ECON 4930 Autumn 2007 Electricity Economics Lecture 12

1. ECON 4930 Autumn 2007Electricity EconomicsLecture 12 Lecturer: Finn R. Førsund Summing up

2. The key theme: drivers of price changes • Point of departure: water as a natural resource in limited supply • All prices equal, Hotelling’s rule • The price of electricity varies over both day and season • We must come up with explanations • NB! price variation in the market may not be optimal Summing up

3. Constraints as price drivers • Reservoir constraint • Threat of overflow • Running empty • Production constraint • Pipes, turbines, generator • Environmental constraints • Ramping up and down • Minimum production (max covered above) Summing up

4. Threat of overflow and empty reservoir Period 2 Period 1 p2 p1 p2(e2H) p1(e1H) λ2 γ1 λ1 e2H D B A C e1H Total available water Ro + w1 + w2 Summing up

5. In between empty and full Period u+1 Period u pu+1 pu λu+1=pT B A C D M Water to period u+2 Summing up

6. Production constraint:constraint in period 2: peak demand p1 p2 Period 1 Period 2 p2=λ2+ρ2 ρ2 λ2 p1=λ1 B’ B’’ C A D B Summing up

7. Production constraint:constraint in period 1:threat of overflow p1 p2 Period 1 Period 2 p2=λ2=γ1 p1=ρ1 γ1 ρ1 λ1=0 D C A B' B Spill Summing up

8. Unregulated generation • Run-of-the-river • Full reservoirs turn a power station into a run-of-the-river station • Windmills • Range of fluctuation large • Geothermal • May take time to regulate steam pressure, etc. • Downward price jumps when hydro plants can do pure accumulation and low demand Summing up

9. Must take: Run-of-the-river and wind power Period 2 Period 1 p2(x2) λ1 = λ2 p2 p1(x1) p1 River flow River flow C e1H e1R D A B e2R e2H Total controllable inflow Summing up

10. Hveding’s conjecture • Assume independent hydropower plants with one limited reservoir each, and perfect manoeuvrability of reservoirs, but plant-specific inflows • The plants can be regarded as a single aggregate plant and the reservoirs can be regarded as a single aggregate reservoir when finding the social optimal solution for operating the hydropower system. • If overflow, then all reservoirs overflow at the same time, if empty then all reservoirs are emptied at the same time Summing up

11. Price fluctuation when hydro interacts with thermal • Thermal sector is used according to merit order ranking of marginal cost • General rule: price equals water value equals marginal cost of thermal • Typical result: price variations less than in a pure hydro system Summing up

12. Bathtub diagram with thermal and hydro with reservoir constraint Period 1 Period 2 p2 p1 λ2 p2 γ1 λ1 p1 c' c' A' A B C D D' Hydro energy Thermal extensions Summing up

13. The impact of trade on prices • Unlimited trade • External exogenous prices determine the regional prices • Limited trade due to transmission • Region may have different prices if trade is limited • If import-constrained higher regional price • If export-constrained lower regional price • Endogenous trade prices • Equal prices without constraints on interconnectors • Different prices with constraints on interconnectors Summing up

14. Impact of trade on prices Period 2 Period 1 p2 p1 p2XI α2 p2=2 γ1 pAU p1=1 β1 p1XI Import Export Prod.1 Cons.2 B C D A x2 x1 Total available water Summing up

15. The impact of transmission on prices • Transmission: connecting all generator nodes and consumption nodes by lines • Fundamental physics: loss of energy on lines • Implication: nodal prices as the optimal price structure; higher consumer price the higher the loss • Limited capacity of lines and congestion • Thermal capacity (Ohm’s law) • More general resistance; impedance when AC • Loop flows and other electric mysteries with AC Summing up

16. Bathtub with loss and congestion Period 2 Period 1 2 p2 p1 λ λ D D' C B A A' Total available water Summing up

17. Uncertainty as price driver • Assuming all information for the present period to be known, price for the next period will be expected price • The construction and use of expected water value table, role of constraints • When time progresses there will be a continuous update of expected prices • Realised price will typically differ from expected price, implying fluctuating price Summing up

18. A general case for period t Period t-1 Period t pt pt A'A B Mt|t-1 MtC Summing up

19. Market power as price driver • Monopoly • No reservoir constraint, no spill • Shifting of water from relatively inelastic periods to more elastic periods • Price will then go down in periods where more is produced and up in periods with less production • Reservoir constraint, no spill • Shifting if constraint not binding • Social price solution if reservoir constraint is binding Summing up

20. Bathtub illustration of two periods Period 2 Period 1 p2M p1S= λS p2S =λS p1M λM Summing up

21. The competitive solution • Second welfare theorem: any efficient allocation can be sustained by a competitive equilibrium • Problems: • Electric externalities due to transmissions with loop flows, reactive power, etc. • Hydraulic externalities for plants along the same river system • Uncertainty and expectation formation Summing up

22. The optimisation problem of producer j at period 1 with certainty for given prices Summing up

23. The Lagrangian Summing up

24. The Kuhn – Tucker conditions Summing up

25. Investments • Deregulation of electricity sector • Unbundling generation and transmission • Investment in generation and investment in transmission made by independent organisations, but investments need coordination both over time and over space • Use of shadow prices on capacities as marginal investment signals Summing up