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ECON 4925 Autumn 2007 Electricity Economics Lecture 7

ECON 4925 Autumn 2007 Electricity Economics Lecture 7. Lecturer: Finn R. Førsund. Trade between Hydro and Thermal. The cooperative social planning problem. The Lagrangian function. Inserting the energy balances Export for one country is import for the other. The Kuhn – Tucker conditions.

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ECON 4925 Autumn 2007 Electricity Economics Lecture 7

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  1. ECON 4925 Autumn 2007Electricity EconomicsLecture 7 Lecturer: Finn R. Førsund Trade and transmission

  2. Trade between Hydro and Thermal • The cooperative social planning problem Trade and transmission

  3. The Lagrangian function • Inserting the energy balances • Export for one country is import for the other Trade and transmission

  4. The Kuhn – Tucker conditions Trade and transmission

  5. Combining the bathtub diagram and the thermal diagram for two periods Period 2 Period 1 θ2 p2Th=p2H= p1Th=p1H= c' c' Export Import A' A M' M B' B Export Import Hydro Thermal Thermal Trade and transmission

  6. Trade Hydro –Thermal with reservoir constraint Period 2 Period 1 θ2 p2Th=p2H=2 γ1 p1Th=p1H=1 c' c' Import Export D' A' A B C D Export Import Thermal Thermal Hydro Trade and transmission

  7. Transmission • The model of Lord Kelvin from 1881 (Smith, 1961) • A single production node connected with a single consumption node • Assumptions • Voltage at consumption node given • No binding capacity limit on the line Consumption node Generating node Electricity flow Trade and transmission

  8. Ohm’s law Symbols PL = loss in kW I = current in amps R = resistance on the line in ohms L = length of line A = area of cross section ρ = specific resistance of the metal The physical laws of transmission Trade and transmission

  9. Constancy of energy Symbols Pi = power produced (kW) PL= loss on the line (kW) Po = power received (kW) Kirchhoff’s laws Current flow into a node must be equal to current flow out (energy cannot be lost) Voltage drops around any loop sum to zero (relevant for loop flow networks) Ohm’s and Kirchhoff’s laws Flows distribute within loops proportional to impedance on lines The physical laws of transmission, cont. Trade and transmission

  10. Definition for AC Symbols Po = power at consumption node in kW Vo = voltage at consumption node I = current in amps cosφ = power factor of the consumer’s load φ = lag between voltage and current variation in an alternating-current circuit The connection between voltage and current Trade and transmission

  11. The transmission production function • Inserting in the power balance • Introducing the weight of the cable K = 2dLA, d= specific weight Renaming Poand Pi , x and e, multiplying each term above with K Trade and transmission

  12. Substitution between capital and power input • Ex ante MRS (marginal rate of substitution) • The explicit ex ante production function • Scale properties ex ante and ex post • Ex ante: constant returns to scale • Ex post (fixed capital): decreasing returns to scale Trade and transmission

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