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Paper Title Optimal Power Flow Considering Wheeling Charges By بسم الله الرحمن الرحيم ندوة التعريفات الكهربائيّة – الرياض 17-18 يناير 2008 Eng. Saleh M. Bamasak Saudi Electricity Company-SEC DTA-Jeddah Dr. M. A. Abido King Fahd University of Petroleum & Minerals KFUPM

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4/15/2015 ندوة التعريفات الكهربائية 2 Outline: Introduction OPF Classical OPF in Deregulation Wheeling Charge Definition. Wheeling Charge Methods Bialek Tracing Algorithms Software Algorithm Case Study Conclusion

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4/15/2015 ندوة التعريفات الكهربائية 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. Wheeling Chargers” 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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4/15/2015 ندوة التعريفات الكهربائية 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.

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4/15/2015 ندوة التعريفات الكهربائية 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.

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4/15/2015 ندوة التعريفات الكهربائية 6 OPF Output AB L2=50MW+j10MVR L2=70MW+j30MVR L2=60MW+j20MVR

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4/15/2015 ندوة التعريفات الكهربائية 7 Gen. W & Var AB L2=50MW+j10MVR L2=70MW+j30MVR L2=60MW+j20MVR 128.091MW+19.947Mvar 55.68MW+22.58Mvar

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4/15/2015 ندوة التعريفات الكهربائية 8 Terminal Volt. AB L2=50MW+j10MVR L2=70MW+j30MVR L2=60MW+j20MVR 1.1@0 1.07@-2.681 1.03@-3.1981.077@-2.79 1.034@-5.255 128.091MW+19.947Mvar 55.68MW+22.58Mvar

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4/15/2015 ندوة التعريفات الكهربائية 9 Lines Flow AB L2=50MW+j10MVR L2=70MW+j30MVR L2=60MW+j20MVR 1.1@0 1.07@-2.681 1.03@-3.1981.077@-2.79 1.034@-5.255 128.091MW+19.947Mvar 55.68MW+22.58Mvar 84.1MW 11.5Mvar 19MW 2.6Mvar 9.7MW 4.8Mvar 42.6MW 14.3Mvar 28.8MW 10.8Mvar

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4/15/2015 ندوة التعريفات الكهربائية 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 Genco Disco Tie lines

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4/15/2015 ندوة التعريفات الكهربائية 11 OPF In Deregulation Objective = Minimize (Fuel Cost + Wheeling Charges) The OPF objective in deregulation environment has to be

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4/15/2015 ندوة التعريفات الكهربائية 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.

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4/15/2015 ندوة التعريفات الكهربائية 13 Wheeling Charges Methods AB LB=60MW+j20MVR LA=60MW+j20MVR

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4/15/2015 ندوة التعريفات الكهربائية 14 Wheeling Charges Methods AB LB=60MW+j20MVR LA=60MW+j20MVR

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4/15/2015 ندوة التعريفات الكهربائية 15 Wheeling Charges Methods AB LB=60MW+j20MVR LA=60MW+j20MVR A B B B

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4/15/2015 ندوة التعريفات الكهربائية 16 From Previous Example: “Postage stamp method”. 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. “MW-Mile Method”. Fair Usage-Based Transmission’s cost allocation methods should be adopted for example “MW-Mile Method”.

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4/15/2015 ندوة التعريفات الكهربائية 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? Bialek Tracing Algorithm 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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4/15/2015 ندوة التعريفات الكهربائية 18 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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4/15/2015 ندوة التعريفات الكهربائية 19 Bialek Mathematical Model P k ij : An unknown gross line flow in line i-j. PigPig : An unknown gross nodal power flow thru node i. AuAu : topological distribution matrix.. P GK : generation in node K. αidαid : Set of nodes supplied directly from node i. αiuαiu : Set of buses supplying bus i. D g ij,k : topological distribution factors.

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4/15/2015 ندوة التعريفات الكهربائية 20 Suppliers Contributions AB L2=50MW+j10MVR L2=70MW+j30MVR L2=60MW+j20MVR 1.1@0 1.07@-2.681 1.03@-3.1981.077@-2.79 1.034@-5.255 128.091MW+19.947Mvar 55.68MW+22.58Mvar 84.1MW 11.5Mvar 19MW 2.6Mvar 9.7MW 4.8Mvar 42.6MW 14.3Mvar 28.8MW 10.8Mvar 1 25

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4/15/2015 ندوة التعريفات الكهربائية 21 Suppliers Contributions AB L2=50MW+j10MVR L2=70MW+j30MVR L2=60MW+j20MVR 1.1@0 1.07@-2.681 1.03@-3.1981.077@-2.79 1.034@-5.255 128.091MW+19.947Mvar 55.68MW+22.58Mvar 84.1MW 11.5Mvar 19MW 2.6Mvar 9.7MW 4.8Mvar 42.6MW 14.3Mvar 28.8MW 10.8Mvar 1 25

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4/15/2015 ندوة التعريفات الكهربائية 22 Suppliers Contributions AB L2=50MW+j10MVR L2=70MW+j30MVR L2=60MW+j20MVR 1.1@0 1.07@-2.681 1.03@-3.1981.077@-2.79 1.034@-5.255 128.091MW+19.947Mvar 55.68MW+22.58Mvar 84.1MW 11.5Mvar 19MW 2.6Mvar 9.7MW 4.8Mvar 42.6MW 14.3Mvar 28.8MW 10.8Mvar 4.388MW 1 25

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4/15/2015 ندوة التعريفات الكهربائية 23 Suppliers Contributions AB L2=50MW+j10MVR L2=70MW+j30MVR L2=60MW+j20MVR 1.1@0 1.07@-2.681 1.03@-3.1981.077@-2.79 1.034@-5.255 128.091MW+19.947Mvar 55.68MW+22.58Mvar 84.1MW 11.5Mvar 19MW 2.6Mvar 9.7MW 4.8Mvar 42.6MW 14.3Mvar 28.8MW 10.8Mvar 38.292MW 4.388MW 1 25

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4/15/2015 ندوة التعريفات الكهربائية 24 Suppliers Contributions AB L2=50MW+j10MVR L2=70MW+j30MVR L2=60MW+j20MVR 1.1@0 1.07@-2.681 1.03@-3.1981.077@-2.79 1.034@-5.255 128.091MW+19.947Mvar 55.68MW+22.58Mvar 84.1MW 11.5Mvar 19MW 2.6Mvar 9.7MW 4.8Mvar 42.6MW 14.3Mvar 28.8MW 10.8Mvar 38.292MW 4.388MW 1 25

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4/15/2015 ندوة التعريفات الكهربائية 25 Suppliers Contributions AB L2=50MW+j10MVR L2=70MW+j30MVR L2=60MW+j20MVR 1.1@0 1.07@-2.681 1.03@-3.1981.077@-2.79 1.034@-5.255 128.091MW+19.947Mvar 55.68MW+22.58Mvar 84.1MW 11.5Mvar 19MW 2.6Mvar 9.7MW 4.8Mvar 42.6MW 14.3Mvar 28.8MW 10.8Mvar 38.292MW 4.388MW 1 25 84.1 MW

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4/15/2015 ندوة التعريفات الكهربائية 26 Suppliers Contributions AB L2=50MW+j10MVR L2=70MW+j30MVR L2=60MW+j20MVR 1.1@0 1.07@-2.681 1.03@-3.1981.077@-2.79 1.034@-5.255 128.091MW+19.947Mvar 55.68MW+22.58Mvar 84.1MW 11.5Mvar 19MW 2.6Mvar 9.7MW 4.8Mvar 42.6MW 14.3Mvar 28.8MW 10.8Mvar 38.292MW 4.388MW 1 25 84.1 MW 0.0 MW

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4/15/2015 ندوة التعريفات الكهربائية 27 Where does the OPF play a role in all of this???

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4/15/2015 ندوة التعريفات الكهربائية 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. based on OPF calculation 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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4/15/2015 ندوة التعريفات الكهربائية 29 Developed Software Network Data Run Newton Raphson LF Power Flow Result Optimization Algorithm POS Objective Function Propose a solutions Revise solutions Using PSO Subroutine Run Bialek Model To find each Gen contribution for all lines Calculate the fuel cost + wheeling cost Check for optimal No Print Result yes

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4/15/2015 ندوة التعريفات الكهربائية 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

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4/15/2015 ندوة التعريفات الكهربائية 31 Simulation Result Total fuel cost Total wheeling cost Total $/hour Min.(Fuel)1797.9639.99082438.7 Min.(Fuel+Wh eeling)1803631.992434.9

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4/15/2015 ندوة التعريفات الكهربائية 32 Simulation Result F2Fuel Cost $/h Wheeling Cost $/h Total $/h G-A1176.3464.462434.9 G-B626.58167.533 F1Fuel Cost $/h Wheeling Cost $/h Total $/h G-A1023.5354.46482438.7 G-B774.38285.5260

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4/15/2015 ندوة التعريفات الكهربائية 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.

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4/15/2015 ندوة التعريفات الكهربائية 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.

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The Floor is Open for Discussion Thank you

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