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Electricity Market Price Forecasting Based on Weighted Nearest Neighbors Techniques

Troncoso Lora, Alicia; Riquelme Santos, Jesús Manuel; Gómez Expósito, Antonio; Martínez Ramos, José Luis; Riquelme Santos, José Cristóbal

Abstract

This paper presents a simple technique to forecast next-day electricity market prices based on the weighted nearest neighbors methodology. First, it is explained how the relevant parameters defining the adopted model are obtained. Such parameters have to do with the window length of the time series and with the number of neighbors chosen for the prediction. Then, results corresponding to the Spanish electricity market during 2002 are presented and discussed. Finally, the performance of the proposed method is compared with that of recently published techniques.

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Mean - S.D. 0 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Hours c ent/kW h Thursday-1st Friday-30th    7        2! 4889       -  2! 4889  ,    ,  3 1"2 "  ,  ,   ,  "  .$A'3  &'$A   !/5  0  0 !   55 0    3AB 0    ,   4AB  &  %5 >, $#   ,!  0   ! 0  3AA$5  ,: 8    0  "    #   #! ,    : ##!  , "   5       #0  0  ==    "       .    == #",  0  (C*  (4*/5  ==    0   # 0   , #!!5          ,      '  0 0  5   7   8 #!,, 0  #   ,  , 5 D!  ==    0  ! .   /    0  ! 0   0   !5           0  == +  E,   ,!  #!  0 :,  # 0       !5  -#,   ,, 0 0  ,  ' 0 .' ,  /5 ,   7         0  ==   0,  0  , 34 5      !    0 34  5  0   #  0        #   #   5 /  ,      #!    34 5 D   !     0,    0    5 #/ ! 0   ,    0   !     #!  0    !5       0 34   5      #  ! 0  #/    !     5 9   0! :  ==   !    # 0      !   # 0 !  0  ,  5 >, 3  0 $3 34  CF     !   , 0,    ,!   ,   ", ! 0 >#' ! 3AA$   #0!     ==5   #   3A !  Æ    ==  # 0   # ,   5 >    #  34     !   #    0    " ,! 5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 5 10 15 20 25 30 35 40 45 Days E rror (cent/kWh ) n12 n24 n36   /    !     #   0   #    .! ' >#! 3AA$/         :     #  ==  ,!   ,  .', 3AA$/     "  0, 5 >, C   #  0   0  0   "  0  ! 0  3AA$ ,   ,    , 5 0 0.5 1 1.5 2 2.5 3 1 3 5 7 9 11 13 15 17 19 21 23 Hours E rror (cent/kWh ) Friday 23 Monday 12 0 0.5 1 1.5 2 2.5 3 3.5 1 4 7 10 13 16 19 22 Hours c ent/kW h Errors Forecasted    /    !   !    &   - *  7   !    &2! 4889*  3 &+6!* /   / 2"       2!%2 44:;; 8<;89 8=5>5 4><9 ?%/ =:5;4 98:@< 854; 48<=>   0   !   >, C#   !  , 0  0 ,!  '  ,   3AA$     ,   .# #! 8     0 :, $/5 =   0,   , ,  " 5 >! # $    ,  55 0     , #  0 0,      0 ,   5   ,  , 0 $3B ./  $)B .,/ 0  !  , 5     ,  55 0   ,   , 0, 5         9    # "== ($$ $C*   ($4* 0 ! " ,!  0,  #5   ,       ,  ,   ,: 5  "== :  ! " ,!    G H   0   !5     ,   0   ! 0   # 0  ,!  0  !  0   ,#  !5        0      ", 0  +   ! #,    # 0  ,#5    0    #     ! (I &*5 ,!     !       !  5 > ' 0,   #    ,       0,  0  , 34   !  # ,   345  0   # 0      !   #!  #   + ! 0   ,    0   !     #!  0    !5   #!      0 34   5          #       ' 5     !     0     ,           #     ' 5   0     !#      !    : 0 0   5   '      0    ,    #  (%*5 9        ! " ,!    2,'   0 #      0  !    @    0  0, !5    : #!    &   *A        &      *  &9*   J ,.  /    (A  $*5     0  " ,!  0  !  K $   ,   ",    , 0    0  !+ $5 ;   #    0  !        ,              , .$/5  #   555      !   !    #! 5 35   +     A 9   B  B                &4*    A   &      *    &      *   &      *    &     ½ * &=*   0     ,  ! 0  0, 5 =  A     $ 55  ,        !          !   5    0    ,#  0      (   ½      *         ,#   0   (   ½        * ! #        5     , ./    #    0        #       !  ,  0 #, ,5           #    #   : 0  ,   # 0     #     , , : 05      #!                5 9            : #!  ,0   ,   !   : 0     0   ,   ./   0  0 , 5  # ,  #    0 ($3*+ $5      ! 5 35  : 0 0     5 C5 ?  !  ,    5 45 ?  #     5 )5       5 F5 #    : 0      5 I5 90   # 0 ,   #   ,   35 =       : 0 0     = =,#  ,  5 9     !  #!  "== 5 9    #!       ,   34  0  !5  # 0 !  0   0            #  0   ! 5 90  #0!         #    0     ,  '  0    ! !   5 9     0  #0!      !   ,5 -   0     0,+  !      ! ! 5 "   : 0  #  #     ,   '  0  !0  15  "==K?E9;9-=  '      ,!  ,  .3/5  : 0  : #!  0   A 9      &       *  &5*     # 0 !     ,5 0          ,#  0  !   #  "5    #     ,   !  ,        #    0  5  ##! 0     #,         : 0 ",       # , 5 ,,         ##!  #     55       #    #    ! #  #    5 ;  # #! ,  ,   0   0  5   >,              ,  ,   ':  ##!5  ,  #     #!  !   !   5    ,   #          ! : ##!5 $ %   "==K  #        #  0 0  ! " ,! 5 >#! 3AA$  #   '   ,0 !  0  ! ,   #    0         # 35   #   0 ', 3AA$  #       "  0, 5  #  0 ,#   #              @   0  ($A*5 0.3 0.35 0.4 1 501 1001 1501 2001 2501 Number of Generations S quare Erro r     !    0,  # #!    ,      0  ==      #    :  0   5 >, 4     0    0  :   ,      5 3 1 988 3     9 3   89 2"     :888   '/   0 0.5 1 1.5 2 2.5 3 3.5 4 1 3 5 7 9 11 13 15 17 19 21 23 Hours P rices (Cent/kWh ) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Weights March 21 March 22 0 0.5 1 1.5 2 2.5 3 3.5 4 1 3 5 7 9 11 13 15 17 19 21 23 Hours P rices (Cent/kWh ) February 28 March 22   ( !  .  ! 6!%  !   >, )    , 0  !  ,   ,!  0   !  33    ,#   ,  2,'  .$/5   ,#     3$5 9  #      , , .$ I $$ $$  $3/      ,! 5 L   C 4 ) F  I   8    ,  ,  ' !   5 >, )#   ,!  0  33 ,   '  ,#   ,   5 9     ,#    >#! 3&5 =  @ 0   '     0   ,# 5 0 0.5 1 1.5 2 2.5 3 1 3 5 7 9 11 13 15 17 19 21 23 Hours E rror (Cent/kWh ) With Euclidean distance With WeightedEuclidean distance   /    !   !    &2! 4=  *  3 &+6!* /   / 2"       2!%2 44:;; 849;> 84:> 49= ?%/ =:5;4 84> 8== 4=>   0     >, F   #  0   0  0   "  0  3C ,      2,' 5     0,  , 0   !  ,! @ #!   0   ,# 5 >! # C    ,  55 0     , #  0 0,      0 ,   5 =    ,  ,  == , 0 $3B ./  $)B .,/ 0  !  ,     ,  # #!  0  "== #    , 0 %B ./  $$B .,/5 # 4    # , #  5   - #, ,         "   0, 0  : # ,  0  , 5 9            0,  +  : = ="   #  = =,#    ,5 M ,   #     34' ' ,!  0, # ,   0   ,! "    0   #  5    2,' "==    0,  0  ,!    ==  5 2!%2 ?%/ ((B'/ /(( ((B'/ /((  849;> 8<;89 84> 98:@< /    84:> 8=5>5 8== 854; 2"  49= 4><9 4=> 48<=> / C  &D* 99 9: @ 94   $     &$+6!*