Hydropower Economics: An Overview

Transcription

1 ydropower Economics: An Overview Finn R Førsund Professor Emerius Universiy of Oslo * Slides prepared for ECON Resource Economics Ocober ydropower economics 1

2 Curriculum ydropower Economics: An Overview. Encyclopedia of energy, Naural Resource and Environmenal Economics, pp ydropower economics 2

3 10 op hydroelecriciy produers ydropower economics 3

4 Renewable power 10 larges producers Rank Counry Year oal renewable ydropower Wind power Biomass Solar power Geoher mal 1 China [1] , , [2] Unied Saes [3] Brazil Canada India [4] Germany [5] Russia Japan Norway [6][5] Ialy ydropower economics 4

5 GWh Weekly inflow and producion of hydropower in Norway Inflow Producion Source: OED: Faka 2005 Weeks ydropower economics 5

6 he basic model for managemen of hydropower wih reservoir ydroelecriciy producion funcion 1 e r a a: waer per kwh Waer accumulaion equaion R R w r R w ae R R 1 w e, 1,.., Reservoir consrain R 1 1 R ydropower economics 6

7 he social planning problem he objecive funcion e 1 z0 p ( z) dz Maximising consumer plus producer surplus Area under he demand curve from 0 o opimal value of e ydropower economics 7

8 he opimisaion problem e max p ( z) dz 1 z0 subjec o R R w e R 1 R, e 0, 1,.., R, w, R, R given, R free o L 1 1 he Lagrangian e 1 z0 p ( z) dz ( R R w e ) 1 ( R R) Shadow prices he envelope heorem ydropower economics 8

9 he necessary firs-order condiions L p ( e ) 0 ( 0 for e 0) e L R 0 ( 0 for R 0) 1 0( 0 for R R w e ) 1 0( 0 for R R ), 1,.., Dynamics of shadow price deerminaion Waer values are he same for and +1 if he reservoir consrain is no binding ydropower economics 9

10 he inerior soluion for he price of elecriciy he price will only change if he waer value changes, and his will only happen if he reservoir consrain is binding (empy or full) ydropower economics 10

11 Bahub diagram for wo periods Inerior soluion for reservoir levels p 1 Period 1 Period 2 p 2 p ( e ) p2( e 2 ) 1 1 p 1=λ1 p 2 =λ 2 e 1 e 2 A e 1 B M R C e 2 D oal available waer R w w o 1 2 ydropower economics 11

12 Upper reservoir consrain binding in period 1 ydropower economics 12

13 Bellman s backward inducion Using up all he available waer in he erminal period e R w 1 Insering in he demand funcion gives he opimal price in period p p ( e ) p ( R w ) 1 We have o solve for Range of ransfer R 1 [0, R] R 1 ydropower economics 13

14 Sepping one period back from e 1 R 2 R 1 w 1 Assuming inerior soluion for p ( e ) p ( R w ) e 1 p 1( p ( R 1 w )) Solving for R R R w e R 1 R w p ( p ( R w )) Soluion for if we have he soluion for ydropower economics 14

15 Repeaing going backward o period 1 assuming inerior soluions for he reservoir levels 1 1 R R w p ( p ( R w )) i i 1 i1 i1 We know R, can hen solve for and hen 0 R 1 all prices, reservoir levels and oupu levels ydropower economics 15

16 Binding reservoir consrains Empy reservoir in period +1 implies = 0 Assuming inerior soluion for he reservoir from o +2 implies same price all periods, and price in period +1 ypically higher han his price ydropower economics 16

17 hrea of overflow in period s, giving a full reservoir o period s+1, s+1<, inerior soluions backward from o s+1, use period +1 as he erminal period 1 s i i 1 1 is1 is1 R R w p ( p ( R w )) 1 i i 1 1 is1 is1 R R w p ( p ( R w )) Lower price in period s, if inerior soluions from s-1 o =1 hen a lower price regime ydropower economics 17

18 Finding he lower price in period 1,,s using s1 s1 1 0 s1 i i s s1 s i1 i1 R R w p ( p ( R w )) R0 known, only Rs-1 unknown ydropower economics 18

19 Limi on producion capaciy period 2 e e, 1,.., p 1 Period 1 p ( e ) 1 1 p ( e ) 2 2 Period 2 p 2 ρ 2 p 2 =λ 2 +ρ 2 p 1 =λ 1 λ 2 e A e 1 B B' B'' C e 2 D ydropower economics 19

20 Muliple producers Energy balance N x e j, j 1,.., N, 1,.., j1 Necessary firs-order condiions L e j L R j N j j j j1 p ( e ) 0( 0 for e 0) 0( 0 for R 0) j j, 1 j j 0( 0 for R R w e ) j j j, 1 j j 0( 0for R R ), 1,..,, j 1,.., N j j j ydropower economics 20

21 ydro ogeher wih oher echnologies hermal echnology h h h c( e ), e e Inermien echnologies Coefficiens I I e a e, a [0,1], i wind,solar,run-of-river i i i i a i Capaciy facor; fracion of use of full insallaion I of power capaciy e i ydropower economics 21

22 he opimisaion problem of he social planner h max [ p ( z) dz c( e )] 1 z0 subjec o 1 h x, e, R, e 0, 1,.., h I, R, R, e, e, w ( 1,..., ) given, free x x e e e h I R R w e R e h R h R e o ydropower economics 22

23 he Lagrangian h L [ p ( z) dz c( e )] h I e e e 1 z0 h h ( e e ) ( R R w e ) 1 ( R R) ydropower economics 23

24 L e he necessary firs-order condiions L e h L R h I p ( e e e ) 0 ( 0 for e 0) h I h h p ( e e e ) c( e ) 0 ( 0 for e 0) 0 ( 0 for R 0) 1 0 ( 0 for R R w e ) 1 0 ( 0 for R R) h h 0 ( 0 for e e ), 1,.., ydropower economics 24

25 Deerminaion of price, inerior soluions p ( e e h e I ) c( e h ) p,, j 1,..., J j j Period j : prices are he same Use of hermal capaciy consan for ydro swing producer I I e e ( x x ) ( e e ) hydroswing demand change inermien change j, j 1,..., J No use of hydro h I p ( e e ) ydropower economics 25

26 Bahub of mix of echnologies Inermien only in period 1 ydropower economics 26

27 Inermien only in period 2 ydropower economics 27

28 Addiional hydropower issues Uncerainy Inflows and demand sochasic variables Maximising he expeced consumer plus producer surplus Marke power he monopoly case: prices can be raised by reducing oupu Bu wasing waer will be sopped by a regulaor he monopolis se flexibiliy-correced prices equal. More waer is used when demand is elasic and less waer when demand is inelasic ydropower economics 28

29 ransmission and many producion-and consumer nodes Nodal pricing: opimal prices vary beween nodes due o loss in he nework (Ohm s law) and congesion on lines Problemaic o implemen in pracice: In Norway 5 price regions rade beween counries Expor impor will make prices more equal Congesion of cables an issue: congesion ren Norway as he baery of Europe Insanly available power capaciy of hydropower ydropower economics 29