Transcript
Hydroelectric and Wind Power Plants
Prof. Paulo Seleghim Jr.Universidade de São Paulo
LBE5010 Renewable Energies and Energy Planning
Coal39.1%
Hydro6.7%
Wind4.2%
Approximately 11% of all electricity generated in the world comes from impulse turbines
Turbinas Parson(r 0,5)
Impulse turbines (r=0)
Coal39.1%
Hydro6.7%
Wind4.2%
Hydroelectric turbines
✓ lowest generation cost (~4 ¢/kWh)
✓ 50 – 100 years useful life
✓ functionality of the reservoir
✓ small growth potential
Parson turbines(r 0,5)
Wind turbines
✓ low generation cost (~8 ¢/kWh)
✓ virtually unlimited potential
✓ complementarity with hydroelectric power plants
✓ intermittent
Approximately 11% of all electricity generated in the world comes from impulse turbines
Impulse turbines (r=0)
ramjet, scramjet, etc. (r = 1)
OPERATION OF THERMO POWERPLANTS BETWEEN 2013 – 2014
WIND ELECTRICITY GENERATION IN BRAZIL
Technical potential: 143 GW(1)
(1) Atlas do Potencial Eólico Brasileiro(2) Assoc. Brasileira de Energia Eólica
Operating (2014): 9,91 GW(2)
Hired (2035): 9,93 GW(2)
Average FAC (2014): 38%(2)
Total generation in 2014: 71,26 GW
WIND38%
Global Mean Wind Speed at 80m
Global Mean Wind Speed at 80m
Chapada do Araripe
TW21,2W 2012,cons =
WORLD HYDROELECTRIC POTENTIAL
Wpot: 0,113 TW
Winst: 0,183 TW
América do Norte
Wpot: 0,235 TW
Winst: 0,143 TW
América do Sul
Wpot: 0,095 TW
Winst: 0,172 TW
Europa
Wpot: 0,169 TW
Winst: 0,026 TW
África
Wpot: 0,340 TW
Winst: 0,341 TW
Ásia
FLUX MACHINES:theoretical analysis
Energy inventory in the control volume... 1ª Law of Thermodynamics
open
systemQ W
entra
kkm sai
kkm
( ) ( )
++−++−−=
entra
2kkkk
sai
2kkkk
VC 2/Vgzhm2/VgzhmWQdt
dE
mechanicalenergy
thermalenergy
mechanicalenergy
thermalenergy
Q W
entra
kkm sai
kkm
( ) ( )
++−++−−=
entra
2kkkk
sai
2kkkk
VC 2/Vgzhm2/VgzhmWQdt
dE
( ) ( )
++−++=
sai
2kkkkk
entra
2kkkkk 2/Vgz/Pm2/Vgz/PmW
T=cte T=cte
Energy inventory in the control volume... 1ª Law of Thermodynamics
open
system
Application to an impulse turbine
1
2 3
4
4V1Vforces on the
fluid exerted by
the turbine
velocity pressure
1 2 3 4
4V1V
1
2 3
4
)VV(mA)PP(F 4123 −=−=
Saint-Venant
momentumvariation
Application to an impulse turbine
forces on the
fluid exerted by
the turbine
)VV(mA)PP(F 4123 −=−=
+
−
+
=
2
VP
2
VPm0
22
2
22
1
1
1
)VV(VAA)PP(F 41med23 −=−=
+
−
+
=
2
VP
2
VPm0
24
4
423
3
3
P1 = P4
V2 = V3
1ª lei
2
VVV 41
med
+=
−=
−
2
V
2
VPP 24
21
2
2
3
3
T = ctez = cte
→ 32
Application to an impulse turbine
)VV(VAVFW 412medmed −==
)VV(2
VVAVFW 41
2
41med −
+==
)1(2
1VAW
2
31 −
+=
14 V/V=
1ou3/10/W −===
2
VA
27
16W
31
max =
Application to an impulse turbine
2
VA
27
16W
31
max =
s/m9maximum
mechanical power
produced by the
turbine
D = 20 m
25°C, 1bar
2
)s/m9(
4
)m20(
m
kg17,1
27
16W
32
3
max
=
kW789,158Wmax =
s/m325°C, 1bar
D = 34,6 m
Application to an impulse turbine
Working Definitions and Equations
)1()1(2
1VA
2
1W)1(
2
1VAW 23
1
2
31 −+=→−
+=
windpower
powercoefficient
)1()1(2
1
power wind
power turbine
2/VA
W)(CP 2
31
−+==
=
= velocity ratio
CP =
coefic
iente
de p
otê
ncia
%3,5927
16CPmax =
2/VA)(CP
W
power maximum
power actual3med
==
design:=1/3
wind powercapacity
V
Working Definitions and Equations
Burgar Hill, Orkney; 60 m measurement height; 4 hour averages
V
2/VA)(CP
W3med
=
V9,8m/s
nominal designvalues
+3−3
Working Definitions and Equations
V
Burgar Hill, Orkney; 60 m measurement height; 4 hour averages
2/VA)(CP
W3med
=
0
loss ofefficiency
Working Definitions and Equations
Factors Causing Efficiency Losses
high pressure
low pressure
high pressure
low pressure
Factors Causing Efficiency Losses
high pressure
low pressurewing tipvortex
wing tipvortex
high pressure
low pressure
Factors Causing Efficiency Losses
high pressure
low pressurewing tipvortex
wing tipvortex
high pressure
low pressure
Evolution of Wind Power Technology
600m
tempo
W
active phase return phase
balloon
400m
lateral wind
200m
HYDROELECTRIC POWER PLANTS:design and operation
1
2
mecW
Kaplan
eleW
W
W
Wmec
=
( ) ( ) 2/Vgz/P2/Vgz/PmW 22222
21111 ++−++=
( ) ( ) 2/Vgz/P2/Vgz/PmW 22222
21111 ++−++=
1
2
mecW
Kaplan
eleW
( ) ( ) ( ) 2/V2/Vzzg/P/PmW 22
21212211 −+−+−=
W
W
Wmec
=
1
2
mecW
Kaplan
eleW
zgmW =
W
W
Wmec
=
Hydroelectric Power Generation Potential in the World
zgmW = Average continental height: 840m
Average annual pluviosity: 505103 km3
at sea: 398 103 km3
on land: 107 103 km3
m840s
m8,9
m
kg997
s360024365
)m10(10107W
23
333
teomax,
=
TW8,27W theomax, =
Assuming that all in land precipitation can be used for power generation
TW84,3W UNDPmax, = World Energy Assessment: 2004 - United Nations Development Programme
TW21,2W 2012,cons =
The potential growth of hydroelectric generation is substantially limited, however...
RESERVOIR: Capacity of storing water for energy generation
COMPLEMENTARITY: Stabilization of supply in face of fluctuations in generation conditions (intermittencies) and also of the demand
Hydroelectric Power Generation Potential in the World
Barra Bonita
Bariri
Promissão
Ibitinga
Nova
AnanhandavaTrêsIrmãos
Jupiá
PortoPrimavera
Institutions of the Electricity Sector in Brazil
Geradores
DistribuidoresConsumidores
Energy Bids Consolidated Results
0
1
2
3
4
5
6
7
8
2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 2055
GW(físicos)
ano
Último leilão: 13/11/2015
Energy Bids Consolidated Results
APPLICATION EXAMPLE:optimized design and operation
HYDROELECTRIC POWER PLANTS OPTIMIZED OPERATION
time
flow rate(m3/s)
100
20
10
01/01 31/1201/04 01/07 30/09
annual averages
seasonal variations of the main river and tributaries
50m100m3/s
100 m3/s
50m110m3/s
10 m3/s
50m130m3/s
20 m3/s
Design Configuration
efficiency curves and optimum operation points (%)
100
Nsp,min Nsp,max
Locus of design points(maximum conversion efficiency)
specificrotation (rps)
4/5
2/1
sp)Hg(
)/W(NN
=
design point
geometric
similarity
50m100m3/s
100 m3/s
50m110m3/s
10 m3/s
50m130m3/s
20 m3/s
HYDROELECTRIC POWER PLANTS OPTIMIZED OPERATION
Design Configuration
(%)
100
0,1
4/5
2/1
sp)Hg(
)/W(
=
0,04 0,2 0,4 1,0 2,0 4,0 10,0
95
90
85KaplanFrancis
Pelton
50m100m3/s
100 m3/s
50m110m3/s
10 m3/s
50m130m3/s
20 m3/s
HYDROELECTRIC POWER PLANTS OPTIMIZED OPERATION
Design Configuration
efficiency curves and optimum operation points
specificrotation (rad)
312rpmsp = 3,14rad
298rpmsp = 3,14rad
274rpmNsp = 0,5
“We chose Kaplan turbines”
50m100m3/s
100 m3/s
50m110m3/s
10 m3/s
50m130m3/s
20 m3/s
(%)
100
0,1
4/5
2/1
sp)Hg(
)/W(
=
0,04 0,2 0,4 1,0 2,0 4,0 10,0
95
90
85KaplanFrancis
Pelton
HYDROELECTRIC POWER PLANTS OPTIMIZED OPERATION
Design Configuration
efficiency curves and optimum operation points
specificrotation (rad)
312rpmsp = 3,14rad
298rpmsp = 3,14rad
274rpmNsp = 0,5
50m100m3/s
100 m3/s
50m110m3/s
10 m3/s
50m130m3/s
20 m3/s
HYDROELECTRIC POWER PLANTS OPTIMIZED OPERATION
Design Configuration
The design is based on nominal parameters (annual or pluriannual averages) that result in an optimized
performance (maximum efficiency)
Operating parameters vary with respect to nominal parameters (tributaries flow rates e.g.)
The problem: how to adjust the overall system operation, acting on controllable variables, in order to optimize
performance ?
( ) =k
ksist maxmax → performance criterium
( ) =k
ksist maxmax
HYDROELECTRIC POWER PLANTS OPTIMIZED OPERATION
→ performance criterium
Hk+1
Vk+1
Qk+1
Ak+1
Wk+1
Hk
Vk
Qk
Ak
Wk
Hk-1
Vk-1
Qk-1
Ak-1
Wk-1
ano
Winst
Wmed
W
W
+
=k W
meddef
sist1.0
W
Wmed W
( ) =k
ksist maxmax
Given the (non controllable) variations of the tributaries flow
rates (A), how to adjust the reservoirs discharges (Q) to optimize the total energy generation ?
HYDROELECTRIC POWER PLANTS OPTIMIZED OPERATION
Hk+1
Vk+1
Qk+1
Ak+1
Wk+1
Hk
Vk
Qk
Ak
Wk
Hk-1
Vk-1
Qk-1
Ak-1
Wk-1
Subjected to the foillowing mass and energy conservation equations:
kk1kk QAQ
dt
dV−+= −
kkkk HQgW =
=
T
kk dtWE )V(fH kkk =
)N( k,spkk =
To which the following performance characterization
equation apply
Efficiency curves
Water height at in function of the
accumulated volume
+k W
med
1.0
Wmax
HYDROELECTRIC POWER PLANTS OPTIMIZED OPERATION
Given the (non controllable) variations of the tributaries flow
rates (A), how to adjust the reservoirs discharges (Q) to optimize the total energy generation ?
TRIBUTARIES FLOW RATES: STOCHASTIC MODELS
Hydrology 2014, 1(1), 89-111; doi:10.3390/hydrology1010089
vazão(m3/s)
100
20
10
0
−=
24365
t2sin1020A3
=8760 horas=2190 horas =4380 horas =6750 horas
365243/4 365244/4
+
=
2190tse878,7
2190t0se21902
t2sin1010
A2
365242/4365241/4
+=
24365
t2sin10100A1
TRIBUTARIES FLOW RATES: STOCHASTIC MODELS
TURBINE PERFORMANCE EQUATIONS
4/3
2/1
sp)Hg(
QNN
=
H
Q
W
cxbxax 2max
^ ++=
7,4c8,6b8,2a =−==
2
NNN
max,spmin,spnom,sp
+=
max?
max
0,0
(%)
Nsp,nom Nsp,max
0,7max
0
0,5 1,0x
design point
model
Nsp,min
RESERVOIR CHARACTERIZATION EQUATIONS
L
H
B
2A+B
A
A
baseAL3
1V =
L
B
2A+B
A
A
L
H)(Tg
=
a
H)(Tg
=
baseAL3
1V =
2
Ha2HbAbase
+=
+=
2
Ha2Hb
3
LV
+
=
)(Tg
Hb
)(Tg3
HV
2
L
H)(Tg
=
a
H)(Tg
=
H
RESERVOIR CHARACTERIZATION EQUATIONS
3nom km025,0V =
3Monte.B km5,2V =
5km
50m
100m
200m
200m
01,05000
50
L
H)(Tg ==
= 25,0
200
50
a
H)(Tg ==
=
+
=
)(Tg
Hb
)(Tg3
HV
2
92
1025,0
50100
01,03
50V −
+
=
3Itaupú km19V =
RESERVOIR CHARACTERIZATION EQUATIONS
H
volume (km3)
altura (m) silting
+
=
)(Tg
Hb
)(Tg3
HV
2
RESERVOIR CHARACTERIZATION EQUATIONS
FORMULATION OF THE OPTIMIZATION PROBLEM
50mQ1
A1(t)
50mQ2
A2(t)
50mQ3
A3(t)
• Maximum total energy generated in a period of time (1 year)
• Maximum regularity of the generated energy (dispatchability)
( ) HQNgW sp =
4/3
2/1
sp)Hg(
QNN
=
cteHQ 4/32/1 −
Q e H must be so that Nsp 0,5to have max
When Q H and when A H
cteHQ 1 −
)A,Q(HH =
conflicting effects: trade-off solution
50mQ1
A1(t)
50mQ2
A2(t)
50mQ3
A3(t)
+
→k k,W
k,med321
1.0
Wmax)t(Qe)t(Q),t(Q
Greater total generation in the period
Smaller dispersion around the average value
Defining an adequate target function combining two optimization aspects (total energy generation and regularity)
FORMULATION OF THE OPTIMIZATION PROBLEM
• Maximum total energy generated in a period of time (1 year)
• Maximum regularity of the generated energy (dispatchability)
50mQ1
A1(t)
50mQ2
A2(t)
50mQ3
A3(t)
+
=k k,W
k,med321
1.0
Wmax)Q,Q,Q(
Initialization
Random change in direction 1
Keep modification only if increases
Random change in direction 2
Keep modification only if increases
Random change in direction N
Keep modification only if increases
Iterate
Q1
Q2
“Bioinpired” search method
não
iso-
FORMULATION OF THE OPTIMIZATION PROBLEM
50mQ1
A1(t)
50mQ2
A2(t)
50mQ3
A3(t)
+
=k k,W
k,med321
1.0
Wmax)Q,Q,Q(
Q1
Q2
iso-
FORMULATION OF THE OPTIMIZATION PROBLEM
Initialization
Random change in direction 1
Keep modification only if increases
Random change in direction 2
Keep modification only if increases
Random change in direction N
Keep modification only if increases
Iterate
“Bioinpired” search method
50mQ1
A1(t)
50mQ2
A2(t)
50mQ3
A3(t)
+
=k k,W
k,med321
1.0
Wmax)Q,Q,Q(
Q1
Q2
iso-
FORMULATION OF THE OPTIMIZATION PROBLEM
Initialization
Random change in direction 1
Keep modification only if increases
Random change in direction 2
Keep modification only if increases
Random change in direction N
Keep modification only if increases
Iterate
“Bioinpired” search method
50mQ1
A1(t)
50mQ2
A2(t)
50mQ3
A3(t)
+
=k k,W
k,med321
1.0
Wmax)Q,Q,Q(
Q1
Q2
iso-
FORMULATION OF THE OPTIMIZATION PROBLEM
Initialization
Random change in direction 1
Keep modification only if increases
Random change in direction 2
Keep modification only if increases
Random change in direction N
Keep modification only if increases
Iterate
“Bioinpired” search method
NUMERICAL SIMULATIONS
+
=k k,W
k,med321
1.0
Wmax)Q,Q,Q(
+
=k k,W
k,med321
1.0
Wmax)Q,Q,Q(SMALL VOLUME RESERVOIR
+
=k k,W
k,med321
1.0
Wmax)Q,Q,Q(LARGE VOLUME RESERVOIR
+
=K k,W
k,med321
1.0
Wmax)Q,Q,Q(SMALL VOLUME RESERVOIR
LARGE VOLUME RESERVOIR +
=K k,W
k,med321
1.0
Wmax)Q,Q,Q(
+
=k k,W
3k,med
3211.0
)W(max)Q,Q,Q(SMALL VOLUME RESERVOIR
LARGE VOLUME RESERVOIR +
=k k,W
3k,med
3211.0
)W(max)Q,Q,Q(
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