al., ( 2021 ), the major ecological impacts of run-of-river projects were reviewed, yet modeling factors were not on major focus. The review in Sasthav and Oladosu ( 2022 ) focused on only low-head run-of-rivers in the United States with some yet limited modeling perspectives. Finally, the authors in Singh and Singal ( 2017 ) reviewed the system operation of several hydro plants, yet the specific detailed models were not in the focus. Therefore, it turns out that reviewing design methodologies for run-of-river projects is not only timely but also needed.

This paper aims at examining numerical models for the optimal design of run-of-river hydropower plants without pondage. This is done with a particular focus on the optimal design of a penstock (calculation of the diameter and thickness), the optimal selection and implantation (admissible suction head) of a turbine, the estimation of energy production for central-grid applications and the estimation of the cost of small hydropower projects. More in detail, the main novelties of this study lay in (a) identifying and reviewing all major technical and economic parameters needed for the optimal design of run-of-river project, based on relevant literature and in-field experience, and (b) proposing a classification of the reviewed models to be possibly used as a reference by scholars and practitioners in the field.

Overview of run-of-river hydropower plants

Run-of-river hydropower plants are characterized by the fact that they do not have a water reserve allowing a seasonal regulation (Bozorg Haddad et al., 2011 ; Goodland, 1994 ; Pagès et al., 2003 ; Yildiz & Vrugt, 2019 ). They use the natural flow on river of water from upstream. Therefore, these plants are less flexible than hydropower plants with large reservoirs because their electricity output depends on the availability of water in the river. This particularity makes the energy generated proportional to water inflow, which is why the amount of power produced by run-of-river hydropower plants varies considerably throughout the year. Multiple hydraulic turbines can be set up to have a better control on these flow variations (Bozorg Haddad et al., 2011 ) and vary depending on the run-of-river hydropower plant configurations.

These configurations, regrouped into the diversion type plants without dams, the weir type plants and the river current systems type plants (using kinetic energy devices), can involve penstock pipes, open channels, barrages and other diversion methods.

In the diversion type plants without dams, a portion of the water diverted from fast flowing rivers can be used directly to feed a penstock. This will move the water down to the turbine (Fig.  2 a), whereas in other cases, the intake system instead feeds a diversion channel first before reaching the penstock passing through a forebay tank (Fig.  2 b) (Aquaret, 2012 ; Publishers, 2015 ).

Run-of-river in diversion type plants a without forebay tank and b with forebay tank

In the weir type plants (Fig.  3 a, c), the capacity of the system is directly linked to the existing flow of water through the dam which maintains the river flow (Penche, 2004 ; Publishers, 2015 ). There is also a weir type plant where the water of the river damned with a weir is allowed to flow through low-head turbines housed in the weir to generate electricity (Fig.  3 b) (Aquaret, 2012 ; Publishers, 2015 ).

Run-of-river in weir type plants a directly linked to the existing flow of water with floating intake b with flow through low-head turbines housed and c directly linked to the existing flow of water with protected intake

The river current systems type plants are using kinetic energy devices (reaction turbines, small bulb turbines, underwater turbines, oscillating hydrofoils, and venturi devices) installed directly into flowing water to harness the kinetic energy of the water of the river; hence, these systems are generally small. This type can make use of existing structures such as bridges (Aquaret, 2012 ; Publishers, 2015 ) (Fig.  4 ).

Run-of-river in river current systems type

Generally, run-of-river hydropower projects deal with two main activities. One main activity includes civil works, such as diversion weir and intake, desilting chamber, power channel including headrace channel, forebay and spillway, penstock, powerhouse building, or tailrace channel. The other main activity includes electromechanical equipment, namely turbines with governing systems and generators with excitation systems, switch gears, control and protection equipment, among others, which are all sheltered by the powerhouse (Mishra et al., 2012 ; Vougioukli et al., 2017 ; Yildiz & Vrugt, 2019 ).

As introduced, there are several configurations and components to take into consideration while dealing with run-of-river hydropower projects, of which the penstock and the turbine turn out to be the most relevant, hence heavily discussed in this study. After discussing the models for the design of a penstock (diameter and thickness), then the choice of the appropriate selection and implementation of the turbine (admissible suction head) for a given run-of-river without pondage project will be detailed.

The models presented in this review are appropriate for the design of a run-of-river hydropower plant that has a penstock and no reservoir, independently of the configuration chosen. Changes can occur if there is a reservoir because its presence will make sure that the flow reaching the turbine is not always the direct flow of the stream available for the plant, but this case will not be discussed in this paper.

Penstock models

To make the right choice of a penstock for a project, materials, diameter, wall thickness, type of joint and relative cost must be taken into account (Fraenkel et al., 1999 ; Penche, 2004 ).

Several methods used to determine the diameter and the wall thickness of the penstock of a small hydropower plant are presented in this subsection (Fig.  5 ).

Calculation models of the penstock diameter

To calculate the diameter of a penstock, one of the equations presented in the Table 1 can be used considering its limits.

Selecting a diameter can also be an iterative process. It is even the best way of selecting the appropriate diameter of a penstock since all the formulae have their limits. This method involves starting with a first estimate of what might be a suitable diameter obtained via one of the formulae of Table 1 and then adjusting that estimate according to the calculated head losses and the price (Fraenkel et al., 1999 ).

For example, the objective can be the restriction of the total head loss between 2 and 10%. Usually, the head loss is less than 4% according to the ESHA standard (Obinna Ajala Chinyere & Emmanuel Osiewundo Ojo, 2017 ). While using this method, one of the formulae of the Table 1 can be used for a first estimation of the diameter, which will serve as a guide diameter; the first value for the iteration process to get the best penstock. Obinna et al. ( 2017 ) proceeded like that using the first empirical Eq. (5) of the Table 1 to calculate the first estimate of a diameter to design a penstock for Kuchigoro Small Hydro Project.

Calculation models of the penstock thickness

The thickness of the penstock must be able to guarantee sufficient rigidity to withstand the maximum possible overpressure, which occurs when the valve that links the penstock to the turbine is closed in a short time (Fraenkel et al., 1999 ). This means that the determination of the minimum thickness of a penstock depends on the expected surge pressure and the properties of the penstock (Fraenkel et al., 1999 ).

The surge pressure head is calculated by the Eqs. ( 1 ), ( 2 ), ( 3 ) and ( 4 ) below:

where h surge

h surge : Surge pressure head (m)

h max : Maximum possible pressure (m)

h gross : Gross head (m)

C : Velocity of the pressure wave through the water (m/s)

V : Flow velocity with valve fully open (m/s)

\(\rho\) : Density of water (kg/m 3 )

\(k\) : Bulk Modulus of water (N/mm 2 )

\(E\) : Young’s Modulus of Elasticity for penstock material (N/m 2 )

\(D\) : Penstock diameter (mm)

\(e\) : Penstock wall thickness (mm)

e min : Penstock minimum wall thickness (mm)

\(:\) Gravitational acceleration (m/s 2 )

\(\sigma\) : Ultimate tensile strength of penstock material (N/mm 2 )

\(F\) : Safety factor, typically 3.

It is worth noticing that the expressions of the minimum thickness \({e}_{\text{min}}\) and the expected surge pressure \({h}_{\text{surge}}\) are mutually dependent. Hence, an iterative approach is needed to estimate the value of the thickness (Fraenkel et al., 1999 ).

The algorithm allowing the calculation of the thickness of a penstock is presented as below (Fraenkel et al., 1999 ):

Initialize a first estimate of \({e}_{0}\)

Calculate c, \({h}_{\text{max}}\) and \({e}_{\text{min}}\) for the current iteration i

Compare \({e}_{i}\) and \({e}_{\text{min}}\) :

if \({e}_{i}<\)   \({e}_{\text{min}}\) , update \({e}_{i+1}={e}_{i}+\Delta {e}_{i}\) and go to 2

if \({e}_{i} \gg\)   \({e}_{\text{min}}\) , set \({e}_{i+1}={e}_{\text{min}}\) , and go to 2

if \({e}_{i} \cong {e}_{\text{min}}\) and \({e}_{i}\ge {e}_{\text{min}}\) , go to 4

\({e}_{i}\) should be increased by 1.5 mm while dealing with mild steel pipes to take into consideration corrosion effects.

According to Ramos et al. ( 2000 ), the most dangerous situation the penstock must withstand occurs when it is subjected to a great depression due to the appearance of the vacuum. Thus, the minimum thickness a steel penstock with a diameter D must have to withstand such condition is calculated through the inequation below:

While using this method, 1 mm must be added to the value of the penstock thickness calculated to take into account the effects of corrosion (Ramos et al., 2000 ). In the numerical model of Yildiz and Vrugt ( 2019 ), the minimum thickness of the penstock is calculated using this method.

ESHA (Penche, 2004 ) also proposed other equations for the estimation of the minimum wall thickness that will make the penstock rigid enough to be handled without danger of deformation in the field. The equations are presented below:

where D is the diameter in m

where D is the diameter in mm.

The Eq. ( 23 ) with an additional margin of 1.2 was also used for feasibility studies of micro-hydro-power plant projects in Cameroon (Kengne Signe et al., 2017 a; Kengne Signe et al., 2017 b).

In conclusion, for the calculation of the thickness of a penstock, Eqs. ( 1 ), ( 2 ), ( 3 ) and ( 4 ) seem to be better appropriate since they can be used for all types of penstock material compared to the other models used only for steel pipes. However, their iteration process makes them a relatively more complex model that needs higher computational time and resources to be used, yet modern computers are well capable of bearing the burden.

Equations ( 22 ) and ( 23 ) guarantee the survival of the penstock during its manipulation in the field. This is why it might be more cautious to calculate three minimum thicknesses using Eq. ( 3 ), ( 22 ) and ( 23 ) to ultimately choose the largest value.

Models for the selection of hydraulic turbines

Turbine is made of (1) a nozzle that directs the flow to the runner, (2) a runner that converts the hydraulic energy into mechanical work and (3) a shaft that transfers the mechanical work to the electrical generator (Sangal et al., 2013 ), components that altogether determine the flexibility options and total energy production from the water flow. Commonly, there are two principal categories of hydro-turbines: impulse turbines, such as Pelton, Cross-flow and Turgo, for sites with high head and reaction turbines, such as propeller, Kaplan, Francis, screw and hydro-kinetic turbines, for sites generally with lower head and higher flows (Okot, 2013 ; Sangal et al., 2013 )). Typically, the head and flow available on a site are the principal criteria that orientate the choice of a hydro turbine for a given project (Paish, 2002 ). Nevertheless, it is also important to use the efficiency curves of turbines (like the one of Fig.  6 ) to know how the turbines will react to variations in flow rates and therefore determine the one which is the most suitable for a given installation site and river system (Okot, 2013 ; Yildiz & Vrugt, 2019 ).

Typical small hydro-turbines efficiencies (Chapallaz et al., 1995 )

Determination models of the nominal discharge

The choice of the nominal flow is important since the height of a proposed site does not really vary meanwhile the available flow varies a lot (Bezabih, 2021 ). Based on the flow duration curve, it is possible to determine the nominal flow of a hydropower plant. It is the maximum flow rate that can pass through the penstock and the turbine without causing inadmissible energy losses (Dubas & Pigueron, 2009 ). The nominal flow must be chosen carefully to have a hydro-project profitable and efficient enough. A good choice should make sure the plant works all the time at its maximum capacity while exploiting efficiently the hydraulic energy of the water (Dubas & Pigueron, 2009 ).

There are different ways to choose the nominal flow of a hydropower plant. The simplest way is to fix the mean annual flow as the nominal flow. In the work of Adejumobi and Shobayo ( 2015 ) on the optimal choice of turbines for small hydropower plants, the average annual flow has been considered as the nominal flow. According to Heteu and Martin ( 2001 ), the choice of the nominal flow depends on the use of the plant. If the hydropower plant is the only source of supply to the consumer or the mini-grid, the nominal flow is the flow reached for at least 250 days a year. Otherwise, the production must be the most important factor and the optimum flow in that case will be around a flow reached for a period between 50 and 90 days a year. This methodology was used for feasibility studies of micro-hydro-power plant projects in Cameroon while assessing the fall river of Kemken and Bakassa (Kengne Signe et al., 2017 a; Kengne Signe et al., 2017 b). For those two projects, systems were decentralized, and the flow rate of equipment used was the one, which exceeded 250 days per year (Kengne Signe et al., 2017 a; Kengne Signe et al., 2017 b). In the same way, Hanggi and Weingartner ( 2012 ) also mentioned in their work that the choice of the nominal flow depends on the desired operation or purpose of the hydropower plant. They recommended that for hydropower plants operating in an isolated network, the approximate values of the nominal flow should be less or equal to the flow reached for at least 255.5 days a year while that for hydropower plants in parallel operation should be between the flow reached for at least 54.75 days to 91.25 days a year.

According to Alexander and Giddens ( 2008 ), the equation below can also be used to find the optimum discharge for any diameter.

where \(\lambda\)  is the friction factor determined by the surface roughness of the penstock material (–), \({H}_{\text{g}}\text{ is}\) the gross head (m), S  is the penstock slope = \({H}_{\text{g}}\)  / L (–), D is the diameter of the penstock (m) and h is the head loss (m).

As with the formula of the calculation of the diameter of a penstock relying on the cost and the slope of the penstock presented in Table 1 (Eq. (17)), the objective is to have the head loss h = \({H}_{\text{g}}\)  /3 to achieve maximum power.

Voros et al. ( 2000 ) worked on how to design small hydroelectric plants while maximizing the economic benefits of the investment and they proposed an empirical equation allowing determining the optimum nominal flow rate of the hydro-turbines and concluded that it can be used safely for short-cut design purposes. This empirical equation is presented below:

where \({q}_{*50}\) is flow rate duration curve parameter, defined as \(/\) , \(q_{*\min }\) is flow rate duration curve parameter, defined as \(Q_{*\min }\) \(/\) , \(q_{\max }\) is hydro turbine maximum working flow rate fraction, Q max is annual highest stream flow rate (m 3 /s) and \(\gamma\) is short-cut model parameter with the values 0.422 for Francis turbines, 0.369 for Pelton turbines and 0.364 for Axial turbines.

In the study of Munir et al. ( 2015 ), a new parameter, known as the inverse incremental energy was used to select the optimum flow of the hydropower plant at head of Upper Chenab Lower (UCC) at Bamanwala. The nominal flow was selected through comparison of increment of energy with respect to change in flow. A relationship between inverse incremental energy and flow was plotted for the selection of the appropriate flow.

In conclusion, as seen above, there are several methodologies for the determination of the nominal discharge of a small hydropower project. Each of these methods can be used in specific contexts and situations as a starting point for the assessment of the potential of hydropower sites. However, to determine the best nominal discharge for a better exploitation of the energy potential of a natural stream or for a more economical project, we recommend using of an optimization algorithm related to appropriate objectives functions.

Selection of the appropriate type of turbine

The net head is the first criterion to estimate a suitable turbine for a hydropower project (Pagès et al., 2003 ; Paish, 2002 ; Penche, 2004 ) and Table 2 gives the range of operating heads by type of turbine.

A first technique used in the selection of turbines makes use of charts like that in Fig.  7 that depict the expected suitable ranges of net head and water flow admissible by technology (Paish, 2002 ; Penche, 2004 ). However, it is important noticing that the specific curve is strictly manufacturer-specific; hence, that plot shall be used as a preliminary reference.

: Typical range chart of turbines (Chapallaz et al., 1995 )

Another criterion that can also orientate in the selection of the appropriate turbine type is the specific speed. The specific speed is the speed in rpm of a turbine with a unit head and a unit output power. Impulse turbines have low specific speeds; Francis turbines have medium specific speeds and propeller or Kaplan have high specific speeds (Ramos et al., 2000 ). The specific speed of a turbine can be calculated as follows:

where \(Q\) is the discharge in m 3 /s, \(n\) the rotational speed of the turbine in rpm, \(E\) the specific hydraulic energy of the machine in J/kg, \(f\) the frequence of the electric system in Hz, \(p\) the number of pairs of poles of the trubine’s generator, \(g\) the gravitational constant in m/s 2 and \({H}_{\text{net}}\) the net head in m.

Without a speed increaser, the rotational speed of the turbine has the same value than the rotational speed of its generator. The rotational speeds of asynchronous generators will be 1 to 2% higher than the value of rotational speeds of the corresponded synchronous generators, a slight over-speed being necessary to create the magnetic field in the machine (Chapallaz et al., 1995 ).

According to Chapallaz et al. ( 1995 ), the maximum speed of the generator must be limited to 1500 rpm to consider the over-speeding of the runaway. Over-speeding causes very significant mechanical stress, and the minimum speed limited to 600 rpm, as because below this speed, the volume of the generator, hence its price compared to the installed power, increases with a decline in yield due to increased losses. When the rotational speed of the turbine is less than 600 rpm, it usually drives a generator with a low number of poles (1000 or 1500 rpm) via a speed increaser.

Thus, after calculating the specific speed of a hydro-project, the appropriate type of turbine can be selected through the Table 3 , which describes the operating speed limits by turbine.

This way of characterizing turbines through the specific speed was even used in the numerical model of Yildiz and Vrugt ( 2019 ).

Generally, in the prefeasibility study phase, the head and the design flow rate are used to select the appropriate type of turbine for a project since usually there is no enough information to calculate the specific speed. The choice of the methodology for selecting the type of turbine requires this level of information.

Cavitation model

The cavitation phenomenon occurs when a high-enough negative pressure occurs at the exit of the wheel, such as when a reaction turbine is located well above the downstream plan. In those conditions, water vaporizes and the corresponding vapor bubbles first detach from the surface of the runner blade and then implode creating strong pressure waves as soon as they reach an area where pressure is higher. As these implosions cause fast erosion of the blades, they must be avoided by accurately design the turbine discharge to limit the depression at its exit. To do so, the so-called suction head H S , which measures the distance between the downstream plan of water and the axis of the wheel of the turbine, shall be limited.

To reduce the construction costs, a reaction turbine shall be placed as high as possible in reference to the downstream level, but this increases the value of H S and cavitation may occur. Therefore, to protect turbines, it is important to know the suction head threshold beyond which cavitation appears relevant enough to damage the wheel during the implantation of a turbine. In mathematical terms, H S is calculated as follows (Penche, 2004 ):

where \({H}_{\text{s}}\) (m) is the limited suction head, \({H}_{\text{a}}\) (m) is the water height equivalent to atmospheric pressure, H v (m) is the water height equivalent to the vaporization pressure, H (m) is the net head, V (m/s 2 ) is the outlet average velocity (as a first approach, one can consider 2 m/s according to ESHA (Penche, 2004 )) and σ is a dimensionless coefficient called the Thomas’s coefficient.

\({H}_{\text{a}}\) can be calculated with the formula below (Yildiz & Vrugt, 2019 ):

where \({P}_{0}\) is the atmospheric pressure in Pa at sea level and \(z\) is the altitude of the power house in m.

\(\sigma\) can be calculated with the equations below (Penche, 2004 ):

where V is the outlet average velocity in m/s 2 and H the net head in m.

In the techno-economical method for sizing the capacity of a small hydropower plant by Santolin et al. ( 2011 ), the limited suction head was also calculated with the equation above but with different equations for the calculation of the Thomas’s coefficient: \(\sigma\) was calculated with the equations below:

where \({\omega }_{\text{s}}\) is the dimensionless specific speed (with values lying in the intervals [0.04, 0.40] for Pelton turbines, [0.4, 1] for Slow Francis turbines, (Safarian et al., 2019 ; Yildiz & Vrugt, 2019 ) for Normal Francis turbines, [2.0, 2.5] for Quick Francis turbines and [2.5, 8.0] for Kaplan turbines) and \(\omega\) the rotation velocity in rad/s.

Turbine operation models

It is worth noticing that each turbine can only operate between a minimum and a maximum flow rate, reflecting its limit in exploiting the available hydraulic energy. Hence, in a hydropower plant where there is only one turbine, the power output of the turbine can be represented as follows (Anagnostopoulos & Papantonis, 2007 ; HOMER, 2019 ):

\({Q}_{\text{exploited}}\) : Exploited discharge (m 3 /s).

\({Q}_{\text{exploitable}}\) : Exploitable discharge (m 3 /s).

Q min : Minimal discharge (m 3 /s).

Q miax : Maximal discharge (m 3 /s).

The minimal discharge is usually given as a percentage of the rated discharge (Penche, 2004 ), whose values by turbine type are reviewed and summarized in Table 4 .

Hanggi and Weingartner ( 2012 ) proposed a new parameter \(Q_{{{\text{safety}}}}\) , which is the safety flow beyond which the turbine operation has to be to avoid damages. By taking into account this new security constraint, the new operating schedule below emerged: (Yildiz & Vrugt, 2019 ):

Hanggi and Weingartner ( 2012 ) recommended to set \(Q_{{{\text{safety}}}}\) equal to the river discharge with an exceedance probability of 2% and it was done by Yildiz and Vrugt ( 2019 ) in their work.

It is worth mentioning that in most hydro-projects, environmental regulation mandates a minimum non-usable to bypass the hydropower plant to limit damages to the ecosystem. There are several hydrological-based environmental flows methods, which allow estimating this minimum flow. According to Kuriqi et al. ( 2019 ), the choice of 10% or 15% daily flow as minimum flow, methods named 10% or 15% Daily Flow, is considered appropriate. One of the methods can be used as reference method and can be combined with other methods.

Accordingly, the exploitable flow is obtained by the equation:

where \(Q\) Exploitable : Exploitable flow (m 3 /s).

\(Q\) river : Flow of the river (m 3 /s).

Q f : Reserved flow (m 3 /s).

However, given the variability of the river flow across the year and the operating schedules above, the efficient exploitation of a hydraulic resource, particularly in run-of-river plants with one turbine, can be challenging. For this reason, multiple turbines of different size operated in parallel may be used to enhance overall exploitation of the potential energy, but project, operation and maintenance costs may rise. This financial constraint limits most models to two turbines in practical terms (Anagnostopoulos & Papantonis, 2004 , 2007 ).

While dealing with two turbines, the operating schedule is a bit more complex. Two examples of operating schedule in the case of two turbines of different size working in parallel have been seen in the literature.

The first example is the methodology of Anagnostopoulos and Papantonis ( 2007 ) that does not consider the parameter \({Q}_{\text{safety}}\) , conversely to the second example of Yildiz and Vrugt ( 2019 ).

Calculation model of the energy production

The electric power generated by each turbine can be calculated using the formula below (RETScreen International, 2001 ):

where D : diameter of the penstock (m), \(L\) \(:\) Penstock length (m), \(:\) friction factor from moody chart of Darcy’s equation (–), \(V\) \(:\) velocity of water at the time t (m/s), \(\Delta H_{{{\text{major}}}}\) : losses due to friction (m), \(\Delta H_{{{\text{minor}}}}\) : singular or local losses (m), \(\varepsilon\) : coefficient of singular loss (–), P elec \(:\) electric power the time t (kW), \(\rho\) : density of water (kg/m 3 ), \(g\) \(:\) gravitational acceleration (m/s 2 ), Q t , k : exploited discharge of the turbine number k at the time t (m 3 /s), \(h_{{{\text{net}}}}\) \(:\) Net head (m) \(,\) : gross head (m) \(,\) : efficiency of the turbine number k at the time t (%) \(, :\) efficiency of the generator (%), \(l_{{{\text{trans}}}}\) \(:\) the transformer losses (–) \(,:\) line losses (–).

The calculation of turbine efficiencies can be done with the efficiency equations presented in the Retscreen engineering and cases textbook (RETScreen International, 2001 ) which are derived from a large number of manufacture efficiency curves for different turbine types and head and flow conditions. Gagliano et al. ( 2014 ) to evaluate the technical feasibility of repowering an old Silican hydro-power plant also used this equation for the calculation of electric power by a turbine. The results of the simulation were sufficiently reliable.

The amount of energy E in kilowatt hours (kWh) produced by n turbines of a run-of-river hydropower plant over a time period \(\Delta\) t can be calculated using the formula below

Equation ( 43 ) is one of the most general energy calculation formulae identified in the literature since it takes into account not only the electrical losses of all equipment (turbine, alternator, transformer), but also all types of line losses, such as those due to a parasitic load or an inappropriate cable section. The efficiency of the increaser should also be considered when it is needed between the turbine and the generator. Although the evolution of the generator efficiency with load is not considered in this equation, it generally gives a good representation of the total energy production, when the average efficiency is considered (Yildiz & Vrugt, 2019 ).

It is important to note that in grid-connected applications, all the potential energy that the hydro-power plant can generate is usually sold, unless grid outages occur. Instead, in off-grid applications depending on the actual load, the hydro-power plant may not be exploited completely and renewable production may be curtailed. This article focuses on the generation system, which can then be connected to the grid or enable a mini-grid or off-grid system. However, the issue of distribution of the generated energy is not discussed in this article.

There are also three indices, namely the energy production index \({E}_{f}\) , the load index \({L}_{f}\) and the water exploitation index \({W}_{f}\) , which can be useful for the assessment of the efficiency of a hydropower plant. \({W}_{f}\) denotes the fraction of the stream flow that passes through the operating turbines, \({E}_{f}\) is the sum of the generated energy divided by the energy potential of the natural stream at a gross head during a year period and \({L}_{f}\) is the ratio of the mean (annually) produced power to the installed nominal power (Anagnostopoulos & Papantonis, 2004 , 2007 ).

Cost estimation models of small hydropower projects

While dealing with a small hydropower project, it is important to evaluate its financial viability along with technical feasibility before taking any investment decision. That is the reason why several researchers developed multiple models for the estimation of the cost of a small hydropower project defining different cost-influencing parameters, which represent the variables of the equations. The most common cost-influencing parameters are the power and the net head.

Singal and Saini ( 2007 ) made an analysis for the cost of canal-based small hydropower schemes in the plains and other regions of the country in which water is used also for other purposes, like irrigation/drinking through canals, small dams, etc., and developed the correlation in Eq. ( 43 ) for estimating the cost of such schemes. The results of the correlation showed a maximum deviation of ± 12%, so the correlation can be used to predict the cost of a small hydropower plant at the planning stage.

Another study carried out by Singal et al. ( 2008 ) on the cost optimization based on electromechanical equipment of canal-based low-head (3–20 m) small hydropower scheme proposed correlations for the cost in Indian Rupees per kilowatt of the main components. These main components include civil works (diversion channel, spillway and power house building) and electromechanical equipment (turbine with governing system, generator with excitation system, control and protection equipment, electrical and mechanical auxiliaries, and main transformer and switchyard equipment). The correlations are presented below:

\(\text{Cost of diversion channel}\) : \(C_{1} = a_{1} P^{{x_{1} }} H^{{y_{1} }}\) (45)

\(\text{Cost of spillway}\) : \(C_{2} = a_{2} P^{{x_{2} }} H^{{y_{2} }}\) (46)

\(\text{Cost of power house building}\) : \(C_{3} = a_{3} P^{{x_{3} }} H^{{y_{3} }}\) (47)

\(\text{Cost of turbines with governing system}\) : \(C_{4} = a_{4} P^{{x_{4} }} H^{{y_{4} }}\) (48)

\(\text{Cost of generator with excitation system}\) : \(C_{5} = a_{5} P^{{x_{5} }} H^{{y_{5} }}\) (49)

\(\text{Cost of electrical }\&\text{ mechanical auxiliaries}\) : \(C_{6} = a_{6} P^{{x_{6} }} H^{{y_{6} }}\) (50)

\(\text{Cost of transformer }\&\text{ switchyard equipment}\) : \(C_{7} = a_{7} P^{{x_{7} }} H^{{y_{7} }}\) (51)

with \({a}_{1}=9904, {x}_{1}=-0.2295, {y}_{1}=-0.0623\)

\({a}_{3}\) , \({x}_{3}\) , and \({y}_{3}\) can be obtained via Table 5 and the other coefficients via Table 6 .

The total project cost includes the cost of civil works, the direct cost of electromechanical equipment and various items, and other indirect costs. This miscellaneous and indirect cost (that includes the costs of designs, indirect costs, tools and plants, communication, preliminary charge of preparing the report, survey and investigation, environmental impact assessment and cost of land) represents 13% of the sum of the cost of civil works and electromechanical equipment. Thus, the total cost of the project in this case can be calculated through the equation below:

In the work of Singal et al. ( 2010 ) on the analysis for cost estimation of low-head (3–20 m) run-of-river small hydropower schemes, other correlations were proposed for estimating the costs of several subcomponents of civil works. This includes diversion weir and intake, desilting chamber, power channel including head race channel, forebay and spillway, penstock, powerhouse building and tail race channel and electromechanical equipment (turbine with governing system, generator with excitation system, control and protection equipment, electrical and mechanical auxiliaries, main transformer and switchyard equipment). The correlations are presented below:

\(\text{Cost of power house building}\) : \(C_{1} = 92615P^{ - 0.2351} H^{ - 0.0585}\) (55)

\(\text{Cost of diversion weir and intake}\) : \(C_{2} = 12415P^{ - 0.2368} H^{ - 0.0597}\) (56)

\(\text{Cost of power channel}\) : \(C_{3} = 85383P^{ - 0.3811} H^{ - 0.0307}\) (57)

\(\text{Cost of desilting chamber}\) : \(C_{4} = 20700P^{ - 0.2385} H^{ - 0.0611}\) (58)

\(\text{Cost of forebay and spillway}\) : \(C_{5} = 25402P^{ - 0.2356} H^{ - 0.0589}\) (59)

\(\text{Cost of penstock}\) : \(C_{6} = 7875P^{ - 0.3806} H^{ - 0.3804}\) (60)

\(\text{Cost of tail race channel}\) : \(C_{7} = 28164P^{ - 0.376} H^{ - 0.624}\) (61)

Finally, the cost in Indian Rupees per kilowatt of civil works is

\(\text{Cost of turbines with governing system}\) :

\(\text{Cost of generator with excitation system}\) :

\(\text{Cost of electrical }\&\text{ mechanical auxiliaries}:\)

\(\text{Cost of transformer }\&\text{ switchyard equipment}\) :

Finally, the cost in Indian Rupees per kilowatt of electromechanical equipment is

For the same reasons mentioned in the work of Singal et al. ( 2008 ), the total cost of the project in this case too will be calculated through the Eq. ( 53 ).

Ogayar and Vidal ( 2009 ) developed correlations to estimate the cost of the electromechanical equipment (turbine, alternator and regulator) based on the head and the power. Here, we have an equation for each type of turbine: Pelton, Francis, Kaplan and semi-Kaplan for a power range below 2 MW. The results of these equations can be used to determine the initial investment at a previous study level when planning refurbishment or new construction of small hydropower plants without developing a complete project. These equations had been validated with real installations in different countries of the world (Spain, France, Italy, Belgium, Portugal, and Morocco) with committed errors lower than 20%. Santolin et al. ( 2011 ) used these equations in their techno-economical method for capacity sizing of a small hydropower plant to determine the machine cost. They were even updated by Gallagher et al. ( 2015 ) in his four-step methodology for assessing potential energy recovery sites in water and wastewater infrastructure in the UK and Ireland.

The correlations obtained were:

\(COST = 17.693P^{( - 0.3644725)} H^{( - 0.281735)}\) (68) in €/kW for Pelton turbine with errors ranged between − 23.83% and 20.015% ( R 2  = 93.16%);

\(COST = 25.698P^{( - 0.560135)} H^{( - 0.127243)}\) (69) in €/kW for Francis turbine with errors ranged between − 15.83% and 22.27% ( R 2  = 72.26%);

\(COST = 33.236P^{( - 0.58338)} H^{( - 0.113901)}\) (70) in €/kW for Kaplan turbine with errors ranged between − 18.53% and 23.5% ( R 2  = 91.7%);

\(COST = 19.498P^{( - 0.58338)} H^{( - 0.113901)}\) (71) in €/kW for Semi-Kaplan turbine with errors ranged between − 18.53% and 23.5% ( R 2  = 91.72%).

Mishra et al. ( 2011a ) also developed correlations for the estimation of the cost of the electromechanical equipment (turbine-alternator) in run-of-river small hydropower projects based on the head and the power. They used three different methods: sigma plot method, linest method and logest method. The results obtained from these correlations were verified from the data of electro-mechanical equipment of installed small hydropower projects. The results of the sigma plot software had a maximum error of ± 10%, the ones of the linest method had a maximum error of ± 5% and the ones of the logest method had a maximum error of ± 18%. Therefore, they are regarded as suitable for the preliminary cost estimation of the electromechanical equipment in small run-of-river hydropower projects.

(Sigma plot method)

(Linest method)

(Logest method)

In the review of Mishra et al. ( 2012 ) on electromechanical equipment applicable to small hydropower plants, other correlations developed for the cost of run-of-river small hydropower projects under low head (3–20 m) considering the head and the power were presented. Here, there is an equation for the cost estimation of turbines with governing system \(( {C}_{\text{t}}\) ), an equation for the cost estimation of generators with excitation system \(( {C}_{\text{g}}\) ), an equation for the cost estimation of electrical and mechanical auxiliaries \(( {C}_{\text{e}}\) ) and another one for the estimation of the cost of transformers and switchyard equipment \(( {C}_{\text{tr}}\) ). The equations are presented below:

where \({C}_{\text{e}\&\text{m}}\) is the cost per kilowatt of electromechanical equipment, H the net head in m and P the power in kW.

Mishra et al. ( 2011b ) proposed other correlations for the estimation of the investment cost of an entire small hydropower scheme under low head plants. There were formulas for civil works and formulas for electromechanical equipment.

For civil works, we have:

Intake (C 1 ): \(14382P^{( - 0.2368)} H^{( - 0.0596)}\) (76) with one unit, \(17940P^{( - 0.2366)} H^{( - 0.0596)}\) (77) with two units, \(21191P^{( - 0.2367)} H^{( - 0.0597)}\) (78) with three units and \(24164P^{( - 0.2371)} H^{( - 0.06)}\) (79) with four units;

Penstock (C 2 ): \(4906P^{( - 0.3722)} H^{( - 0.3866)}\) (80) with one unit, \(7875P^{( - 0.3806)} H^{( - 0.3804)}\) (81) with two units, \(9001P^{( - 0.369)} H^{( - 0.389)}\) (82) with three units and \(10649P^{( - 0.3669)} H^{( - 0.3905)}\) (83) with four units;

Power house building (C 3 ): \(62246P^{( - 0.2354)} H^{( - 0.0587)}\) (84) with one unit, \(92615P^{( - 0.2351)} H^{( - 0.0585)}\) (85) with two units, \(121027P^{( - 0.2354)} H^{( - 0.0587)}\) (86) with three units and \(146311P^{( - 0.2357)} H^{( - 0.0589)}\) (87) with four units;

Tailrace channel (C 4 ): \(28164P^{( - 0.376)} H^{( - 0.624)}\) (88) with one unit, \(28164P^{( - 0.376)} H^{( - 0.624)}\) (89) with two units, \(28164P^{( - 0.376)} H^{( - 0.624)}\) (90) with three units and \(28164P^{( - 0.376)} H^{( - 0.624)}\) (91) with four units.

For electromechanical equipment, we have:

Turbine with governing system (C 5 ): \(39485P^{( - 0.1902)} H^{( - 0.2167)}\) (92) with one unit, \(63346P^{( - 0.1913)} H^{( - 0.217)}\) (92) with two units, \(83464P^{( - 0.1922)} H^{( - 0.2178)}\) (93) with three units and \(101464P^{( - 0.1920)} H^{( - 0.2177)}\) (94) with four units;

Generator with excitation system (C 6 ): \(48568P^{( - 0.1867)} H^{( - 0.2090)}\) (95) with one unit, \(78661P^{( - 0.1855)} H^{( - 0.2090)}\) (96) with two units, \(105046P^{( - 0.1859)} H^{( - 0.2085)}\) (97) with three units and \(127038P^{( - 0.1858)} H^{( - 0.2085)}\) (98) with four units;

Mechanical and electrical auxiliaries (C 7 ): \(31712P^{( - 0.1900)} H^{( - 0.2122)}\) (99) with one unit, \(40860P^{( - 0.1892)} H^{( - 0.2118)}\) (100) with two units, \(49338P^{( - 0.1898)} H^{( - 0.2080)}\) (101) with three units and \(56625P^{( - 0.1896)} H^{( - 0.2121)}\) (102) with four units;

Main transformer and switchyard equipment (C 8 ): \(14062P^{( - 0.1817)} H^{( - 0.2082)}\) (103) with one unit, \(18739P^{( - 0.1803)} H^{( - 0.2075)}\) (104) with two units, \(23051P^{( - 0.1811)} H^{( - 0.2080)}\) (105) with three units and \(26398P^{( - 0.1809)} H^{( - 0.2079)}\) (106) with four units.

Thus, the formula to calculate the total cost per kW (Rs) is \({\mathbf{1}}.{\mathbf{13}}(C_{1} + \, C_{2} + \, C_{3} + \, C_{4} + C_{5} + \, C_{6} + \, C_{7} + \, C_{8} )\) (107).

Yildiz and Vrugt ( 2019 ) computed the cost of electromechanical equipment (turbine, generator and power transformer) using the equation of Ogayar and Vidal ( 2009 ):

where j is the exchange rate of euro to US dollar, P is the installed capacity of the plant in MW, a , b and c are coefficients of calculation depending on the type of turbine used. The multiplication factor 1/1000 converts the units of P from MW to kW. The cost of the penstock was calculated with the equation below:

where \(D\) , \(k\) and \(L\) are the diameter, the thickness and the length of the penstock in units of meters, \({d}_{s}\) in ton/m 3 denotes the steel density and \({c}_{\text{ton}}\) in $/ton is the penstock cost per ton weight.

The total cost of civil works was calculated with the Eq.  110 below:

where \(\alpha\) is a unitless coefficient called site factor (it can take on values between 0 and 1.5). The yearly maintenance and operation cost \({C}_{\text{om}}\) are estimated using the expression \({C}_{\text{om}}={\beta C}_{\text{em}}\) with \(\beta\) a unitless coefficient whose value ranges between 0.01 and 0.04. It was considered here that the electromechanical equipment has a life-span of about 25 years and the plant has a lifespan of 50 years. Hence, the total monetary investment in this numerical model is estimated using Eq.  111 below:

Dubas and Pigueron ( 2009 ) established a formula given the price, dated September 2009, of electromechanical equipment (the guard valve, the turbine, the generator as well as control-command, safety devices and cabinets) based on series of invoices and offers for this equipment. The formula relies on the maximum hydraulic power as presented in Eq. ( 112 ):

While using this formula, if the price obtained is lower than 20′000 CHF, then 20′000 CHF should be considered as the price. However, this price may vary from single to double depending on the supplier. In addition, this price was related to the specific economic and market situation of that time: when mini-turbines are in great demand, or when the prices of steel or copper prices are high, such as in recent periods, prices increase, making it difficult to be precise.

More recently, Mishra et al. ( 2018 ) developed a methodology for cost assessment of high head (beyond 100 m) run-of-river small hydropower plant projects to determine their techno-economic viability before undergoing detailed investigation. In this work, it is still the capacity and the head that have been considered as cost-influencing parameters. The correlations for cost proposed in this study were based on different types of head race conduit, penstock materials, types of turbine and types of generator for various layouts. It was concluded that these correlations could be used for reasonable cost estimation of hydropower projects for planning of such projects. The costs obtained through these correlations are in Indian Rupees. The correlations of costs are presented in Eqs.  113 and 114 :

Cost per kilowatt of civil works

The equations for the calculation of costs of civil works components presented above are used with Table 7 and considering the prices as per schedule of rates prevailing for the year 2012 in India (Penche, 2004 ). Thus, the prices used are as follows:

The price for earthwork in excavation with all leads and lifts in ordinary soil is 265 Indian Rupee/m 3 ;

The price for earthwork in excavation with all leads and lifts in soft rock, where blasting is not required is 330 Indian Rupee/m 3 ;

The price for earthwork in excavation with all leads and lifts in hard rock, including blasting is 550 Indian Rupee/m 3 ;

The price for M20 grade concrete work in plain cement concrete as well as in reinforced cement concrete, including shuttering, mixing, placing in position, compacting, and curing is 3640 Indian Rupee/m 3 ;

The price for reinforcement steel bars of iron 500 grade, including cutting, bending, binding, and placing in position is 55,000 Indian Rupee/MT;

The price for structural steel, including fabrication, transportation to site, and erection is 75,000 Indian Rupee/MT.

Cost per kilowatt of electromechanical equipment

The electromechanical equipment considered and the value of the constants \({a}_{1}\) , \({x}_{1}\) and \({x}_{2}\) are presented in Table 8 .

For the same reasons mentioned in the work of Singal et al. ( 2008 ), the total cost of a high head run-of-river small hydropower plant project can be calculated through Eq. ( 53 ).

These equations for the estimation of the cost of small hydropower projects presented in this part should be used carefully because they give a rough estimation of the costs of specific markets at specific times.

Conclusion and future scope

This paper presents a detailed review of models for the techno-economic design of a run-of-river hydropower plants. In particular, the technical modeling of the diameter and thickness of a penstock, the optimal selection and implantation (admissible suction head) of the turbine, the estimation of energy production systems and the estimation of the cost of small hydropower projects were extensively reviewed and discussed. These modeling approaches provide a powerful tool for the technical, economical, and financial feasibility study of run-of-river hydropower sites, to feed Artificial Intelligence and optimization algorithms. The limitation and validity of each have been clarified to inform readers on the generalizability of the study, as technology and market conditions evolve.

Therefore, this study can be of interest for scholars and developers interested in developing run-of-river feasibility studies and further research activity, especially in the context of Sub-Saharan Africa. The results of this review could also be used to develop a tool for the preliminary studies of run-of-river hydropower projects.

Availability of data and materials

All data analyzed during this study are included in this published article.

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Acknowledgements

The Cameroon Ministry of Scientific Research and Innovation supported this work under the SETaDiSMA project. The SETaDiSMA project is part of the LEAP-RE programme. LEAP-RE has received funding from the European Union’s Horizon 2020 Research and Innovation Program under Grant Agreement 963530.

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Renewable energy is one of the best option for challenging situation to supply and demand of electricity. Out of all renewable energy sources, hydro gives effective results at different phase. The hydro power plant helps us to generate the electricity from the potential energy of water. Site selection and huge investment are major drawbacks for huge hydro power plant. Instead of creating one large source of energy, we can install the same amount of source by using small or micro hydropower plant on the local river. River being rich source of water and location for installation of small hydro power plant are in favor of India. The design and components of small hydro power plant to be discuss in this paper apart from that, there is a wide range of possibility to improve the performance efficiency of small hydro power plant.

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Chaudhari, A., Chaudhari, G.C. (2023). Review on Micro Hydro Power Plant. In: Banerjee, J., Shah, R.D., Agarwal, R.K., Mitra, S. (eds) Recent Advances in Fluid Dynamics . Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-19-3379-0_34

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Original research article, the effect of precipitation on hydropower generation capacity: a perspective of climate change.

• 1 Ministry of Education Key Laboratory of Resources and Environmental Systems Optimization, North China Electric Power University, Beijing, China
• 2 The Electricity Engineering School, Guangxi University, Nanning, China
• 3 State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing, China

Hydropower, which is the most extensively used renewable energy, is sensitive to the change of streamflow under the great impact of precipitation. According to the relationship between the hydropower station generation and local precipitation, the impact of precipitation on hydropower can be analyzed. In this paper, the global climate model and regional climate model simulations in precipitation are compared firstly, and the high-resolution precipitation data are then calculated by stepwise clustering analysis statistical downscaling method. Secondly, based on the hydropower potential (HP), the hydropower response model driven by precipitation is established. Finally, the simulated generation of a hydropower station in Dadu River basin is used as a case to validate this proposed model. The results show that precipitation will increase by around 42% from May to August in study region, while it will decrease by 40% in other months in RCP4.5. For different periods of reservoir scheduling, the precipitation will increase by about 40% in the Neutral I and Wet period, while it will decrease by around 30% in other periods, which will lead to the shortening of the peak period of hydropower generation and the peak value will be decreased. Correspondingly, the results show power generation will decrease by around 12% from June to December and increase by around 4% in the rest months. On the other hand, owing to the changes in precipitation, the future power generation will increase by 25% in Neutral I and decrease by 13.5% in other periods, but the total hydropower generation will remain. The results can provide some decision support for future water resources management in Dadu river basin, especially for the planning and operation of hydropower stations.

Introduction

According to the IPCC AR5, with the increase of global populations and economies, the man-made emissions of greenhouse gases have remained rising and reached the industrial history peak at the beginning of the 21st century ( IPCC, 2013 ). The global mean temperature at the end of the 21st century will probably be 1.5°C higher than that in 1899–1990 under the influence of current emission trends ( Arnette, 2017 ).

China, which is located in East Asia, has a vast territory, abundant climate zones and complex topography ( Guo et al., 2017a ). Owing to the stronger regional seasonal wind led by global warming, more moisture in the atmosphere will be transported to land areas from ocean, then resulting in more extreme precipitation events in China recently ( Hui et al., 2018 ). For example, ten million residents were displaced and billion dollars economy cost was caused by the Yangtze River flood in 1998 ( Chen and Zong, 2000 ). The serious urban waterlogging events in Beijing in 2012 caused thousands people death and 11.6 billion economic losses ( Zhang D.L. et al., 2013 ).

As one of the effective energies to alleviate the greenhouse effect caused by fossil energy, renewable energy is in a fast-growing demand. Renewable energy has taken 18.2% in world total energy consumption in 2016 ( REN21, 2018 ). In the meantime, the development of renewable energy in China is also rapidly developed. Renewable energy generation, which is up to 1676 TWh, has taken 30% in total national power generation in 2017 ( CREO, 2018 ). Relative to other types of renewable energy, owing to the lowest cost, easier to control and manage and lower intermittent and uncertainly means, hydropower is a kind of the most widely used renewable energies ( Panwar et al., 2011 ; Chu and Majumdar, 2012 ; Jiang et al., 2018 ). In 2017, the new generating capacity of hydropower in China is 9.12 GW, and the total installed capacity reached 341 GW. The hydropower generation has taken almost 20% of total power generation, which is far more than the generation of wind energy (5%) and solar energy (2%). Therefore, more hydropower is planned by China’s government to generate electricity and replace fuel energy ( IHA, 2018 ).

Hydropower is sensitive to climate change, especially for precipitation. Based on the change of runoff, Ali et al. (2018) evaluated and predicted the power generation of seven large hydropower stations in India. Results illustrated that the specific future climate may increase hydropower generation by about 25%. Liu et al. (2016) thought runoff and reservoir storage has a great influence on hydropower, then Generation Hydropower Potential (GHP) and Development Hydropower Potential (DHP) are tested based on 8 Global Hydro Models (GHMs), indicating that GHP will have a 3–6% increase between 2070 and 2099. Obviously, precipitation has a direct influence on basin runoff change, which will finally affect hydropower generation ( Berghuijs et al., 2014 ; Wasko and Sharma, 2017 ). Based on the observed data, Chilkoti et al. (2017) found that generation of hydropower stations and the precipitation have close links, the generation of hydropower stations may rise 39% when the precipitation rise 43%. Above all, climate change has a more direct impact on precipitation, but few studies are analyzing the influence of precipitation changes under the context of global warming on hydropower generation ( Guo et al., 2018 ). Hence, it is significant to explore the relationship between precipitation changes and hydropower generation, and the results could provide some suggestions and measures to the government policy makers in hydropower to response the climate change better.

In this study, stepwise cluster analysis (SCA) statistic method is used to downscale future climate data from PRECIS regional climate model (RCM). Then, the hydropower response model driven by precipitation (HRMDP) is established. Finally, a hydropower station in Dadu River basin is taken as a case to quantitatively analyze future climate change influence on hydropower generation.

Data and Methods

As shown in the Figure 1 , four analysis steps are divided in this paper. The first step is collecting precipitation and power generation data, which include large-scale HadGEM2-ES climate data, observation of meteorological stations and generation data of hydropower stations. Then, the statistical downscaling simulation in precipitation using SCA method is conducted. Specifically, some independent variables in large scale grids in PRECIS RCM, such as precipitation, temperature, humidity and pressure are extracted firstly, afterward, the precipitation in station scale is simulated and projected by the SCA statistic downscaling method. The third step is the establishment of a HRMDP based on the hydropower potential (HP). In the end, we use the projected precipitation under RCP4.5 and RCP8.5 climate emission scenarios to drive the HRMDP to analyze the change in hydropower in the case.

Figure 1. Study flow chart.

Hydropower Response Model Driven by Precipitation

In general, hydropower generation has a close relationship to precipitation. The increase in precipitation will lead to an increase in power generation, and continuous non-precipitation will cause a decrease in power generation ( Chilkoti et al., 2017 ). Figure 2 shows that the daily precipitation and daily power generation of station A in Dadu River basin. The high power generation can be found in a high precipitation period (such as from June to September), while low power generation in low precipitation periods (such as from January to April and December). At the same period, power generation shows an increasing trend with increasing precipitation, and vice versa. According to Figure 2 , we can find that there is a certain relationship between precipitation and power generation, and the power generation is sensitive to the change of precipitation.

Figure 2. Daily precipitation and power generation of a hydropower station in Dadu River basin.

Before establishing the hydropower response model, a new conception – HP is introduced. Hydropower potential is the perfect state power generation which only considers the precipitation as the influence condition, it can be calculated by daily precipitation without considering the actual generating capacity. In this paper, HP mainly depends on the daily precipitation. In addition, continually precipitation factor and non-precipitation factor also have influence on HP, which respectively represents the increased coefficient of power generation in the period of continue precipitation and the decline coefficient of power generation in the period of non-precipitation. The detailed calculation method is as follows:

HP n – HP in the day n , kWh; R n – Precipitation in the day n , mm; σ 1 – The increasing coefficient of generation in the period of continue precipitation, dimensionless; σ 2 – The decline coefficient of generation in the period of non-precipitation, dimensionless; P n – The power generation in the day n , kWh; j – The number of days in some periods.

Hydropower potential represents the optimal power generation under the current precipitation status. Station power generation is not only restricted by natural factors but also influenced by human society factors (such as power policies and plans). Hence, the controllable coefficient, which represents human characteristics, is added to the formula. Formula b is used to restrict the power generation of actual production, and finally achieves the amount of constrained power generation.

HP max – Maximum HP during this period, kWh; HP min – Minimum HP during this period, kWh; P max – Maximum power generation of generator set under the power plan of this period; P m in – Minimum power generation of generator set under the power plan of this period; P F,n – The constrained power generation in day n of the period; δ – The controllable factor, which affected by actual power plan, power policy and more, and it shows as power generation fluctuates at a certain range.

Regional Climate Model

The future precipitation forecasting data are from two climate numerical simulations, which includes HadGEM2-ES and PRECIS. The former is a global climate model (GCM) and is used as the initial and boundary field data to drive the RCM PRECIS for dynamic downscaling. Developed by the UK’s The Met Office Hadley Centre, PRECIS is a high-resolution (25 km) RCM and it has been widely used in regional climate simulations and extreme events forecasting ( Xu et al., 2009 ; Kerkhoff et al., 2014 ; Saini et al., 2015 ; Guo et al., 2017b , 2018 ; Hui et al., 2018 ).

SCA Statistical Downscaling Method

Although the results from RCMs can simulate the climate change of the whole region or basin, the higher-resolution simulations (i.e., station scale) still cannot be met through dynamical downscaling. Therefore, based on the results of RCM, statistical downscaling can be achieved by establishing the numerical statistical relation between the large-scale circulation fields and station-scale climate variables (i.e., precipitation). There are rich methods to be applied, the statistical downscaling has been widely applied in climate change influence analysis on precipitation and hydrology ( Bellouin et al., 2011 ; Jones et al., 2011 ; Wang et al., 2015 ). However, it is necessary to select an appropriate statistical downscaling method to reflect the discrete and random characteristics for precipitation. The SCA uses a cluster tree to illustrate the relationship between the large-scale atmosphere fields and high spatial-resolution variables, especially in effectively dealing with the stochastic and non-linear relationships. Through the integration of missing data detection, correlation analysis, model calibration, cluster tree mapping and other auxiliary function modules, SCA can rapidly develop downscaling scenarios of local weather variables under current and future climate forcing, and performs well in predicting precipitation during the verification ( Chen et al., 2011 ; Yang et al., 2016 ).

As shown in Figure 3 , the first step in the SCA statistical downscaling is to select large-scale forecast factors. Following previous studies, the variables, including mean sea level pressure, surface airflow strength, surface wind direction, near-surface temperature, surface specific humidity, surface relative humidity, surface divergence, surface meridional velocity and more are selected as initial variables ( Duan and Mei, 2013 ; Li and Yan, 2017 ). According to correlation analyze, Near-surface temperature, Surface relative humidity and Mean sea level pressure are selected as independent variables in statistical downscaling ( Wood et al., 2004 ; Perkins et al., 2007 ; Liu et al., 2011 ). The meteorological station precipitation data are selected as dependent variable. Then, the independent variables of statistical downscaling are constituted as X matrix. The dependent variable is constituted as Y matrix. And using R Studio to create site scale precipitation SCA statistical downscaling training model, and build the clustering tree predictor to establish the quantitative relationship between precipitation and large-scale prediction factors.

Figure 3. Stepwise cluster analysis downscaling flow chart.

The data used for validation is divided into the following categories:

1. Climate simulation data. The future climate data from PRECIS are used to drive the power forecasting model. Its initial field and boundary field data as the driving data is from HadGEM2-ES(GCM). HadGEM2-ES is a coupled AOGCM with atmospheric resolution of N96 (1.875° × 1.25°) with 38 vertical levels and an ocean resolution of 1° (increasing to 1/3° at the equator) and 40 vertical levels. HadGEM2-ES also represents interactive land and ocean carbon cycles and dynamic vegetation with an option to prescribe either atmospheric CO 2 concentrations or to prescribe anthropogenic CO 2 emissions and simulate CO 2 concentrations as described. An interactive tropospheric chemistry scheme is also included, which simulates the evolution of atmospheric composition and interactions with atmospheric aerosols. The model time step is 30 min (atmosphere and land) and 1 h (ocean) ( Jones et al., 2011 ). The PRECIS is able to run at two different horizontal resolutions: 0.44° × 0.44° (approximately 50 km × 50 km) and 0.22° × 0.22° (approximately 25 km × 25 km), with 19 atmospheric levels in the vertical using a hybrid coordinate system ( Guo et al., 2017b ).

2. Climate Observation data. The CN05 precipitation data set is used to validate the precipitation results of GCM and RCM. CN05 is a dataset consisting of daily mean, maximum, and minimum temperature on a 0.25 × 0.25° grid has been constructed over mainland China for the 45-years period of 1961–2005. CN05 is derived from interpolating observations from 751 stations distributed throughout the entire Chinese territory except Taiwan. The interpolation follows basically the same approach used in generating the CRU dataset, whereby a gridded climatology is calculated first, and then a gridded anomaly is added to obtain the final data ( Xu et al., 2009 ).

3. Meteorological station data. The observation is used to validate the results of RCM and build the HRMDP. It is from the real-time monitoring stations, including daily precipitation, near-surface temperature, surface relative humidity and surface wind speed.

4. Hydropower station data. The daily power generation data is used to calibrate and verify the simulation results of the power forecasting model.

The Dadu River basin which shown in Figure 4 , is located between 99°42’E–103°48’E and 28°15’N–33°33’N and lies in the transition area of Tibet Plateau and Sichuan Basin. Dadu River basin meets the Minjiang River in Leshan. It is the largest tributary of the Minjiang River and the secondary tributary of the Yangzi River. Dadu River Basin has an abundant hydro resource, which has 7.74 × 10 4 km 2 basin area and a total of 149 tributaries. The mainstream, which is 1062 km long and 48.8 km 3 annual net flow, and has 33730 MW water resource reserve. The annual precipitation of Dadu River Basin is about 800–1000 mm, and the precipitation from May to October takes up 80% of the whole year ( Yang et al., 2017 ). As a key hydropower development area in China, Dadu River basin has many large power stations.

Figure 4. Dadu River basin.

Station A is one of the largest hydropower stations in China, the power capacity of station A is nearly 3.6 million KW, and the reservoir capacity is 5.337 billion km 3 . Due to the greatest power generation in Dadu River Basin and the most abundant water resources, station A is selected as the research object ( Zhang and Xu, 2014 ).

Moreover, according to the precipitation feature of Dadu River basin and power generation plan for station A. Five main power generation periods in a year are divided, which include Dry I (from January to April), Neutral I (May), Wet (from June to October), Neutral II (November) and Dry II (December).

In this paper, we take the power station A as a case and use HRMDP model to build the relationship between meteorological factors and power generation capacity. Then based on the projection in precipitation from dynamical and statistical downscaling results, the influence of precipitation on power generation from 2025 to 2035 will be analyzed.

Simulation and Verification

The results of climate models and their deviations with CN05 in different periods are shown in Figure 5 . Compared with the results of CN05, GCM underestimates the precipitation in most regions of the basin but overestimates the precipitation in the middle of basin. Due to the rough resolutions in GCM, the results of most areas only show a single value. On the other hand, PRECIS improves the spatial resolutions and shows more details in reproducing the precipitation in Dadu River basin, especially in autumn in Figure 6 . The results in PRECIS are similar to the observation, and the deviation is between -1 mm and 1 mm in the midstream. In terms of different periods, Dry II shows a better performance (±1 mm biases) than that in Dry I (∼2 mm). From the spatial distribution, the deviation is between 0 and 1 mm in the upstream, while the value is larger (∼2 mm) in the downstream.

Figure 5. Simulation results and deviation of difference scale models in each period.

Figure 6. Simulation results and deviation of difference scale models in each season.

Figure 7 shows simulation results in annual cycle obtained from GCM and PRECIS. Compared to CN05, PRECIS can simulate the monthly precipitation in Dadu River Basin reasonably. For example, the highest precipitation occurs in June, while the precipitation in January is smaller. Meanwhile, PRECIS shows a great advantage in simulating the monthly mean precipitation relative to its driving GCM. Lots of overestimations in HadGEM2-ES (especially from May to October) are corrected by PRECIS in dynamic downscaling. Overall, the bias of RCM is kept between −0.34 and 3.67 mm, especially in August (∼−0.34 mm).

Figure 7. Monthly mean precipitation and deviation of different scale models and observation data.

Figure 8 is the comparison results between simulation and observation in precipitation data at different spatial scales. The higher in resolutions for climate model, the simulation trend and value of precipitation are closer to the observed data. Specifically, comparing to observation, the simulation results of GCM are overestimated obviously, especially in June or Neutral I, the error is even exceeding 20 mm/day. While the results downscaled by PRECIS have numerous improvements relative to its GCM. However, PRECIS still cannot solve effectively the accuracy in simulating station-scale precipitation. For example, the error is still high in June (about 10 mm) and in Neutral I (about 8 mm). On the other hand, the results from SCA statistical downscaling show the best performance than other simulations. The simulated precipitation is consistent with the observation well. The errors in GCM and PRECIS are reduced greatly, particularly in August and Dry II.

Figure 8. Comparison of precipitation simulation and observed data in different scale models: (A) monthly precipitation; (B) monthly precipitation error; (C) precipitation in period; (D) precipitation error in period.

In terms of the correlations between simulations and observation, SCA downscaling also show its advantage, with a correlation coefficient (about 0.97) and low RMSE value (about 0.16), meaning that there is a great fitting degree and lower biases between the results and observation ( Figure 9 ). Moreover, with the improvement of resolution, the decrease of RMSE is more pronounced. For example, the RMSE is about 68.9 mm/day in July for GCM and about 10.2mm/day for PRECIS, while the RMSE of SCA statistical downscaling is only about 0.5 mm/day. In addition, the RMSEs are different in periods and SCA shows a better performance (∼ 0.16 mm/day) in Dry II periods than that in other periods.

Figure 9. Verification of precipitation simulation and observed data in different scale models: (A) monthly correlation coefficient; (B) monthly RMSE; (C) correlation coefficient in period; (D) RMSE in period.

Overall, compared with coarser-resolution climate models, the simulation results of SCA statistical downscaling can reasonably reproduce the precipitation trend and value. Thus, these results can be used as the input of a subsequent power forecasting model to simulate the power generation of hydropower stations.

Then, through the HRMDP model, we compare the simulated power generation and actual power generation in different months and periods for Station A, which is shown in Figure 10 . Overall, the performance in correlation coefficients and RMSE values are quite satisfactory especially from May to July, which are 0.85 and 232 kWh respectively. The simulation results demonstrate a great performance in Wet period, and the correlation coefficients and RMSE values in different periods are 0.95 and 611 kWh, respectively.

Figure 10. Simulation power generation compare with actual power generation: (A) monthly power generation; (B) power generation in period.

Future Forecasting

The projection in precipitation is the first step to forecast the future power generation through the HRMDP model. The future precipitation and percentage change through SCA downscaling in annual cycle and different periods are shown in Figure 11 . Compared with the historical period, the projected precipitation in annual cycle shows different change trends. Specifically, precipitation will increase by about 20–80% from May to July, while it will decrease in other months. For different periods, precipitation will increase in Neutral I and Wet, which are 79 and 4% respectively. The projected precipitation in other periods shows a decreasing trend, particularly in Neutral II (about 58%).

Figure 11. Future precipitation forecasting: (A) future monthly precipitation; (B) monthly precipitation change; (C) future precipitation in period; (D) precipitation change in period.

The changes in power generation resulting from the precipitation changes in station A in the future are shown in Figure 12 . Compared with the historical period, there is an ascending trend in power generation in station A from January to February and May to July in the future, especially in February with the most increase by about 25%. However, in the rest months, there is a decreasing trend in power generation in station A, for example, the decrease in September will be 36%. Similarly, the power generation will increase by about 20% in future Neutral I period, while there is no obvious change in other three periods relative to the historical period.

Figure 12. Future power generation change: (A) future monthly power generation; (B) monthly power generation change; (C) future power generation in period; (D) power generation change in period.

It is noted that there is more power generation in September in tradition, but the decrease in future precipitation will lead to a decrease in power generation in this month. On the other hand, though the power generation is less in May in the historical, the value will increase because of the increased precipitation in future. In addition, the peak of the generation will change from July to August, and the value will decrease about 8%. Meanwhile, the peak period of power generation will be shortened from June to August, because of the influence of precipitation.

Conclusion and Discussion

In this paper, based on the results from HadGEM2-ES and PRECIS climate models, the precipitation and power generation in power station A over Dadu River basin in China were simulated and projected using SCA statistical downscaling. The results from SCA downscaling show a great performance relative former climate models in simulating the precipitation at station scale. On the other hand, we used the observed meteorological and hydropower data in station A to establish a HRMDP. Meanwhile, we also validated the performance of HRMDP, and the results show that the HRMDP model can reflect the relationship between the precipitation and power generation, with the correlation coefficient of 0.95 and RMSE of 611 kWh.

In future, the precipitation of station A is projected an ascending trend from May to July while it will decrease in other months. For different periods, the precipitation will increase in Neutral I and Wet, but it will decrease in other periods. As the response from precipitation, the power generation will also show a similarly trend. There is an increasing trend in power generation in station A from January to February and May to July, while there is a decreasing trend in other months. For different periods, the power generation in Neutral I will increase by about 20% in future, while there is no obvious change in other three periods relative to the historical period.

Climate change has a great impact on precipitation, which affects hydropower generation. Therefore, it is of great significance to study the future precipitation change and power generation forecasting model of hydropower station to adapt climate change. As far as we know, there are many studies on future precipitation changes using climate models, but relatively few on hydropower generation forecasting model. For example, for precipitation, future climate change will lead to a general increase in precipitation over the most regions of China ( Lin and Zhou, 2015 ; Zhao et al., 2019 ). Future precipitation of Dadu river basin in our study also shows an increase trend, which is consistent with other similar basins ( Zhang J. et al., 2013 ; Zheng et al., 2017 ). In addition, although there are many researches on power generation forecasting methods, which focus on the runoff forecast, there are few studies on hydropower generation forecasting directly. For example, Cheng et al. (2013) used linear trend estimation method, Morlet wavelet transform and Kendall rank correlation method to forecast future runoff over the Dadu river basin, and shows that runoff will appear an increase trend. Our results show that hydropower generation has an increase trend in the future, which means the increase of precipitation will lead to increase of runoff, and further promote the increase of hydropower generation. The results can provide some decision support for future water resources management in Dadu river basin, especially for the planning and operation of hydropower stations.

Data Availability Statement

The datasets generated for this study are available on request to the corresponding author.

Author Contributions

LW, LJ, and GJ conceived and designed the research, collected the data, and performed the data analyses and manuscript preparation. LW, LJ, GJ, and BZ formulated the optimization model. LW, LJ, GJ, and FL wrote the manuscript. LW, GJ, and HB gave the comments and helped to revise the manuscript. All authors contributed to the article and approved the submitted version.

This research was supported by the National Key Research and Development Plan (2018YFE0196000), Natural Sciences Foundation (51190095), and the 111 Project (B14008).

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Keywords : hydropower, precipitation, regional climate model, stepwise clustering analysis, downscaling

Citation: Wei L, Jiheng L, Junhong G, Zhe B, Lingbo F and Baodeng H (2020) The Effect of Precipitation on Hydropower Generation Capacity: A Perspective of Climate Change. Front. Earth Sci. 8:268. doi: 10.3389/feart.2020.00268

Received: 28 October 2019; Accepted: 15 June 2020; Published: 08 September 2020.

Reviewed by:

Copyright © 2020 Wei, Jiheng, Junhong, Zhe, Lingbo and Baodeng. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Li Jiheng, [email protected] ; Guo Junhong, [email protected]

This article is part of the Research Topic

Future Climate Scenarios: Regional Climate Modelling and Data Analysis