Lecture 4 Economics for Energy Systems Analysis

Gang He

September 12, 2022

Sample analytic questions

  • What’s the LCOE of a new technology?
  • When to retire a nuclear/coal power plant?
  • Should I install rooftop solar? Buy an EV?
  • How long should the government subsidies heatpumps?
  • When can offshore wind achieve grid parity?

Project economics

  • Simple payback
  • Discounting
  • Present/future value
  • Uniform payments (annuities)
  • Capital recovery factor
  • Comparing technologies/costs (LCOE)
  • Learning curve
  • Market and technology drivers

Time is money

  • Money value changes in time: a dollar today worth more than a dollar tomorrow.
  • When money is invested, its amount changes with the return.
  • When money is transferred into assets, its value change due to depreciation and/or inflation.
  • Discounted cash flow is a technique that allow us to evaluate values as they change over time.

Payback period

\(Payback\ Period = Initial\ Investment ÷ Annual\ Cash\ Flow\)

Simple payback: no discounting
Payback: with discounting

Capital Recovery Factor (CRF)

Ratio of a constant annunity to the present value of receiving that annuity for a given length of time.

\(CRF = \frac{i(1+i)^n}{(1+i)^n - 1}\)


\(discount\ rate (r) = interest\ rate (i) + inflation\)

The power of discounting

Declining discounting


\(LCOE=\frac{\text{sum of costs over lifetime}}{\text{sum of electricity produced over life time}}=\frac{\sum_{t=1}^{n}{\frac{I_t+M_t+F_t}{(1+r)^t}}}{\sum_{t=1}^{n}{E_t}}\)

I: Investment costs
M: Operation and maintaince costs
F: Fuel costs

Comparing LCOE

Limitations of LCOE

  • Fossil: not include other costs (e.g. enviromental, carbon, etc.)
  • RE: not include integraton costs
  • Focus on economics, not include social cultural acceptance

Learning curve

Empircial relations between unit costs and cumulative production.

\(Y = aX^b\)



Y: Unit costs
a: Cost of first unit
X: Units
b: Slope of the learning curve
Pr: Progress ratio
Lr: Learing rate

Learning of differrent technologies

Drivers of learning

Source of learning

Learning by doing

  • Economy of scale
  • Economy of scope

Learning by researching

How renewables are getting cheap

Why nuclear costs are going up?

Role of global supply chain in PV


  • Project economics is useful for basic cost-benefit analysis
  • Getting the price (discounting) right
  • Understanding technology dynamics will help to model future projections
  • Aware of the limitations


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