Hydropower and thermal1 ECON 4925 Autumn 2007 Electricity Economics Lecture 5 Lecturer: Finn R. Førsund

Hydropower and thermal 2 Thermal capacity Primary energy source coal, oil, gas, wood uranium  Water is heated up to produce steam that drives the turbines producing electricity  Burning gas directly like a jet engine: CCGT; combined cycle gas turbine  Emission of pollutants; acid rain, climate gases, nuclear waste Thermal capacity is power-restricted

Hydropower and thermal 3 Thermal capacity, cont. Variable cost of thermal electricity production as a function of output based on the consumption of primary fuel

Hydropower and thermal 4 Least cost combination of thermal plants

Hydropower and thermal 5 The Lagrangian (formulating a maximisation problem)

Hydropower and thermal 6 The Kuhn – Tucker conditions

Hydropower and thermal 7 The three states of a plant Condition for not activating plants for a given level of total production Conditions for activating plants  Interior solution for production  Capacity-constrained production

Hydropower and thermal 8 A'A' Merit-order ranking No intersection of marginal cost curves e Th c'c' B C D θiθi υ A B'B' Shoulder Base Peak

Hydropower and thermal 9 Merit-order aggregation of cost curves e Th c'c' c'c' Base Shoulder Peak

Hydropower and thermal 10 Mixed hydro and thermal capacity The social planning problem

Hydropower and thermal 11 The Lagrangian function

Hydropower and thermal 12 The Kuhn – Tucker conditions

Hydropower and thermal 13 The use of hydro and thermal No use of thermal (NB! Applies to all periods) Use of both thermal and hydro Hydro will always be used if

Hydropower and thermal 14 Bathtub diagram with hydro and thermal p1p1 λ Period 2 Period 1 λ Thermal extensions p2p2 p1p1 p2p2 c' A' A M' M D D' Hydro energy

Hydropower and thermal 15 Thermal and hydro with a reservoir constraint The social planning problem

Hydropower and thermal 16 The Lagrangian

Hydropower and thermal 17 The Kuhn – Tucker conditions

Hydropower and thermal 18 The use of hydro and thermal Thermal will not be used in period t if Hydro will not be used in period t if Both thermal and hydro in use

Hydropower and thermal 19 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

Hydropower and thermal 20 Start-up costs of thermal Base e Th b1b1 b2b2 b3b3 Loss a3a3 p 1, p 3 p2p2 b i, p i ShoulderPeak Start-up