Generation Adequacy Planning in MultiArea Power Systems

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Generation Adequacy Planning in Multi-Area Power
Systems

• Panida Jirutitijaroen

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Outline

• Overview
• Multi-area power systems
• Reliability indices
• System modeling
• Problem statement
• Problem formulation
• Implementation
• References

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Multi-Area Power Systems

• Consists of generators, transmission lines, and
  load.
• Power systems can be divided geographically into
  several areas.
• Each area has its generation units, transmission
  lines in the area, and load.
• Tie lines are transmission lines that
  interconnect from one area to another.

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Reliability Indices

• Power systems are expected to operate within
  reliability limit.
• Examples of reliability index are
• Loss of load probability (LOLP) Probability that
  load in any area is not satisfied.
• Expected Unserved Energy (EUE) Expected energy
  not supplied to load.

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System Modeling

• Capacity flow network a node in the network
  represents an area.
• Source node for generation
• Sink node for load
• Network random variables
• Area generation capacity
• Area load
• Tie line capacity between areas
• Discrete probability distribution functions of
  all random variables are constructed.

s
.
.
t
Power system network (only tie line capacity)
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Problem Statement

• Multi-area power systems with prospective
  generation locations.
• To ensure resource adequacy, ISOs need to guide
  generation expansion in a competitive market.
• The optimal location will yield favorable
  trade-off between reliability and cost.
• At present, generation requirement is computed
  from simulation or ad hoc procedure.

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Problem Formulation

• Two-stage recourse model
• Mixed-integer stochastic programming.
• Use expected unserved energy as reliability
  index.
• Decision variables
• First stage
• number of additional generators at area
  i, integer
• Second stage
• flow from arc i to j
• Objective function Minimize expansion cost in
  the first stage and expected unserved energy in
  the second stage.

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• minimize
• s.t.
• where
• s.t.

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Implementation

• Implementation to three-area power systems.
• L-shaped algorithm with integer variable in the
  first stage.
• Problem stats
• 3 integer variables
• 12 positive continuous variables
• 16 constraints
• 10080 scenarios

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Input parameters

• Discrete generation capacity distribution in each
  area.
• Discrete tie line capacity distribution in the
  network.
• Discrete area load distribution.
• Dependent among areas
• Independent with respect to generation and
  tie-line capacity.
• BLOCK structure for STOCH file

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References

• Introduction to Stochastic Programming, John R.
  Birge and Francois Louveaux.
• INEN 689 Large Scale Stochastic Optimization
  class notes.
• ELEN 643 Power System Reliability class notes.

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Thank you! ?