5 - IIT - Universidad Pontificia Comillas

ESD.S30
Electric Power System Modeling for a Low Carbon Economy
Impact of renewable energy sources in
short-term generation planning
Prof. Andres Ramos
http://www.iit.upcomillas.es/aramos/
Andres.Ramos@upcomillas.es
arght@mit.edu
Massachusetts Institute of Technology (MIT). October 2014
Contents
1.
Wind generation in Spain
2.
Impact of wind generation in medium and long-term planning
3.
Impact of wind generation in short-term planning
4.
Impact of wind generation in real time operation
5.
Stochastic Unit Commitment
6.
Prototype stochastic unit commitment. Mathematical formulation
7.
Prototype stochastic unit commitment. Computer implementation
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
2
1
Wind generation in Spain
Impact of WG in medium and long-term planning
Impact of WG in short-term planning
Impact of WG in real time operation
Stochastic UC
Prototype stochastic UC. Mathematical formulation
Prototype stochastic UC. Computer implementation
Wind generation in Spain
Renewable Energy Sources (RES)
•
Renewable Energy Sources
Wind generation (WG)
– Solar Thermal
– Photovoltaic Solar
– Small Hydro
– Biomass
– Solid Waste
–
•
Cogeneration or Combined Heat and Power (CHP)
and as another uncertain resources
•
•
Demand Response (DR)
Electric Vehicle (EV)
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
4
Cecre: control centre of renewable energies
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
5
WG in mainland Spain
•
Year 2013:
21.1 % wind energy
– 22746 MW (22.2 % of total installed capacity) installed on
Dec-31-2013
Energy
[GWh]
–
•
Year 2016 (NREAP):
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Winter Peak
[MW]
Summer Peak
[MW]
Min Load
[MW]
Max Up Reserve
[MW]
Max Down Reserve
[MW]
Nuclear
[MW]
Coal
[MW]
CCGT
[MW]
Gas Turbines
[MW]
Max Hydro Output
[MW]
Pure Pumped Storage Hydro
[MW]
Combined Pumped Storage Hydro [MW]
Wind Generation
[MW]
CHP
[MW]
Other RES
[MW]
Natural Hydro Inflows
[GWh]
Coal Price
[€/Mcal]
Natural Gas Price
[€/Mcal]
CO2 Price
[€/t CO2]
# of Electric Vehicles
[units]
Impact of RES in Short-Term Generation Planning
6
323408
59135
44511
18385
6155
1183
7000
6338
25026
2100
10000
2432
2985
29778
9008
10758
28517
0.014
0.025
30
50000
Solar and wind generation
http://www.iit.upcomillas.es/aramos/Productores_Regimen_Especial.kmz
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
8
Installed capacity of WG
Installed Capacity [MW]
25000
22746
22573
21011
19569
18722
20000
15977
15000
13529
11290
9654
10000
7777
5816
4391
5000
1
2817
1829
6341022
375
146
97
1 30 34 39
Source: REE
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
0
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
9
Demand share of WG
25
22
19
Demand share[%]
20
17 16
15
15
12
10
10
8
9
7
4
5
0
0
0
0
0
0
0
0
1
1
2
5
3
Source: REE
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
0
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
10
Monthly WG capacity factor
Spanish saying:
Febrero revuelto,
marzo ventoso y
abril lluvioso,
sacan a mayo
florido y hermoso
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Impact of RES in Short-Term Generation Planning
11
WG Operation hours at full capacity
2440
2421
2341
Operation Hours at Full Capacity [h]
2500
2078
2097
2000
1873
1951
2395
2208
2161
2132
2109
2 026 2027
2024 2004
2015
2 014
1988
1656 1651
1500
1000
570
500
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
0
Source: REE
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
12
Yearly WG Capacity factor
29%
30%
28%28%
27%
25%
24%
Capacity facotr [p.u.]
21%
19%
20%
22%
27%
25%
25%
24%
24%
23%23% 23%23%23%23% 23%
10%
19%
15%
10%
7%
5%
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
0%
Source: REE
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
13
Maximum WG output (Wednesday, 2012-04-18)
52%
16593 MW
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Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
14
Maximum WG output (Tuesday, 2010-11-09)
14901 MW
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
53%
Impact of RES in Short-Term Generation Planning
15
Maximum WG output (Thursday, 2010-02-24)
12843 MW
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
45 %
16
Maximum WG output (Thursday, 2009-03-05)
11180 MW
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
42 %
17
Maximum hourly WG share 64.2 %
(Monday, 2012-09-24 3 am)
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Impact of RES in Short-Term Generation Planning
18
Maximum hourly WG share 59.7 %
(Sunday, 2011-11-06 2 am)
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Impact of RES in Short-Term Generation Planning
19
Maximum daily WG share (Sunday, 2009-11-08)
11536 MW
53 %
45% daily
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Impact of RES in Short-Term Generation Planning
20
Maximum monthly WG share (April 2012)
Solar PV
Wind
Hydro
Solar thermal
Thermal RES
Nuclear
Cogeneration
and other RES
Combined Cycle
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Coal
Impact of RES in Short-Term Generation Planning
22
2
Wind generation in Spain
Impact of WG in medium and long-term planning
Impact of WG in short-term planning
Impact of WG in real time operation
Stochastic UC
Prototype stochastic UC. Mathematical formulation
Prototype stochastic UC. Computer implementation
Impact of WG in medium and longterm planning
Maximum WG share (Monday, 2012-09-24)
13333 MW
64.2 %
3 am
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Impact of RES in Short-Term Generation Planning
25
Minimum WG share (Saturday, 2010-06-26)
<1 %
192 MW
10 am
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Impact of RES in Short-Term Generation Planning
26
Probability density function f(x) (2006)
Potencia (% potencia instalada)
Source: REE
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
27
95 -100
90 -95
85 -90
80 -85
75 -80
70 -75
65 - 70
60 -65
55 -60
50 -55
45 -50
40 -45
35 -40
30 -35
25 -30
20 -25
15 - 20
10 - 15
5 - 10
0-5
18
16
14
12
10
8
6
4
2
0
0
Frecuencia (% tiempo)
Distribución de frecuencias producción eólica
Total peninsular
Probability distribution f(x) and F(x)
400
100.00%
350
90.00%
80.00%
Frecuency [h]
300
250
60.00%
200
50.00%
150
40.00%
30.00%
100
20.00%
50
10.00%
0
0.00%
100
1800
3500
5200
6900
8600
10300
12000
13700
15400
17100
18800
20500
22200
23900
25600
27300
5.2 % of installed
capacity 95 % of
being exceeded
70.00%
Mean value: 24.15
% of installed
capacity
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73.5 % of installed
capacity in 2020
Output [MW]
Source: REE
Impact of RES in Short-Term Generation Planning
28
Number of hours of low WG per year
200
180
160
# of hours per year
140
120
IG
v
12hMA
100
24hMA
48hMA
80
72hMA
v
96hMA
60
40
v
20
0
0.6%
1.3%
1.9%
2.5%
3.1%
3.8%
4.4%
5.0%
5.6%
6.3%
6.9%
7.5%
8.1%
8.8%
% of installed capacity
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Impact of RES in Short-Term Generation Planning
29
9.4%
10.0%
Number of occurrences of low WG per year
100
Occurrence: any number of consecutive hours
90
80
# of low wind periods per year
70
60
IG
v
12hMA
50
24hMA
48hMA
40
72hMA
96hMA
30
20
10
v
v
0
2.0%
3.0%
4.0%
5.0%
6.0%
7.0%
8.0%
9.0%
% of installed capacity
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Impact of RES in Short-Term Generation Planning
30
10.0%
Demand vs. Intermittent Generation (2008)
50000
No correlation
45000
40000
Hourly demand [MW]
35000
30000
Intermittent
25000
20000
15000
10000
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Hourly generation [MW]
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Impact of RES in Short-Term Generation Planning
31
10000
Impact of WG in medium and long-term planning
•
Reliability assessment
Low coincidence with yearly peak loads (January and July)
– Almost no dispatchability of WG
– Will there be enough generation to meet peak loads?
Determine some system adequacy reliability measures for the
system.
Determine WG contribution to the system reliability: capacity
credit.
NEED OF COMPLEMENTARY UNITS
–
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Impact of RES in Short-Term Generation Planning
32
3
Wind generation in Spain
Impact of WG in medium and long-term planning
Impact of WG in short-term planning
Impact of WG in real time operation
Stochastic UC
Prototype stochastic UC. Mathematical formulation
Prototype stochastic UC. Computer implementation
Impact of WG in short-term
planning
High ramp rates of WG (Monday, 2005-05-09)
•
Approx. 10400 MW of installed capacity
Decrement of 1000 MW
in 1 h and 45 minutes
Ramp rate: -570 MW/h
Increment of 800 MW in
45 minutes
Ramp rate: 1067 MW/h
Source: REE
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Impact of RES in Short-Term Generation Planning
34
Hourly ramp rates of WG (2006)
Rampas horarias de generación eólica en 2006 (MW)
Total peninsular
V a ria c ió n h o ra ria (M W )
1000
500
0
-500
-1000
-1500
-2000
Source: REE
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Impact of RES in Short-Term Generation Planning
35
Load demand (Wednesday, 2010-03-03)
No downward
tertiary reserve
from 2-6 am
39183 MW
23653 MW
1 CCGT in offpeak hours
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Impact of RES in Short-Term Generation Planning
27 CCGT in
peak hours
36
Load demand (Wednesday, 2010-03-03)
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Impact of RES in Short-Term Generation Planning
37
Load demand (Wednesday, 2010-03-03, 4:30 h)
CCGT 1.3 %
Wind 21.1 %
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Impact of RES in Short-Term Generation Planning
38
Load demand (Wednesday, 2010-03-03, 20:20 h)
CCGT 30.2 %
Wind 9.6 %
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Impact of RES in Short-Term Generation Planning
39
Load demand (Wednesday, 2010-03-03)
WG 4000 MW
CCGT 12000 MW
WG 6000 MW
CCGT 200 MW
No support from
neighbors
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Impact of RES in Short-Term Generation Planning
40
Nuclear units decrease production 20 % (Friday
2013-03-29)
WG 6990 MW
NUC 7080 MW
HYD 8520 MW
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Impact of RES in Short-Term Generation Planning
NUC 5960 MW
41
Iberian daily market prices (March, 2013)
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Impact of RES in Short-Term Generation Planning
42
Impact of WG in short-term planning
•
Variability. Unit commitment
Strong variability of WG over the day. Opposite behavior with
respect to the demand in certain periods
– Ramps, minimum load, startups and shutdowns.
NEED OF FLEXIBLE UNITS
–
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Impact of RES in Short-Term Generation Planning
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4
Wind generation in Spain
Impact of WG in medium and long-term planning
Impact of WG in short-term planning
Impact of WG in real time operation
Stochastic UC
Prototype stochastic UC. Mathematical formulation
Prototype stochastic UC. Computer implementation
Impact of WG in real time
operation
WG Forecast error
Source: EPRI The Integration of Large-Scale Renewable
Resources into the Spanish Power System 2010
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Impact of RES in Short-Term Generation Planning
45
WG Forecast error wrt. WG output
19 % in 24 h
18 % in 12 h
15 % in 6 h
Source: G. González (REE) Wind power prediction in the Spanish system
operation (peninsula and islands) Sipreólico 2008
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Impact of RES in Short-Term Generation Planning
46
WG Forecast error wrt. WG installed capacity
NRMSE: normalized root mean square error
SIPREOLICO 2007
4.9 % in 24 h
4.4 % in 12 h
4 % in 6 h
Source: EPRI The Integration of Large-Scale Renewable Resources
into the Spanish Power System 2010
Instituto de Investigación Tecnológica
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Impact of RES in Short-Term Generation Planning
47
WG curtailment (Thursday, 2012-11-01)
1000 MW
due to excess of
generation
Instituto de Investigación Tecnológica
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1000 MW
to commit one
CCGT
Impact of RES in Short-Term Generation Planning
48
Load demand (Thursday, 2012-11-01)
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Impact of RES in Short-Term Generation Planning
49
WG curtailment (Tuesday, 2008-03-04)
•
•
Instantaneous peak 10032 MW at 15:53 h (28 % of demand).
Hourly peak 9803 MW between 15:00 and 16:00 h
A reduction order of 500 MW of wind generation was sent
500 MW
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Impact of RES in Short-Term Generation Planning
50
WG curtailment (Sunday, 2008-11-02)
2800 MW
due to stability
reasons
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Impact of RES in Short-Term Generation Planning
51
Load demand (Sunday, 2008-11-02)
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Impact of RES in Short-Term Generation Planning
52
ERCOT Texas incident (Tuesday, 2008-02-26)
•
•
•
•
The wind production dropped from over 1700 MW (out of
8000 MW), three hours before the event, down to 300 MW
and that led to some system constraints in moving power from
the generation in the north zone to load in the west zone
Evening electricity load was increasing
Multiple power providers falling below their scheduled energy
production
ERCOT activated demand response program known as Loads
Acting as Resource (LAARs), which added approximately 1100
MW of resources within a 10-minute period. LAARs are
typically large industrial and commercial users who are paid to
curtail their electricity use as needed for reliable grid
operation. Most of the interruptible loads were restored after
approximately an hour and a half.
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Impact of RES in Short-Term Generation Planning
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Impact of WG in real time operation
•
Predictability. Forecast error. Operating reserves. Wind
curtailment
– Limited predictability or uncertainty: errors increasing
with forecast horizon
– Critical time horizons are 24 or 36 hours in advance for D1 reserve evaluation and 6 hours for real-time unit
commitment.
– Rapid dynamic adjustments to fix WG forecast errors.
Balancing mechanisms, operating reserves. NEED OF
OPERATING RESERVES
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Impact of RES in Short-Term Generation Planning
54
Short-term operation scheduling
Market Operator
System Operator: Red Eléctrica de España
< 9.00 h
< 11.00 h
< 12.00 h
Previous information
Day-Ahead Market
Nomination schedules
Technical constraints management (DM)
Secondary regulation capacity
Intra-Day Market:
Sessions 1 a 6
Technical constraints management (IM)
Generation-load unbalance mechanism
Tertiary reserve
Technical constraints management (RT)
14.00 h
16.00 h
18.30 h
…
19.20 h
21.00 h
…
15 min
before
Real
Time
Source: M. de la Torre, J. Paradinas Integration of renewable generation. The case of Spain
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Impact of RES in Short-Term Generation Planning
55
55
Operating reserves in the Iberian market
•
Secondary reserve
Offered and cleared one day in advance (at 16 h D-1)
– Can be asked for at any time
– Has to be deployed in less than 15 min
–
•
Tertiary reserve
Offered one day in advance (at 23 h D-1) and updated
continuously
– Asked with 10 min in advance
–
•
Can the WG contribute these operating reserves?
One single wind farm can only guaranty approximately 30 % of
the installed capacity one day in advance
– The whole system may have a 15-20 % of forecast error of the
output one day in advance
–
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Impact of RES in Short-Term Generation Planning
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Impact of WG at different time scopes
•
•
•
Medium and long-term planning. Reliability assessment
– Will there be enough generation to meet peak loads? Determine
some system adequacy reliability measures for the system. NEED OF
COMPLEMENTARY UNITS
Short-term operation planning. Unit commitment
– Strong variability of WG over the day. Opposite behavior with
respect to the demand in certain periods. Ramps, minimum load,
startups and shutdowns. NEED OF FLEXIBLE UNITS
Real time operation. Operating reserves
– Limited predictability or uncertainty: errors increasing with forecast
horizon
– Critical time horizons are 24 or 36 hours in advance for D-1 reserve
evaluation and 6 hours for real-time unit commitment.
– Rapid dynamic adjustments to fix WG forecast errors. Balancing
mechanisms, operating reserves. NEED OF OPERATING RESERVES
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Impact of RES in Short-Term Generation Planning
57
5
Wind generation in Spain
Impact of WG in medium and long-term planning
Impact of WG in short-term planning
Impact of WG in real time operation
Stochastic UC
Prototype stochastic UC. Mathematical formulation
Prototype stochastic UC. Computer implementation
Stochastic Unit Commitment
Introduction
•
Deterministic unit commitment (UC)
–
•
Stochastic unit commitment
–
•
Given load forecasts and available generators, decide when to
start up and shut down generators so as to minimize costs and
maintain reliability. Plant ramp rates and minimum down and uptimes must be respected, and fixed start-up costs must be
considered.
Some parameters are uncertain. Only their distribution is known
Sources of uncertainty
Generation
• Intermittent generation (wind, solar)
• Failure of connected units (security constrained UC)
– Demand
–
•
ROM Model (Reliability and Operation Model for Renewable Energy
Sources) (http://www.iit.upcomillas.es/aramos/ROM.htm)
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Impact of RES in Short-Term Generation Planning
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Solution methods
•
Heuristics
–
•
Priority ordering
Classical optimization
Direct solution of MIP problem (Branch and cut)
– Dynamic programming (time decomposition)
– Lagrangian relaxation (unit decomposition)
–
•
Metaheuristics
Genetic algorithm
– Tabu search
–
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References (i)
•
B. F. Hobbs, M. H. Rothkopf, R. P. O'Neill, H-P.
Chao (eds.) The Next Generation of Electric
Power Unit Commitment Models Kluwer
Academic Publishers 2001
•
Unit commitment survey
N. Padhy Unit commitment-a bibliographical survey IEEE Transactions on Power
Systems, vol. 19, no. 2, pp. 1196–1205, 2004
• S. Takriti, J. R. Birge, and E. Long A stochastic model for the unit commitment problem
IEEE Trans. Power Syst., vol. 11, pp. 1497–1508, Aug. 1996.
•
•
Centralized framework. Lagrangian relaxation
–
•
Growe-Kuska, N., K.C. Kiwiel, M.P. Nowak, W. Romisch, I. Wegner (2002). Power
management in a hydro-thermal system under uncertainty by Lagrangian relaxation, in:
C. Greengard, A. Ruszczynski (eds.), Decision Making under Uncertainty: Energy and
Power. Vol. 128 of IMA volumes on Mathematics and its Applications, Springer-Verlag,
pp. 39–70.
Deregulated framework. Benders decomposition
–
S. Cerisola, A. Baillo, J.M. Fernandez-Lopez, A. Ramos, R. Gollmer Stochastic Power
Generation Unit Commitment in Electricity Markets: A Novel Formulation and A
Comparison of Solution Methods Operations Research 57 (1): 32-46 Jan-Feb 2009
10.1287/opre.1080.0593
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Impact of RES in Short-Term Generation Planning
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References (ii)
•
Tight and compact unit commitment
G. Morales-España, J.M. Latorre, and A. Ramos Tight and Compact MILP Formulation for
the Thermal Unit Commitment Problem IEEE Transactions on Power Systems 28 (4):
4897-4908, Nov 2013 10.1109/TPWRS.2013.2251373
• G. Morales-España, J.M. Latorre, and A. Ramos Tight and Compact MILP Formulation of
Start-Up and Shut-Down Ramping in Unit Commitment IEEE Transactions on Power
Systems 28 (2): 1288-1296, May 2013 10.1109/TPWRS.2012.2222938
•
•
Impact on operating reserves
G. Morales-España, A. Ramos, and J. Garcia-Gonzalez An MIP Formulation for Joint
Market-Clearing of Energy and Reserves Based on Ramp Scheduling IEEE Transactions on
Power Systems 10.1109/TPWRS.2013.2259601
• G. Morales-España, J. García-González, A. Ramos Impact on Reserves and Energy
Delivery of Current UC-based Market-Clearing Formulations 9th International
Conference on the European Energy Market (EEM 12). Florence, Italy. May 2012
10.1109/EEM.2012.6254749
•
Tight: small integrality gap, initial LP relaxation close to the final MIP solution
• Compact: small optimization problem, few constraints and variables
•
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6
Wind generation in Spain
Impact of WG in medium and long-term planning
Impact of WG in short-term planning
Impact of WG in real time operation
Stochastic UC
Prototype stochastic UC. Mathematical formulation
Prototype stochastic UC. Computer implementation
Prototype Stochastic UC.
Mathematical Formulation
Mathematical formulation
•
Objective function
–
•
Variables
–
–
•
Minimize the total expected variable costs plus penalties for
energy not served
BINARY: commitment, startup and shutdown of thermal units
Thermal output
Operation constraints
Load balance and operating reserve
– Thermal operation constraints
–
•
Mixed integer linear programming (MIP)
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Indices
• Time scope
– 1 day
• Period
– 1 hour
Hour
n
Scenario ω
• Scenario
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Demand (5 weekdays)
Chronological Load Curve (5 Working Days)
Demand [MW ] Dn
50000
45000
40000
Demand [MW]
35000
30000
25000
20000
15000
10000
5000
0
1
5
9
13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117
Hours
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Intermittent generation (IG)
Intermittent generation [MW ] ignω
Intermittent Generation [MW]
1200
1000
800
600
400
200
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hours
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67
Technical characteristics of thermal units (t)
•
•
•
•
Maximum and minimum output
Fuel cost
Slope and intercept of the heat rate straight line
Operation and maintenance (O&M) variable cost
No load cost = fuel cost x heat rate intercept
– Variable cost = fuel cost x heat rate slope
+ O&M cost
–
•
•
Cold startup and shutdown cost
Up and down ramps
Max and min output [MW ]
pt , pt
No load cost
[€ / h ]
ft
Variable cost
[€ / MWh ] vt
Startup cost
Shutdown cost
Instituto de Investigación Tecnológica
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[€]
[€]
Ramp up
[MW / h ] rupt
Ramp down [MW / h ] rdwt
sut
sdt
Impact of RES in Short-Term Generation Planning
68
Scenario tree
•
•
•
Stage
1
Represents how the stochasticity is revealed over time, i.e.,
the different states of the random parameters and
simultaneously the non anticipative decisions over time
Nodes: where decisions are taken.
Scenarios: instances of the random process.
Stage
2
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Stage
3
Stage
4
Scenario
Impact of RES in Short-Term Generation Planning
69
Weekly load, a 4-scenario tree example
4
3
x 10
2.8
Historical series (green)
2.6
2.4
Scenario tree (black)
2.2
2
1.8
1.6
1.4
0
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20
40
60
80
100
120
Impact of RES in Short-Term Generation Planning
140
70
160
180
Weekly load,
x 10 a 32-scenario tree example
4
3
2.8
2.6
2.4
Scenario tree (colored)
2.2
2
1.8
1.6
1.4
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0
20
40
60
80
100
120
140
Impact of RES in Short-Term Generation Planning
160
71
180
Scenario tree for the SDUC
•
Commitment decisions of thermal units (the set of committed
units) are unique under different stochastic scenarios
(intermittent generation IG, demand, etc.)
Hour 1
Hour 24
Scenario 1
Hour 1
Scenario 3
Hour 24
Scenario 5
FIRST-STAGE DECISIONS
Unique commitment
decisions for every hour
TWO-STAGE
DECISION
PROBLEM
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Scenario 7
SECOND-STAGE DECISIONS
Generator output for every
hour depend on the scenario
Probability of scenario pω
Impact of RES in Short-Term Generation Planning
72
Scenario tree example with IG uncertainty
Hour 2
Hour 1
IG Output 400 MW
IG Output 410 MW
Prob: 0.3
IG Output 430 MW
IG Output 420 MW
Prob: 0.2
IG Output 630 MW
Prob: 0.25
IG Output 560 MW
IG Output 550 MW
Prob: 0.25
IG Output 600 MW
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Variables
•
Commitment, startup and shutdown of thermal units (BINARY)
Commitment, startup and shutdown
•
{0,1}
UCnt , SUnt , SDnt
Production of thermal units
Production of a thermal unit [MW ] Pntω
•
Intermittent generation
Intermittent generation [MW ] IGnω
•
Energy not served
Energy not served [MW ] ENSnω
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Constraints: Operating power reserve
Committed output of thermal units
+ Maximum output of hydro plants
>= Demand
+ Operating reserve
for each load level and scenario
∑ pUC
t
t
nt
+ ∑ ph ≥ Dn + On
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∀n
h
Impact of RES in Short-Term Generation Planning
75
Constraints: Generation and load balance
Generation of thermal units
+ Energy not served
= Demand
for each load level and scenario
∑P
ω
nt
+ IGnω + ENSnω = Dn
∀ωn
t
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Constraints: Production in consecutive load levels
Unit output in any hour - Unit output in previous one ≤ ramp up
Unit output in any hour - Unit output in previous one ≥ – ramp down
Pntω − Pnω−1t ≤ rupt
∀ωnt
Pntω − Pnω−1t ≥ −rdwt
∀ωnt
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Constraints: Commitment, startup and shutdown
Commitment of a thermal unit in an hour
– Commitment of a thermal unit in the previous hour
= Startup of a thermal unit in this hour
– Shutdown of a thermal unit in this hour
UCnt −UCn−1t = SUnt − SDnt
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∀nt
Impact of RES in Short-Term Generation Planning
78
Constraints: Commitment and production
Production of a thermal unit on every scenario
≤ Commitment of a thermal unit x the maximum output
Production of a thermal unit on every scenario
≥ Commitment of a thermal unit x the minimum output
UCnt pt ≤ Pntω ≤UCnt pt
∀ωnt
• If the thermal unit is committed (UCnt = 1) it can produce
between its minimum and maximum output
• If the thermal unit is not committed (UCnt = 0) it can’t produce
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Constraints: Operation limits
Power output between limits for each unit
0 ≤ Pntω ≤ pt
∀ωnt
Commitment, startup and shutdown for each unit
UCnt , SUnt , SDnt ∈ {0,1} ∀nt
Intermittent generation limit
0 ≤ IGnω ≤ ignω ∀ωn
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Multiobjective function
•
Minimize
–
Thermal unit expected variable costs
ω
ω
su
SU
+
sd
SD
+
fUC
+
v
P
p
∑ t nt ∑ t nt ∑ t nt ∑ t nt
nt
–
nt
nt
ωnt
Expected penalty introduced in the objective function for
energy not served
ω
ω
′
v
ENS
p
∑
n
ωn
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Short Run Marginal Cost (SRMC)
•
Short Run Marginal Cost = Dual variable of generation and load
balance when binary variables are fixed [€/MWh]
–
Change in the objective function due to a marginal increment in
the demand
ω
ω
ω
P
+
IG
+
ENS
= Dn
∑ nt
n
n
: σnω
∀ωn
t
SRMCnω = σnω
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∀ωn
Impact of RES in Short-Term Generation Planning
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7
Wind generation in Spain
Impact of WG in medium and long-term planning
Impact of WG in short-term planning
Impact of WG in real time operation
Stochastic UC
Prototype stochastic UC. Mathematical formulation
Prototype stochastic UC. Computer implementation
Prototype Stochastic UC.
Computer implementation
StarGenLite_SDUC Stochastic Daily Unit Commitment
Model (http://www.iit.upcomillas.es/aramos/StarGenLite_SDUC.zip)
•
Files
Microsoft Excel interface for input and output data
StarGenLite_SDUC.xlsm
– GAMS file StarGenLite_SDUC.gms
–
•
How to use it
Save the Excel workbook if data have changed
– Run the model
Run
– The model creates
• tmp.xlsx with the output data and
• StarGenLite_SDUC.lst as the listing file of the GAMS execution
– Load the results into the Excel interface
Load results
–
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StarGenLite_SDUC (i)
$title StarGen Lite Stochastic Daily Unit Commitment of Thermal Units (SDUC)
$ontext
Model name
Developed by
Andrés Ramos
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería - ICAI
UNIVERSIDAD PONTIFICIA COMILLAS
Alberto Aguilera 23
28015 Madrid, Spain
Andres.Ramos@upcomillas.es
Authorship and version
Allow declaration of
empty sets and multiple
declaration. Suppress
listing
October 14, 2014
$offtext
$onempty onmulti offlisting
* solve the optimization problems until optimality
option OptcR = 0 ;
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Obtain the optimal solution
Impact of RES in Short-Term Generation Planning
85
StarGenLite_SDUC (ii)
* definitions
sets
n
hour
n1(n) first hour of the day
sc
scenario
Set definition
g
generating unit
t (g) thermal
unit
h (g) hydro
plant
parameters
pDemand
(n
)
pOperReserve(n
)
pOperReserveUp(n )
pOperReserveDw(n )
pIntermGen (n,sc)
pScenProb
(sc )
pCommitt (
g,n)
pProduct (sc,g,n)
pSRMC
(sc, n)
pMaxProd
(g)
pMinProd
(g)
pMaxCons
(g)
pIniOut
(g)
pIniUC
(g)
pRampUp
(g)
pRampDw
(g)
pSlopeVarCost (g)
pInterVarCost (g)
pEmissionCost (g)
pStartupCost
(g)
pShutdownCost (g)
pMaxReserve
(g)
pMinReserve
(g)
pIniReserve
(g)
pEffic
(g)
pInflows
(g,n)
pENSCost
pCO2Cost
hourly load
hourly operating reserve
hourly operating reserve up
hourly operating reserve down
stochastic IG generation
probability of scenarios
commitment of the unit
output
of the unit
short run marginal cost
[GW]
[GW]
[GW]
[GW]
[GW]
[p.u.]
[0-1]
[GW]
[ € per MWh]
maximum output
minimum output
maximum consumption
initial output > min load
initial commitment
ramp up
ramp down
slope
variable cost
intercept variable cost
emission
cost
startup
cost
shutdown
cost
maximum reserve
minimum reserve
initial reserve
pumping efficiency
inflows
energy not served cost
CO2 emission
cost
[GW]
[GW]
[GW]
[GW]
[0-1]
[GW per
h]
[GW per
h]
[M€ per GWh]
[M€ per
h]
[M€]
[M€]
[M€]
[GWh]
[GWh]
[GWh]
[p.u.]
[GWh]
[M€ per GWh]
[M€ per tCO2]
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Impact of RES in Short-Term Generation Planning
Parameter
definition
86
StarGenLite_SDUC (iii)
variables
vTotalVCost
total system variable cost
[M€]
binary
variables
vCommitt (
n,g) commitment of the unit
vStartup (
n,g) startup
of the unit
vShutdown (
n,g) shutdown
of the unit
[0-1]
[0-1]
[0-1]
positive variables
vProduct (sc,n,g)
vProduct1 (sc,n,g)
vConsump (sc,n,g)
vENS
(sc,n )
vIG
(sc,n )
vReserve (sc,n,g)
vSpillage (sc,n,g)
output of the unit
output of the unit > min load
consumption of the unit
energy not served
intermittent generation
reserve at the end of period
spillage
[GW]
[GW]
[GW]
[GW]
[GW]
[GWh]
[GWh]
equations
eTotalVCost
eBalance (sc,n )
eOpReserve(
n )
eReserveUp(sc,n )
eReserveDw(sc,n )
eMaxOutput(sc,n,g)
eMinOutput(sc,n,g)
eTotOutput(sc,n,g)
eRampUp
(sc,n,g)
eRampDw
(sc,n,g)
eUCStrShut(
n,g)
eWtReserve(sc,n,g)
total system variable cost
[M€]
load generation balance
[GW]
operating reserve
[GW]
operating reserve upwards
[GW]
operating reserve downwards
[GW]
max output of a committed unit [GW]
min output of a committed unit [GW]
tot output of a committed unit [GW]
bound on ramp up
[GW]
bound on ramp down
[GW]
relation among commitment startup and shutdown
water reserve
[GWh] ;
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Impact of RES in Short-Term Generation Planning
Variables
87
Equation
definition
StarGenLite_SDUC (iv)
* mathematical formulation
eTotalVCost
.. vTotalVCost =e= sum[(sc,n ),
sum[(sc,n,g),
sum[(sc,n,g),
n,g),
sum[(
n,g),
sum[(
n,g),
sum[(
pENSCost
*vENS
(sc,n )*pScenProb(sc)] +
pSlopeVarCost(g)*vProduct (sc,n,g)*pScenProb(sc)] +
pEmissionCost(g)*vProduct (sc,n,g)*pScenProb(sc)] +
pInterVarCost(g)*vCommitt (
n,g)] +
pStartupCost (g)*vStartup (
n,g)] +
pShutdownCost(g)*vShutdown(
n,g)] ;
eBalance (sc,n ) .. sum[t, vProduct(sc,n,t)] + sum[h, vProduct(sc,n,h)] - sum[h, vConsump(sc,n,h)/pEffic(h)] +
vIG(sc,n) + vENS(sc,n) =e= pDemand(n) ;
eOpReserve(
n ) .. sum[t, pMaxProd(t) * vCommitt(n,t)
] + sum[h, pMaxProd(h)] =g=
pOperReserve (n) + pDemand(n) ;
eReserveUp(sc,n ) .. sum[t, pMaxProd(t) * vCommitt(n,t) - vProduct(sc,n,t)] =g=
pOperReserveUp(n) ;
eReserveDw(sc,n ) .. sum[t, pMinProd(t) * vCommitt(n,t) - vProduct(sc,n,t)] =l= - pOperReserveDw(n) ;
eMaxOutput(sc,n,t) $pMaxProd(t) .. vProduct(sc,n,t) / pMaxProd(t) =l= vCommitt(n,t) ;
eMinOutput(sc,n,t) $pMinProd(t) .. vProduct(sc,n,t) / pMinProd(t) =g= vCommitt(n,t) ;
eTotOutput(sc,n,t)
eRampUp
eRampDw
.. vProduct(sc,n,t) =e= pMinProd(t)*vCommitt(n,t) + vProduct1(sc,n,t) ;
(sc,n,t) .. vProduct1(sc,n,t) - vProduct1(sc,n-1,t) - pIniOut(t) $n1(n) =l=
pRampUp(t) ;
(sc,n,t) .. vProduct1(sc,n,t) - vProduct1(sc,n-1,t) - pIniOut(t) $n1(n) =g= - pRampDw(t) ;
eUCStrShut(
n,t) .. vCommitt(n,t) - vCommitt(n-1,t) - pIniUC(t) $n1(n) =e= vStartup(n,t) - vShutdown(n,t) ;
eWtReserve(sc,n,h) .. vReserve(sc,n-1,h) + pIniReserve(h) $n1(n) + pInflows(h,n) - vSpillage(sc,n,h) vProduct(sc,n,h) + vConsump(sc,n,h) =e= vReserve(sc,n,h) ;
model SDUC / all / ;
SDUC.solprint = 1 ; SDUC.holdfixed = 1 ;
Reduced solution output
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Model includes
all the equations
Eliminate fixed variables
Impact of RES in Short-Term Generation Planning
Mathematical
formulation of
equations
88
StarGenLite_SDUC (v)
* read input data from Excel and include into the model
file TMP / tmp.txt /
$onecho > tmp.txt
i="%gams.user1%.xlsm"
r1=indices
o1=indices
r2=param
o2=param
r3=demand
o3=demand
r4=oprres
o4=oprres
r5=oprresup
o5=oprresup
r6=oprresdw
o6=oprresdw
r7=IGgen
o7=IGgen
r8=thermalgen
o8=thermalgen
r9=hydrogen
o9=hydrogen
r10=inflows
o10=inflows
Read input from Excel
named ranges and
write into text files
$offecho
$call xls2gms m @"tmp.txt"
sets
$include
;
$include
parameter
$include
indices
param
pDemand(n)
demand
parameter pOperReserve(n)
$include oprres
hourly load
[MW] /
/
hourly operating reserve [MW] /
/
parameter pOperReserveUp(n) hourly operating reserve [MW] /
$include oprresup
/
parameter pOperReserveDw(n) hourly operating reserve [MW] /
$include oprresdw
/
pIntermGen(n,sc) stochastic IG generation [MW]
table
$include IGgen
pThermalGen(g,*)
table
$include thermalgen
pHydroGen (g,*)
table
$include hydrogen
pInflows
(g,n)
table
$include inflows
Input from text files
into GAMS
Delete read text files
Instituto de Investigación Tecnológica
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89
Escuela Técnica
Superior
de Ingeniería
ICAI
'del
tmp.txt indices
param demand oprres oprresup oprresdw IGgen thermalgen hydrogen inflows' ;
execute
StarGenLite_SDUC (vi)
* determine the first hour of the day
First hour of the day
n1(n) $[ord(n) = 1] = yes ;
* assignment of thermal units, storage hydro and pumped storage hydro plants
t (g) $[
pThermalGen(g,'FuelCost') *
pThermalGen(g,'MaxProd')] = yes ;
h (g) $[not pThermalGen(g,'FuelCost') and pHydroGen (g,'MaxProd')] = yes ;
* scaling of parameters to GW and M€
pDemand
(n
) = pDemand
(n
)
pOperReserve(n
) = pOperReserve(n
)
pIntermGen (n,sc) = pIntermGen (n,sc)
* 1e-3 ;
* 1e-3 ;
* 1e-3 ;
pENSCost
pMaxProd
(g)
pMinProd
(g)
pIniOut
(g)
pRampUp
(g)
(g)
pRampDw
pSlopeVarCost(g)
=
=
=
=
=
=
=
pEmissionCost(g)
pInterVarCost(g)
pStartupCost (g)
pShutdownCost(g)
=
=
=
=
pENSCost
pThermalGen(g,'MaxProd'
)
pThermalGen(g,'MinProd'
)
pThermalGen(g,'IniProd'
)
pThermalGen(g,'RampUp'
)
pThermalGen(g,'RampDw'
)
pThermalGen(g,'OMVarCost'
)
pThermalGen(g,'SlopeVarCost')
pThermalGen(g,'EmissionRate')
pThermalGen(g,'InterVarCost')
pThermalGen(g,'StartupCost' )
pThermalGen(g,'ShutdownCost')
*
*
*
*
*
*
*
*
*
*
*
*
pMaxProd
pMinProd
pMaxCons
pEffic
pMaxReserve
pMinReserve
pIniReserve
=
=
=
=
=
=
=
pHydroGen
pHydroGen
pHydroGen
pHydroGen
pHydroGen
pHydroGen
pHydroGen
* 1e-3 ;
* 1e-3 ;
* 1e-3 ;
;
* 1e-3 ;
* 1e-3 ;
* 1e-3 ;
(h)
(h)
(h)
(h)
(h)
(h)
(h)
(h,'MaxProd'
(h,'MinProd'
(h,'MaxCons'
(h,'Efficiency'
(h,'MaxReserve'
(h,'MinReserve'
(h,'IniReserve'
)
)
)
)
)
)
)
1e-3
1e-3
1e-3
1e-3
1e-3
1e-3
1e-3
1e-3
1e-3
1e-6
1e-6
1e-6
;
;
;
;
;
;
+
*
*
*
*
*
Scaling of parameters
pThermalGen(g,'FuelCost')
pCO2Cost ;
pThermalGen(g,'FuelCost')
pThermalGen(g,'FuelCost')
pThermalGen(g,'FuelCost')
;
;
;
;
Initial committed units
* if the initial output of the unit is above its minimum load then the unit is committed, otherwise it is not
committed
pIniUC
(g)
= 1 $[pIniOut(g) >= pMinProd(g)] ;
* if the efficiency
pEffic
(h) $[pEffic
Instituto de Investigación Tecnológica
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of a hydro plant is 0, it is changed to 1
(h) = 0] =
1 ;
Impact of RES in Short-Term Generation Planning
90
StarGenLite_SDUC (vii)
* bounds on variables
Bounds on variables
vProduct.up(sc,n,g) = pMaxProd (g
) ;
vIG.up
(sc,n ) = pIntermGen(n,sc) ;
vConsump.up(sc,n,g) = pMaxCons (g
) ;
* solve stochastic daily unit commitment model
Solve the optimization
problem
solve SDUC using MIP minimizing vTotalVCost ;
* scaling of results
pCommitt(
g,n) = vCommitt.l(
n,g)
+ eps ;
pProduct(sc,g,n) = vProduct.l(sc,n,g)*1e3 + eps ;
(sc, n) = eBalance.m(sc,n )*1e3 + eps ;
pSRMC
Scaling the results
* data output to xls file
put TMP putclose 'par=pCommitt rdim=1 rng=UC!a1' / 'par=pProduct rdim=2 rng=Output!a1' /
'par=pSRMC rdim=1 rng=SRMC!a1'
'tmp.gdx' pProduct pCommitt pSRMC
execute_unload
'gdxxrw.exe tmp.gdx SQ=n EpsOut=0 O="tmp.xlsx" @tmp.txt'
execute
'del
tmp.gdx
tmp.txt'
execute
$onlisting
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Write output to Excel
Impact of RES in Short-Term Generation Planning
91
Interface StarGenLite_SDUC. Menu
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
92
Interface StarGenLite_SDUC. Indices
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
93
Interface StarGenLite_SDUC. Parameters
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
94
Interface StarGenLite_SDUC. DemandReserveIG
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
95
Interface StarGenLite_SDUC. Generation
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
96
Task assignment
•
•
•
•
•
•
Run a deterministic version of the model for every scenario (three
different cases)
Run the stochastic daily unit commitment model
– Determine the committed units and the output of each unit
Compare the results of the four cases
– Total expected variable costs
– Committed thermal units
– Thermal unit output
Introduce two additional extreme intermittent generation scenarios with
low probability and analyze the results
– Do the main results depend on the scenarios defined?
Introduce a constraint with a emission maximum allowance
Formulate mathematically the introduction of Demand Side Management
strategies in the model
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
97
Deterministic solution for scenario 1
10
9
8
FuelOilGas
7
OCGT_3
OCGT_2
OCGT_1
6
CCGT_4
CCGT_3
5
CCGT_2
CCGT_1
ImportedCoal_Bituminous
4
ImportedCoal_SubBituminous
BrownLignite
3
DomesticCoal_Anthracite
Nuclear
2
1
0
h01 h02 h03 h04 h05 h06 h07 h08 h09 h10 h11 h12 h13 h14 h15 h16 h17 h18 h19 h20 h21 h22 h23 h24
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
98
Deterministic solution for scenario 2
10
9
8
FuelOilGas
7
OCGT_3
OCGT_2
OCGT_1
6
CCGT_4
CCGT_3
5
CCGT_2
CCGT_1
ImportedCoal_Bituminous
4
ImportedCoal_SubBituminous
BrownLignite
3
DomesticCoal_Anthracite
Nuclear
2
1
0
h01 h02 h03 h04 h05 h06 h07 h08 h09 h10 h11 h12 h13 h14 h15 h16 h17 h18 h19 h20 h21 h22 h23 h24
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
99
Deterministic solution for scenario 3
10
9
8
FuelOilGas
7
OCGT_3
OCGT_2
OCGT_1
6
CCGT_4
CCGT_3
5
CCGT_2
CCGT_1
ImportedCoal_Bituminous
4
ImportedCoal_SubBituminous
BrownLignite
3
DomesticCoal_Anthracite
Nuclear
2
1
0
h01 h02 h03 h04 h05 h06 h07 h08 h09 h10 h11 h12 h13 h14 h15 h16 h17 h18 h19 h20 h21 h22 h23 h24
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
100
Deterministic solution for mean scenario
10
9
8
FuelOilGas
7
OCGT_3
OCGT_2
OCGT_1
6
CCGT_4
CCGT_3
5
CCGT_2
CCGT_1
ImportedCoal_Bituminous
4
ImportedCoal_SubBituminous
BrownLignite
3
DomesticCoal_Anthracite
Nuclear
2
1
0
h01 h02 h03 h04 h05 h06 h07 h08 h09 h10 h11 h12 h13 h14 h15 h16 h17 h18 h19 h20 h21 h22 h23 h24
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
101
Deterministic solution for the scenario tree
10
9
8
FuelOilGas
7
OCGT_3
OCGT_2
OCGT_1
6
CCGT_4
CCGT_3
5
CCGT_2
CCGT_1
ImportedCoal_Bituminous
4
ImportedCoal_SubBituminous
BrownLignite
3
DomesticCoal_Anthracite
Nuclear
2
1
0
h01 h02 h03 h04 h05 h06 h07 h08 h09 h10 h11 h12 h13 h14 h15 h16 h17 h18 h19 h20 h21 h22 h23 h24
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
102
Summary of results
Scenario 1
p=0.3
Scenario 2
p=0.5
Scenario 3
p=0.2
Mean
scenario
Stochastic
Solution
2.563975
2.514956
2.328417
2.488835
2.493131
3.0
1.0
-6.4
62329
61386
56270
Thermal generation [%]
2.8
1.2
-7.2
Wind generation [MWh]
13805
14748
19863
Wind generation [%]
-10.9
-4.8
28.2
Objective function [M€]
Objective function [%]
Thermal generation [MWh]
Instituto de Investigación Tecnológica
Escuela Técnica Superior de Ingeniería ICAI
Impact of RES in Short-Term Generation Planning
0.2
60646
60646
0.0
15488
15488
0.0
103
Prof. Andres Ramos
http://www.iit.upcomillas.es/aramos/
Andres.Ramos@upcomillas.es
arght@mit.edu
Instituto de Investigación Tecnológica
Santa Cruz de Marcenado, 26
28015 Madrid
Tel +34 91 542 28 00
Fax + 34 91 542 31 76
info@iit.upcomillas.es
www.upcomillas.es