Hydropower Optimal Power Flow

8/10/2019 Hydropower Optimal Power Flow

1/26

Dimensional Analysis for Determining OptimalDischarge and Optimal Penstock Diameter inImpulse and Reaction Water Turbines

1

Arturo Leon1and Ling Zhu

1

School of Civil and Construction Engineering, Oregon State University2Department of Civil and Environmental Engineering, Louisiana State University

X Congreso Latinoamericano de Estudiantes de Ingenieria Civil - XXII Congreso

Nacional de Estudiantes de Ingenieria Civil del Per, August 4-8, !"4#


2/26

Ackno!ledgements"

#inancial support"

$onneville Po%er Administration o& the'#(# )e*artment o& Energ+ )E. undera%ard num/er 0IP128#


3/26

Presentation outline

$ac3ground5otivation

)imensional anal+sis A**lication Conclusions

$


4/26

%ydropo!er systems

&arkamis hydroelectric po!er plant' Turkey

Three (orges hydropo!er

plant' )hina

%%%#%ater-technolog+#net

%oo*er Dam' +,

%%%#hdrinc#com

%%%#*o%er-technolog+#com


5/26

-ackground./oti*ation

6"7 o& glo/al electricit+ *roduction came &romh+dro*o%er in !!9

6)evelo*ment o& all the remaining h+droelectric*otential could not ho*e to cover total &uture %orld

demand

6:+dro*o%er due to its associated reservoirstorage, can *rovide i/ilit+ and relia/ilit+ &or

energ+ *roduction in integrated s+stems# therdi&&use and varia/le rene%a/le energ+ sources

%ind, %ave, solar. can *la+ a larger role in

*roviding electrical *o%er o& commercial


6/26

-ackground./oti*ation 0)ont2

6Im*lementation o& remaining h+droelectric *otentialcan ma3e a vast contri/ution to im*roving livingstandards in the develo*ing %orld (outh America, Asia

and A&rica., %here the greatest *otential still e;ists#

65inimi=ing %ater consum*tion &or *roducingh+dro*o%er is critical given that overuse o& &lo%s &or

energ+ *roduction ma+ result in a shortage o& &lo%s &or

other *ur*oses such as irrigation or navigation

60heoretical &rame%or3 &or determining o*timal design&lo% and o*timal *enstoc3 diameter &or im*ulse and

reaction tur/ines is N0availa/lein literature


7/26

3lectrical po!er 0P2 of impulse andreaction turbines 0)ont2

4

( )g LP Q H h=

= t g = const

Hg : gross head

hL : total head losses

: specific weight of water = g( )

: water densityg : acceleration of gravity

Q : flow discharge

t : turbine efficiency

g : generator efficiency


8/26

3lectrical po!er 0P2 of impulse andreaction turbines 0)ont2

5

P =Q Hg hL( )h

L =

Q2

2gA22 C

L

2

21 2

2

2

21 2

2

for an impulse turbine

for a reaction turbine

N

N

L

d

ALf k k

D AC

ALf k

D A

+ + =

+ +

L : length

D2 : diameter of penstock

A2 : cross - section area of penstock

AN : nozzle area at exit

f : friction factor

1-2

N

2

: draft tube cross-sectional area at outlet

k : sum of local losses in penstock

due to entrance, bends, penstock fittings and gates

k : nozzle head loss coefficient

11, : 0.98 0.99

d

N V

V

A

k CC

=


9/26

A dimensionless relationship bet!eenpo!er and flo! discharge 0)ont2

6

6Choose re&erence *o%er Pr. and re&erence discharge Qr.

6Choose Pras the ma;imum *o%er can /e generated %ith

&i;ed CL and o& "!!

2

2

22

g LQP Q H CgA

=

dP dQ = 0

Qr= 2A3

1

3gH

g , Pr =4

3H

gA3

1

3gH

g

A3 = A

N for an impulse turbine

Ad

for a reaction turbine


10/26

A dimensionless relationship bet!eenpo!er and flo! discharge 0)ont2

17

2

2

2

2g L

QP Q H C

gA

=

P+ = P Pr, Q+ = Q Qr

with

= CLA3

A2

2

= f L, D2, f, k , A3 A2(

!!

2

P Q Q + + + =

[ ]

[ ]

21

0.01, 1.0 for impulse turbines"n applications,

10, 1000 for reaction turbines

D


11/26

11

Im*ulse tur/ines > !#8.

Dimensionless discharge *ersus Dimensionless Po!er


12/26

1

?eaction tur/ines > !#8.

Dimensionless discharge *ersus Dimensionless Po!er


13/26

Determine optimal 8 and optimal D 0)ont2

1$

2! !! 0,2 2

dP QdQ

+ ++

=

@P @Q> !achieve ma;imum Pho%ever, not o*timalB

P+( )max =1

2

, Q+( )max =1

2

5inimi=ing %ater

consum*tion

Achieving large @P

%ith small @

5a;imi=e @P @


14/26


19

2! !! 0,2 2

dPQ

dQ + +

+

=

5inimi=ing %ater

consum*tion

Achieving large @P

%ith small @

5a;imi=e @P @

@P @Q> D

Ideal condition to

save %ater /ut *o%er

*roduced is small


15/26

1:

Im*ulse tur/ines > !#8.;P


16/26

1?

Im*ulse tur/ines > !#8.;P


17/26

14


o*timal head loss hL > hL/ Hg. "2#7

Qopt upper =2

3A2

7

10

gHg

CL

Popt upper =

76

135 HgA27

10

gHg

CL

dP+dQ+

opt

= 0.8

Q+( )opt upper =7

30

P+( )opt upper =19

15

7

30


18/26

15

Influence of changing penstock

diameter on po!er *ariation

P+

= Q

+

3

!!

2P Q Q + + +

=

!

!!

2

P QP

Q Q

+ +

++ +

=


19/26

Im*ulse tur/ines Q+> D.

;P


20/26

Qopt upper =2

3A2

7

10

gHg

CL

Popt upper =76

135HgA2

7

10

gHg

CL

Qopt = 4538

PHg

P s*eci&ied

Popt =38

45

HgQ

CL( )opt

A22

14

45

gHg

Q2

Q s*eci&ied

Turbine design !ith P or Qspecified


21/26

3@ample" Impulse Turbine design

( )

( )

( )

( )( )

2

1 2

# 2

$onditions:%ross head 200 m

&enstock length '00 m

1#

Nozzle (elocit) coefficient 0.98'

1.'

*oughness height of penstock material 0.0+' mm

inematic (iscosit) 10 m -s

urbine efficien

g

N

V

H

L

A

A

C

k

=

=

=

=

=

==

( )

( )

c) 82/

%enerator efficienc) 90/

t

g

=

=


22/26

Impulse Turbine design 0)ont2

)ase A1F design an im*ulse tur/ine %ith Q> !#7 mD

s

( )( )

( )

( ) ( )

opt -+

2 2

2

2

10 0.9

2

2

1+1#9!.8 m 1

+'

1 1 0.0!0

0.2' 2

'.+log!. *e

'001.' 1# !

L g

N

V

L N

C gH

A Q

kC

f

D

fC k

D

= =

= =

=

+

= + +

D2 = 0.3968 m


23/26

Impulse Turbine design0)ont2

Case A"F design an im*ulse tur/ine %ith Q> !#7 mD

sssuming that a schedule 80 steel pipe is reuired due to structural

considerations, a 18 in outside diameter pipe 3ould be selected.

3all thickness 4 0.9!8 in

internal diameter 4 1#.12+ in 5+09.' mm6

LC

( )

2

272

2

2

2'.!'

dimensionless head loss 0.1!+ 51!.+/6 1'.#/2

electrical po3er 0.82 0.90 1000 9.8 0.#

0.#200 2'.!' 4'1+21 4'1.+ k

2 9.8 0.1!1

L L

g

Qh C

gH A

P

=

= =

=


24/26

/ATLA- toolbo@ for turbine designhtt*F%e/#engr#oregonstate#eduGleonCodes#html
http://web.engr.oregonstate.edu/~leon/Codes.htmlhttp://web.engr.oregonstate.edu/~leon/Codes.html


25/26

)O)L+,IO, 0he *resent anal+sis resulted in various

dimensionless relationshi*s /et%een P, Qand hL&or

determining o*timal design &lo% and *enstoc3

diameter &or designing im*ulse and reaction tur/ines

0he derived relationshi*s %ere used to %ithdra%general insights on h+dro*o%er o*timi=ation# Hor

instance, it %as &ound that &or minimi=ing %ater

consum*tion, the ratio o& head loss to gross head

hL:g. should not e;ceed "2# 0o &acilitate the calculations, a 5A0LA$ h+dro*o%er

tool/o; %as develo*ed#


26/26

/any thanks for your attentionB/any thanks for your attentionB

)ontact")ontact"Arturo LeonArturo Leon(chool o& Civil and Construction Engineering,(chool o& Civil and Construction Engineering,regon (tate 'niversit+regon (tate 'niversit+

3Cmail"3Cmail"arturo#leonoregonstate#eduarturo#leonoregonstate#eduResearch Web page"htt*F%e/#engr#oregonstate#eduGleon

?
mailto:[email protected]:[email protected]://web.engr.oregonstate.edu/~leonhttp://web.engr.oregonstate.edu/~leonmailto:[email protected]

Date post:	02-Jun-2018
Category:	Documents
Upload:	alejandro-cardenas
View:	232 times
Download:	0 times

Hydropower Optimal Power Flow

Documents