Masters G.M. Renewable and Efficient Electric Power Systems

Подождите немного. Документ загружается.

588 PHOTOVOLTAIC SYSTEMS

the equivalent of 5.0 ft of pipe; the gate valve (assuming it is totally open) adds

the equivalent of 0.5 ft of pipe. The total equivalent length of pipe is therefore

240 + 6 + 5 + 0.5 = 251.5 ft.

From Table 9.17, 100 ft of 3/4-in. pipe at 4 gpm has a pressure drop of

4.2 ft/100



of tube. Our friction-head requirement is therefore 4.2 × 251.5/100 =

10.5 ft of water.

The water must be lifted 150 +10 = 160 ft (static head). Total head requirement

is the sum of static and friction heads, or 160 + 10.5 = 170.5 ft of water pressure.

If the process followed in Example 9.21 is repeated for varying ﬂow rates,

a plot of total dynamic head H (static plus friction) versus ﬂow rate, called

the hydraulic system curve, can be derived. The hydraulic system curve for

Example 9.21 is given in Fig. 9.57.

9.6.2 Hydraulic Pump Curves

The hydraulic system curve tells us the amount of head that the pump must

provide to supply a given ﬂow rate Q. To determine the actual ﬂow that a given

pump will provide, we need to know something about the characteristics of the

pump that will be used. Pumps suitable for PV-powered systems generally fall

into one of two categories: centrifugal and positive displacement pumps.

Centrifugal pumps have fast-spinning impellers that literally throw the water

out of the pump, creating suction on the input side of the pump and creating

pressure on the delivery side. When these are installed above the water, they

are limited by the ability of atmospheric pressure to push water up into the

suction side of the pump—that is, to a theoretical maximum of about 32 ft. In

240

220

200

180

160

140

120

100

024681012

Flow Rate

(gpm)

Total Dynamic Head H (ft of H

Figure 9.57 The hydraulic system curve for Example 9.21.

PV-POWERED WATER PUMPING 589

practice, this is more like 20 ft. When the pump is installed below the water

line, however, the pump can push water up hundreds of feet. Submersible pumps

with waterproof housings for the motor are suspended in a well using the same

pipe that the water is pumped through. In this conﬁguration, centrifugal pumps

can push water over 1000 vertical feet. One of the disadvantages of centrifugal

pumps, however, is that their speedy impellers are susceptible to abrasion and

clogging by grit in the water. When powered by PVs, they are also particularly

sensitive to changes in solar intensity during the day.

Positive displacement pumps come in several types, including helical pumps,

which use a rotating shaft to push water up a cavity, jack pumps, which have

an above-ground oscillating arm that pulls a long drive shaft up and down (like

the classic oil-rig pumper), and diaphragm pumps, which use a rotating cam to

open and close valves. The traditional hand pump as well as the wind-powered

water pumps are versions of jack pumps. Jack pumps use simple ﬂap valves

that work very much like hydraulic diodes. During each upward stroke of the

shaft, a ﬂap closes and a gulp of water is carried upward; during the downward

stroke, the valve opens and new water enters a chamber to be carried upward on

the next stroke. In general, positive displacement pumps pump at slower rates

so they are most useful in low volume applications. They easily handle high

heads, however, and they are much less susceptible to gritty water problems than

centrifugal pumps. They also are less sensitive to changes in solar intensity. A

brief comparison of the two types of pumps is presented in Table 9.19.

The graphical relationship between head and ﬂow is called the hydraulic pump

curve, two examples of which are shown in Fig. 9.58. Notice that the fundamen-

tal difference in processes that produce the pumping for centrifugal and positive

displacement pumps yield quite different shapes to their pump curves. For a cen-

trifugal pump, as the height of the water column above the pump increases, more

and more of the pump’s energy is devoted to simply holding up the water so ﬂow

rates rapidly diminish. For example, imagine a small centrifugal pump connected

to a hose. Raising the open end of the hose higher and higher (increasing the

head) will result in less and less ﬂow until a point is reached at which there is no

ﬂow at all. On the other hand, the ﬂapper valve, diaphragm, or rotating screw in

TABLE 9.19 A Comparison Between Centrifugal and Positive-Displacement

Pumps

Centrifugal Positive Displacement

High-speed impellers Volumetric movement

Large ﬂow rates Lower ﬂow rates

Loss of ﬂow with higher heads Flow rate less affected by head

Low irradiance reduces ability to achieve

head

Low irradiance has little effect on head

Potential grit abrasion Unaffected by grit

590 PHOTOVOLTAIC SYSTEMS

Centrifugal pump

Positive

displacement pump

Flow rate

Head

Figure 9.58 The pump curves for positive displacement pumps and centrifugal pumps

have quite different shapes.

a positive displacement pump holds up the water column mechanically, so their

ﬂow rates are much less affected by increasing head.

Electrical I –V curves and hydraulic Q–H curves share many similar features.

For example, recall that the electrical power delivered by a PV is the product of

I times V and the maximum power point is at the knee of the I –V curve. For

the hydraulic side, the power delivered by the pump to the ﬂuid is given by

P = ρHQ (9.56)

where ρ is ﬂuid density. In American units,

P(watts) = 8.34 lb/gal × H(ft) × Q(gal/ min) × (1min/60 s)

× 1.356 W/(ft-lb/s)

P(watts) = 0.1885 × H(ft) × Q(gpm) (9.57)

In SI units,

P(watts) = 9.81 × H(m) × Q(L/s)(9.58)

When Q is zero, there is no power delivered to the ﬂuid; when the head H is

zero, there is no power delivered either.

To complicate matters, for directly coupled PV-to-pump systems the voltage

delivered to the pump will vary as insolation changes. In turn, the pump curve

will shift as the pump voltage changes, which means that the pump curves vary

with insolation. Many manufacturers of pumps intended for solar applications will

supply pump curves for voltages corresponding to nominal 12-V module voltages.

Figure 9.59 shows an example of a set of pump curves for the Jacuzzi SJ1C11

dc centrifugal pump, which is intended for use with photovoltaics. Individual

curves have been given for 15-V, 30-V, 45-V, and 60-V inputs. A typical “12-

V” PV module operating near the knee of its I –V curve delivers about 15 V,

PV-POWERED WATER PUMPING 591

350

300

250

200

150

100

Total Head (ft)

Flow rate (gpm)

0 2 4 6 8 10121416

60 V

45 V

30 V

15 V

30%

40%

43%

44%

40%

30%

Figure 9.59 Pump curves for the Jacuzzi SJ1C11 pump showing pump efﬁciency for

various input voltages. Pump efﬁciencies are also shown, with the peak along the knee

of the curves.

so these pump voltages are meant to correspond to 1, 2, 3, and 4, typical “12-V”

PV modules wired in series. Also shown are indications of the efﬁciency of the

pump as a function of ﬂow rate and head. Notice that the peak in efﬁciency (about

44%) occurs along the knee of the pump curves, which is exactly analogous to

the case for a PV I –V curve.

9.6.3 Hydraulic System Curve and Pump Curve Combined

Just as an I –V curve for a PV load is superimposed onto the I –V curves

for the photovoltaics, so too is the Q–H system curve superimposed onto the

Q–H pump curve to determine the hydraulic operating point. For example,

superimposing the system curve of Fig. 9.57 onto the pump curves in Fig. 9.59

gives us the diagram in Fig. 9.60. A glance at the ﬁgure tells us a lot. For

example, this pump will not deliver any water unless the voltage applied to the

pump is at least about 36 V. At 45 V, about 5 gpm would be pumped, while at

60 V the ﬂow would be about 9.5 gpm.

592 PHOTOVOLTAIC SYSTEMS

350

300

250

200

150

100

Total head (ft)

60 V

45 V

30 V

15 V

30%

40%

43%

44%

40%

30%

0 2 4 6 8 10 12 14 16

Flow rate (gpm)

System curve

Figure 9.60 The system curve for the example, superimposed onto the pump curves for

the Jacuzzi SJ1C11. No ﬂow occurs until pump voltage exceeds about 36 V.

9.6.4 A Simple Directly Coupled PV–Pump Design Approach

The easiest approach to estimating average performance of directly coupled

PV–pump systems is based on the familiar concept of “peak sun hours.” That is,

insolation expressed as kWh/m

-day is treated as if it is numerically equivalent

to “peak hours” at 1-sun. This lets us base the analysis of PV performance on

its 1-sun rated voltage, current, and power. And it lets us assume that the ﬂow

rates on a pump curve are deliverable for the number of peak sun hours per day.

This procedure assumes that a linear current booster (LCB) is included in the

system to help start the pump in the morning and keep it running under conditions

of low insolation. Starting a pump requires high current at low voltage, but under

low-light conditions the maximum power point on the PV I –V curve has just

the opposite characteristic. An LCB is the clever dc-to-dc converter described

in Section 9.2.2 that enables the PVs to operate at their highest efﬁciency in

low light—that is, at low current and relatively high voltage—while providing

the pump with what it needs to start or keep running—that is, high current and

low voltage.

Usually manufacturers provide a nominal voltage and power for their pump

curves. From pump power (W) and 1-sun PV power (W/module) we can deter-

mine the needed number of photovoltaic modules. If pump voltage and efﬁciency

PV-POWERED WATER PUMPING 593

are given, as is the case with the pump curves in Fig. 9.60, pump power can be

determined using (9.57).

(W) to pump =

Power to ﬂuid

Pump efﬁciency

0.1885 × H(ft) × Q(gpm)

(9.59)

The sizing procedure is based on the following simple steps (Thomas, 1987):

1. Determine the water production goal (gallons/day) in the design month

(highest water need and lowest insolation).

2. Use design-month insolation (hours @ 1-sun) as the hours of pumping to

ﬁnd the pumping rate:

Q(gpm) =

Daily demand (gal/day)

Insolation(h/day@1-sun) × 60 min /h

(9.60)

3. Find the total dynamic head H @ Q (gpm). As a default, the friction head

maybeassumedtobe5%ofthestatichead.

4. Find a pump capable of delivering the desired head H and ﬂow Q.Note

its input power P

and nominal voltage. Pump input power can also be

estimated from (9.59) along with estimated pump efﬁciency η

(defaults:

suction pumps 25%; submersible pumps 35%)

5. The number of PV modules in series (assuming that modules will operate

at about 15 V) is an integer number based on

Modules in series =

Pump voltage(V)

15 V/module

(9.61)

6. The number of PV strings in parallel will be an integer number based on

# strings =

Pump input power P

(W)

# mods in series × 15 V/mod ×I

(A) × de-rating

(9.62)

where I

is the PV rated current at STC. The de-rating factor takes into

account dirt and temperature effects. A reasonable default value is 0.80.

7. After having sized the system, the water pumped can be estimated by

rearranging (9.59) and adding in the de-rating factor:

Q(gal/day) = 15 V/mod × I

(A) × (# mods) ×(Peak h/day) × 60 min /h

× de-rating × η

/[0.1885 × H(ft)] (9.63)

Example 9.22 Sizing an Array for a 150-ft Well in Santa Maria, Califor-

nia. Suppose that the goal is to pump at least 1200 gallons per day from the

594 PHOTOVOLTAIC SYSTEMS

150-ft well described in Example 9.21 using the Jacuzzi SJ1C11 pump. Size the

PV array based on Siemens SR100 modules with rated current 5.9 A, mounted

at an L + 15

◦

tilt.

Solution. From the solar radiation tables given in Appendix E, the worst month

is December, with an insolation of 4.9 kwh/m

-day. From (9.60)

Q =

1200 gal/day

4.9 (h/day @1-sun) × 60 min /h

= 4.1 gpm

From Fig. 9.60, at 4.1 gpm the total dynamic head is about 170 ft and the pump

efﬁciency is about 34%. From (9.59), the estimated pump input power is

(W) =

0.1885 × H(ft) × Q(gpm)

Pump efﬁciency

0.1885 × 170 × 4.1

0.34

= 386 W

From Fig. 9.60, at 4.1 gpm and 170 ft of head, the pump voltage is a little under

45 V, which means that at 15 V per module, three modules in series should

be sufﬁcient.

Using (9.62), we can decide upon the number of parallel strings of modules

# strings =

386 W

3 modules string × 15 V/module × 5.9 A × 0.80

= 1.8

so choose two parallel strings.

−−

Array

disconnect

Linear

current

booster

Surge

protector

Well

Pump

Storage

tank

Figure 9.61 PV water pumping system for Example 9.22.

PROBLEMS 595

From (9.63), estimated delivery in January with two strings of three modules

would be

Q ≈

15 V × 5.9 A × 6 modules × 4.9 h/day × 60 min /h × 0.80 × 0.34

0.1885 × 170 ft

= 1325 gal/day

A system diagram is shown in Fig. 9.61.

REFERENCES

Applebaum, J. (1981). Performance Analysis of D.C. Motor Photovoltaic Converter Sys-

tem II, Solar Energy, vol 27, no. 5, pp. 421–431.

Chang, A. (2000). Residential Systems Summary Report: Analysis of TEAM-UP Residen-

tial Installations, Utility Photovoltaic Group, Washington, D.C.

Linden, D. (1995). Handbook of Batteries, McGraw-Hill, New York.

Patel, M. R. (1999). Wind and Solar Power Systems, CRC Press, Boca Raton, FL.

Real Goods Trading Corporation (2002). Solar Living Source Book,Ukiah,CA.

Roger, J. A. (1979). Theory of the Direct Coupling Between D. C. Motors and Photo-

voltaic Solar Arrays, Solar Energy, vol 23, pp 193–198.

Rosen, K., and A. Meier (1999). Energy Use of Televisions and Videocasette Recorders in

the U.S., Lawrence Berkeley National Labs, LBNL-42393.

Rosen, K., and A. Meier (2000). Energy Use of U.S. Consumer Electronics At the End of

the 20th Century, Lawrence Berkeley National Labs, LBNL-46212.

Sandia National Laboratories (1991). Maintenance and Operation of Stand-Alone Photo-

voltaic Systems, U.S. Department of Energy, Albuquerque, NM.

Sandia National Laboratories (1995). Stand-Alone. Photovoltaic Systems Handbook of

Recommended Design Practices, U.S. Department of Energy, Albuquerque, NM.

Scheuermann, K., D. R. Boleyn, P. N. Lilly, and S. Miller (2002). Measured Output for

nineteen residential PV systems: Updated analysis of actual system Performance and

net metering impacts, Proceedings of the 31st American Solar Energy Society Annual

Conference, Reno, NV.

Thomas, M. G. (1987), Water Pumping, the Solar Alternative, Sandia National Laborato-

ries, SAND87-0804, Albuquerque, NM.

Wiles, J. (2001). Photovoltaic Power Systems and the National Electrical Code: Suggested

Practices, Sandia National Laboratories, SAND2001-0674, Albuquerque, NM.

PROBLEMS

9.1 Suppose the I –V curve for a PV module exposed to 1-sun (1 kW/m

)of

insolation is as shown below:

596 PHOTOVOLTAIC SYSTEMS

20181614121086420

V (volts)

Current (amps)

1-sun = 1000 w/m

Figure P9.1

a. What load resistance R would result in the maximum power delivered

to the panel at 1-sun? How much power would that be (watts)?

b. Suppose the hour-by-hour insolation striking this single panel is given

in the following table (e.g., from 7:30

A.M. to 8:30 A.M. the insolation

averages 200 W/m

Time

Insolation (W/m

)

8A.M.,4P.M. 200

9, 3

400

10, 2

600

11, 1

800

noon

1000

Daily total

5000 W-hr/m

If current (at any given voltage) is directly proportional to insolation,

carefully draw the hour-by-hour I –V curves for the module. For the

resistive load determined in (a), what would be the energy (watt-hr)

delivered by this panel in a day’s time?

c. If the module is equipped with a maximum-power-point tracker, what

energy would be delivered in a day’s time? What percentage improve-

ment does it provide?

9.2 Consider a single PV module supplying power to a resistance load. The

hour-by-hour I –V curves for the PV module are shown below along

with the I –V curve for the resistance. For simplicity, consider each I –V

curve to apply for one hour (e.g., the “8-

A.M.” curve is from 7:30 A.M. to

8:30

A.M.).

PROBLEMS 597

20181614121086420

Current (amps)

1-sun = 1000 w/m

Noon

11am and 1 pm

10 am and 2 pm

9 am and 3 pm

8 am and 4 pm

Resistance load

V (volts)

Figure P9.2a

a. What is the resistance of the load?

−

Modules in series

(b)

−

Modules in parallel

(c)

Figure P9.2b

b. Suppose the same resistive load is connected to two such modules wired

together in series (so their voltages add). Draw the I –V curves for the

pair of modules and from that, determine the daily energy delivered

(W-hr). Compare that with the energy that would have been delivered

with just a single module.

c. If two modules are connected in parallel (so their currents add), what

would be the daily energy delivered to the same resistive load?

9.3 A dc pump connected to a PV module runs a garden water fountain. The

pump I –V curve and the hourly I –V curves for the module are shown.

Once the pump starts running, it needs 8 V to keep spinning. At what

time in the morning will the pump start running? At what time will it stop

running?