2009-10-06 Energy Management Systems II

2009-10-06 Energy Management Systems II - Energy Management...

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Energy Management Systems II Jovan Ilić ECE 18-418 Fall 2009
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Bus Types [1] Bus Type P Q |E| Th Comments Load X X Load bus Voltage Controlled X X |E| constant regardless of Q Generator or Sync Condenser X X Qmin<Qg<Qmax VAR limits must be enforced by changing |E| X X Qmin>Qg>Qmax Fixed Z Only Z given Reference X X Swing (slack) bus
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Power Flow (PF) formulation • Calculate voltages for all buses • Calculate power flows, contingencies, real and reactive losses, etc. • Network consists of PV, PQ, and a slack bus. • Unknowns for PV buses are voltage angle and reactive power. • Unknowns for PQ buses are voltage angle and magnitude. • Slack bus is completely determined
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The variables of interest are:         1 1 | || | cos | | sin n i i k ik ik k i k n i i k ik ik k i k P V V Y Q V V Y   The non-linear system of equations: 2 2 g N N N V V V   
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Mismatch between the specified and injected bus P and Q must be zero at the solution V                     2 2 2 2 2 1 2, 2 , 1 2, 2 , | || || | cos , , , | || | cos , , , g gg n k k k k k specified n N specified N N N k Nk Nk k N k N N specified N N specified N P V V Y P P V PV P P V P V V Y Q Q Q V QV Q Q V             2 2 2, 2, 2 1 ,, 1 | || | sin | || | sin g g g g n N k N k N k k N k n N N k N k N k k N k V V Y Q V V Y       , ,0 , hV 
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From the Taylor series around   ** ,0 hV       2 0 0 0 2 2 1 0 0 0 2 0, || , g g N N N N N N h V J V V J h V V V      0 x h Jx V x 
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Calculating power flow Jacobian: 11 12 21 22 JJ J    22 2 11 2 N NN N PP J   Voltage angle of all the buses, except the slack bus, are unknown, so the first equation is removed.
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22 2 12 2 | | | | | | | | g g NN PP VV J     |V| of all PV (generator) are known so Ng+1 equations are removed Q for generator buses can be found from the calculated voltages and must be between the limits If a generator’s Var limits are exceeded during Newton-Raphson iterations, the bus is converted to a PQ bus.
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This note was uploaded on 09/20/2010 for the course ECE 18418 taught by Professor Illic during the Fall '09 term at Carnegie Mellon.

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2009-10-06 Energy Management Systems II - Energy Management...

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