How to Design a Mini-Hydro Power Plant

November 13th, 2015 Posted in hydro power

How to Design a Mini-Hydro Power Plant


Excel programs to help you automate your design, optimize penstock diameter and determine economic viability and prepare feasibility studies

Take advantage of the Christmas Holiday Big Discount Sale.

Order now your top-of-the-line this December your advanced Excel programs for designing a mini-hydro to develop a number of design alternatives and run the project finance models at various exceedance (% of the time a given flow is exceeded) in order to optimize hydro plant capacity and configuration as well as determine the optimal penstock diameters.

Mini-hydro Power Plant Design Toolkit.xlsm

ADV Mini-hydro Power Plant Project Finance Model.xlsm

Sample Feasibility Study for a Mini-Hydro Power Project.pdf

To order, email me at my Gmail account:

To remit payment, use my PayPal account:

To download the complete article with the tables, pictures and graphs – please download the file below (click the link below):

How to Design a Mini-Hydro Power Plant – Copy

Here is the article (minus the tables, pictures and graphs):

Since time immemorial, the earth has been blessed with an endless cycle of rain falling from the sky, onto the watershed, flowing as run-off into the rivers, lakes, groundwater, and finally into the oceans where it picks up the Sun’s limitless energy to evaporate again and join the clouds, only to be cooled by the shadow of the earth as cold winds precipitate the saturated vapors that falls again to repeat the cycle.

This manual presents the technology and design concepts of hydro power. The reader will be able to follow the methodology applied in determining rainfall, drainage area,  river flow for gauged and un-gauged rivers, gross head, head loss and friction loss, net head, efficiency of turbine and generator, electrical power output, capital and operating costs, development schemes (long headrace vs. short tunnel) and demand scenarios (low, high, most likely), penstock diameter and wall thickness, and economic analysis of alternative scheme and scenario of a mini-hydro project.

Figure 1.1 – Hydrologic Cycle

Figure 1.1 - Hydrologic Cycle

When rain falls unto two watersheds, tunnels have to be built to utilize it in another watershed (trans-basin). An example of this is the Casecnan River Trans-basin Hydro Project that utilizes head waters from the Cagayan River Basin to generate power in a water turbine that releases its tailwater into the Pantabangan River.

1.1     Types of Hydro Power Plants

Because of this endless hydrologic cycle, the change in energy of water as it moves from high elevation to a lower elevation can be captured in hydro power stations using three basic technologies, namely impoundment, pumped storage, and diversion (run-of-river):

  • Impoundment – typical large hydropower system use an impoundment facility like a dam to store river water in a reservoir; water may be released either to meet changing electricity needs or to maintain a constant reservoir level or to meet irrigation needs (Figure 1.2)
  • Pumped storage – when demand for electricity is low, say at night or weekend, a cheap source of electricity like nuclear power will pump water from a lower reservoir to an upper reservoir, where it is released back to the lower reservoir to generate electricity during periods of high or peak electrical demand (Figure 1.3)
  • Diversion – also called run-of-river, channels a portion of a river through a canal or penstock to run a turbine; may not require the use of a dam (Figure 1.4)

Figure 1.2 – Hydroelectric Dam (Impoundment)


Figure 1.3 – Pumped Storage Dam


Figure 1.4 – Diversion Dam (Run-of-River)


1.2     Mini-Hydro Power Plant

A mini-hydro system (Figure 1.5) normally consists of a weir (diversion dam, thrash rack and intake), desander (desilting, spillway), headrace (open canal, culvert, pipe, tunnel), forebay (temporary storage, pressure relief, surge tank, spillway), penstock (pressurized pipe), water turbine (converts static head and velocity head to rotating mechanical energy), generator (converts rotating mechanical energy to electrical energy), tailrace (directs diverted water back into the main river), power house (protects turbine-generator and other electro-mechanical equipment, metering, monitoring and control), sub-station and transformer (raises low voltage of generator to high voltage of transmission line), and transmission line (connects the transformer to the main grid).

Here is a summary of input data for a case study we will be using in this design exercise:

Hydrologic Data:

The upstream gauged station (1) has a drainage area (DA) of 955 km2 while the downstream ungauged station (2) where the mini-hydro dam will be built has a drainage area of 969 km2. When two catchment areas are similar in terms topography, land-use, geomorphology and lithology,  the discharge of the un-gauged station can be estimated from  of drainage areas:

Q2 = Q1 (A2 / A1)

Flow duration curve (FDC) is a simple graphical depiction of variability of flow at a location without any reference to the chronological sequence in which this flow would be available. It is a cumulative frequency curve that expresses the magnitude of mean discharge that is equaled or exceeded as a percentage of the period of record at a gauging station.

A sample FDC of the un-gauged stations is shown below:

x = Duration (%) y = Discharge (m3/s)
100% 11.88
95% 20.29
90% 30.44
85% 40.59
80% 50.73
75% 55.96
70% 65.95
65% 71.87
60% 80.65
55% 89.29
50% 96.39
45% 101.47
40% 111.61
35% 116.75
30% 121.76
25% 129.84
20% 131.91
15% 136.98
10% 144.55
5% 152.20
Q, maximum flow = 152.20
Q, design flow = 88.06
Q, firm flow = 11.88

The FDC  is best represented by a polynomial equation (y* = a + b x + c x2) whose  constants a, b and c are determined using the method of least squares:

Q = y* = 154.4535 – 91.73343 x – 50.8371 x2

Topographic Data:

E = River bottom elevation = 104.310 m EL (above sea level)

Ogee weir height = 8 m (you can run a sensitivity at 12 m)

Ogee weir length = f1 to f2 = 161.498 m long

F = Head water elevation = Weir crest elevation = E + Ogee weir height = 112.310 m EL

f10 = Tail water elevation = 97.469 m EL

Gross head = F – f10 = 112.310 – 97.469 = 14.841 m of head

Head race length = Settling basin to Forebay = 416.786 m long

Forebay elevation = f11 = 110.134 m EL

Headrace drop = Head water elevation – Forebay elevation = 112.310 – 110.134 = 2.176 m

Penstock length = Forebay to Powerhouse turbine = f11 to f9 = 233.350 m long

Tailrace length = Powerhouse turbine to Tail water = 117.968 m long

Headrace loss = hh = S L = (headrace slope) x (headrace length) = headrace drop = 2.176 m of head

Penstock Diameter and Friction Loss:

To optimize penstock diameter, we assume a number of pipe diameters (5.30 to 5.90 m) and calculate the power output and compare the value of the power saved with the incremental cost of the penstock of pipe diameter D:

Penstock friction loss  at 5.6 m diameter = hf = f (L / D) V2 / (2 g) = 0.060 m of head

where D = 5.60 m (pipe diameter)

A = pi / 4 D2 = 24.630 m2 = cross-sectional area of pipe

Q = 98.71 m3/s = river discharge at 48% exceedance (maximum scenario)

V = Q / A = 4.008 m/s = velocity

K = Kinematic viscosity of water = u / d = 8.60 E-07

NR = Reynolds Number = V D / K = 2.61 E+07

e/D = Relative Roughness = 10 mm / 5.60 m = 0.00018

f = friction factor (from Moody Diagram for NR and e/D) = 0.00175

Miscellaneous Losses (add 10% allowance) = hm = (hh + hf) x 10% = 0.224 of head

Total Head Loss = Hloss = hh + hf + hm = 2.459 m of head

Net Head = H = Hgross – Hloss = 14.841 – 2.459 = 12.382 m of head

Power Output of Francis Turbine:

Pelec (kW) = g × d × (Et × Eg) × H × Q / 1000

= 9.81 × 1000 × (84.97% × 95.00%) × 12.382 × 98.71 / 1000 = 10,191 kW

Figure 1.5 – Mini-hydro Components


The power output of a mini-hydro is dependent on river flow and effective or net head (gross elevation at the weir less tailrace elevation less head losses due to the desander, headrace or tunnel, and forebay less friction losses at the inlet valves, penstock, turbine, and tail water pipe).

Figure 1.6 – Gross Head and Net Head of a Mini-Hydro System


The head loss (or friction loss) in the penstock could be very significant if the pressurized pipe is too small and its surface is rough. However, as you increase the pipe diameter, the cost of the penstock will rise but the friction loss will decrease. So it becomes an optimization problem of balancing the capital cost of the pipe of given diameter and thickness against the higher revenue of electricity sales arising from lower friction loss or pressure drop inside the penstock. Optimal diameter is reached once economic returns from increasing pipe diameter becomes marginal or smaller than acceptable returns (or payback period becomes too long).

The headrace (open canal, culvert, pipe or tunnel) also needs to be optimized to minimize water spillage and must be designed in such a way that it can convey the needed quantity of water to the forebay and penstock to generate the desired power output. It has to be optimized with respect to dimensions (cross-section and depth of water), type of material (concrete canal, concrete culvert, and GRP pipe), roughness and shape (rectangular, trapezoidal, and circular).

1.3     Main Parts of a Mini-Hydro Power Plant

This section will cover the design of the civil structures of a mini-hydro power plant, namely: diversion weir, intake, settling basin or desander, headrace or tunnel, forebay, power house (turbine, generator, and controls), sub-station, transformer and transmission line to grid.

1.3.1    Diversion Weir and Intake Channel

The diversion weir is a barrier built across the river to divert water through an opening in the riverside (intake opening) into a settling basin.

The next Figure 1.7 shows the diversion weir may be made of concrete, earth, rocks, masonry, wood and gravel.

Its design would include gravity dam, floating dam, wet masonry, gabion, brushwood and wooden frame.

Figure 1.7 – Diversion Weir


1.3.1    Intake Structure

The intake structure may be of the side intake type that is perpendicular to river direction, or of the Tyrolean intake design which is along the weir but is susceptible to sedimentation during flooding and requires more maintenance.

Figure 1.8 – Intake Structure


1.3.1    Settling Basin (Desander, Sand Trap, Siltation Basin)

The settling basin is used to trap sand or suspended silt from the water before entering the penstock. It may be built at the intake structure or at the forebay. Its main function is to ensure that all suspended materials that could damage the water turbine is removed. The minimum specification for safe turbine operation is 0.5 – 1.0 mm diameter of suspended materials. It is designed to have sediment marginal settling speed of 0.1 m/s while flow velocity in settling basin should be less than 0.3 m/s. These design specs are met by sizing the length, width and depth properly.

Figure 1.9 – Settling Basin


1.3.1    Headrace (Open Canal, Culvert, Pipe, Tunnel)

The headrace is a channel leading water to a forebay or turbine. The headrace follows the contour of the hillside so as to preserve the elevation of the diverted water, but with sufficient slope to move the water at the right velocity without spilling water along the bends and capable of providing the needed volumetric flow rate given the cross-section of the channel. Since it is open and not pressurized, the head loss is basically the elevation change from the top of the water surface at the diversion weir and the end of the headrace before the forebay and penstock.

Figure 1.10 – Headrace (Open Canal, Culvert, Tunnel)


The Manning’s equation for uniform flow in long pipes or channel is given by:

Q = ( 1 / n ) A r2/3 S1/2 = ( 1 / n ) (b d) (b d / (b + 2 d)2/3 S1/2

1.3.1    Forebay (Head Tank, Head Pond, Surge Tank)

The forebay or head tank is a small pond at the top of a penstock or pipeline; serves as final settling basin, provides submergence of penstock inlet and accommodation of trash rack / screen and overflow / spillway arrangement. In the event that the water turbine is closed and stops operation, the flowing water from the headrace to the forebay is dumped via a spillway back into the river. It acts like a surge tank also to protect the pressurized penstock from water hammer effects when water is suddenly stopped from flowing freely by the inlet valves.

Figure 1.11 – Forebay (Head Tank, Head Pond)


1.3.1    Penstock (Pressure Pipe)

The penstock is a closed conduit or pressure pipe for supplying water under pressure to a water turbine that is connected to an electric generator. It is designed based on the route, slope and geological conditions. It must be of sufficient thickness to withstand pressure, bending moments and carry its own weight and that of the water (hydrostatic load, dynamic load and water hammer inertia), as well as external forces such as earth quake. It must be durable and withstand impact from falling earth and trees. Its diameter and pipe thickness (pipe size) must be optimized to balance the capital cost of a much larger pipe vs. the economic gain from higher electricity sales due to lower friction loss at larger pipe diameter and therefore higher pressure acting on the turbine. An Excel program was developed to automate the optimization of the penstock diameter.

Figure 1.12 – Penstock (Pressure Pipe)


There are many variations on the design layout of the system. As an example, the water is entered directly to the turbine from a channel without a penstock. This type is the simplest method to get the waterpower.

Another variation is that the channel could be eliminated, and the penstock will run directly to the turbine. Instead of a headrace, a tunnel is used to convey water from another side of a hill or mountain to the other side in case of a winding river. Variations like this will depend on the characteristics of the particular site and the requirements of the user of system.

1.3.1    Powerhouse and Tailrace

The main function of the Powerhouse is to provide shelter for the electro-mechanical equipment (turbine, generator, control panels, etc.). The size of the powerhouse and the layout is determined by taking into account convenience during installation, operation and maintenance.

Location of Powerhouse

The location of the powerhouse must avoid the level and section where the water flows to avoid scouring and to prevent inundation of the powerhouse during high flows. The flood water level could be assumed based on the information listed below that could be used in determining the ground elevation of the powerhouse with sufficient margin for error:

  • Information obtained from local residents
  • Ground elevation of nearby structures (roads, embankments and bridges, etc.)
  • Traces of flooding and vegetation boundary

Foundation of Powerhouse

The foundations of the powerhouse must be strong enough to withstand the installation of heavy loads like the electro-mechanical equipment. For a mini-hydropower plant, a compacted gravel layer may be sufficient because of the relatively lightweight equipment (approximately 2 – 3 tons/m2).

The foundation is classified into two types:

For Impulse Turbine

–          Pelton turbine, Turgo turbine or Cross-Flow Turbine, etc.

For Reaction Turbine

–          Francis turbine or Propeller turbine, etc.

Figure 1.13 – Foundation for Impulse and Reaction Turbines


Location of Tailrace

The location of the tailrace is determined using the same conditions as the powerhouse location because it is located adjacent to the powerhouse. It is decided by the following considerations:

(1) Flood Water Level

The tailrace channel should be preferably placed above the expected flood water level. When the base elevation of the tailrace is planned to be lower than the flood level, the location and base elevation of the tailrace must be decided in consideration of (a) suitable measures to deal with the inundation or seepage of water into the powerhouse due to flooding, and (b) a method to remove sediment which may occur in the tailrace canal.

(2) Existence of Riverbed Fluctuation at Tailrace

When riverbed fluctuation is expected to take place in the future, the location of the water outlet must be selected so as to avoid any trouble to its operation due to sedimentation near the tailrace.

(3) Possibility of Scouring

Careful attention must be made to avoid the scouring of the riverbed and nearby ground. The selection of a location where protective measures can be easily applied is essential.

(4) Flow Direction of River Water

The tailrace must be directed (in principle, facing downstream) so as not to disrupt the smooth flow of the river water or a location which allows the direction of the tailrace as that of the river flow should be selected.

1.3.1    Water Turbine and Generator

A water turbine is a machine to directly convert the kinetic energy of the flowing water into a useful rotational mechanical energy while a generator is a device used to convert rotational mechanical energy into electrical energy.

Figure 1.14 – Water Turbine and Generator


1.3.1    Electro-Mechanical Equipment

The water coming from the conveyance components (diversion weir, inlet structure, settling basin, headrace or tunnel, forebay and penstock) needs to be controlled as it enters the power house that encloses the water turbine and generator.

A list of the electro-mechanical equipment in a mini-hydro power plant is shown in Figure 1.15. The inlet valve controls the supply of water from the penstock to the turbine that converts water energy (static head and velocity head) into rotating mechanical energy that drives a generator to convert rotating mechanical energy to electrical energy thru a mechanical drive, gear and clutch. A control facility measures, logs and controls the speed and power output of the unit. The sub-station with the switchgear and transformer controls the voltage and export of power to the transmission line connected to the regional grids (Luzon, Visayas, and Mindanao).

Figure 1.15 – Electro-Mechanical Equipment


Inlet Valve

The inlet valve controls the supply of water from the penstock to the turbine, and as such, must be able to shut-off the water flow during repairs and don’t contribute too much to the head loss. Among the types of inlet valves are the butterfly valve, bi-plane valve and sluice valve.

The application of each valve is shown in Figure 1.16. For instance, a butterfly valve can handle up to 200 meters of head and up to 2,500 mm (2.5 m) of pipe diameter. It has a high head loss due to friction in its vane body located at the center of the valve, leakage is higher than the other types at complete closure, but is cheap, occupies less space and simple in construction.

The other extreme is the sluice valve than can handle over 200 meters of head but small diameter up to 500 mm (0.5 m). Head loss is small, occupies larger vertical space and is heavier, but head loss and leakage at complete closing are both very small.

In between is the bi-plane valve that can handle up to 350 meters of head but larger diameter of over 500 mm (0.5 m). Head loss and leakage at complete closure is little, construction is simple and maintenance is easy. It is costly for small diameter but cheaper for large diameter.

Figure 1.16 – Inlet Valve


Water Turbine

The next series of figures show the various types of water turbines, when applicable, turbine efficiency curves, best efficiency and head range, and pictures of various types of turbines.

Figure 1.17 – Water Turbine Performance and Selection Criteria


For low head application (3 – 20 meters) and small discharge (1.5 – 40 m3/s), the Kaplan Propeller Turbine is most appropriate and has a high turbine efficiency of 91% to 93%.

For medium head application (15 – 300 meters) and small discharge (0.40 – 20 m3/s), the Francis Turbine is the choice with the highest turbine efficiency of 94%.

For high head application (75 – 400 meters) but smallest discharge (0.2 – 3 m3/s), the Pelton Turbine is selected and has a lower turbine efficiency of 89% to 90%.

For the medium head application (2 – 200 meters) but smallest discharge (0.1 – 10 m3/s), the Crossflow (Turgo) Turbine is chosen and has the lowest turbine efficiency of 85%.

The minimum technical flows of turbines are listed below for comparison:

Turbine Type Qmin (% of Qdesign)
Francis 50%
Semi Kaplan 30%
Kaplan 15%
Pelton 10%
Turgo 20%
Propeller 75%

The above table shows that Francis Turbine and Propeller Turbine can be throttled down up to 50% and 75% of their design capacity, respectively; while the other turbines, can be throttled down much lower to 10% to 30% of design capacity.

Pictures showing the cut-out design of the four major water turbine types are shown in the next four slides (Propeller, Francis, Pelton and Crossflow).

xxx Propeller

xxx Francis

xxx Pelton

xxx Crossflow

xxx Sample Problem – Turbine Selection

In the above sample problem, select the appropriate turbine type for a proposed mini-hydro project that has a water discharge of 0.45 m3/s (15.88 ft3/s) and a net head of 25 m (82 ft). By plotting the points, the intersection (yellow star) selects the Cross Flow Turbine as the appropriate type.

Electric Generator

The electric generator is connected to the water turbine with a drive mechanism consisting of a set of gears, clutch and shaft. It is classified as synchronous or asynchronous (induction) type.

Figure 1.18 – Electric Generator


The synchronous generator needs an independent exciter rotor and synchronizer. The exciter is necessary for supplying field current to the generator and keeps the terminal voltage constant even though the load fluctuates. The type of exciter is classified as DC exciter, AC exciter and Static exciter. Each type has varying capital costs, maintenance requirements and operating costs. On the other hand, the asynchronous generator needs no excitation and synchronizer but needs to be connected to capacitors to be able to generate electricity.

Driving Facility (Gear Box, Belt)

To match the speed of the generator and the turbine, a gear box type or belt type driving facility is needed to couple the generator shaft and turbine shaft according to the speed ratio between the turbine and generator. A gear box type has long life but costlier and provides mechanical efficiency of 95% to 97%. On the other hand, the belt type with pulleys, flywheels and belts are designed according to the speed ratio. The cost is lower but the life is shorter while providing mechanical efficiency of 95% to 98%.

Figure 1.19 – Driving Facility (Speed Increaser, Gearbox)


Control Facility of Turbine and Generator

Because the speed of the turbine may vary due to changes in load, water head or flow, it is important to keep the turbine speed constant. The speed governor does this job and can either be of the mechanical / electrical type or a dummy load that varies in response to changes in the external electrical load. The speed governor keeps the frequency constant by maintaining equilibrium in the relationship:

Generator Output = Customer Load + Dummy Load

When the Customer Load varies, the Dummy Load (an electric heating coil) compensates and is adjusted by an electronic load controller (ELC) to satisfy the above equation.

Figure 1.20 – Control Facility of Turbine and Generator



The switchgear controls the electric power and increases the voltage of transmission lines, if required. It isolates the hydro plant from the load or grid and connects it vice versa.

Figure 1.21 – Switchgears


Control Panels

Shown in Figure 1.22 are the control methods employed in a mini-hydro system, namely: supervisory control, operational control, and output control methods.

Instrumentation is built into the control panels to display pressure gauge readings at the penstock, volt meter and ammeter readings at the output of generator and dummy load, frequency meter for the rotational speed of the generator, hour meter for operating time, and kWh meter and kVh meter for the energy output of the mini-hydro plant.

To minimize capital cost, a minimal protection system is in place to protect a mini-hydro plant such as: over-speed of turbine and generator (from frequency), under voltage, over voltage, and over current at the breakers of low tension circuits.

Figure 1.22 – Control Panels


1.4     Calculation of Hydro Power Output

A hydro scheme requires both water flow and a drop in height (referred to as ‘Head’) to produce useful power. The power conversion absorbs power in the form of head and flow, and delivering power in the form of electricity or mechanical shaft power. No power conversion system can compare to hydropower, which can deliver as much useful power as it absorbs.

Overall efficiency of a hydropower system can range from 85% to 94%, whereas other thermal technologies have much lower thermal efficiencies: diesel genset (32%), oil thermal (38%), geothermal (28%), biomass (27%), coal CFB (41%), coal PC sub-critical (45%), coal PC super-critical (48%), coal PC ultra-super-critical (51%), gas thermal (45%), open cycle GT (38%), combined cycle GT (54%), and nuclear (33%). RE systems have capacity factors instead for comparison: wind (27.5%), biomass (72%), solar (22%), and mini-hydro (47%).

Figure 1.23 – Gross Head


Head is the vertical height through which the water drops. The power conversion equation is:

Power input = Power output + Loss

or         Power output = Power input × Conversion Efficiency

The power input, or total power absorbed by the hydro scheme, is the gross power, (Pgross).

The power output is the net power (Pnet) which is gross power less losses.

The overall efficiency of the scheme (Figure 1.24) is termed Eo.

Pnet = Pgross – Plosses = Pgross × Eo

Figure 1.24 – Typical system efficiencies for a scheme running at full design flow


The gross power (P) is the product of the gross head (Hgross), the design flow (Q), a coefficient factor (acceleration due to gravity, g = 9.81 m/s2, and density of water, d = 1,000 kg/m3), and overall efficiency Eo, so the fundamental hydropower equation is:

P = g × d × Hgross × Q × Eo

Where the gross head is in meters and the design flow is in cubic meters per second.

Eo is derived as follows:

Eo = Ecivil work × Epenstock × Eturbine × Egenerator × Edrive system × Eline × Etransformer

The usual values of the efficiency terms are:

Ecivil work      = 1.0 – (Channel length × 0.002 ~ 0.005) / Hgross

Epenstock       = 0.90 ~ 0.95 (it depends on length, surface condition)

Eturbine          = 0.70 ~ 0.85 (it depends on the type of turbine)

Egenerator      = 0.80 ~ 0.95 (it depends on the capacity of generator)

Edrive system = 0.97             (it depends on the gearbox)

Eline                = 0.90 ~ 0.98 (it depends on the transmission length)

Etransformer  = 0.98             (it depends on transformer)

Ecivil work and Epenstock are usually computed as ‘Head Loss (Hloss)’. In this case, the hydropower equation becomes:

P = g × d × (Eo – Ecivil work – Epenstock) × (Hgross – Hloss) × Q

The above equation for net mechanical power output (P) can be re-written as the product of a constant (g × d), hydraulic turbine efficiency (Et), net head (H) and volume flow rate (Q).

P = g × d × Et × H × Q


P is the mechanical power produced at the turbine shaft (Watts)

g is the acceleration due to gravity (9.81 m/s2)

d is the density of water (1000 kg/m3)

Et = Eo – Ecivil work – Epenstock = hydraulic turbine efficiency of the turbine

Q is the volume flow rate passing through the turbine (m3/s)

H = Hgross – Hloss = effective pressure head of water across the turbine (m)

If we include further the generator and transformer efficiencies, then the net power output available for export to the transmission line and grid is given by the final formula:

Pelec = g × d × (Et × Eg) × H × Q

= g × d × E × H × Q


Pelec is the electrical power exported to the grid (Watts)

Eg is the mechanical drive (gear, clutch), generator, and transformer efficiencies

E = Et × Eg = overall hydropower plant efficiency

1.5     Optimizing Penstock Diameter

As mentioned in a previous section, the losses occurring in the penstock have the potential to significantly affect the power available to the turbine. When sizing a penstock, the pipe length and diameter, design flow, and gross head must be considered as they contribute to the head loss in the system.

In general, the pipe length, design flow and gross head are fixed variables, meaning they are unalterable. As such, the primary alternative to reduce head loss in the system is to adjust the penstock diameter to minimize the velocity in the pipe, and thus, the friction created. However, an increased penstock diameter leads to additional material cost; therefore, an optimum balance should be considered between the two.

When sizing a penstock, a good place to start is calculating a rough diameter of pipe that would adequately pass a flow velocity of 3.0 meters per second (10 feet per second). The flow velocity can be calculated by dividing the flow rate by the area of the pipe opening, taking care to ensure that units are identical. When beginning the design process with an initial 3.0 m/s flow velocity, this relationship can be used to obtain a preliminary inside pipe diameter.

Once an initial pipe diameter is reached, head loss analysis can take place to further refine the penstock sizing. According to Canyon Hydro, a good rule of thumb is to size the pipe such that no more than 10% to 20% of the gross head is lost due to pipe friction.

Figure 1.25 – Effective Head (Net Head)


The head loss at the penstock can be calculated from the friction loss at the penstock, inlet loss and valve loss as shown in the next boxes.


The general procedure is to assume a pipe diameter (D) with a given thickness (t) of given cost per unit length (Cunit cost).

The pipe inner cross-sectional area (Ap) is calculated from inner pipe diameter (Dp):

Ap = 3.1416 Dp2 / 4

From the design discharge (Q) and the pipe inner cross-sectional area (Ap), calculate the flow velocity:

Vp = Q / Ap

From the given pipe material of given roughness (see Manning’s coefficient n) and pipe diameter (Dp), calculate the coefficient:

f = 124.5 n2 / Dp1/3

Then, calculate the penstock head loss (hf) from the above friction loss formula (1).

Then, calculate the inlet valve loss using formula (2) and the valve loss using formula (3).

Then, calculate the other losses by providing 5% to 10% allowance on previous totals of head losses using formula (4).

Then, total all the losses using the formula:

HL2 = hf + he + hv + ho

Then, calculate the net head:

H = Hg – (HL1 + HL2 + HL3)

Then, calculate the net power output:

Pelec (kW) = g × d × (Et × Eg) × H × Q / 1000

Then, calculate the total cost of the penstock from its price per unit length and the length of the penstock:

Cpenstock (PhP) = Cunit cost (PhP/meter) × Lpenstock (meters)

Then, calculate the annual energy generation from the capacity factor and annual operating hours:

Energy (kWh/year) = Pelec (kW) × CF (%) × 8760 (hours/year)

Then, calculate the revenue from the sale of the annual energy generation to the grid:

Rpower (PhP/year) = (Energy, kWh/year) × (5.90 PhP/kWh feed-in-tariff)

Repeat the above steps for several pipe diameters and tabulate the results.

Then make an incremental analysis by comparing the increase in cost of the penstock (incremental investment) to the value of the reduction in head loss which results in higher net power output and thus annual energy sales.

The return on investment is thus:

ROI (% per year) = [Cpenstock2 – Cpenstok1] / (Rpower2 – Rpower1] ×100%

As you increase the pipe diameter, the penstock pipe cost will gradually rise while the value of energy sales will also rise at say 100%, 80%, 50%, 30%, 15%, 12%, 10%, 5% until the annual returns on incremental investments become marginal or nil.

The optimal penstock pipe diameter will correspond to the point where the diminishing returns cuts the minimum acceptable returns of say 12% per year.

An Excel model has been prepared to automate this calculation. The model user simply enters the input data and presses the macro ctrl + f in the worksheet Table 15 in order to optimize the penstock diameter.

The actual formulas used in the excel model is shown in the box below. The friction factor f may be read from the Moody Diagram shown on the next page using the Reynold’s number from the velocity of the flow (v), pipe diameter (D) and kinematic viscosity of water (K = u / d):

NR = V D / K

Alternatively, the friction factor f may be computed from the formula below or read from the Moody Diagram:

f = 124.5 n2 / Dp1/3


Design to deliver water to water turbine
Design Flow m3 / s Q
Pipe length m L
Pipe diameter m D
Roughness mm e
for Moody chart e / D
for Moody chart 1.2 Q / D
Pipe area m2 A = pi D2 / 4
Velocity in pipe m / s V = Q / A
Kinematic viscosity of water K = u / d
Reynold’s Number NR = V D / K
Relative roughness e / D
Friction factor (read Moody Diagram) f
Friction factor (from equation) f = 124.5 n2 / Dp1/3
Head loss due to friction hf = f (L / D) V2 / (2 g)

Penstock Pipe Diameter

If the gross head is available and an upper limit of say 20% of gross head as the total allowable head loss, then the minimum pipe diameter may be computed as follows:

The penstock line is the high pressure component of the system. Hence, the Darcy-Weishbach equation is used in lieu of the Manning’s formula for gravity flow for sizing:

Hf = f (L / D) V2 / (2 g)


Hf = friction loss, m of head

L = penstock length, m

D = penstock diameter, m

A = 3.1416 D2 / 4 = cross-sectional area, m2

V = Q / A = penstock velocity, m/s

Q = turbine discharge, m3/s

g = acceleration due to gravity = 9.81 m/sec2

f = friction factor

Penstock Diameter

Substituting area of flow (A) in the equation and rearranging terms, the Darcy-Weishbach equation is reduced to the formula for pipe diameter (D) as follows:

D = (0.0827 f L Q2 / hf)0.20

The friction factor ‘f’ is conservatively around 0.015, although it may be lesser (see Moody Diagram).

Penstock Wall Thickness

Wall thickness of the penstock is calculated considering the static pressure owing to the difference in water level from the weir crest level to the powerhouse’s tailrace plus (gross head) the dynamic pressure in the event of the rapid closure of the intake valve before the turbine which is taken as 40% of the static pressure to comprise the designed internal bursting pressure. The thickness is calculated as follows:

2 × (tensile force) = (diameter) × (static pressure of water from crest to tailrace)

2 × T = D × (9.81 × H)

2 × [ t × (allowable stress for A-36 steel) ] = D × (9.81 × H)

2 × [ t × (0.60 by code) × (248,000 mpa yield strength of A-36) ] = D × (9.81 × H)

If we include 40% allowance for rapid closure and 10% corrosion allowance, the equation becomes:

2 × [ t × (0.60 × 248,000) ] = D × (9.81 × H) × 1.40 × 1.10

t × [ (2 × 0.60 × 248,000) / (9.81 × 1.40 × 1.10) ] = D × H

t = [ (9.81 × 1.40 × 1.10) / (2 × 0.60 × 248,000) ] × D × H

Hence, the minimum penstock wall thickness in mm for an A-36 steel material is given by:

t = [ 5.0764 × 10-5 ] × D × H × 1000

The thickness ts includes a 15% additional safety allowance:

ts = t × 1.15

1.6     Validation of Geological Conditions

The survey on the ground stability of the surface layer is required for the construction of a small-scale hydropower plant due to: (a) the exposed structure of most of the main civil structures and (b) the rooting of the waterway on a sloping hillside.

The results of investigation should be presented in the form of sketch drawings (Figure 1.26) for reference purposes when determining the basic structures for civil works.

Figure 1.26 – A geological sketch based on site observations


Field reconnaissance by the hydropower specialist is important to establish a waterway route based on an existing topographical map and other relevant information for the planning of a mini-hydropower plant. The results of the reconnaissance survey will determine if the project will proceed or not.

The items to be checked during this survey are listed below. It is necessary to repeat the field reconnaissance in line with the progress of the planning and design. When uncertainties emerge, particularly at the design stage, field verification is necessary.

Moreover, there is a need to keep the expected demand in mind. Therefore, this survey should be conducted in parallel with the demand survey.

It is important not only to select suitable locations for such individual facilities as the intake weir and waterway, etc. but also to carefully examine the locations of their tie-in sites to the grid.

1.7     Survey on Locations of Civil Structures

Field reconnaissance by the hydropower specialist is important to establish a waterway route based on an existing topographical map and other relevant information for the planning of a mini-hydropower plant. The results of the reconnaissance survey will determine if the project will proceed or not.

The items to be checked during this survey are listed in the next sections. It is necessary to repeat the field reconnaissance in line with the progress of the planning and design. When uncertainties emerge, particularly at the design stage, field verification is necessary.

Moreover, there is a need to keep the expected demand in mind. Therefore, this survey should be conducted in parallel with the demand survey. The potential off-takers may be the LGUs, ECs and DUs, as well as the NGCP using the feed-in-tariff program of the country.

It is important not only to select suitable locations for such individual facilities as the intake weir and waterway, etc. but also to carefully examine the locations of their tie-in sites to the grid.

For the development of mini-hydro, the maximum use of natural topographical features is important from the viewpoint of cost reduction.

1.8     Measurement of River Flow

The estimated river flow at a project site is considered reasonably reliable if it is based on data from a nearby gauging station. As such, it may not be necessary to conduct actual discharge measurement at the project site. Alternatively, a water balance on the watershed or catchment area may provide an estimate of the river flow.

However, when river flow data is difficult to obtain, it is preferable to measure the river discharge in the dry season, by means of simple method, to confirm the appropriateness of the estimated flow duration. Any stoppage of power generation due to a reduced water flow volume significantly affects the generation of a mini-hydropower plant, thus it is essential to check the discharge at dry season. Although it is necessary to record the river flow for at least one year in mini hydropower development, the river flow during the dry season should be checked even for micro hydropower development.

Should there be a need to measure the discharge, the observation period must be carefully determined based on past rainfall records and information relative to the climate.

It is also necessary to check and evaluate the observation results in connection with the characteristics (for example, drought year or wet year) of the year of observation based on past rainfall records, etc.

Data on river flow throughout the country can be obtained from government agencies such as PAGASA, DPWH, NWRC and NIA These records can be used to assess stream flow at the proposed site, as long as due allowance is made for the actual site location in relation to the gauging station (upstream or downstream).

If no data is available, it is also possible to use hydrological methods (water balance) that are based on long-term rainfall and evaporation records, and on discharge records for similar catchment areas. This allows initial conclusions to be drawn on the overall hydraulic potential without taking actual site observations. It is advisable to follow this up with site measurements once the project looks likely to be feasible.

The reference books provide for sophisticated methods both for estimating the hydrology of a catchment area and for measuring the flow in streams. The most accurate and reliable flow measurement method is to install a measuring weir, as summarized below.

1.8.1  Measuring Weirs

A flow measurement weir has a rectangular notch in it through which all the water in the stream flows. It is useful typically for flows in the region of 50-1000 liters per second (l/s). The flow rate can be determined from a single reading of the difference in height between the upstream water level and the bottom of the notch (Figure 1.27). For reliable results, the crest of the weir must be kept ‘sharp’ and sediment must be prevented from accumulating behind the weir.

The formula for a rectangular notched weir is:

Q = (2/3) Cd (2 g) 0.5 (L – 0.2 h) h1.5


Q = flow rate, m3/s

Cd = the coefficient of discharge

L = the notch width, m

h = the head difference, m

g = acceleration due to gravity = 9.81m/s2

If Cd is taken, typically, as 0.6, then the equation becomes:

Q = 1.8 (L – 0.2 h) h1.5

Since stream flow varies both from day to day and with the season, measurements should ideally be taken over a long period of time, preferably several years.

Figure 1.27 – Measuring Weir for River Flow


Flow Duration Curve (FDC)

There are two ways of expressing the variation in river flow over the year: the annual hydrograph and the Flow Duration Curve or FDC, as illustrated below. The annual hydrograph is the easiest to understand, since it simply shows the day-by-day (chronological) variation in flow over a calendar year. However, the FDC is more useful when calculating the energy available for a hydro-power scheme.

The FDC shows how flow is distributed over a period (usually a year). The vertical axis gives the flow, the horizontal axis gives the percentage of the year that the flow exceeds the value given on the y-axis. Hence, for example, the FDC can immediately indicate the level of flow which will be available for at least 50% of the year (known as Q50). The flow exceeded for 95% of the year (Q95) is often taken as the characteristic value for minimum river flow.

FDCs are often very similar for a region, but can be affected by soil conditions, vegetation cover, and to a lesser extent by catchment shape. They are also modified by man-made reservoirs, abstractions and discharges. A flatter FDC (characterizing a heavily spring-fed river) is preferable to a steeply sloping one, and means that the total annual flow will be spread more evenly over the year, giving useful flow for a longer period, and less severe floods

Compensation Flow

A portion of the flow, termed the compensation flow (riparian flow), will need to by-pass the scheme for environmental or aesthetic reasons. In abstraction schemes, where water is diverted from the main course of the river, this compensation flow is needed to maintain the ecology and aesthetic appearance of the river in the depleted stretch. The amount of compensation flow will depend on site-specific concerns, but a reasonable first estimate will lie between the Q90 and Q99 values of river flow.

Figure 1.28 – Annual Hydrograph and Flow Duration Curve (FDC)


Measuring Head

After measuring river flow, the next important parameter is measuring the head or height of water from the top of the water surface in the diversion weir and the tailrace level (usually the river surface elevation since the tailrace pipe may be submerged).The head of water available at any one site can be determined by measuring the height difference between the water surface at the proposed intake and the river level at the point where the water will be returned.

A number of reference books can provide details of basic survey techniques to measure or estimate the available head. The most common methods are summarized as follows.

An initial estimate for a high-head site (> 50m) can be taken from a large-scale map, simply by counting the contours between the inlet and discharge points: the distance between contours on standard NAMRIA maps is 10 m. Altimeters can also be useful for high-head pre-feasibility studies. Surveying altimeters or hand-held GPS in experienced hands will give errors of as little as 3% in 100 meters. Atmospheric pressure variations need to be corrected for, however, and this method cannot be generally recommended except for approximate readings.

The use of a Dumpy level (Theodolite or builder’s level) or a Surveyor’s Transit is the conventional method for measuring head accurately and should be used wherever time and funds allow. Such equipment should be used by experienced operators who are capable of checking the calibration of the device. Surveyor’s Transit is a surveying instrument for measuring horizontal and vertical angles, consisting of a small tripod-mounted telescope that is free to move in both the horizontal and vertical planes.

Figure 1.29 – Measuring Head


When no actual site visit has not been commissioned yet, nor a topographic survey has been made and completed, a desktop survey using Google Earth maps that display location (latitude, longitude) and elevation can be made with a computer (laptop, desktop) with internet connection. A sample of such point of interest is shown in Figure 1.31.

Figure 1.31 – Google Earth Points of Interest


Preliminary Power and Energy Calculation

Design Flow

It is unlikely that schemes using significantly more than the mean river flow (Qmean) will be either environmentally acceptable or economically attractive. Therefore the turbine design flow for a run-of-river scheme (a scheme operating with no water storage) will not normally be greater than Qmean. The exception would be a scheme specifically designed to capture very high winter flows, which is very rare in mini-hydro applications.

The greater the chosen value of the design flow, the smaller proportion of the year that the system will be operating on full power, i.e. it will have a lower ‘Capacity factor’.

Capacity Factor

The ‘Capacity factor’ is a ratio summarizing how hard a turbine is working, expressed as follows:

Capacity factor (%) = Energy generated per year (kWh/year) / (Installed capacity (kW) x 8760 hours/year)

The power Pelec can be estimated from the design flow Q and head H as follows:

Pelec (kW) = g × d × (Et × Eg) × H × Q / 1000

Energy Output

The annual energy output is then estimated using the Capacity Factor (CF) as follows:

Energy (kWh/year) = Pelec (kW) × CF (%) × 8760 (hours/year)

There is clearly a balance to be struck between choosing a larger, more expensive turbine which takes a high flow but operates at a low Capacity factor, and selecting a smaller turbine which will generate less energy over the year, but will be working flat out for more of the time, i.e. a higher Capacity factor. The Capacity factor for most mini-hydro schemes would normally fall within the range 50% to 70% in order to give a satisfactory return on the investment. Most turbines can operate over a range of flows (typically down to 20-40% of their rated flow) in order to increase their energy capture and sustain a reduced output during the drier months.

1.8.5    Power and Energy Demand Survey

There can be many types of power demand facilities for small-scale hydropower generation to respond to the conditions of the subject area for development. In the preparation of development plan, accurate understanding of the power demand facilities in the subject area for development is essential.

What is important is to ensure the efficiency and practicality of a demand survey. It is necessary to estimate a slightly higher demand level than the assumed scale of power generation so that it would adequately respond to the scale of development as well as to the seasonal fluctuations of the power demand as well as accommodate future growth arising from increasing population and economic activity.

When there is more than one power demand facility or electric cooperative or distribution utility, each facility should be surveyed. The demand survey items are described below:

(1) Location

The suitable route and distance, etc. to each power demand facility should be surveyed to examine the optimal transmission and distribution lines.

(2) Owners

The opinions and intentions of the owners of power demand facilities regarding the introduction of a new power supply source should be clarified.

(3) Types and required quality of equipment

The situation of power use by equipment (for power, heating, lighting and electrical control, etc.) and the required level of accuracy (in terms of the allowable voltage fluctuation and frequency fluctuation) should be surveyed.

(4) Equipment capacity, etc.

The equipment capacity, power consumption level and electricity tariff (or estimated electricity tariff in the case of planning) should be surveyed.

(5) Period of use

Any seasonal or daily fluctuation of power use and the range of fluctuation should be surveyed.

(6) Year of installation and service life

The year (date) of installation of each power demand equipment and its service life or planned period of use should be surveyed.

(7) Likely problems associated with power cut

The likely problems and financial losses associated with a power cut to power demand facilities should be surveyed.

1.8.6    Use of Land

No project can proceed unless you have the right to utilize all the land in question. It is also important to establish how contractors will access the different parts of the scheme with the necessary equipment, and to confirm that these routes will be available.

It is therefore wise to approach the relevant land-owners at an early stage to establish any objections to the proposed scheme and to negotiate access. Since water courses often form property boundaries, the ownership of the banks and existing structures may be complex. Failure to settle this issue at an early stage may result in delays and cost penalties later in a project.

Leasing agreements will need to be drawn up which establish the right to use the necessary land areas and also to define the responsibilities of the tenant in maintaining it.

1.8.7    Grid Connect or Stand-Alone

It is important to determine at the outset what the value of the electricity generated by the scheme will be, i.e. to whom the power will be sold. In this case, will it be feed-in-tariff to the national grid (NGCP) or as merchant plant (WESM) or bilateral contract (off-taker like an LGU, EC or DU or a commercial or industrial facility).

The electricity generated by a scheme may be used at the point of generation, in place of electricity supplied by the local electricity company.

Alternatively it may be exported via the local distribution network by agreement with the DU.

It is nearly always financially advantageous to consume as much of the power as possible on site, and only export the surplus into the network in order to minimize transmission line losses.

1.9    How to Develop and Plan a Mini-Hydro Project

The definitive project or scheme comes as the result of a complex and iterative process, where consideration is given to the environmental impact and different technological options. These are then costed and an economic evaluation carried out.

Additionally, in the Philippines, the process must meet the requirements of government regulations regarding implementation of new hydro sites. The two relevant pieces of legislation are the implementing rules and regulations (IRR) of the Renewable Energy Law, RA 9513 and RA 7156, An Act Granting Incentives to Mini-Hydro-Electric Power Developers and for Other Purposes.

It is necessary to secure the two (2) stages of contract with the Department of Energy (DOE) in order to qualify for all of the available incentives, namely:

  1. Hydropower Pre-Development Service Contract (PDSC), and
  2. Hydropower Operating Service Contract from the Department of Energy (DOE)

This involves reporting on an initial feasibility study that is then followed by a detailed analysis of the project, including the following steps:

  1. Topographic Survey

Conduct feasibility level topographic survey for the ground contours for dam, headrace, and power plant sites including river cross-sections and profiling work.

  1. Geologic & Geotechnical Investigation

Conduct feasibility level geologic and geotechnical investigations to establish soil and rock characteristics, earthquake magnitude and frequency and structural stability for structure’s design. Methodology will include rock sampling, test pittings, laboratory analysis, mathematical analysis and interpretation.

  1. Social-Environment Investigation & Surveys

Conduct sampling and interviews on social acceptability, area’s baseline flora and fauna survey and analysis of impacts and mitigation measures including social surveys on Indigenous People in the area (thru the NCIP).

  1. Hydrologic Investigation and Analysis

Establish vertical staff gaging station and conduct daily flow measurement and analysis by use of a flow meter, & take gage heights readings of flows. Prepare Q-H (discharge-gage height) flow measurement curve. Calibrate the gaging station for about a month. Take daily gage readings for majority duration of the FS. Also conduct mathematical statistical modeling using established methods of hydrology and correlate resulting values to those gathered at the field.

  1. Hydraulic Study

Conduct water level analysis at normal and flood conditions using non-uniform flow computations.

  1. Power Supply & Demand Study

Determine present power supply in the area, past and current demand of power and prepare forecast of energy demand based on data available at government Electrification Administration (NEA), Power Corporation (NPC) and local Electric Cooperative.

  1. Outline Design of Plant Facilities

Based on the inputs from the conduct of topographic survey, geologic study hydrologic study, power market study and facilities evaluation, prepare the scheme of development of the power systems including preliminary and concept design of the various facilities such as the weir, mechanical gates turbines, power house and sub-station including the coordination of equipment fabrication with local and foreign based manufacturers and suppliers.

  1. Cost Estimates

Conduct unit pricing analysis, bill of quantities and prepare cost estimates of the entire mini-hydro development.

  1. Financial / Economic Viability Study

Conduct economic and financial viability studies such as generation / production cost analysis, benefit – cost analysis, financial and economic internal rate of return analysis. 

  1. Packaging and Submittal of FS reports

The FS reports are reviewed, finalized, packaged and submitted to relevant government agencies (DOE, DENR, EMB, BOI, ERC, NREB, NWRB, NIA, NEA, NCIP, LGUs, etc.) as well as potential investors and join venture partners as well as banks and funding institutions for equity and debt financing.

  1. Additional work and certification is required for the following
  1. Municipal Resolution Endorsing Proponent for the Development of the Project. This involves drafting of and presentation of resolutions to the Municipal council and the Mayor. Upon passage of the resolution, the Company will receive a Mayor’s letter of no objection to the project.
  2. Preparation of documentation to secure of DOE Pre-development Service Contract (PDSC) and assistance in follow up.
  3. Water Rights from the National Water Resources Board (NWRB). Applications will present the case for the projects to acquire the necessary approvals for rights to use the river water to support the mini-hydro stations.
  4. National Commission for Indigenous People (NCIP) Certification involves public hearings related to getting approval for the project construction.
  5. Preparation of Initial Environmental Examination (IEE) and other documentation needed to apply for an Environmental Compliance Certificate (ECC), which involves applications and attendance at public meetings and hearings to obtain approval for the projects.

The following Figure 1.32 and Figure 1.33 show the flowchart for developing a mini-hydro and micro-hydro project (DOE) and planning a mini-hydro project (JICA).

The following Figure 1.32 and Figure 1.33 show the flowchart for developing a mini-hydro and micro-hydro project (DOE) and planning a mini-hydro project (JICA). 

Figure 1.32 – Flowchart of Mini-hydropower Development (DOE)


Figure 1.33 – Flowchart for Planning a Mini-Hydro Project (JICA)



If you need the complete article with tables (xxx) and figures (xxx), email the expert to place your order:

You may order the mini-hydro project finance model to determine all-in capital cost (equipment, installation, project development, initial working capital, financing, taxes and contingency), equity and project returns (IRR, NPV, PAYBACK), capacity and generation forecast, income and expense statement, net cash flow statement, balance sheet, levelized cost breakdown, financial ratios, and benefit vs. cost analysis.

Also available is the mini-hydro power plant design tool box kit to automate your design and optimization calculations and estimate the construction costs of each mini-hydro component (diversion weir, dam, settling basin, headrace, forebay, penstock, powerhouse, turbine, generator, switchyard and transformer, transmission line and other indirect costs.



Leave a Reply

XHTML: You can use these tags: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>