ECON 4930 Autumn 2007
Electricity Economics
Lecture 1
Lecturer:
Finn R. Førsund
Introduction to electricity economics
1
Overview of the course

Basic learning objectives
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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
2
Book: Hydropower Economics
Finn R. Førsund (forthcoming)
Introduction to electricity economics
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Introduction

Why dynamics
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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
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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
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Power (kW)
Energy (kWh)
Volt
Introduction to electricity economics
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The use of electricity in Norwegian
households
35
31
30
25
20
17
15
10
11
10
3
5
11
9
5
2
2
0
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Introduction to electricity economics
g
in
y
Dr
PC
er
th
O
8
Load curves for consumption
20000
18000
Wed.20.07
GWh
16000
Mon.24.01
14000
Sun.17.07
12000
Sun.23.01
10000
8000
1
3
5
7
9
11 13 15 17 19 21 23
Hours
Introduction to electricity economics
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Load-duration curve
MWh
21000
18000
15000
12000
9000
6000
3000
0
0
1000
2000
3000
4000
5000
6000
7000
8000
8760
Hours
Introduction to electricity economics
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Hydropower

The dynamics of water accumulation:
Rt  Rt-1 + wt – rt , t =1,..,T
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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
10000
9000
8000
Inflow GWh
7000
Production GWh
GWh
6000
5000
4000
3000
2000
1000
0
1
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46
49
52
Weeks
Introduction to electricity economics
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A social planning problem

The objective function:
Maximising consumer plus
producer surplus
T
t 1 z  0
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Illustration of the objective
function
etH

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pt ( z ) dz
pt(etH)
etH : consumption of
hydropower in period t
pt(etH): demand function on
price form, period t
Discrete time, period from
hour, week, month, season,
year
Variable production costs zero
etH
0

Area under the demand curve
Introduction to electricity economics
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A social planning problem, cont.

Reservoir dynamics in energy variables
Rt  Rt 1  wt  rt  Rt 1  wt  aetH 
Rt Rt 1 wt
H

  et
a
a
a


Assuming equality in the production function
All variables expressed in energy units by
deflating with the fabrication coefficient
Introduction to electricity economics
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A social planning problem, cont.
T
max
etH

t 1 z  0
pt ( z ) dz
subject to
Rt  Rt 1  wt  etH
Rt  R
Rt , etH  0 , t  1,.., T
T , wt , Ro , R given, RT free
Introduction to electricity economics
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