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Paper TitlePaper Title
Optimal Power Flow Considering Optimal Power Flow Considering Wheeling ChargesWheeling Charges
By
بسم الله الرحمن الرحيم
ندوة التعريفات الكهربائي*ة – الرياض
2008 يناير 17-18
Eng. Saleh M. BamasakSaudi Electricity Company-SEC
DTA-Jeddah
Dr. M. A. AbidoKing Fahd University of
Petroleum & Minerals KFUPM
04/18/23الكهربائية التعريفات ندوة 2
Outline: Introduction OPF
Classical OPF in Deregulation
Wheeling Charge Definition. Wheeling Charge Methods Bialek Tracing Algorithms
Software Algorithm Case Study Conclusion
04/18/23الكهربائية التعريفات ندوة 3
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 Wheeling Chargers”Chargers”.
04/18/23الكهربائية التعريفات ندوة 4
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.
04/18/23الكهربائية التعريفات ندوة 5
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.
04/18/23الكهربائية التعريفات ندوة 6
OPF Output
A B
L2=50MW+j10MVR L2=70MW+j30MVR
L2=60MW+j20MVR
04/18/23الكهربائية التعريفات ندوة 7
Gen. W & Var
A B
L2=50MW+j10MVR L2=70MW+j30MVR
L2=60MW+j20MVR128.091MW+19.947Mvar 55.68MW+22.58Mvar
04/18/23الكهربائية التعريفات ندوة 8
Terminal Volt.
A B
L2=50MW+j10MVR L2=70MW+j30MVR
L2=60MW+j20MVR
1.1@0
1.07@-2.681
1.03@-3.198 1.077@-2.79
1.034@-5.255
128.091MW+19.947Mvar 55.68MW+22.58Mvar
04/18/23الكهربائية التعريفات ندوة 9
Lines Flow
A B
L2=50MW+j10MVR L2=70MW+j30MVR
L2=60MW+j20MVR
1.1@0
1.07@-2.681
1.03@-3.198 1.077@-2.79
1.034@-5.255
128.091MW+19.947Mvar 55.68MW+22.58Mvar
84.1MW11.5Mvar
19MW2.6Mvar
9.7MW4.8Mvar
42.6MW14.3Mvar
28.8MW10.8Mvar
04/18/23الكهربائية التعريفات ندوة 10
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.
The role of the ISO is to manage the transmission system such that reliable power is provided to the users at a minimum price.
Transco
GencoGencoGenco
DiscoDisco
Tie lines
04/18/23الكهربائية التعريفات ندوة 11
OPF In Deregulation
Objective = Objective = Minimize (Fuel Cost + Wheeling Charges)Minimize (Fuel Cost + Wheeling Charges)
The OPF objective in deregulation environment has to be
04/18/23الكهربائية التعريفات ندوة 12
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.
04/18/23الكهربائية التعريفات ندوة 13
Wheeling Charges Methods
A B
LB=60MW+j20MVR
LA=60MW+j20MVR
04/18/23الكهربائية التعريفات ندوة 14
Wheeling Charges Methods
A B
LB=60MW+j20MVR
LA=60MW+j20MVR
04/18/23الكهربائية التعريفات ندوة 15
Wheeling Charges Methods
A B
LB=60MW+j20MVR
LA=60MW+j20MVR
A
BB
B
04/18/23الكهربائية التعريفات ندوة 16
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”. “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-“MW-Mile Method”. Mile Method”.
04/18/23الكهربائية التعريفات ندوة 17
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 Bialek Tracing AlgorithmAlgorithm
04/18/23الكهربائية التعريفات ندوة 18
Bialek Tracing AlgorithmBialek 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.
04/18/23الكهربائية التعريفات ندوة 19
Bialek Mathematical Bialek Mathematical ModelModel
di
n
kGK
gkij
n
kGKikug
i
gijg
ij
jPD
PAp
pp
;1
,
1
1
niPppdij
Gigij
gi ,,2,1;
otherwise
jp
pji
A dig
i
gij
iju
0
1
1
i
ikugij
gi
ikugijg
ij p
Ap
p
ApD
11
Pkij : An unknown gross line flow in line i-j.
Pig : 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 : Set of buses supplying bus i.
Dgij,k : topological distribution factors.
04/18/23الكهربائية التعريفات ندوة 20
Suppliers Contributions
A B
L2=50MW+j10MVR L2=70MW+j30MVR
L2=60MW+j20MVR
1.1@0
1.07@-2.681
1.03@-3.198 1.077@-2.79
1.034@-5.255
128.091MW+19.947Mvar 55.68MW+22.58Mvar
84.1MW11.5Mvar
19MW2.6Mvar
9.7MW4.8Mvar
42.6MW14.3Mvar
28.8MW10.8Mvar
1
2 5
04/18/23الكهربائية التعريفات ندوة 21
Suppliers Contributions
A B
L2=50MW+j10MVR L2=70MW+j30MVR
L2=60MW+j20MVR
1.1@0
1.07@-2.681
1.03@-3.198 1.077@-2.79
1.034@-5.255
128.091MW+19.947Mvar 55.68MW+22.58Mvar
84.1MW11.5Mvar
19MW2.6Mvar
9.7MW4.8Mvar
42.6MW14.3Mvar
28.8MW10.8Mvar
1
2 5
04/18/23الكهربائية التعريفات ندوة 22
Suppliers Contributions
A B
L2=50MW+j10MVR L2=70MW+j30MVR
L2=60MW+j20MVR
1.1@0
1.07@-2.681
1.03@-3.198 1.077@-2.79
1.034@-5.255
128.091MW+19.947Mvar 55.68MW+22.58Mvar
84.1MW11.5Mvar
19MW2.6Mvar
9.7MW4.8Mvar
42.6MW14.3Mvar
28.8MW10.8Mvar
4.388MW
1
2 5
04/18/23الكهربائية التعريفات ندوة 23
Suppliers Contributions
A B
L2=50MW+j10MVR L2=70MW+j30MVR
L2=60MW+j20MVR
1.1@0
1.07@-2.681
1.03@-3.198 1.077@-2.79
1.034@-5.255
128.091MW+19.947Mvar 55.68MW+22.58Mvar
84.1MW11.5Mvar
19MW2.6Mvar
9.7MW4.8Mvar
42.6MW14.3Mvar
28.8MW10.8Mvar
38.292MW
4.388MW
1
2 5
04/18/23الكهربائية التعريفات ندوة 24
Suppliers Contributions
A B
L2=50MW+j10MVR L2=70MW+j30MVR
L2=60MW+j20MVR
1.1@0
1.07@-2.681
1.03@-3.198 1.077@-2.79
1.034@-5.255
128.091MW+19.947Mvar 55.68MW+22.58Mvar
84.1MW11.5Mvar
19MW2.6Mvar
9.7MW4.8Mvar
42.6MW14.3Mvar
28.8MW10.8Mvar
38.292MW
4.388MW
1
2 5
04/18/23الكهربائية التعريفات ندوة 25
Suppliers Contributions
A B
L2=50MW+j10MVR L2=70MW+j30MVR
L2=60MW+j20MVR
1.1@0
1.07@-2.681
1.03@-3.198 1.077@-2.79
1.034@-5.255
128.091MW+19.947Mvar 55.68MW+22.58Mvar
84.1MW11.5Mvar
19MW2.6Mvar
9.7MW4.8Mvar
42.6MW14.3Mvar
28.8MW10.8Mvar
38.292MW
4.388MW
1
2 5
84.1 MW
04/18/23الكهربائية التعريفات ندوة 26
Suppliers Contributions
A B
L2=50MW+j10MVR L2=70MW+j30MVR
L2=60MW+j20MVR
1.1@0
1.07@-2.681
1.03@-3.198 1.077@-2.79
1.034@-5.255
128.091MW+19.947Mvar 55.68MW+22.58Mvar
84.1MW11.5Mvar
19MW2.6Mvar
9.7MW4.8Mvar
42.6MW14.3Mvar
28.8MW10.8Mvar
38.292MW
4.388MW
1
2 5
84.1 MW
0.0 MW
04/18/23الكهربائية التعريفات ندوة 27
Where does the OPF play a role in all of
this???
04/18/23الكهربائية التعريفات ندوة 28
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 calculationbased on OPF calculation that optimally clear the market while respecting the security constraints imposed by the transmission network.
04/18/23الكهربائية التعريفات ندوة 29
Developed SoftwareNetwork Data
Run Newton Raphson LF
Power Flow Result
Optimization AlgorithmPOS
Objective FunctionPropose a solutions
Revise solutionsUsing PSO Subroutine
Run Bialek ModelTo find each Gen
contribution for all lines
Calculate the fuel cost + wheeling cost
Check for optimal
No
Print Resultyes
04/18/23الكهربائية التعريفات ندوة 30
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
04/18/23الكهربائية التعريفات ندوة 31
Simulation Result
Total fuel cost
Total wheeling
cost
Total$/hour
Min.(Fuel) 1797.9 1797.9 639.9908 639.9908 2438.7 2438.7
Min.(Fuel+Whee
ling)
1803 1803 631.99 631.99 2434.9 2434.9
04/18/23الكهربائية التعريفات ندوة 32
Simulation Result
F2 Fuel Cost $/h
WheelingCost $/h
Total $/h
G-A 1176.3 464.46 2434.9
G-B 626.58 167.533
F1 Fuel Cost $/h
WheelingCost $/h
Total $/h
G-A 1023.5 354.4648 2438.7
G-B 774.38 285.5260
04/18/23الكهربائية التعريفات ندوة 33
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.
04/18/23الكهربائية التعريفات ندوة 34
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.
The Floor is Open for Discussion
Thank youThank you
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