Transcript King Fahd University of Petroleum and Minerals Department

‫بسم هللا الرحمن الرحيم‬
ّ
‫الكهربائية – الرياض‬
‫ندوة التعريفات‬
2008 ‫ يناير‬18-17
Paper Title
Optimal Power Flow Considering Wheeling
Charges
By
Eng. Saleh M. Bamasak
Dr. M. A. Abido
Saudi Electricity Company-SEC
DTA-Jeddah
King Fahd University of
Petroleum & Minerals KFUPM
Outline:


Introduction
OPF



Wheeling Charge






Classical
OPF in Deregulation
Definition.
Wheeling Charge Methods
Bialek Tracing Algorithms
Software Algorithm
Case Study
Conclusion
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2
Introduction

Power transmission engineers perform many system
studies … Stability, Transmission Expansion, Protection,
OPF, etc. with objective functions suitable to vertically
integrated electricity sectors.

Continuing trend towards deregulation and unbundling of
electricity sectors has resulted in the need to reformulate
many of power system objectives.

Optimal Power Flow OPF problem has to be
reformulated in order to incorporate other objectives
that resulted from deregulation such as “Wheeling
Chargers”.
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Classical OPF


The classical OPF problem is a constrained
optimization problem.
Two types of variables appear in this problem,




state variables, denoted x, and
control variables denoted u .
The state variables consist of bus voltage magnitudes
and angles.
The control variables consist of adjustable quantities
such as generator MW, terminal voltage, and
transformer taps.
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
The mathematical formulation of the classical OPF problem is the
following
 Minimize c(x,u)
 Subject to : g(x,u)=0

The function is typically generation cost.


The equality constraints g(x,u)=0 result from Kirchhoff’s current law.
They are written as real and reactive power balance equations at
each network node.
The inequality constraints f(x,u)<= 0 model physical and operational
limits on the system components.
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OPF Output
A
L2=60MW+j20MVR
L2=50MW+j10MVR
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B
L2=70MW+j30MVR
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Gen. W & Var
128.091MW+19.947Mvar
A
L2=60MW+j20MVR
L2=50MW+j10MVR
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55.68MW+22.58Mvar
B
L2=70MW+j30MVR
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Terminal Volt.
128.091MW+19.947Mvar
A
1.1@0
L2=60MW+j20MVR
[email protected]
[email protected]
B
[email protected]
[email protected]
L2=50MW+j10MVR
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55.68MW+22.58Mvar
L2=70MW+j30MVR
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Lines Flow
128.091MW+19.947Mvar
A
1.1@0
L2=60MW+j20MVR
55.68MW+22.58Mvar
[email protected]
B
[email protected]
19MW
2.6Mvar
84.1MW
11.5Mvar
9.7MW
4.8Mvar
28.8MW
10.8Mvar
42.6MW
14.3Mvar
[email protected]
[email protected]
L2=50MW+j10MVR
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L2=70MW+j30MVR
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OPF In Deregulation


Consider a power system in which the
generation, transmission and
distribution services are unbundled.
In this structure, we have competing
generation companies, (GENCOS), the
regional transmission is operated by an
independent system operator (ISO), and
the customers are the distribution
companies (DISCOS) as well as some
large industrial loads.
Genco
Tie lines
Genco
Transco
Disco

Genco
Disco
The role of the ISO is to manage the
transmission system such that reliable
power is provided to the users at a
minimum price.
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OPF In Deregulation

The OPF objective in deregulation
environment has to be
Objective =
Minimize (Fuel Cost + Wheeling Charges)
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Wheeling Def.


The term of wheeling is defined as “The use of
transmission or distribution facilities of a system
to transmit power of and for another entity or
entities.”
Wheeling costs when applied to a transmission
network, also called transmission costs, are the
costs charged against generator companies and
suppliers for their use of the transmission
services.
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Wheeling Charges Methods
A
LA=60MW+j20MVR
B
LB=60MW+j20MVR
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Wheeling Charges Methods
A
LA=60MW+j20MVR
B
LB=60MW+j20MVR
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Wheeling Charges Methods
LA=60MW+j20MVR
A
B
A
B
B
B
LB=60MW+j20MVR
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
From Previous Example:



It is not fare that Trans. Company charge Supplier (A)
similar amount as Supplier (B) even though they
generate same amount of Power??? “Postage stamp
method”.
The usage of transmission network is vary from supplier
to supplier based on suppliers and customers locations .
Fair Usage-Based Transmission’s cost allocation
methods should be adopted for example “MW-Mile
Method”.
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MW-Mile Method




Power flow calculations are used to determine the actual
paths that the power follows through the network.
This amount of MW is then multiplied by agreed per-unit
cost of transmission capacity to get wheeling charge.
How to allocate the cost?
From engineering point of view, it is possible and acceptable
to apply approximate models or sensitivity indices to
estimate the contributions to the network flows from
individual users such as Bialek Tracing Algorithm
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Bialek Tracing Algorithm




Is design for recovery of fixed transmission cost in a pool
based market
The basic assumption used by tracing algorithms is the
proportional sharing principle.
it is assumed that the nodal inflows are shared
proportionally among the nodal outflows.
Extensive studies have shown its capability and efficiency
in allocating transmission usage charge among different
generators or loads.
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Bialek Mathematical Model
p 
g
ij
pijg
 A 
n
1
u ik
g
k 1
i
p
n
  Dijg, k PGK
k 1
pig 

pijg  PGi
j id
D 
g
ij
g
ij
p
PGK
A 
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1
u ij
; i  1,2,, n
1
u
ik
g
i
p
A 
; j   id

g
ij
p
A 
1

 pg

ij
  g
 pi

0
i j
j   id
otherwise
1
u
ik
pi
Pkij
: An unknown gross line flow in line i-j.
Pi g
: An unknown gross nodal power flow thru node i.
Au
: topological distribution matrix..
PGK
: generation in node K.
αid
: Set of nodes supplied directly from node i.
αiu
Dg
ij,k
: Set of buses
supplying
‫الكهربائية‬
‫التعريفات‬
‫ندوة‬bus i.
: topological distribution factors.
19
Suppliers Contributions
128.091MW+19.947Mvar
A
1.1@0
1
L2=60MW+j20MVR
55.68MW+22.58Mvar
B
[email protected]
[email protected]
19MW
2.6Mvar
84.1MW
11.5Mvar
9.7MW
4.8Mvar
2
42.6MW
14.3Mvar
[email protected]
L2=50MW+j10MVR
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28.8MW
10.8Mvar
5
[email protected]
L2=70MW+j30MVR
‫ندوة التعريفات الكهربائية‬
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Suppliers Contributions
128.091MW+19.947Mvar
A
1.1@0
1
L2=60MW+j20MVR
55.68MW+22.58Mvar
B
[email protected]
[email protected]
19MW
2.6Mvar
84.1MW
11.5Mvar
9.7MW
4.8Mvar
2
42.6MW
14.3Mvar
[email protected]
L2=50MW+j10MVR
7/18/2015
28.8MW
10.8Mvar
5
[email protected]
L2=70MW+j30MVR
‫ندوة التعريفات الكهربائية‬
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Suppliers Contributions
128.091MW+19.947Mvar
A
1.1@0
1
L2=60MW+j20MVR
55.68MW+22.58Mvar
B
[email protected]
[email protected]
19MW
2.6Mvar
84.1MW
11.5Mvar
9.7MW
4.8Mvar
4.388MW
2
42.6MW
14.3Mvar
[email protected]
L2=50MW+j10MVR
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28.8MW
10.8Mvar
5
[email protected]
L2=70MW+j30MVR
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Suppliers Contributions
128.091MW+19.947Mvar
A
1.1@0
1
L2=60MW+j20MVR
55.68MW+22.58Mvar
B
[email protected]
[email protected]
19MW
2.6Mvar
84.1MW
11.5Mvar
9.7MW
4.8Mvar
4.388MW
2
38.292MW
42.6MW
14.3Mvar
[email protected]
L2=50MW+j10MVR
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28.8MW
10.8Mvar
5
[email protected]
L2=70MW+j30MVR
‫ندوة التعريفات الكهربائية‬
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Suppliers Contributions
128.091MW+19.947Mvar
A
1.1@0
1
L2=60MW+j20MVR
55.68MW+22.58Mvar
B
[email protected]
[email protected]
19MW
2.6Mvar
84.1MW
11.5Mvar
9.7MW
4.8Mvar
4.388MW
2
38.292MW
42.6MW
14.3Mvar
[email protected]
L2=50MW+j10MVR
7/18/2015
28.8MW
10.8Mvar
5
[email protected]
L2=70MW+j30MVR
‫ندوة التعريفات الكهربائية‬
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Suppliers Contributions
128.091MW+19.947Mvar
A
1.1@0
1
B
[email protected]
[email protected]
19MW
2.6Mvar
84.1MW
11.5Mvar
9.7MW
4.8Mvar
84.1 MW
4.388MW
2
L2=60MW+j20MVR
55.68MW+22.58Mvar
38.292MW
42.6MW
14.3Mvar
[email protected]
L2=50MW+j10MVR
7/18/2015
28.8MW
10.8Mvar
5
[email protected]
L2=70MW+j30MVR
‫ندوة التعريفات الكهربائية‬
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Suppliers Contributions
128.091MW+19.947Mvar
A
1.1@0
1
B
[email protected]
[email protected]
19MW
2.6Mvar
84.1MW
11.5Mvar
9.7MW
4.8Mvar
84.1 MW
0.0 MW
2
L2=60MW+j20MVR
55.68MW+22.58Mvar
4.388MW
38.292MW
42.6MW
14.3Mvar
[email protected]
L2=50MW+j10MVR
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28.8MW
10.8Mvar
5
[email protected]
L2=70MW+j30MVR
‫ندوة التعريفات الكهربائية‬
26
Where does the OPF play a
role in all of this???
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27

In Centralized or pool-based trading system,
producers and customers submit their bids and
offers to the system operator, who also acts as
market operator.

The system operator which must be independent
from all the other parties, selects the bids and
offers based on OPF calculation that optimally
clear the market while respecting the security
constraints imposed by the transmission network.
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Developed Software
Network Data
Propose a solutions
Run Newton Raphson LF
Optimization Algorithm
POS
Objective Function
Revise solutions
Using PSO Subroutine
Power Flow Result
Run Bialek Model
To find each Gen
contribution for all lines
No
Calculate the fuel cost +
wheeling cost
Check for
optimal
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‫ندوة التعريفات الكهربائية‬
yes
Print Result
29
Case Study


6-Bus system
Two Objective Function



F1=Minimize (fuel cost)
F2=minimize (fuel cost+ wheeling cost)
Output:



Transmission Cost allocation
Fuel cost
Total cost
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Simulation Result
Total fuel
cost
Total wheeling
cost
Total
$/hour
Min.(Fuel)
1797.9
639.9908
2438.7
Min.(Fuel+Wh
eeling)
1803
631.99
2434.9
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Simulation Result
F1
Fuel Cost Wheeling
$/h
Cost $/h
1023.5
354.4648
774.38
285.5260
Total $/h
Fuel Cost Wheeling
$/h
Cost $/h
1176.3
464.46
626.58
167.533
Total $/h
G-A
G-B
F2
G-A
G-B
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2438.7
‫ندوة التعريفات الكهربائية‬
2434.9
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Conclusion


This paper uses optimization technique as the
dispatch algorithm for the economic dispatch
problem, considering the wheeling charges.
The wheeling charges are calculated with a power
flow based MW-Mile approach, where the power
tracing from each generator is carried out using the
Bialek’s tracing method.
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

The proposed OPF algorithm is tested on a small
test system, showing that the optimization
algorithm is capable of dealing with non-linear and
multi-objective problems.
The OPF algorithm can be scaled up as a useful
tool for transmission companies to dispatch power
at the least possible cost, where the cost to be
minimized includes both fuel and wheeling cost.
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Thank you
The Floor is Open for Discussion