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3.1.2. KERUGIAN TRANSMISI DIPERHITUNGKAN

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Consider a similar system, which now has atransmission network that connects the generating

units to the load◦  The Economic Dispatch Problem is slightly more

complicated

◦  the constraint equation must include the network losses,P loss

◦

 the objective function,FT

is the same as before◦  the constraint equation must be expanded as :

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1 1

( )

1 0

 N N 

i i load load  

i i

i loss i loss

i i i i

 L F F P P P Pi

dF P dF P   y

 x dP P dP P 

     

 

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Contoh :

Dengan nilai fuel cost perunitnya sama seperti soal

diatas dan pernyataan rugi-rugi dinyatakan denganpersamaan :

Persamaan rugi-rugi menjadi lebih lengkap dengan :

2 2 2

1 2 30.00003 0.00009 0.00012loss P P P P 

1 1

2 2

3 3

2 2 2

1 2 3 1 2 3

1

23.76 0.009372 [1 2(0.00003) ]

23.55 0.01164 [1 2(0.00009) ]

23.70 0.02892 [1 2(0.00012) ]

850 0.00003 0.00009 0.00012

i loss

i i

i

i

i

i

i

i

loss

dF P 

dP P 

dF  P P 

dP 

dF  P P 

dP 

dF  P P 

dP 

 P P P P P P P 

 

 

 

 

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Prosedure iterasi terbaru diselesaikan dengan urutan

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Nilai pembangkitan puncak

Diperoleh pertambahan rugi-rugi sebesar

1 2 3400 , 300 , 150 , P MW P MW P MW 

2(0.00003)(400) 0.0240

2(0.00009)(300) 0.0540

2(0.00012)(150) 0.0360

loss

i

loss

i

loss

i

 P 

 P 

 P 

 P 

 P 

 P 

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Total rugi-rugi

Penyelesaian nilai langrange

5 2 5 2 5 23*10 (400) 9*10 (300) 12*10 (150) 15.6loss

 P MW 

1

2

3

1 2 3

23.76 0.009372 (1 0.024)

23.55 0.01164 (1 0.054)

23.70 0.02892 (1 0.036)

(850 15.6) 0

 P 

 P 

 P 

 P P P 

 

 

 

1

2

3

1 2 3

0.009372 0 0 0.976 23.76

0 0.01164 0 0.946 23.55

0 0 0.02892 0.964 23.70

1 1 1 0 865.6

437.20, 296.49, 131.91, 28.54

 P 

 P 

 P 

 P P P 

 

 

 

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Kesimpulan dari proses iterasi langrange

iteration count P1 (MW) P2 (MW) P3 (MW) losses (MW) ($/MWh)

1 400.00 300.00 150.00 15.60 28.54

2 437.20 296.49 131.91 15.73 28.55

3 431.03 298.38 136.33 15.82 28.55

4 432.45 297.92 135.45 15.80 28.55

5 432.11 298.06 135.63 15.81 28.55

6 432.19 298.02 135.59 15.80 28.55

7 432.17 298.03 135.60 15.80 28.55