Capacity Expansion Model

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Capacity Expansion Model
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Load Duration Curve
Demand
time
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Piecewise Constant Approximation of Load Duration
Curve
Demand
Demand during time
time
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Static Deterministic Analysis
Optimal power plant can be found from equation

• type of power plant
• investment cost per 1 MW
• operating cost per 1 MW
• availability factor

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Motivation for Multistage Model

• Long-term evolution of equipment costs
• long-term evolution of load curve
• appearance of new technologies
• obsolescence of currently available equipment.

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Multistage Model Notations

• index periods of stages
• index the available
  technologies
• index operating modes in load
  duration curve

• availability factor of
• lifetime of
• existing capacity of at time
  , decided before
• unit investment cost for at time
  (assuming a fixed kkkkk plant
  life cycle for each type of plant).

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Multistage Model Notations (contd)

• index periods of stages
• index the available technologies
• index operating modes in load duration
  curve

Set of decisions

• new technology made available for
  technology at time
• total capacity of available at
  time
• capacity effectively used at time
  in mode .

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H-Stage Problem Deterministic Statement
s.t.
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H-Stage Problem Stochastic Statement
s.t.

• new capacity decided at time for
  equipment ,
• total capacity of available and in
  order at time
• vector of random parameters at time
  (demands ).

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H-Stage Problem Stochastic Statement(contd)
If decisions variables do not
depend upon then problem is
deterministic
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Example Problem Variables

• technologies
• construction delay
• existing equipment
• full availability
• takes values 3, 5, 7 with probabilities 0.3,
  0.4, 0.3

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Example Problem Model
investment costs
production costs
s.t.
investment constraint
random demand, first duration mode
deterministic demand
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Optimal Solution of Stochastic Problem
Value of performance function 381.85
Expected value solution
Value of performance function 365
is not feasible in stochastic problem
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Alternative Approaches
Chance constraints
Quantile constraints
In example