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Unformatted text preview: EEL 6266 Power System Operation and Control Chapter 11 Power System Security © 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 2 Security Analysis c To be useful to the system operators in any way, a security analysis study must be executed very quickly r on the order of 5 to 10 minutes c Three approaches r fast algorithms using linear approximating models of the power system that can cover all possible cases r traditional algorithms for a selection of only the most important cases r multiple processors / vector processors modifications of traditional algorithms to gain speed to cover a larger selection of cases © 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 3 Sensitivity Factors c Linear sensitivity factors r useful for reaching an approximate analysis of the effect of each outage c limitations and attributes to the linear (DC) power flow method c only branch active power flows (MW) are calculated with approximately 5% accuracy r show the approximate change in line flows for changes in generation and network configuration r two types of sensitivity factors c generation shift factors: s change on line l w.r.t. gen. i c line outage distribution factors: s change on line l w.r.t. line k i l i l P f a ∆ ∆ = , , k l k l f f d ∆ = © 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 4 Sensitivity Factors c Derivation of sensitivity factors r begin with the linear load flow model θ = [ X ] P c the incremental changes of the bus voltage angles for perturbations of power injections ∆θ ∆θ ∆θ ∆θ = [ X ] ∆ P r first consider the generation shift sensitivity for the generator on bus i c set the perturbation on bus i to +1 and the perturbation on all other buses to zero s an equal but opposite perturbation (–1) must occur on the reference bus (that is, the reference bus absorbs any changes and all other generation buses remain fixed) © 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 5 Sensitivity Factors c Derivation of sensitivity factors c the change in bus phase angles are found using matrix calculations s this is equivalent to a 1 pu power increase at bus i with a compensating 1 pu power decrease at the reference bus s the ∆ θ values are equal to the derivative of the bus angle with respect to a change in power injection at bus i r the sensitivity factor for the change in power of line l with respect to a change in generation at bus i is c line l is connected between buses n and m  + = ∆ row ref at row at 1 1 ] [ i X θ ( 29 ( 29 mi ni l i m i n l m n l i i l i l X X x P P x x P P f a =  =  = = 1 d d d d 1 1 d d d d , θ θ θ θ © 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 6 Sensitivity Factors c Derivation of sensitivity factors r a line outage is modeled by adding two power injections, one...
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 Fall '04
 THOMASBALDWIN
 Electrical Engineering, Madrid Metro, Metropolitana di Napoli, Florida State University, Electric power transmission, Power System Operation and Control

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