ECON 4930 Spring 2013 Electricity Economics Lecture 1 Lecturer: Finn R. Førsund Introduction to electricity economics 1 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 2 Book: Hydropower Economics Finn R. Førsund (forthcoming) Introduction to electricity economics 3 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 4 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 5 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 Introducing intermittent generating capacity Trade between countries Transmission network Market power Uncertainty Introduction to electricity economics 6 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 Introduction to electricity economics 7 The use of electricity in Norwegian households 35 31 30 25 20 17 15 10 11 10 3 5 11 9 5 2 2 O th er PC Dr yin g hw as he Re r fr i ge ra tin De g ep fre ez W in g as hi ng m a. Di s Li gh t at er Ho tw Sp ac eh ea tin g 0 Introduction to electricity economics 8 Load curves for consumption 20000 18000 GWh 16000 Wed.20.07 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 9 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 10 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 11 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 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 Weeks Introduction to electricity economics 12 A social planning problem The objective function: Maximising consumer plus producer surplus T t 1 z 0 Illustration of the objective function etH 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 et H 0 Area under the demand curve Introduction to electricity economics 13 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 14 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 15