NOMOR 1.A (LEVEL BEBAN 450 MW) A. MANUAL

Tugas 2 OOSTL

Nama : Mufidah Sa’adah

NRP : 2214105041

B. MATLAB PROGRAM

% Pembebanan optimal generator untuk level beban 450 MW

% Iterative solution Using Newton method alpha =[350; 500; 600 ]; beta =[7.2; 7.3; 6.74]; gama =[.004; .0025; .003];

PD=450; DelP = 10; % Error in DelP is set to a high value lambda = input('Enter estimated value of Lambda = '); fprintf('\n ') disp([' Lambda P1 P2 P3 DP'... ' grad Delambda']) iter = 0; % Iteration counter while abs(DelP) >= 0.001 % Test for convergence iter = iter + 1; % No. of iterations P = (lambda - beta)./(2*gama); DelP =PD - sum(P); % Residual J = sum( ones(length(gama), 1)./(2*gama)); % Gradient sum Delambda = DelP/J; % Change in variable disp([lambda, P(1), P(2), P(3), DelP, J, Delambda]) lambda = lambda + Delambda; % Successive solution end totalcost = sum(alpha + beta.*P + gama.*P.^2) %Graphical Demonstration of Example 7.4 axis([0 450 6.5 10.5]); P1=250:10:450; P2 = 150:10:350; P3=100:10:250; IC1= 5.3 + 0.008*P1; IC2= 5.5 + 0.012*P2; IC3= 5.8 + 0.018*P3; Px = 0:100:400; plot(P1, IC1, P2, IC2, P3, IC3, Px, lambda*ones(1, length(Px)),'-m'), xlabel('P, MW'), ylabel(' $/MWh'), grid

OUTPUT

C. PERHITUNGAN PENGHEMATAN ($/h)

D. PERBANDINGAN (LEVEL BEBAN 450MW)

METODE PERHITUNGAN UNIT OUTPUT

(MW) TOTAL GEN COST

($/H)

MANUAL DENGAN PEMBAGIAN OPTIMAL

P1 100 4828.7

P2 140

P3 210

MANUAL DENGAN PEMBAGIAN RATA

P1 150 4849.75

P2 150

P3 150

MATLAB P1 100 4828.7

P2 140

P3 210

NOMOR 1.A (LEVEL BEBAN 1335 MW) A. MANUAL

B. MATLAB PROGRAM

% Pembebanan optimal generator untuk level beban 1335 MW

% Iterative solution Using Newton method alpha =[350; 500; 600 ]; beta =[7.2; 7.3; 6.74]; gama =[.004; .0025; .003];

PD=1335; DelP = 10; % Error in DelP is set to a high value lambda = input('Enter estimated value of Lambda = '); fprintf('\n ') disp([' Lambda P1 P2 P3 DP'... ' grad Delambda']) iter = 0; % Iteration counter while abs(DelP) >= 0.001 % Test for convergence iter = iter + 1; % No. of iterations P = (lambda - beta)./(2*gama); DelP =PD - sum(P); % Residual J = sum( ones(length(gama), 1)./(2*gama)); % Gradient sum Delambda = DelP/J; % Change in variable disp([lambda, P(1), P(2), P(3), DelP, J, Delambda]) lambda = lambda + Delambda; % Successive solution end totalcost = sum(alpha + beta.*P + gama.*P.^2) %Graphical Demonstration of Example 7.4 axis([0 450 6.5 10.5]); P1=250:10:450; P2 = 150:10:350; P3=100:10:250; IC1= 5.3 + 0.008*P1; IC2= 5.5 + 0.012*P2; IC3= 5.8 + 0.018*P3; Px = 0:100:400; plot(P1, IC1, P2, IC2, P3, IC3, Px, lambda*ones(1, length(Px)),'-m'), xlabel('P, MW'), ylabel(' $/MWh'), grid

OUTPUT

C. PERHITUNGAN PENGHEMATAN ($/h)

D. PERBANDINGAN (LEVEL BEBAN 1335MW)

METODE PERHITUNGAN UNIT OUTPUT

(MW) TOTAL GEN COST

($/H)

MANUAL DENGAN PEMBAGIAN OPTIMAL

P1 325 12,705.2

P2 500

P3 510

MANUAL DENGAN PEMBAGIAN RATA

P1 445 12,783

P2 445

P3 445

MATLAB P1 325 12,705

P2 500

P3 510

NOMOR 1.B (LEVEL BEBAN 450 MW DENGAN LIMIT GENERATOR) A. MANUAL

B. MATLAB PROGRAM

cost = [350 7.2 0.004 %P1 (c bx ax2) 500 7.3 0.0025 %P2 600 6.74 0.003]; mwlimits=[122 400 260 600 50 445]; Pdt = 450; dispatch gencost

OUTPUT

C. PERHITUNGAN PENGHEMATAN ($/h)

D. PERBANDINGAN (LEVEL BEBAN 450MW DENGAN LIMIT)

METODE PERHITUNGAN UNIT OUTPUT

(MW) TOTAL GEN COST

($/H)

MANUAL DENGAN PEMBAGIAN OPTIMAL

P1 122 4927.132

P2 260

P3 68

MANUAL DENGAN PEMBAGIAN RATA

P1 150 4849.75

P2 (under limit) 150

P3 150

MATLAB P1 122 4927.13

P2 260

P3 68

NOMOR 1.B (LEVEL BEBAN 1335 MW DENGAN LIMIT GENERATOR) A. MANUAL

B. MATLAB PROGRAM % Pembebanan optimal generator untuk level beban 1335 MW dengan limit

cost = [350 7.2 0.004 %P1 (c bx ax2) 500 7.3 0.0025 %P2 600 6.74 0.003 ];%P3 limits = [122 400 260 600 50 445]; Pdt = 1335; dispatch %memanggil gencost gencost %menghitung cost

OUTPUT

C. PERHITUNGAN PENGHEMATAN ($/h)

D. PERBANDINGAN (LEVEL BEBAN 1335MW DENGAN LIMIT)

METODE PERHITUNGAN UNIT OUTPUT

(MW) TOTAL GEN COST

($/H)

MANUAL DENGAN PEMBAGIAN OPTIMAL

P1 445 12,724.375

P2 350

P3 540

MANUAL DENGAN PEMBAGIAN RATA

P1 445 12,783

P2 445

P3 445

MATLAB P1 445 12,724.38

P2 350

P3 540

NOMOR 2A A. POWERGEN

B. MATLAB PROGRAM

cost = [220 5.9 0.009 80 6.1 0.009 60 6.5 0.007 40 6.7 0.007 34 6.8 0.007]; mwlimits=[60 200 45 150 30 100 25 80 25 75]; Pdt = 450; dispatch gencost

OUTPUT

NOMOR 2B A. MANUAL

PERBANDINGAN PEMBEBANAN

METODE PERHITUNGAN

UNIT OUTPUT

(MW) LAMBDA ($/MWh)

TOTAL GEN COST ($/H)

POWERGEN P1 106.8 7.8225 3624.28

P2 95.7

P3 94.5

P4 80.0

P5 73.0

MATLAB P1 106.8056 7.8225 3624.24

P2 95.6944

P3 94.4643

P4 80.0000

P5 73.0357

MANUAL P1 106.78 7.822 3624.38

P2 95.67

P3 94.43

P4 80.14

P5 73.00

Dari hasil perhitungan maupun simulasi menunjukkan angka total generation cost yang hampir sama. Hal

ini menunjukkan bahwa dengan output-output yang telah didapatkan dapat menghasilkan biaya operasi

yang minimal, karena pencarian nilai lambda mempertimbangkan nilai peningkatan biaya serta batas

generator.

NOMOR 3A (RUGI-RUGI TRANSMISI DIABAIKAN) A. MATLAB

PROGRAM

cost = [312.5*1.05 8.25*1.05 0.005*1.05 112.5*1.217 8.25*1.217 0.005*1.217 50*1.1831 8.25*1.1831 0.005*1.1831]; mwlimits =[50 250 5 150 15 100]; Pdt = 400; B = [0.000136255 0.0000 0.000 0.0000 0.00015448 0.000 0.000 0.000 0.0016147]; basemva = 100; dispatch gencost

OUTPUT

B. POWERGEN

NOMOR 3B (RUGI-RUGI TRANSMISI DIPERHITUNGKAN) A. MATLAB

PROGRAM

cost = [312.5*1.05 8.25*1.05 0.005*1.05 112.5*1.217 8.25*1.217 0.005*1.217 50*1.1831 8.25*1.1831 0.005*1.1831]; mwlimits =[50 250 5 150 15 100]; Pdt = 400; B = [0.000136255 0.00001753 0.00018394 0.00001753 0.00015448 0.000282765 0.00018394 0.000282765 0.0016147]; basemva = 100; dispatch gencost

OUTPUT

B. POWERGEN

NOMOR 3C

A. TOTAL BIAYA OPERASI RUGI-RUGI TRANSMISI DIABAIKAN

F1 = ( 312.5 + 8.25 ( 221.8 ) + 0.005 ( 221.8 )2 ) * 1.05= 2507.74 $/h F2 = ( 112.5 + 8.25 ( 78.5 ) + 0.005 ( 78.5 )2 ) * 1.217 = 962.569 $/h F3 = ( 50 + 8.25 ( 100 ) + 0.005 ( 100 )2 ) * 1.1831 = 1094.367 $/h FTOTAL = 4564.676 $/h

RUGI-RUGI TRANSMISI DIPERHITUNGKAN F1 = ( 312.5 + 8.25 ( 222 ) + 0.005 ( 222 )2 ) * 1.05 = 2509.94 $/h F2 = ( 112.5 + 8.25 ( 78.4 ) + 0.005 ( 78.4 )2 ) * 1.217 = 961.469 $/h F3 = ( 50 + 8.25 ( 100 ) + 0.005 ( 100 )2 ) * 1.1831 = 1094.367 $/h FTOTAL = 4565.776 $/h

B. PERBANDINGAN

CASE UNIT OUTPUT (MW)

TOTAL SYSTEM LOSS (MW)

TOTAL GEN COST ($/H)

MATLAB POWERGEN MATLAB POWERGEN MATLAB POWERGEN

RUGI-RUGI TRANSMISI DIABAIKAN

P1 221.7762 221.8 0.237997 0.2 4564 4564.02

P2 78.4618 78.5

P3 100.000 100.0

RUGI-RUGI TRANSMISI DIPERHITUNGKAN

P1 221.8714 222.0 0.370185 0.4 4565.45 4565.43

P2 78.4988 78.4

P3 100.000 100.0