1. Summing up1 ECON 4930 Autumn 2007 Electricity Economics Lecture 12 Lecturer: Finn R. Førsund

2. 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

3. 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)

4. Summing up 4 Threat of overflow and empty reservoir p 2 (e 2 H ) e2He2H p 1 (e 1 H ) D C Period 2 Period 1 λ1λ1 λ2λ2 B A e1He1H γ1γ1 p2p2 p1p1 Total available water R o + w 1 + w 2

5. Summing up 5 In between empty and full M λ u+1 =p T p u p u+1 Period u Period u+1 BC D A Water to period u+2

6. Summing up 6 Production constraint: constraint in period 2: peak demand p1p1 p 1 =λ 1 D C A Period 2Period 1 ρ2ρ2 p2p2 λ2λ2 p 2 =λ 2 +ρ 2 B B’B’ B ’’

7. Summing up 7 Production constraint: constraint in period 1:threat of overflow Spill p1p1 p 1 =ρ 1 D C A Period 2Period 1 ρ1ρ1 p2p2 p 2 =λ 2 =γ 1 BB' γ1γ1 λ 1 =0

8. 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

9. Summing up 9 Must take: Run-of-the-river and wind power Total controllable inflow p1p1 p2p2 B D River flow e1Re1R p 2 (x 2 ) e2He2H p 1 (x 1 ) C Period 2 Period 1 λ 1 = λ 2 e1He1H River flow e2Re2R A

10. 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

11. 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

12. Summing up 12 Bathtub diagram with thermal and hydro with reservoir constraint p1p1 λ1λ1 Period 2 Period 1 Thermal extensions p1p1 c'c' c'c' A' A B C D D' Hydro energy γ1γ1 λ2λ2 p2p2 p2p2

13. 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

14. Summing up 14 Impact of trade on prices p1p1 Prod.1Cons.2 Import Export Total available water p2p2 α2α2 β1β1 γ1γ1 p AU Period 1 Period 2 x1x1 A BCD x2x2 p 1 = 1 p 1 XI p 2 XI p 2 = 2

15. 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

16. Summing up 16 Bathtub with loss and congestion p1p1 λ D B D' A λ Total available water p2p2 A' Period 1 Period 2 22 C

17. 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

18. Summing up 18 A general case for period t A' A B M t|t-1 M t C ptpt Period t ptpt Period t-1

19. 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

20. Summing up 20 Bathtub illustration of two periods p2Mp2M Period 1 Period 2 p 2 S = λ S p 1 S = λ S p1Mp1M λMλM

21. 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

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

23. Summing up 23 The Lagrangian

24. Summing up 24 The Kuhn – Tucker conditions

25. 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