Introduction to electricity economics1 ECON 4930 Autumn 2007 Electricity Economics Lecture 1 Lecturer: Finn R. Førsund.

Introduction to electricity economics

1

ECON 4930 Autumn 2007 Electricity Economics Lecture 1

Lecturer:

Finn R. Førsund

Introduction to electricity economics

2

Overview of the course

Basic learning objectives Know key qualitative results as to optimal social planning in

electricity economics when hydropower is involved Have a satisfactory understanding of how to formulate

dynamic management models using standard non-linear programming

Understand how constraints on the generating system and uncertainty of inflows of water to hydro reservoirs affect the optimal path of social prices

Be able to discuss actual market organisations in view of theoretical results obtained from the social planning analyses

Introduction to electricity economics

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Book: Hydropower EconomicsFinn R. Førsund (forthcoming)

Introduction to electricity economics

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Introduction

Why dynamics Hydropower plants can store energy in the form of

water if there is a dam or reservoir Water used today can alternatively be used

tomorrow; there is an opportunity cost attached to current water use

A dynamic analysis is then necessary in order to determine the time profile of the use of water in reservoirs

Introduction to electricity economics

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Introduction, cont.

Why standard non-linear programming Can use more specialised methods (dynamics

programming, Bellman) But will use a more basic tool

Baumol the Kuhn – Tucker conditions may perhaps

constitute the most powerful single weapon provided to economics theory by mathematical programming

Introduction to electricity economics

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Overview of the course Main themes

Introduction to electricity and hydropower The formulation of a dynamic social planning

problem Understanding price changes over time Multiple hydro plants and aggregation Introducing thermal generating capacity Trade between countries Transmission network Market power Uncertainty

Introduction to electricity economics

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Electricity

One of the key goods in a modern economy Supply and demand must be in continuous

physical equilibrium Key variables

Power (kW) Energy (kWh) Volt

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The use of electricity in Norwegian households

31

10 11

3

9

5

11

2 2

17

0

5

10

15

20

25

30

35

Space

heatin

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Hotwat

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Dishwash

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Refriger

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Deepfre

ezing

Wash

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Drying PC

Other

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Load curves for consumption

8000

10000

12000

14000

16000

18000

20000

1 3 5 7 9 11 13 15 17 19 21 23

Hours

GWh

Wed.20.07

Mon.24.01

Sun.17.07

Sun.23.01

Introduction to electricity economics

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Load-duration curve

0 1000 2000 3000 4000 5000 6000 7000 8000

0

3000

6000

9000

12000

15000

18000

21000

8760

Hours

MWh

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Hydropower The dynamics of water accumulation:

Rt Rt-1 + wt – rt , t =1,..,T Reservoir, stock of water R Inflows w Releases r

Inequality implies overflow Converting water from the dam to electricity

eHt (1/a)rt

Fabrication coefficient a assumed to be constant

Introduction to electricity economics

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Storage and production of hydropower in Norway 2003

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52

Weeks

GWh

Inflow GWh

Production GWh

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A social planning problem

The objective function: Maximising consumer plus producer surplus

etH : consumption of

hydropower in period t pt(et

H): demand function on price form, period t

Discrete time, period from hour, week, month, season, year

Variable production costs zero

Illustration of the objective function

Area under the demand curve

1 0

( )

HteT

tt z

p z dz pt(et

H)

etH0

Introduction to electricity economics

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A social planning problem, cont. Reservoir dynamics in energy variables

Assuming equality in the production function All variables expressed in energy units by

deflating with the fabrication coefficient

1 1

1

Ht t t t t t t

Ht t tt

R R w r R w ae

R R we

a a a

Introduction to electricity economics

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A social planning problem, cont.

1 0

1

max ( )

subject to

, 0 , 1,..,

, , , given, free

HteT

tt z

Ht t t t

t

Ht t

t o T

p z dz

R R w e

R R

R e t T

T w R R R