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u Efficient Solution of Optimal Multimarket Electricity Bid Models 1/16 d Efficient Solution of Optimal Multimarket Electricity Bid Models e F.J. Heredia 1 , C. Corchero 1 , E.Mijangos 2 . 1 Department of Statistics and Operations Research c

  1. u Efficient Solution of Optimal Multimarket Electricity Bid Models 1/16 d Efficient Solution of Optimal Multimarket Electricity Bid Models e F.J. Heredia 1 , C. Corchero 1 , E.Mijangos 2 . 1 Department of Statistics and Operations Research c Universitat Polit` ecnica de Catalunya (UPC) 2 Department of Applied Mathematics, Statistics and Operations Research Universidad del Pais Vasco (UPV/EHU) p Project DPI2008-02154, Ministry of Science and Innovation, Spain EEM11 - Zagreb, May 2011 u . Efficient Solution of Optimal Multimarket Electricity Bid Models 2/16 m Introduction 1 Iberian Electricity Market (MIBEL) o GenCo’s optimal DAM bid problem Multimarket in the MIBEL Model Description 2 n Variables Objective function and constraints Optimization and results g 3 Optimization by means of perspective cuts Results Conclusions 4

  2. u Efficient Solution of Optimal Multimarket Electricity Bid Models 3/16 Introduction Iberian Electricity Market (MIBEL) Iberian Electricity Market d The MIBEL (created in 2007) joins Spanish VPP options e and Portuguese electricity system. GenCo Physical derivatives bids It complements the previous mechanisms of products the Spanish Electricity Market with a Buyers’ Bilateral DAY-AHEAD contracts offers MARKET execution Derivatives Market. . It established a fully competitive framework Technical Restrictions c for the generation of electricity, with a set of ANCILLARY Buyers’ and market mechanism centralized and managed sellers’ offers SERVICES by the market operator . p INTRADAY Buyers and sellers offers It included a Day Ahead Market, a Reserve MARKETS Market and a set of Intraday Markets to REAL-TIME which the generation companies (GenCo) MANAGEMENT could submit their sell bids. u . Efficient Solution of Optimal Multimarket Electricity Bid Models 4/16 m Introduction GenCo’s optimal DAM bid problem The GenCo’s optimal DAM bid problem The GenCo’s optimal DAM bid problem considers a Price-Taker o generation company with: A set of thermal generation GenCo Derivatives bids physical units, I , with quadratic products n generation costs, start-up and Buyers Bilateral DAY-AHEAD contracts offers shut-down costs and minimum MARKET execution operation and idle times. g Each generation unit can submit sell bids to the 24 auctions of the DAM. A set of physical futures contracts, F , of energy L F j j ∈ F . A pool of bilateral contracts B of energy L B k , k ∈ B .

  3. u Efficient Solution of Optimal Multimarket Electricity Bid Models 5/16 Introduction Multimarket in the MIBEL Sequence of markets in the MIBEL d ��� � � �� �� �� �� � � � �� �� �� �� ���������������� ����������������� e ��������������������� ���������������������� ��������������������� ���������������������� ��������������������� ������ �!������ ��������������������� "�������!!#������� . c Ancillary Services Participants send bids to potentially increase or decrease the matched energy of the matched units in the day-ahead market. p Intraday Markets It works exactly as the day-ahead market does, except that the GenCo can participate as a buying as well as selling agent. u . Efficient Solution of Optimal Multimarket Electricity Bid Models 6/16 m Introduction Multimarket in the MIBEL Integration of the market sequence in the day-ahead market bid o Our starting point is the DAM optimal bid models developed in Corchero et al. 2011 and Heredia et al. 2010 and 2011. n In the present work the market sequence is integrated in the DAM bid model with the following considerations: A GenCo that participates in the ancillary services always bids the AGC capacity of the unit and, the only decision to be g optimized is whether it participates or not. In order to participate in the ancillary services the generation output of a unit along two successive intervals must be constant. Just the first intraday market is considered.

  4. u Efficient Solution of Optimal Multimarket Electricity Bid Models 7/16 Introduction Multimarket in the MIBEL Objectives of the model d A multistage stochastic programming model has been developed to decide: e the optimal bid in the day-ahead market abiding by the MIBEL rules the optimal economic dispatch of the physical futures and . bilateral contract among the thermal units c the optimal unit commitment of the thermal units maximizing the expected profit of the market sequence p taking into account the commitments deriving from futures contracts and bilateral contracts, the technical production constraints, the sequence of markets rules and the stochasticity of the DAM, reserve and intraday market prices. u . Efficient Solution of Optimal Multimarket Electricity Bid Models 8/16 m Model Description Variables OMEB: Variables First stage variables: for each period t and unit i o The unit commitment variables: u ti ∈ { 0 , 1 } . The instrumental price offer bid variables: q ti . n The scheduled energy for futures contract j variables: f tij . The scheduled energy for bilateral contract variables: b ti . Second and third stage variables: for each t , i and scenario s g Total generation: g s ti Matched energy in the day-ahead market: p s ti Reserve market related variables: r s ti ∈ { 0 , 1 } Intraday market related variables: m s ti

  5. u Efficient Solution of Optimal Multimarket Electricity Bid Models 9/16 Model Description Objective function and constraints OMEB: Model description d OMEB e Max Expected benefit of the markets’ sequence s.t. Physical futures and bilateral contract coverage . Day-ahead market rules Reserve market rules c Intraday market rules Unit commitment p Nonanticipativity Mixed integer quadratic multistage stochastic program. u . Efficient Solution of Optimal Multimarket Electricity Bid Models 10/16 m Optimization and results Optimization by means of perspective cuts Perspective cuts: Motivation o The OMEB model is a Mixed-Integer Quadratic Program (MIQP), which is difficult to solve efficiently, especially for large-scale instances. n A possibility is to use a polyhedral outer approximation of the quadratic generation cost function f ( g , u ) f ( g , u ) = c q g 2 + c l g + c b u g by means of perspective cuts (Frangioni and Gentile 2006), so that this problem can be solved as a Mixed-Integer Linear Program (MILP) by general-purpose MILP solvers.

  6. u Efficient Solution of Optimal Multimarket Electricity Bid Models 11/16 Optimization and results Optimization by means of perspective cuts Perspective cuts: Implementation d The numerical experiments solved instances of the OMEB problem with three different procedures: e MIQP1 The MIQP solver of Cplex 12.1 MIQP24 The MIQP solver of Cplex 12.1 with multithreading (24 threads). . PCF The MILP solver of Cplex 12.1 were the dynamic generation of PCs was implemented by means of the cutcallback procedure. c Method Time (h) c.v. b.v. Constraints S 120 h 30 ′∗ MIQP1 145.680 48.240 381.796 200 p 8 h 45 ′ MIQP24 145.680 48.240 381.796 200 2 h 58 ′ PCF 261.857 48.240 641.151 200 ∗ Execution aborted Fuji RX200 S6 (2 x CPUs Intel Xeon X5680 Six Core / 12T 3.33 GHz, 64Gb RAM) u . Efficient Solution of Optimal Multimarket Electricity Bid Models 12/16 m Optimization and results Results OMEB: Scenario Set 50 scenarios from a reduced equiprobable set of historical data of DAM, reserve and intraday market prices. o 7 8.94 x 10 (a) 8.92 Objective function 8.9 8.88 8.86 n 8.84 8.82 8.8 25 50 75 100 120 140 160 180 Objective function 1 (b) 0.8 � x s − x 180 � 0.6 � x 180 � g 0.4 0.2 0 25 50 75 100 120 140 160 First-stage variables Number of scenarios � x s − x 200 � | S | c.v. b.v. CPU(s) Objective function � x 200 � 25 19680 6240 210 89230500 1,000 50 37680 12240 745 88268300 0,001 75 55680 18240 1664 88624200 0,002 24 hours, 9 thermal units, 3 FCs, 1 BC portfolio. CPU Time: Perspective cuts with CPLEX.

  7. � ✝ ✢ ✢ ✞ ☛ u Efficient Solution of Optimal Multimarket Electricity Bid Models 13/16 Optimization and results Results Results (1/3): optimal bidding curve d 4 Thermal Unit 6 3.5 e ✞✥✤ ✞✩★ ✏✧✦ 3 2.5 ✔✣✖ 2 . 1.5 Spot price (c�/kWh) 1 c ✝✟✞ ✁✡✠✆✂ 0.5 ✁✄✂✆☎ �✜✁✌☞✍✂✆✂ 20 40 80 100 120 140 ✁✚☞✍✛✆✠ ✁✌☞✍☎✆✎ ✏✒✑✌✓✕✔✗✖✙✘ Energy(x1000kWh) Optimal bidding curve for thermal unit 6 at interval 18 p u Bilateral and futures coverage of unit 6 along 24h . Efficient Solution of Optimal Multimarket Electricity Bid Models 14/16 m Optimization and results Results Results (2/3): commitment of the bilateral and future contracts Only DAM o DAM + RM + IM (multimarket) n g Blue: bilateral contracts; orange: future contracts

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