Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium Constraints

Transcription

1 Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium Mariano Ventosa Andrés Ramos Michel Rivier 13 th PSCC Trondheim, 29 June 1999

2 Outline Introduction Modelling Approaches Model Description: Model Overview Scheme of a production cost model with Equilibrium How the Equilibrium work Case Study Model Applications Conclusion Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium - 2

3 Introduction (I) Changes in global electric industry: Deregulation Competition Spanish electricity market Beginning in January, 1998 Based on a simple merit order of the bids Market clearing price is the highest accepted bid Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium - 3

4 Introduction (II) New Framework: Deregulated Power Market Increased opportunities and increased risks New responsibilities: Unit commitment Hydrothermal coordination Biding prices and quantities Electric companies need original models that consider: The technical operation constraints The new competitive framework: Profit maximisation behaviour Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium - 4

5 Modelling Approaches Other modelling approaches: Based on the market equilibrium Theoretical and practical advances However, with some limitations Our approach: Detailed modelling operation of thermal, hydro and pumped units Single shot optimisation procedure Competitive behaviour of the market Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium - 5

6 Model Overview (I): Traditional Production Cost Models Traditional Production Cost Models: Medium term operation planning studies Minimum generation cost subject to operating constraints Two relevant characteristics of these models: A detailed representation of the electric system operation Their main decision variables are the generation output levels offered to the market Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium - 6

7 Model Overview (II): Equilibrium Equilibrium reproduce the first order optimality conditions of the firms profit maximisation objective Pr ofit firm = Pr ice Power firm Cost firm Profit Profit E. C. Profit C.M. Market Equilibrium with Cost Minimization and Equilibrium Market Equilibrium with Cost Minimization Pr ofit Power firm = firm 0 Price Price E. C. Power E.C. Power C.M. Electricity demand function Output = Power Marginal Cost Pr ice Pr ice + Powerfirm = Power firm M arg inalcost Price C.M. firm Market Equilibrium with Cost Minimization Marginal Revenue Marginal Revenue Power E.C. Power C.M. Output = Power Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium - 7

8 Scheme of the production cost model with Equilibrium Minimisation of: Objective Function Total Generation Variable Costs + + Costs of non accepted demand bids Subject to: Operating Interperiod Intraperiod Market Equilibrium Price equation Market Share Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium - 8

9 Objective Function Objective Objective Function Function Operating Market Minimisation of: Subject to: Total Generation Variable Costs + + Costs of non accepted demand bids Fuel Costs + O&M variable costs + Start-up costs + Penalty by unmet reserve margin + Costs of non Price accepted equation demand bids Interperiod Intraperiod Equilibrium Market Share Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium - 9

10 Operating Objective Function Minimisation of: Subject to: Total Generation Variable Costs + + Costs of non accepted demand bids Interperiod Operating Operating Interperiod Hydro management Seasonal Intraperiod operation of pumped-hydro units Fuel management Maintenance scheduling Intraperiod Equilibrium Market Balance between Price equation generation and demand Generation Limits Daily/Weekly pumped-storage units Reserve Margin Market Share Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium - 10

11 Market Objective Function Minimisation of: Subject to: Total Generation Variable Costs + + Costs of non accepted demand bids Equilibrium Marginal revenues equal marginal cost for each Operating strategic firm Interperiod Marginal cost of each firm as a function of its committed Intraperiod units System Marginal Price equation The price is a function of the served demand Market Market Share Equilibrium Market The market Price share of equation each leader in quantity must be equal to its market share objective Market Share Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium - 11

12 How the Equilibrium Work The Cost Minimisation achieves the cheapest feasible scheduling of hydro generation of each firm for the entire scope Total Output of Firm e For each firm, the Equilibrium choose the output that maximises its profits for each load level Thermal Unit 2 Thermal Unit 1 Must run thermal generation Run-of-the-river generation Time The Cost Minimisation achieves the cheapest feasible commitment of thermal units of each firm for each load level Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium - 12

13 Case Study Our model has been applied to the Spanish power market: 73 thermal units and 30 equivalent hydro units. The size of the MIP is 25,000 continuous variables, 2,000 binary variables and 33,000 constraints. System Marginal Price Total ($/MWh) Output (GW) System Total Output Marginal with Price Cost with Minimisation Cost Minimisation and with and with Equilibrium Output Price C. C. M. M. Output Price E. E. C. C Time Time (h) (h) Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium - 13

14 Model Applications Use of results for analysing strategies: In the long term, it is essential to find specific quantities in order to maximise the profit In the short term, forecasted prices help in defining bidding tactics in the wholesale market Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium - 14

15 Conclusion Power market approach based on MPEC Maximise the producer profit while taking into account operating constraints The equilibrium constraints implies only minor modifications to traditional models Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium - 15