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Biogeography-Based Optimization of Power Flow

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Biogeography-Based Optimization of Power FlowOutlineSlide Number 3IntroductionPower Flow ProblemPower Flow ProblemPower Flow ProblemSimulationSimulation SimulationSimulation SimulationSimulationConclusionThank you !BiogeographyBiogeography--Based OptimizationBased Optimization of Power Flowof Power FlowRick Rick RarickRarickDepartment of Electrical Department of Electrical and Computer Engineeringand Computer EngineeringCleveland State UniversityCleveland State UniversityIEEE International Conference onIEEE International Conference onSystems, Man, and CyberneticsSystems, Man, and CyberneticsSan Antonio, TXSan Antonio, TXOctober 13, 2009October 13, 2009All authors should be listed on the first page, just like in your paper2OutlineOutlineI. IntroductionII. Power Flow ProblemIII. Simulation ResultsIV. Conclusion3IntroductionIEEE 30-Bus BenchmarkPower SystemVirginia, 1960s4IntroductionIntroductionPower System Design Problems Large number of variables (5,000) and constraints (10,000) Nonlinear and non-differentiable Multiple local minima Numerical methods unreliable under high loads and faults5Power Flow ProblemPower Flow Problem1GBus 1Bus 3Bus 2Load 1Load 32G10V∠22Vθ∠33Vθ∠6Power Flow ProblemPower Flow Problem()()()()cos( ) sin( )sin( ) cos( )bbiijijijijijjNiijijijijijjNPVVG BQVVG Bθθθθ∈∈=−=−∑∑V, θV, θBus i2 ConstraintEqs30x2 = 60ConstraintEqs()()12 30 12 30,,, , ,,,VV Vθθθ==V θ……30-Bus SystemBus voltage magnitude and phase angle vectors:60 unknowns7Power Flow ProblemPower Flow ProblemCost Function = Power / Voltage Mismatch (Ideally = 0)()()(){}222miniQiVii Gen i PQ i PVPQVλλ∈∈∈Δ+Δ+Δ∑∑∑V,θV, θ V, θ Vest spest spest spii iii iii iPPPQQ QVV VΔ= −Δ= −Δ= −Numerically Heuristically DesignEstimated SpecifiedΔ= −8SimulationIEEE 30-BusEach Chromosome/Island - 60 genes()12 3012 301258131,,, ,,,,, , , , , --- FixedVV VVVVVVθθθθ……Population = 100Generations = 100Monte Carlo Trials = 1000Probability of Mutation = 0.0019Simulation Heuristic Crossover for GA()()0,1Child Best Parent Best Parent Worst ParentUαα=+ −∼Worst ParentWorst ParentBest ParentBest ParentChildChild10SimulationImmigration and Emigration:Probabilistically determined by lambda, mu, and fitnessMigration Scheme for BBOMigrationRateFitness- Immigrationλ - Emigrationμmore clear to use a colon or equal sign instead of a hyphen after "Immigration" or "Emigration" so it is not confused with a minus sign11-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 001234567891011[ ]Angle( deg )Generation G[ ][ ][][][][][][][]gg'b'a'Simulation Non-Uniform Mutation for GA and BBO()()()()()21/max'()'(')( )'''0,1fG GGagfGgabgfGbgga baUαα=−=− −=+ −=+ −∼ab12SimulationGA and BBO Performance()cost cost individual, generation, trial=indtrialgen() ( )()ave avetrials indAveCost gen cost ind, gen, trial=⎡⎤⎣⎦genAveCost13Simulation14Conclusion BBO performs better than GA on Power Flow problem First application of BBO to engineering problem Not restricted to differentiable system equations Need statistical significance of result Need to apply to more difficult Optimal Power Flow problem15Thank you


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