Generation Adequacy
Planning in Multi-Area
Power Systems
Panida Jirutitijaroen
Outline
Overview
Multi-area power systems
Reliability indices
System modeling
Problem statement
Problem formulation
Implementation
References
Multi-Area Power Systems
http://www.ercot.com/
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.
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.
System Modeling
Capacity flow network: a node
in the network represents an
area.
g i (ω )
Network random variables
Area generation capacity
Area load
Tie line capacity between areas
Discrete probability distribution
functions of all random
variables are constructed.
Power system
network
(only tie line capacity)
li (ω )
…….
s
…….
Source node for generation
Sink node for load
tij (ω )
t
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.
Problem Formulation
Two-stage recourse model
Mixed-integer stochastic programming.
Use expected unserved energy as reliability
index.
Decision variables:
First stage
xig : number of additional generators at area i, integer
Second stage
yij (ω ): flow from arc i to j
Objective function: Minimize expansion cost in
the first stage and expected unserved energy in
the second stage.
z = ∑ cig xig + Eω~ [ f ( x, ω~ )]
minimize
i∈I
g g
s.t.
∑ ci xi ≤ R
xig ≥ 0
i∈I
f ( x, ω ) = Min ∑ (li (ω ) − yit (ω ))
where
s.t.
i∈I
ysi (ω ) ≤ g i (ω ) + M ig xig
y ji (ω ) − yij (ω ) ≤ tij (ω )
∀i ∈ I
∀i , j ∈ I , i ≠ j
yit (ω ) ≤ li (ω )
∀i ∈ I
ysi (ω ) + ∑ y ji (ω ) = ∑ yij (ω ) + yit (ω )
∀i ∈ I
j∈I
j ≠i
j∈I
j ≠i
yij (ω ), ysj (ω ), yit (ω ) ≥ 0
∀i, j ∈ I
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
Area
1
Area
2
Area
3
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
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.
Thank you!
☺