paper title optimal power flow considering wheeling charges by

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

04/19/23الكهربائية التعريفات ندوة 2

Outline: Introduction OPF

Classical OPF in Deregulation

Wheeling Charge Definition. Wheeling Charge Methods Bialek Tracing Algorithms

Software Algorithm Case Study Conclusion


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”.


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.


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.


OPF Output

A B

L2=50MW+j10MVR L2=70MW+j30MVR

L2=60MW+j20MVR


Gen. W & Var

A B


L2=60MW+j20MVR128.091MW+19.947Mvar 55.68MW+22.58Mvar


Terminal Volt.

A B


L2=60MW+j20MVR

1.1@0

[email protected]

[email protected] [email protected]

[email protected]

128.091MW+19.947Mvar 55.68MW+22.58Mvar


Lines Flow

A B


L2=60MW+j20MVR

1.1@0

[email protected]


[email protected]

128.091MW+19.947Mvar 55.68MW+22.58Mvar

84.1MW11.5Mvar

19MW2.6Mvar

9.7MW4.8Mvar

42.6MW14.3Mvar

28.8MW10.8Mvar


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


OPF In Deregulation

Objective = Objective = Minimize (Fuel Cost + Wheeling Charges)Minimize (Fuel Cost + Wheeling Charges)

The OPF objective in deregulation environment has to be


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.


Wheeling Charges Methods

A B

LB=60MW+j20MVR

LA=60MW+j20MVR



A B

LB=60MW+j20MVR

LA=60MW+j20MVR



A B

LB=60MW+j20MVR

LA=60MW+j20MVR

A

BB

B


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”.


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


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.


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.


Suppliers Contributions

A B


L2=60MW+j20MVR

1.1@0

[email protected]


[email protected]

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



A B


L2=60MW+j20MVR

1.1@0

[email protected]


[email protected]

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



A B


L2=60MW+j20MVR

1.1@0

[email protected]


[email protected]

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



A B


L2=60MW+j20MVR

1.1@0

[email protected]


[email protected]

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



A B


L2=60MW+j20MVR

1.1@0

[email protected]


[email protected]

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



A B


L2=60MW+j20MVR

1.1@0

[email protected]


[email protected]

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


Where does the OPF play a role in all of

this???


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.


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


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


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


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


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.


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

paper title optimal power flow considering wheeling charges by

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