lecture6- Transmission line

lecture6- Transmission line - EEL 6266 Power System...

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EEL 6266 Power System Operation and Control Chapter 4 Transmission System Effects
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© 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 2 Transmission Losses c An illustration using a simple system r consider a two generator system c the generating units are identical c production costs are modeled using a quadratic equation c the losses on the transmission line are proportional to the square of the power flow r let both units be loaded to 250 MW c the load would be under served by 12.5 MW 500 MW P loss = 0.0002 P 1 2 P 1 Min = 70 MW Max = 400 MW P 2 Min = 70 MW Max = 400 MW ( 29 ( 29 ( 29 2 2 2 1 1 002 . 0 7 400 i i i i P P P F P F P F + + = = = 487.5 MW P loss = 12.5 MW P 1 250 MW P 2 250 MW
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© 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 3 Transmission Losses r solution using the Lagrange equation then r solution: P 1 = 178.88, P 2 = 327.50, P loss = 6.38 MW cost = F 1 ( P 1 ) + F 2 ( P 2 ) = 4623.15 ( 29 ( 29 ( 29 ( 29 0 0002 . 0 500 0 004 . 0 0 . 7 0 0004 . 0 1 004 . 0 0 . 7 0002 . 0 500 2 1 2 1 2 2 1 1 1 2 1 2 1 2 2 1 1 = - - + = = - + = = - - + = = - - + + + = P P P L P P L P P P L P P P P P P F P F L loss loss λ
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© 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 4 Transmission Losses r if the optimal dispatch is ignored and generator 1 is set to supply all the losses, then c P 1 = 263.93 and P loss = 13.93 MW c total cost = F 1 (263.93) + F 2 (250) = 4661.84 s optimum dispatch tends toward supplying the losses from the unit close to the load, resulting in a lower value of losses r the best economics are not necessarily attained at minimum losses c the minimum loss solution: P 1 = 102.08 and P 2 = 400 MW P loss = 2.08 MW c total cost = 4655.43 500 MW P loss = 13.93 MW P 1 263.93 MW P 2 250 MW 500 MW P loss = 2.08 MW P 1 102.08 MW P 2 400 MW (at limit)
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© 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 5 Transmission Losses c Derivation of the penalty factor from incremental losses r start with the Lagrange equation for the economic dispatch r then r rearranging the equation ( 29 ( 29 max min 1 1 2 1 1 0 min , , , i i i i N i P N i i N loss load N i i i P P P P L L P P P P P P P F L i 2200 = - + + = = 2200 = = K K λ ( 29 = - - i i i i loss P P F P P d d 1 1 ( 29 0 1 d d = - - = i loss i i i i P P P P F P L
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© 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 6 Transmission Losses r the incremental loss for bus i is defined as r the penalty factor for bus i is given as c if the losses increase for an increase in power from bus
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This note was uploaded on 07/15/2011 for the course EEL 6266 taught by Professor Thomasbaldwin during the Fall '04 term at FSU.

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lecture6- Transmission line - EEL 6266 Power System...

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