Equilibria in an Oligopolistic Electricity Pool with Stepwise Offer Curves. Antonio J. Conejo, Carlos Ruiz Univ. Castilla La Mancha 2012
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1 Equilibria in an Oligopolistic Electricity Pool with Stepwise Offer Curves Antonio J. Conejo, Carlos Ruiz Univ. Castilla La Mancha 2012
2 EQULIBRIA January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 2
3 What Single producer : Bilevel, MPEC, MILP, NLP All producers: EPEC All producers: system of mixed-integer linear equations All producer: MILP Example and case study Concluding remarks January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 3
4 Single producer Bilevel Offering curve Maximize profit (production price) subject to: Own constraints Maximize social welfare subject to: Market clearing constraints (price) January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 4
5 Single producer Bilevel January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 5
6 Single producer Bilevel (lower-level linear) January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 6
7 Single producer Bilevel to MPEC Bilevel Model MPEC Model s.t. Min ULOF ULC Min LLOF s.t. LLC s.t. Min ULOF ULC LL Optimallity Conditions January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 7
8 Single producer Bilevel to MPEC Maximize profit subject to: Own constraints Market clearing KKTs Nonlinear: Production price Nonlinear: Complementarity January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 8
9 Single producer MPEC-MILP Maximize profit subject to: Own constraints Market clearing KKTs Linearization via strong duality equality Linearization via Fortuny - Amat January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 9
10 Single producer MPEC-MILP January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 10
11 Single producer MPEC-NLP Nonlinear: production price Maximize profit subject to: Own constraints Market clearing primal constraints Market clearing dual constraints Market clearing strong duality equality No Complementarity! January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 11
12 Single producer MPEC-NLP January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 12
13 Single producer MPEC NLP: KKT KKTs of MPEC NLP constitutes a system of nonlinear equations Mangasarian-Fromovitz constraint qualification (MFCQ) does not hold: degrees of freedom January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 13
14 All producers Joint solution of the interrelated MPECs of all producers Multiple-leaders-single-follower game Generalized Nash equilibria EPEC January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 14
15 All producers: Equilibria January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 15
16 All producers EPEC MPEC 1 Max Profit 1 s.t. Upp-level Const. Primal Const. Dual Const. SDE MPEC 2 Max Profit 2 s.t. Upp-level Const. Primal Const. Dual Const. SDE MPEC J Max Profit J s.t. Upp-level Const. Primal Const. Dual Const. SDE January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 16
17 All producers: EPEC MPECs of all producers Solution: joint consideration of: KKT of MPEC NLP for producer 1 KKT of MPEC NLP for producer 2 KKT of MPEC NLP for producer J January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 17
18 All producers: EPEC Strong Stationarity Conditions associated to the EPEC KKTs of MPEC 1 KKTs of MPEC 2 KKTs of MPEC J Multiple equilibria January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 18
19 All producers: EPEC Multiple equilibria January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 19
20 All producers: EPEC Set of MPEC NLPs do not meet constraint qualifications (Mangasarian-Fromovitz). Set of KKTs above constitutes a system of nonlinear equations with degrees of freedom. Clever parameterization results in a system of mixed-integer linear equations. January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 20
21 All producers: MIL Strong Stationarity Conditions associated to the EPEC (γj) MIL constraints 1 MIL constraints 2 MIL constraints J January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 21
22 All producer: MILP Alternative objective functions (Linear) subject to: Systems of mixed-integer linear equations describing EPEC solutions The alternative objective functions allow identifying desirable equilibria January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 22
23 All producers: MILP Maximize Linear Objective Function Subject to: MIL Constraints 1 MIL Constraints 2 MIL Constraints J January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 23
24 Example Data: system January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 24
25 Example Data: generating units and demands Data for the generating units Data for the demand January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 25
26 Example Results Uncongested network case January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 26
27 Example Results Congested network case January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 27
28 Example Equilibrium 1: offering Strategic offer: dash January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 28
29 Example Equilibrium 2: offering January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 29
30 Example Equilibrium 3: offering January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 30
31 Example Total profit vs. parameters (subspace) January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 31
32 Example Parameters vs. parameters (subspace) January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 32
33 Example parameters vs. parameters (subspace) January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 33
34 Case study: System January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 34
35 Case study Data for generating units January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 35
36 Case study Data: location of units Duopoly A Duopoly B January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 36
37 Case study Data: location of units Duopoly A Duopoly B Producer 1 Producer 2 January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 37
38 Case study Demand data and location January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 38
39 Case study Results Uncongested network case (Duopoly A=Duopoly B) January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 39
40 Case study Results Congested network case, Duopoly A January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 40
41 Case study Results Congested network case, Duopoly B January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 41
42 Concluding remarks Supply function equilibria EPEC No diagonalization! Analytical insight Efficient solution January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 42
43 Future work Pre-filtering of equilibria Uncertainty modeling Multi-period case January 12, 2012 A. J. Conejo, Univ. Castilla - La Mancha 43
44 Research is important! Stay Hungry, Stay Foolish 1/12/2012 A. J. Conejo, Univ. Castilla - La Mancha 44
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