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Short-term hydrothermal coordination by augmented lagrangean relaxation: a new multiplier updating

Beltrán Royo, César,Heredia, F.-Javier (Francisco Javier)

Abstract

The Augmented Lagrangean Relaxation (ALR) method is one of the most powerful techniques to solve the Short-Term Hydrothermal Coordination (STHC) problem. A crucial step when using the ALR method is the updating of the multipliers. In this paper we present a new multiplier updating procedure: the Gradient with Radar Step (GRS) method. The method has been successfully tested by solving medium-scale examples of the STHC problem

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 H ¤å KJML*N$OQP fä FH ¤å SRTLVU Vä  H ¤å W X[Z;X H\ ]N$O^P  H\ ]U HDJ  H _` ` ` a ` ` ` b ä Q , å 3 d ÛËÚ7ÎSãÒ¤îÕ(ÊË×ãÒìÚ7ËÒÒìÔfÐÌÍ%ÎÏÐËwѦ×Ù ( ÑáÔ   \ + "  ` ` ` ` `  ` ` ` ` `  Ñ×ã   %ä FH W?  H C?  å W X[Z;X H\ ]N$O^P  H\ ] U _` ` ` ` `a ` ` ` ` ` b ? ä Q - å Ö!ÊËwÍ(Ë   %ä FH C?  H W?  å 8( J LEN$O^P fä FH ¤å SRL U ä  H "å R  / ä FH #  H ¤å R   H #  H   ä Q & å d ÉÊ×Í7Ò¤î   '×Ù*ãÎÕÔáÙ«ËwÌÔ^Í_Ô^ÏÐË]éaìãÚ7Õ«×ÎSãXî¤Õ(ÊnìÙ×ãÎÍ_ÒËwÍÕ(Î&Ѿ×ã×Ñ×ëwË×Õ×ã ÔÙAËwÌÔZÍ_Ô^ÏÐËÖÔfß&ÖË =e Í_ÙAÕVÒÎcÙAÎÑ&ËÑáÔZã×ÌìÐÔ^Õ«×ÎSãÙwæ   ä FH C?  H W?  å J L N$O^P ä FH ¤å RL U ä  H så R  / H #  /  H/R    H # H   R    H # H   J J  LN$O^P ä IH ¤å R  / H R    H # H    R  L U *ä  H ¤å #  /  H/R    H #  H    ä Q 2 å  ¸Ù¾Ö4ËÚwÔZã ÙAËwËc×ãEä Q 2 å   Ú7ÎãÙ×ÙAÕ_ÙÎ^éVÕAÖÎòÔfÐÑ&ÎnÙAÕáÙ«ËwÌÔ^Í_Ô^ÏÐË3Ñ&ËwÑÏËwÍ7Ù]×ã MH Ô^ãÒ  H <Ë $ Ú7ËwÌÕ]éaÎÍÕ%ÊË  SìÔÒÍ_Ô^Õ«×êÚÕ(ËwÍ(Ñ  H # H   æ ) ã Õ%ÊËéaÍ7Ô^Ñ&Ë&Î^éÕ(ÊË  0ÐÎàÚ%ñ â9ÎÎÍ_ÒS×ãÔ^Õ(ËÒ  *ËÙ%Ú7ËwãnÕä F !â  ]åÑ&ËwÕ(ÊÎÒ¤îXÖËáÙAÌÐ×Õ   !×ãÕ(ÎÕAÖÎ&éìãÚ7ÕA×ÎãÙ ( ÎSãËî  "  ä IH C? " å_îÕ(ÎÏË]Ñ×ã×Ñ×ëwËÒ3×ã;Õ(Ê˸ÒÎSÑáÔf×ã ]N$O^P ^îÔ^ãÒcÕ%ÊËÎÕ(ÊËwÍ   "  ä  H C? " å7înÕ%Î ÏËcÑ×ã×Ñ×ëwËÒ<×ã ]U ÓÏß 'e  ×ãïÎãËcÎ^éÕ(ÊË&èSËÚ7Õ(ÎÍ_Ù H <ÎÍ  H ðËÔÚ%Ê ÕA×Ñ&Ëæ  ÎSÍ(Ë ÌÍ(ËÚ%×ÙAË7Ðßî  "  ä IH C? " å ( J L N$OQP ä FH ¤å R  / " H R  !  H #  H "   ? ä Q 3 å   "  ä  H C? " å ( J L U ä  H ¤å #  / "  H R  !  H "   #  H   ? ä Q 4 å ÖÊËwÍ(Ë  H " Ô^ãÒ /H "  !Ô^Í(Ël×Õ(ËwÍ7Ô^Õ(ËÙÎ^é¤Õ(ÊËÒËÚ%×êÙ×ÎSãáè^Ô^ÍA×Ô^ÏÐËÙ  H &ÔZãÒ H Í(ËÙAÌ"ËÚ7ÕA×èË7Ðßæ ÉÊËwã×ãÕ(ÊË  VìïÑËwãnÕ(ËÒ  XÔ^ïÍ7Ô^ãïËÔ^ã  Ë7ÐÔ  Ô^ÕA×Îãcä  *åXÔfÐïÎÍ«×Õ%ÊÑ Õ(ÊÔZÕÙAÎ^ÐèËÙ Õ(ÊËÒìÔfÐÌÍ%ÎÏÐËwÑ ä Q - ålÕ(ÊËÑ×ã×Ñ×ëÔ^ÕA×ÎãÎ^élÕ(ÊËÔ^ìïÑ&ËwãÕ(ËÒ  XÔZïÍ_Ô^ãïËÔZã3ÎNèSËwÍ ]N$O^P Ô^ãÒ ]U ×ÙÍ(ËwÌÐÔÚ7ËÒFÏnß3ÕAÖÎÙ«ìÏÌÍ(ÎÏÐËwÑáÙwî"ÎãË×ã;ËÔÚ(ÊÒÎSÑáÔf×ã ( d Ý!ßÒÍ(ÎÕ(ÊËwÍ(ÑcÔfÐÙAìÏÌÍ(ÎÏÐËwÑæ Ñ×ã  "  ä FH C? " å WYX[Z$X H\] N$OQP _ ` a ` b ä I! @ å 4 Q + î n !Îæ + î  *ìïìÙAÕ Q 4Y4Y3 îSÌÌXæ Q @ - *Q Ü Q @ - & æ  Q +   'Ë7ÐÕ(Í_Ô^ãâ*æÔ^ãÒ3Ý!ËwÍ(ËÒS×Ôî  æ  æ % gR (h  qZW$& (epVq(" B SbepV E ,VjS#epT'U, (SYX P Q="S9epVq (SYXZj d(S9"^p\,Zef^p\ % S9   'X  wî  ËÙ«ËÔ^Í(Ê  ËwÌÎÍ%Õ  4Y3  2@ 4 Î^é Õ(ÊËÛÕ_Ô^Õ«×êÙ«ÕA×ÚwÙÔ^ãÒ % ÌËwÍ_Ô^Õ«×ÎSãÙ  ËÙ«ËÔ^Í_Ú%Ê  *ËwÌÕæÎ^éÕ(ÊË  ã×èËwÍ_Ù×Õ_Ô^Õ = ÎÜ Ð×Õ%ËÚ7ã×êÚwÔ3ÒËâ4Ô^Õ_ÔNÐìãßnÔcä I 4ÔZÍ_Ú7Ë7ÐÎãÔå_î"ÛËwÌÕ(ËwÑÏËwÍ Q 4Y4 3 æ Q &