Masters G.M. Renewable and Efficient Electric Power Systems

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198 DISTRIBUTED GENERATION

well as smaller, less expensive turbines. Home-scale projects with modest ﬂows

and decent heads can lead to quick, simple, cost-effective systems.

The head H given in (4.5) is called the gross head,callitH

, because it does

not include pipe losses that decrease the power available for the turbine. The net

head, H

, will be the gross head (the actual elevation difference) minus the head

loss in the piping. Those losses are a function of the pipe diameter, the ﬂow rate,

the length of the pipe, how smooth the pipe is, and how many bends, valves,

and elbows the water has to pass through on its way to the turbine. Figure 4.18

illustrates the difference between gross and net head.

4.5.2 Pipe Losses

Figure 4.19 shows the friction loss, expressed as feet of head per 100 feet of

pipe, for PVC and for polyethylene (poly) pipe of various diameters. PVC pipe

has lower friction losses and it is also less expensive than poly pipe, but small-

diameter poly may be easier to install since it is somewhat ﬂexible and can

be purchased in rolls from 100 to 300 feet long. Larger-diameter poly comes

in shorter lengths that can be butt-welded on site. Both need to be protected

from sunlight, since ultraviolet exposure makes these materials brittle and easier

to crack.

From (4.5), we can write that the energy delivered by a micro-hydro system

is given by

P(W)

delivered

eQ(gpm)H

(ft)

5.30

,P(kW) = 9.81eQ(m

/s)H

(m)(4.6)

where e is the efﬁciency of the turbine/generator. From (4.6) comes the following

very handy rules-of-thumb for ≈50%-efﬁcient turbine/generator systems (which

is in the right ballpark for a micro-hydro plant):

P(W)≈

Q(gpm)H

(ft)

,P(kW) ≈ 5Q(m

/s)H

(m)(4.7)

Head Loss ∆

Net (dynamic) Head

Penstock

Powerhouse

Gross Head

Figure 4.18 Net head is what remains after pipe losses are accounted for.

MICRO-HYDROPOWER SYSTEMS 199

400350300250200150100500

Flow Rate (gpm)

Friction Loss (ft of head per 100 ft of pipe)

PVCPoly

1.5-in 2-in

Poly PVC

2.5-in

Poly

2.5-in

PVC

3-in Poly

3-in PVC

4-in PVC

5-in PVC

Figure 4.19 Friction head loss, in feet of head per 100 ft of pipe, for 160 psi PVC

piping and for polyethylene, SDR pressure-rated pipe.

Example 4.4 Power from a Small Source. Suppose 150 gpm of water is taken

from a creek and delivered through 1000 ft of 3-in.-diameter polyethylene pipe to

a turbine 100 ft lower than the source. Use the rule-of-thumb (4.7) to estimate the

power delivered by the turbine/generator. In a 30-day month, how much electric

energy would be generated?

Solution. From Fig. 4.19, at 150 gpm, 3-in. poly loses about 5 ft of head for

every 100 ft of length. Since we have 1000 ft of pipe, the friction loss is

1000 ft × 5ft/100 ft = 50 ft of head loss

The net head available to the turbine is

Net head = Gross head − Friction head = 100 ft − 50 ft = 50 ft

The rule-of-thumb estimate for electrical power delivered is

P(W)≈

Q(gpm) × H

(ft)

150 gpm × 50 ft

= 750 W

The monthly electricity supplied would be about 24 hr × 30 d/mo ×0.75 kW =

540 kWh. This is roughly the average electrical energy used by a typical U.S.

household that does not use electricity for heating, cooling, or water heating.

200 DISTRIBUTED GENERATION

Example 4.4 would be a poor design since half of the power potentially

available is lost in the piping. Larger-diameter pipe will always reduce losses

and increase power delivered, so bigger is deﬁnitely better from an energy per-

spective. But, large pipe costs more, especially when the cost of larger valves and

other ﬁttings is included, and it is more difﬁcult to work with. Since the cost of

the piping is often a signiﬁcant fraction of the total cost of a micro-hydro project,

an economic analysis should be used to decide upon the optimum pipe diameter.

Suppose, however, that the pipe size has already been determined for one rea-

son or another. Perhaps it is already the largest diameter conveniently available,

perhaps it is as much as can be afforded, or perhaps it has already been pur-

chased. The question arises as to whether there is an optimum ﬂow rate through

the pipe. If ﬂow is too high, friction eats up too much of the power and output

drops. By slowing down the ﬂow rate, friction losses are reduced but so is the

power delivered. So, there must be some ideal ﬂow rate that balances these two

competing phenomena and produces the maximum power for a given pipe size.

A derivation of the theoretical maximum power delivered by a pipeline is

quite straightforward. The curves given in Fig. 4.19 can be approximated quite

accurately by the following relationship:

H = kQ

(4.8)

where k is just an arbitrary constant. The power delivered by the pipeline will

be the net head times the ﬂow, with an appropriate constant of proportionality c

that depends on the units used:

P = cH

Q = c(H

− H )Q = c(H

− kQ

)Q (4.9)

For maximum power, we can take the derivative with respect to Q and set it

equal to zero:

= 0 = H

− 3kQ

= H

− 3H (4.10)

That leads to the conclusion that the theoretical maximum power delivered by a

pipeline occurs when pipe losses are one-third of the gross head:

H =

(4.11)

Example 4.5 Optimum Flow Rate. Find the optimum ﬂow rate for the 1000 ft

of 3-in. poly pipe in Example 4.4. Gross head is 100 ft.

Solution. Applying (4.11), for friction to be one-third of 100 ft of gross head

means 33.3 ft of pipe losses in 1000 ft of pipe. That translates to 3.33 ft of loss

per 100 ft of pipe. For 3-in. poly, Fig. 4.19 indicates that a ﬂow rate of about

120 gpm will be optimum.

MICRO-HYDROPOWER SYSTEMS 201

200180160140120100806040200

100

200

300

400

500

600

700

800

900

Flow Rate

(gpm)

Power (Watts)

∆

Figure 4.20 Showing the inﬂuence of ﬂow rate on power delivered from a penstock

(values correspond to Example 4.4).

At 120 gpm and with net head equal to two-thirds of the gross head, power

delivered will be

P(W)≈

Q(gpm) × H

(ft)

120 gpm ×

× 100 ft

= 800 W

For comparison, in Example 4.3, with 150 gpm of ﬂow only 750 W were gen-

erated. The relationship between ﬂow and power for this pipeline is shown in

Fig. 4.20.

While the above illustrates how slowing the ﬂow may increase power delivered

by the pipeline, that doesn’t mean it would help to simply put a valve in line that

is then partially shut off. That would waste more power than would have been

gained. Instead, it is the function of a properly designed nozzle to control that

ﬂow without much power loss. And, once again, it should be pointed out that the

ﬁrst approach to increasing power delivered is always to consider a larger pipe.

Keeping ﬂow rates less than about 5 ft per second and friction losses less than

20% seem to be good design guidelines.

4.5.3 Measuring Flow

Obviously, a determination of the available water ﬂow is essential to planning

and designing a system. In some circumstances, the source may be so abundant

and the demand so low that a very crude assessment may be all that is necessary.

If, however, the source is a modest creek, or perhaps just a spring, especially if it

is one whose ﬂow is seasonal, much more careful observations and measurements

may be required before making a hydropower investment. In those circumstances,

regular measurements taken over at least a full year should be made.

202 DISTRIBUTED GENERATION

W > 3 h> 2 h > 2 h

> 2 h

> 4 h

Ruler

v < 0.15 m/s

< 0.5 ft/s

Figure 4.21 A rectangular weir used to measure ﬂows. Based on Inversin (1986).

Methods of estimating stream ﬂow vary from the very simplest bucket-and-

stopwatch approach to more sophisticated approaches, including one in which

stream velocity measurements are made across the entire cross section of the

creek using a propeller-or-cup-driven current meter. For micro-hydro systems,

oftentimes the best approach involves building a temporary plywood, concrete,

or metal wall, called a weir, across the creek. The height of the water as it ﬂows

through a notch in the weir can be used to determine ﬂow.

The notch in the weir may have a number of different shapes, including

rectangular, triangular, and trapezoidal. It needs to have a sharp edge to it so

that the water drops off immediately as it crosses the weir. For accuracy, it

must create a very slow moving pool of water behind it so that the surface is

completely smooth as it approaches the weir, and a ruler of some sort needs to

be set up so that the height of the water upstream can be measured. When the

geometric relationships for the rectangular weir shown in Fig. 4.21 are followed,

and height h is more than about 5 cm, or 2 in., the ﬂow can be estimated from

the following:

Q = 1.8(W − 0.2 h)h

3/2

with Q(m

/s), h(m), W (m) (4.12)

Q = 2.9(W − 0.2 h)h

3/2

with Q(gpm), h(in.), W (in.) (4.13)

Example 4.6 Designing a Weir. Design a weir to be able to measure ﬂows

expected to be at least 100 gpm following the constraints given in Fig. 4.21.

MICRO-HYDROPOWER SYSTEMS 203

Solution. At the 100-gpm low-ﬂow rate, we’ll use the suggested minimum water

surface height above the notch of 2 in. From (4.13),

W ≤

2.9 h

3/2

+ 0.2 h =

100

2.9 × 2

3/2

+ 0.2 × 2 = 12.6in

To give the weir the greatest measurement range under the constraint that h ≤

W/3, suggests making W = 12.6 in. The maximum water height above the weir

can then be h = 12.6/3 = 4.2in.

From (4.13), the greatest ﬂow that could be measured with the 12.6in. ×

4.2 in. notch would be

Q = 2.9(W − 0.2 h)h

3/2

= 2.9(12.6 −0.2 × 4.2)4.2

3/2

= 294 gpm

4.5.4 Turbines

Just as energy in water manifests itself in three forms—potential, pressure, and

kinetic head—there are also three different approaches to transforming that

waterpower into the mechanical energy needed to rotate the shaft of an elec-

trical generator. Impulse turbines capture the kinetic energy of high-speed jets

of water squirting onto buckets along the circumference of a wheel. In contrast,

water velocity in a reaction turbine plays only a modest role, and instead it is

mostly the pressure difference across the runners, or blades, of these turbines

that creates the desired torque. Generally speaking, impulse turbines are most

appropriate in high-head, low-ﬂow circumstances, while the opposite is the case

for reaction turbines. And, ﬁnally, the slow-moving, but powerful, traditional

overshot waterwheel converts potential energy into mechanical energy. The slow

rotational rates of waterwheels are a poor match to the high speeds needed by

generators, so they are not used for electric power.

Impulse turbines are the most commonly used turbines in micro-hydro systems.

The original impulse turbine was developed and patented by Lester Pelton in

1880, and its modern counterparts continue to carry his name. In a Pelton wheel,

water squirts out of nozzles onto sets of twin buckets attached to the rotating

wheel. The buckets are carefully designed to extract as much of the water’s

kinetic energy as possible while leaving enough energy in the water to enable it

to leave the buckets without interfering with the incoming water. A diagram of a

four-nozzle Pelton wheel is shown in Fig. 4.22. These turbines have efﬁciencies

typically in the range of 70–90%.

The ﬂow rate to a Pelton wheel is controlled by nozzles, which for simple

residential systems are much like those found on ordinary irrigation sprinklers.

When water exits a nozzle, its pressure head is converted to kinetic energy, which

204 DISTRIBUTED GENERATION

Twin

Buckets

Jet

Nozzle

Figure 4.22 A four-nozzle Pelton turbine.

means that we can use (4.3) to determine the ﬂow velocity.

so that v =



2gH

(4.14)

From ﬂow velocity v and ﬂow rate Q we can determine an appropriate diameter

for the water jets. For nozzles with needle valves, the jet diameter is on the order

of 10–20% smaller than the nozzle, but for simple, home-scale systems, the jet

and nozzle diameters are nearly equal. Using Q = vA along with (4.14), we can

determine the jet diameter d for a turbine with n nozzles:

Q = vA =



2gH





(4.15)

Solving for jet diameter gives

d =

0.949

(gH

)

1/4



(4.16)

Example 4.7 Nozzles for a Pelton Turbine. A penstock provides 150 gpm

(0.334 cfs) with 50 ft of head to a Pelton turbine with 4 nozzles. Assuming jet

and nozzle diameters are the same, pick a nozzle diameter.

Solution. From (4.16)

d =

0.949

(32.2 ft/s

× 50 ft)

1/4



0.334 ft

= 0.0433 ft = 0.52 in.

The efﬁciency of the original Pelton design suffers somewhat at higher ﬂow

rates because water trying to leave the buckets tends to interfere with the incoming

MICRO-HYDROPOWER SYSTEMS 205

jet. Another impulse turbine, called a Turgo wheel, is similar to a Pelton, but

the runner has a different shape and the incoming jet of water hits the blades

somewhat from one side, allowing exiting water to leave from the other, which

greatly reduces the interference problem. The Turgo design also allows the jet

to spray several buckets at once; this spins the turbine at a higher speed than a

Pelton, which makes it somewhat more compatible with generator speeds.

There is another impulse turbine, called a cross-ﬂow turbine, which is espe-

cially useful in low-to-medium head situations (5–20 m). This turbine is also

known as a Banki, Mitchell, or Ossberger turbine—names that reﬂect its inven-

tor, principal developer, and current manufacturer. These turbines are especially

simple to fabricate, which makes them popular in developing countries where

they can be built locally.

For low head installations with large ﬂow rates, reaction turbines are the ones

most commonly used. Rather than having the runner be shot at by a stream

of water, as is the case with impulse turbines, reaction turbine runners are com-

pletely immersed in water and derive their power from the mass of water moving

through them rather than the velocity. Most reaction turbines used in micro-hydro

installations have runners that look like an outboard motor propeller. The pro-

peller may have anywhere from three to six blades, which for small systems

are usually ﬁxed pitch. Larger units that include variable-pitch blades and other

adjustable features are referred to as Kaplan turbines. An example of a right-

angle-drive system in which a bulb contains the gearing between the turbine and

an externally mounted generator is shown in Fig. 4.23.

4.5.5 Electrical Aspects of Micro-Hydro

Larger micro-hydro systems may be used as a source of ac power that is fed

directly into utility lines using conventional synchronous generators and grid

interfaces. Since the output frequency is determined by the rpm of the genera-

tor, very precise speed controls are necessary. While mechanical governors and

hand-operated control valves have been traditionally used, modern systems have

electronic governors controlled by microprocessors.

Figure 4.23 A right-angle-drive propeller turbine. Inversin (1986).

206 DISTRIBUTED GENERATION

Charge

Controller

Shunt

Load

Generator

Turbine

Batteries

DC to AC

Inverter

Loads

Figure 4.24 Electrical block diagram of a battery-based micro-hydro system.

On the other end of the scale, home-size micro-hydro systems usually generate

dc, which is used to charge batteries. An exception would be the case in which

utility power is conveniently available, in which case a grid-connected system in

which the meter spins in one direction when demand is less than the hydro system

provides, and the other way when it doesn’t, would be simpler and cheaper than

the battery-storage approach. The electrical details of grid-connected systems as

well as stand-alone systems with battery storage are covered in some detail in

the Photovoltaic Systems chapter of this text (Chapter 9).

The battery bank in a stand-alone micro-hydro system allows the hydro sys-

tem, including pipes, valves, turbine, and generator, to be designed to meet just

the average daily power demand, rather than the peak, which means that every-

thing can be smaller and cheaper. Loads vary throughout the day, of course, as

appliances are turned on and off, but the real peaks in demand are associated with

the surges of current needed to start the motors in major appliances and power

tools. Batteries handle that with ease. Since daily variations in water ﬂow are

modest, micro-hydro battery storage systems can be sized to cover much shorter

outages than weather-dependent PV systems must handle. Two days of storage

is considered reasonable.

A diagram of the principal electrical components in a typical battery-based

micro-hydro system is given in Fig. 4.24. To keep the batteries from being dam-

aged by overcharging, the system shown includes a charge controller that diverts

excess power from the generator to a shunt load, which could be, for example, the

heating element in an electric water heater tank. Other control schemes are pos-

sible, including use of regulators that either (a) adjust the ﬂow of water through

the turbine or (b) modulate the generator output by adjusting the current to its

ﬁeld windings. As shown, batteries can provide dc power directly to some loads,

while other loads receive ac from an inverter.

4.6 FUEL CELLS

I believe that water will one day be employed as a fuel, that hydrogen and oxygen

which constitute it, used singly or together, will furnish an inexhaustible source of

heat and light.

—Jules Verne, Mysterious Island, 1874

FUEL CELLS 207

The portion of the above quote in which Jules Verne describes the joining

of hydrogen and oxygen to provide a source of heat and light is a remarkably

accurate description of one of the most promising new technologies now nearing

commercial reality—the fuel cell. However, he didn’t get it quite right since

more energy is needed to dissociate water into hydrogen and oxygen than can be

recovered so water itself cannot be considered a fuel.

Fuel cells convert chemical energy contained in a fuel (hydrogen, natural

gas, methanol, gasoline, etc.) directly into electrical power. By avoiding the

intermediate step of converting fuel energy ﬁrst into heat, which is then used

to create mechanical motion and ﬁnally electrical power, fuel cell efﬁciency is

not constrained by the Carnot limits of heat engines (Fig. 4.25). Fuel-to-electric

power efﬁciencies as high as 65% are likely, which gives fuel cells the potential to

be roughly twice as efﬁcient as the average central power station operating today.

Fuel cells have other properties besides high efﬁciency that make them espe-

cially appealing. The usual combustion products (SO

, particulates, CO, and

various unburned or partially burned hydrocarbons) are not emitted, although

there may be some thermal NO

when fuel cells operate at high temperatures.

They are vibration-free and almost silent, which, when coupled with their lack

of emissions, means they can be located very close to their loads—for example,

in the basement of a building. Being close to their loads, they not only avoid

transmission and distribution system losses, but their waste heat can be used

to cogenerate electricity and useful heat for applications such as space heating,

air-conditioning, and hot water. Fuel-cell cogeneration systems can have overall

efﬁciencies from fuel to electricity and heat of over 80%. High overall efﬁciency

not only saves fuel but also, if that fuel is a hydrocarbon such as natural gas,

emissions of the principal greenhouse gas, CO

, are reduced as well. In fact,

CHEMICAL

ENERGY

HEAT

MECHANICAL

MOTION

ELECTRICITY

CHEMICAL

ENERGY

CONVENTIONAL

COMBUSTION

FUEL

CELL

Figure 4.25 Conversion of chemical energy to electricity in a fuel cell is not limited by

the Carnot efﬁciency constraints of heat engines.