Electric Power Markets

Lecture 1

Intro to electric power markets

Slides

  • How we generate electricity
    • Technologies have different characteristics (size, dispatchability, cost, etc)
    • Electricity is an undifferentiated commodity. Regardless of how it’s made, utility from consumption is the same.
  • What’s special about electricity?
    • Demand and supply have to balance exactly at every point in time and space
    • It’s not economical to store electricity (although this is slowly changing)
  • Goals for power markets
    • Keep the lights on
    • At the lowest social cost
  • How deregulated electricity markets work
    • Plants bid in willingness to supply. Price received is the bid of the marginal producer each period.
  • Start Energy Market Game

Pre-class

Post-class

Conceptual questions

  1. What are some unique aspects of electricity supply and demand, compared to other markets?
    Answer
    • No straight line between supply and demand. Production and consumption inherently systemic.
    • System has to perfectly balance at all points in space and time.
    • Electricity is not (cheaply) storable.

Equilibrium in a wholesale market

Consider a market with the following technologies:

Fuel Capacity (MW) MC
Nuclear 20 10
Coal 50 35
Gas 40 55
Oil 15 90

And demand periods:

  • Off-peak demand 60
  • Peak demand = 120

Question 1: Computing Equilibrium

  • For each period, what is the market clearing price?
  • For each technology, compute total revenue, cost and profit in each period.
  • Which technologies are marginal in each period? Which earn inframarginal rents?
Answers

Off-peak (Coal on the margin)

Fuel Capacity MC Dispatched Price Revenue Cost Profit
Nuclear 20 10 20 35 700 200 500
Coal 50 35 40 35 1400 1400 0
Gas 40 55 0 35 0 0 0
Oil 15 90 0 35 0 0 0

Notes: Nuclear earns inframarginal rents; coal is marginal and breaks even.

Peak (Oil on the margin)

Fuel Capacity MC Dispatched Price Revenue Cost Profit
Nuclear 20 10 20 90 1800 200 1600
Coal 50 35 50 90 4500 1750 2750
Gas 40 55 40 90 3600 2200 1400
Oil 15 90 10 90 900 900 0

Notes: Oil is marginal and breaks even; all others earn inframarginal rents that rise with the higher MCP.

Question 2: Average costs and prices

Assume off-peak and peak each occur for half of the hours in the year.
Using your answers from the previous question,

  • What is the average cost of electricity over the year?
  • What is the average price of electricity over the year?

(Note: The average should be quantity weighted, not just the arithmetic average of the two prices)

Answer
  • Average cost = (Total cost in off-peak + Total cost in peak) / Total quantity

    • Total cost in off-peak = 200 + 1400 = 1600

    • Total cost in peak = 200 + 1750 + 2200 + 900 = 5050

    • Total quantity in off-peak = 20 + 40 = 60

    • Total quantity in peak = 20 + 50 + 40 + 10 = 120

    • Average cost = (1600 + 5050) / (60 + 120) = 6650 / 180 = 36.94

    • Average price = (Total revenue in off-peak + Total revenue in peak) / Total quantity

      • Total revenue in off-peak = 700 + 1400 = 2100
      • Total revenue in peak = 1800 + 4500 + 3600 + 900 = 10800
      • Average price = (2100 + 10800) / (60 + 120) = 12900 / 180 = 71.67

Question 3: Changes in costs and prices

Now imagine that the marginal cost of oil increases to $120 due to sanctions on Russia.

  • Recompute the price and production for each tech in the peak period.
  • By what % do the total costs of electricity generation increase in the peak period? By what percent does the price of electricity increase?
  • How much would prices have increased if the cost of gas had increased by 50% (instead of oil)? Why are these so different?
Answer

Dispatch & Payments — New Peak (MC_oil = 120)

Fuel Capacity MC Dispatched Price Revenue Cost Profit
Nuclear 20 10 20 120 2400 200 2200
Coal 50 35 50 120 6000 1750 4250
Gas 40 55 40 120 4800 2200 2600
Oil 15 120 10 120 1200 1200 0

Totals: Revenue = 14,400 ; Cost = 5,350

Cost & Price Changes (vs. previous peak)

  • Previous peak totals (MC_oil = 90):
    • Price P = 90
    • Cost = 5,050
    • New peak totals (MC_oil = 120):
      • Price P = 120
      • Cost = 5,350
    Percent changes:
    • Total cost: ((5350 - 5050)/5050 %)
    • Price: ((120 - 90)/90 = 33.33%)
    Interpretation: A higher marginal technology MC raises the uniform price substantially (33%), while total system cost rises more modestly (~6%) because only the final 10 MWh are affected directly by the oil cost increase; the price lift, however, is paid on all dispatched MWh.

Additional material

  • Many of the figures in the slides are from the EIA’s Annual Energy Outlook. Worth scrolling through the presentation slides to see policy scenarios.
  • FERC’s Energy Primer has a great overview of electric power markets in the US (Chapter 4)

Lecture 2

Market power in deregulated electricity markets

Market Power Slides

  • Electric power markets will not supply the socially efficient level of power when firms have market power.
  • We review what characteristics of markets lead to market power generally, and then discuss these in the context of the electric power sector.
  • When firms own many plants, incentives to bid above marginal cost depends on both marginal and inframarginal plant profits.

Pre-Class

Post-Class

In class we reviewed monopoly pricing, and then extend the concept to a setting where firms own multiple plants. The two key features were: 1) the elasticity of demand and 2) the share of plant capacity that was marginal (could set the price) and inframarginal (would sell power no matter what the price is). As an exercise, draw some graphical examples similar to the ones in the slides. Can you label the gains from raising price and the losses from lost sales when price increase? Can you see visually how these change with the two factors above?

Additional material

  • Explainer “Electricity Markets 101” from RFF
  • Borenstein, Severin. 2002. “The Trouble with Electricity Markets: Understanding California’s Restructuring Disaster.” The Journal of Economic Perspectives. link.

Lecture 3

Slides (jump to lecture 3 section)

Long-run investment

  • So far we’ve considered optimal dispatch given the set of plants available. We now consider what plants we should be building.

Pre-class

  • Watch this video explaining the levelized cost of energy (LCOE)
    • For a more econ-focused perspective, (rather than finance), here is another video (only need to watch one).
  • Read Lazard’s 2025 Report
    • Only need to read sections I and II, on energy generation.
    • Think about: Which technologies are currently cheapest? What is the range of uncertainty? How sensitive is the answer to modelling assumptions? Tax credits?

Post-class

Conceptual questions

  1. What is levelized cost of energy (LCOE)? Why do we need this measure to compare different generation technologies? What does it miss?
    Answer
    • LCOE is total average cost of output over the lifetime of a plant. We need this because it allows us to compare different plants with different lifetimes and mixes of upfront, on going fixed and marginal costs.
    • It is also useful because it tells use the average price a plant needs to receive over its lifetime to break even.

Computing and comparing LCOE

Question 1

A wind farm costs $1,200/kW to build, has fixed O&M costs of $30/kW-year, and a 25-year lifetime. It has a 40% capacity factor, which means that the it only produces power 40% of the time. It has no variable costs. What is the approximate LCOE? Assume a discount rate (cost of capital) of 5%, no variable O&M or fuel cost.

Note: You can either discount the expenses each year and divide by \((1 + r)^t\), where \(r\) is the discount rate and \(t\) is the year, or use the capital recovery factor (CRF) formula to compute the annuitized capital cost

Answers
  • Annual generation: hours in year \(\times\) capacity factor
    • \(8760 \times 0.40 = 3504\) kWh
    • divide by 1000 to put in MWh: 3.504 MWh
  • Capital Recovery Factor (CRF): \[\tfrac{0.05(1.05)^{25}}{(1.05)^{25} - 1} = 0.07095\]
  • Annualize the capital cost by multiplying it by the CRF: \(1200 \times 0.07095 =\) $85.1/ kW-yr
  • Add O&M to get the total fixed costs: \(85.1 + 30 =\) $115.1 / kW-yr
  • Divide by annual generation to get the average fixed costs per year
    • we’ll divide by MWh since variable cost and prices typically quoted per MWh
    • $ 115.1/ 3.504 = $ $32.9 / MWh
  • LCOE is average fixed cost + variable cost.
    • since there is no variable cost, this is just = $32.9 / MWh

Question 2

A gas plant has capital cost $900/kW, fixed O&M $15/kW-year, fuel cost $20/MWh, and a lifetime of 30 years. What utilization rate (capacity factor) does the gas plant need to achieve to have a lower LCOE than the wind plant? Assume the same discount rate.

Answers
  • First need to update the Capital Recovery Factor (CRF):
    \[ CRF = \tfrac{0.05(1.05)^{30}}{(1.05)^{30} - 1} = 0.0650 \]
  • Can now compute the Annualized capital cost:
    \(900 \times 0.0650 = 58.5 \,\$/\text{kW-yr}\)
  • Add O&M to get the total fixed costs: \(58.5 + 15 =\) \(73.5 / kW-year\)
  • Given Capacity Factor CF - Annual generation in kWh is \(8760 \times CF\)
    • divide by 1000 to get \(8.76 \times CF\) in MWh
  • Fixed cost per MWh:
    \[ \tfrac{73.5}{8.76 \times CF} = \tfrac{8.39}{CF} \,\$/\text{MWh} \]
  • Total LCOE for gas = Fixed cost per MWh + Fuel cost = \(8.39/CF + 20\)
  • Set equal to wind LCOE (32.9 $/MWh):
    \[ \tfrac{8.39}{CF} + 20 = 32.9 \] \[ \tfrac{8.39}{CF} = 12.9 \quad \Rightarrow \quad CF = \approx 0.65 \]
  • Answer: The gas plant must operate at a capacity factor of about 65% or higher to be cheaper than the wind plant.

See Excel calculations for more details.

Additional material