ENERGI LISTRIK YANG DIJUAL
4.1.2 Pengolahan Data
Dalam p enelitian ini s oftware y ang d igunakan ad alah Ms. Exc el. Untuk mencari forecast error dengan menggunakan metode eksponensial ganda dari Brown dengan besar parameter pemulusan α. Nilai α terletak antara 0 sampai 1. Tidak ada ketentuan dalam pengambilan nilai α untuk memilih antara 0 sampai 1. Dalam penelitian ini nilai α yang di gunakan yaitu 0,1 s ampai 0,9. J ika dalam perhitungan nilai α antara 0 sampai 1 diperoleh MSE terkecil dibandingkan dengan nilai α yang lain, m aka n ilai α.itulah y ang t epat u ntuk p eramalan j umlah p enumpang u ntuk m periode ke de pan. Parameter pemulusan t erbaik adalah parameter pemulusan y ang menghasilkan nilai Mean Square Error yang minimum.
Langkah-langkah yang di tempuh unt uk menentukan b entuk p ersamaan p eramalan dengan m enggunakan m etode p emulusan ek sponensial g anda: m etode l inier s atu-parameter dari Brown adalah:
1. Menentukan harga parameter smoothing eksponensial ganda yang besarnya.
2. Menghitung harga smoothing eksponensial tunggal.
S ′t = 𝛼𝑋𝑡+ (1 − 𝛼)𝑆𝑡−1′
Perhitungan untuk energi listrik yang disalurkan
• 𝛼 = 0,1
𝑆1′ = 2.381.693.000
𝑆2′ = (0,1)(2.934.732.684) + (1 − 0,1)(2.381.693.000) = 2.436.996.968
𝑆3′ = (0,1)(3.015.459.439) + (1 − 0,1)(2.436.996.968) = 2.494.843.215
dst.
• 𝛼 = 0,2
𝑆1′ = 2.381.693.000
𝑆2′ = (0,2)(2.934.732.684) + (1 − 0,2)(2.381.693.000)
Perhitungan untuk energi listrik yang dijual
• 𝛼 = 0,1
.
3. Menghitung harga smoothing eksponensial ganda.
Perhitungan untuk energi listrik yang disalurkan
• 𝛼 = 0,1
𝑆1′′ = 2.381.693.000
Perhitungan untuk energi listrik yang dijual
• 𝛼 = 0,1
4. Menghitung koefisien 𝑎𝑡 dan 𝑏𝑡
Perhitungan untuk energi listrik yang disalurkan
• 𝛼 = 0,1
1 − 0,1( 2.436.996.968) − (2.387.223.397) = 5.530.397 𝑏3 = 0,1
1 − 0,1(2.494.843.215) − (2.397.985.379) = 10.761.982 dst.
1 − 0,2(2.492.300.937) − (2.403.814.587) = 22.121.587 𝑏3 = 0,2
1 − 0,2(2.596.932.637 − 2.442.438.197) = 38.623.610 dst.
𝑎2 = 2(2.879.428.716) − (2.829.655.144) = 2.929.202.287 𝑎3 = 2(3.001.856.367) − (2.984.636.244) = 3.019.076.489 dst.
𝑏1 = − 𝑏2 = 0,9
1 − 0,9(2.879.428.716 − 2.829.655.144) = 447.962.144 𝑏3 = 0,9
1 − 0,9(3.001.856.367 − 2.984.636.244) = 154.981.100 dst.
Perhitungan untuk energi listrik yang dijual
• 𝛼 = 0,1
1 − 0,1(2.681.823.541 − 2.686.273.872) = −494.481 𝑏3 = 0,1
1 − 0,1 (279.111.005,85 − 274.749.990,42) = 20.839 dst.
1 − 0,2(2.676.878.730 − 2.684.790.428) = −1.977.925 𝑏3 = 0,2
1 − 0,2(2.687.185.142 − 2.685.269.371) = 478.943 dst.
. . .
• 𝛼 = 0,9
𝑎1 = −
𝑎2 = 2(2.642.265.048) − (2.646.715.378) = 2.637.814.717 𝑎3 = 2(2.719.796.217) − (2.712.488.133) = 2.727.104.301 dst.
𝑏1 = − 𝑏2 = 0,9
1 − 0,9(2.642.265.048 − 2.646.715.378) = −40.052.975 𝑏3 = 0,9
1 − 0,9(2.719.796.217 − 2.712.488.133) = 65.772.755 dst.
5. Menghitung trend peramalan 𝐹𝑡+𝑚
Perhitungan untuk energi listrik yang disalurkan
• 𝛼 = 0,1 𝐹1 = − 𝐹2 = −
𝐹3 = (2.486.770.540 + 5.530.397)(1) = 2.492.300.937 𝐹4 = (2.591.701.052 + 10.761.982)(1) = 2.602.463.034 dst.
• 𝛼 = 0,2 𝐹1 = − 𝐹2 = −
𝐹3 = (2.580.787.286+22.121.587)(1) = 2.602.908.874 𝐹4 = (2.751.427.077+ 38.623.610)(1) = 2.790.050.687 dst.
𝐹4 = (3.019.076.489+154.981.100)(1) = 3.174.057.589 dst.
Perhitungan untuk energi listrik yang dijual
• 𝛼 = 0,1 𝐹1 = − 𝐹2 = −
𝐹3 = (2.677.373.211 + (−494.481))(1) = 2.676.878.730 𝐹4 = (2.686.669.821 + 20.839)(1) = 2.686.690.661 dst.
• 𝛼 = 0,2 𝐹1 = − 𝐹2 = −
𝐹3 = (2.668.967.031 + (−1.977.925))(1) = 2.666.989.106 𝐹4 = (2.689.100.913 + 478.943)(1) = 2.689.579.855 dst.
𝐹3 = (2.637.814.717 + (−40.052.975))(1) = 2.597.761.742 𝐹4 = (2.727.104.301 + 65.772.755)(1) = 2.792.877.055 dst.
6. Menghitung nilai kesalahan (error)
Perhitungan untuk energi listrik yang disalurkan
• 𝛼 = 0,1 𝑒1 = − 𝑒2 = −
𝑒3 = 3.015.459.439 − 2.492.300.937 = 523.158.502 𝑒4 = 3.015.459.439 − 2.602.463.034 = 412.996.405 dst.
• 𝛼 = 0,2 𝑒1 = − 𝑒2 = −
𝑒3 = 3.015.459.439 − 2.602.908.874 = 412.550.565 𝑒4 = 3.015.459.439 − 2.790.050.687 = 225.408.752 dst. 𝑒4 = 3.015.459.439 − 3.174.057.589 = −158.598.150 dst.
Perhitungan energi listrik yang dijual
• 𝛼 = 0,1 𝑒1 = − 𝑒2 = −
𝑒3 = 2.728.410.791 − 2.676.878.730 = 51.532.061 𝑒4 = 2.924.924.483 − 2.686.690.661 = 238.233.822 dst.
• 𝛼 = 0,2 𝑒1 = − 𝑒2 = −
𝑒3 = 2.728.410.791 − 2.666.989.106 = 61.421.685 𝑒4 = 2.924.924.483 − 2.689.579.855 = 235.344.628 dst.
. . .
• 𝛼 = 0,9 𝑒1 = − 𝑒2 = −
𝑒3 = 2.728.410.791 − 2.597.761.742 = 130.649.049 𝑒4 = 2.924.924.483 − 2.792.877.055 = 132.047.428 dst.
Tabel 4.2 Perhitungan Peramalan Banyaknya Energi Listrik yang Disalurkan PT. P LN (Persero) Ca bang Medan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,1
Tahun Xt St' St" at bt Ft et et2
2007 2.381.693.000 2.381.693.000 2.381.693.000 - - - - -
2008 2.934.732.684 2.436.996.968 2.387.223.397 2.486.770.540 5.530.397 - - -
2009 3.015.459.439 2.494.843.215 2.397.985.379 2.591.701.052 10.761.982 2.492.300.937 523.158.502 273.694.818.424.147.000 2010 3.015.459.439 2.546.904.838 2.412.877.325 2.680.932.351 14.891.946 2.602.463.034 412.996.405 170.566.030.476.845.000 2011 3.531.333.729 2.645.347.727 2.436.124.365 2.854.571.089 23.247.040 2.695.824.297 835.509.432 698.076.011.084.618.000 2012 4.159.259.769 2.796.738.931 2.472.185.821 3.121.292.041 36.061.457 2.877.818.129 1.281.441.640 1.642.092.676.080.040.000 2013 4.360.477.994 2.953.112.837 2.520.278.523 3.385.947.152 48.092.702 3.157.353.497 1.203.124.497 1.447.508.554.238.300.000 2014 4.388.722.350 3.096.673.789 2.577.918.050 3.615.429.528 57.639.527 3.434.039.853 954.682.497 911.418.669.359.752.000 2015 4.556.602.274 3.242.666.637 2.644.392.908 3.840.940.366 66.474.859 3.673.069.054 883.533.220 780.630.950.320.363.000 2016 4.776.380.310 3.396.038.004 2.719.557.418 4.072.518.591 75.164.510 3.907.415.225 868.965.085 755.100.319.299.786.000 6.679.088.029.283.850.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,1 dan N = 8 MSE = �et2
N
N
i=1
MSE = 6.679.088.029.283.850.000 MSE = 834.886.003.660.482.000 8
Tabel 4.3 Perhitungan Peramalan Banyaknya Energi Listrik yang Disalurkan PT. P LN (Persero) Ca bang Medan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,2
Tahun Xt St' St" at bt Ft et et2
2007 2.381.693.000 2.381.693.000 2.381.693.000 - - - - -
2008 2.934.732.684 2.492.300.937 2.403.814.587 2.580.787.286 22.121.587 - - -
2009 3.015.459.439 2.596.932.637 2.442.438.197 2.751.427.077 38.623.610 2.602.908.874 412.550.565 170.197.969.011.859.000 2010 3.015.459.439 2.680.637.998 2.490.078.157 2.871.197.838 47.639.960 2.790.050.687 225.408.752 50.809.105.424.099.500 2011 3.531.333.729 2.850.777.144 2.562.217.955 3.139.336.333 72.139.797 2.918.837.798 612.495.931 375.151.265.677.755.000 2012 4.159.259.769 3.112.473.669 2.672.269.098 3.552.678.240 110.051.143 3.211.476.130 947.783.639 898.293.825.673.678.000 2013 4.360.477.994 3.362.074.534 2.810.230.185 3.913.918.883 137.961.087 3.662.729.383 697.748.611 486.853.123.994.348.000 2014 4.388.722.350 3.567.404.097 2.961.664.967 4.173.143.227 151.434.782 4.051.879.970 336.842.380 113.462.788.754.651.000 2015 4.556.602.274 3.765.243.733 3.122.380.720 4.408.106.745 160.715.753 4.324.578.009 232.024.265 53.835.259.333.073.500 2016 4.776.380.310 3.967.471.048 3.291.398.786 4.643.543.310 169.018.066 4.568.822.498 207.557.812 43.080.245.428.152.300 2.191.683.583.297.620.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,2 dan N = 8 SE = �et2
N
N
i=1
MSE = 2.191.683.583.297.620.000 MSE = 273.960.447.912.202.000 8
Tabel 4.4 Perhitungan Peramalan Banyaknya Energi Listrik yang Disalurkan PT. P LN (Persero) Ca bang Medan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,3
Tahun Xt St' St" at bt Ft et et2
2007 2.381.693.000 2.381.693.000 2.381.693.000 - - - - -
2008 2.934.732.684 2.547.604.905 2.431.466.572 2.663.743.239 49.773.572 - - -
2009 3.015.459.439 2.687.961.265 2.508.414.980 2.867.507.551 76.948.408 2.713.516.810 301.942.629 91.169.350.965.877.800 2010 3.015.459.439 2.786.210.717 2.591.753.701 2.980.667.734 83.338.721 2.944.455.959 71.003.480 5.041.494.155.069.650 2011 3.531.333.729 3.009.747.621 2.717.151.877 3.302.343.365 125.398.176 3.064.006.455 467.327.274 218.394.780.854.164.000 2012 4.159.259.769 3.354.601.265 2.908.386.693 3.800.815.837 191.234.817 3.427.741.541 731.518.228 535.118.918.194.719.000 2013 4.360.477.994 3.656.364.284 3.132.779.971 4.179.948.597 224.393.277 3.992.050.654 368.427.340 135.738.705.091.423.000 2014 4.388.722.350 3.876.071.704 3.355.767.491 4.396.375.917 222.987.520 4.404.341.874 -15.619.524 243.969.541.834.568 2015 4.556.602.274 4.080.230.875 3.573.106.506 4.587.355.244 217.339.015 4.619.363.437 -62.761.163 3.938.963.566.704.940 2016 4.776.380.310 4.289.075.705 3.787.897.266 4.790.254.145 214.790.760 4.804.694.259 -28.313.949 801.679.713.267.265
990.447.862.083.060.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,3 dan N = 8 SE = �et2
N
N
i=1
MSE = 990.447.862.083.060.000 MSE = 123.805.982.760.383.000 8
Tabel 4.5 Perhitungan Peramalan Banyaknya Energi Listrik yang Disalurkan PT. P LN (Persero) Ca bang Medan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,4
Tahun Xt St' St" at bt Ft et et2
2007 2.381.693.000 2.381.693.000 2.381.693.000 - - - - -
2008 2.934.732.684 2.602.908.874 2.470.179.349 2.735.638.398 88.486.349 - - -
2009 3.015.459.439 2.767.929.100 2.589.279.250 2.946.578.950 119.099.900 2.824.124.747 191.334.692 36.608.964.286.200.700 2010 3.015.459.439 2.866.941.235 2.700.344.044 3.033.538.427 111.064.794 3.065.678.850 -50.219.411 2.521.989.249.222.110 2011 3.531.333.729 3.132.698.233 2.873.285.720 3.392.110.746 172.941.676 3.144.603.221 386.730.508 149.560.485.551.867.000 2012 4.159.259.769 3.543.322.847 3.141.300.571 3.945.345.124 268.014.851 3.565.052.422 594.207.347 353.082.371.437.939.000 2013 4.360.477.994 3.870.184.906 3.432.854.305 4.307.515.507 291.553.734 4.213.359.975 147.118.019 21.643.711.471.831.800 2014 4.388.722.350 4.077.599.884 3.690.752.536 4.464.447.231 257.898.232 4.599.069.241 -210.346.891 44.245.814.703.684.900 2015 4.556.602.274 4.269.200.840 3.922.131.858 4.616.269.822 231.379.321 4.722.345.462 -165.743.188 27.470.804.506.496.500 2016 4.776.380.310 4.472.072.628 4.142.108.166 4.802.037.090 219.976.308 4.847.649.143 -71.268.833 5.079.246.587.296.280
640.213.387.794.538.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,4 dan N = 8 SE = �et2
N
N
i=1
MSE = 640.213.387.794.538.000 MSE = 80.026.673.474.317.300 8
Tabel 4.6 Perhitungan Peramalan Banyaknya Energi Listrik yang Disalurkan PT. P LN (Persero) Ca bang Medan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,5
Tahun Xt St' St" at bt Ft et et2
2007 2.381.693.000 2.381.693.000 2.381.693.000 - - - - -
2008 2.934.732.684 2.658.212.842 2.519.952.921 2.796.472.763 138.259.921 - - -
2009 3.015.459.439 2.836.836.141 2.678.394.531 2.995.277.750 158.441.610 2.934.732.684 80.726.755 6.516.808.972.830.020 2010 3.015.459.439 2.926.147.790 2.802.271.160 3.050.024.419 123.876.630 3.153.719.360 -138.259.921 19.115.805.754.926.200 2011 3.531.333.729 3.228.740.759 3.015.505.960 3.441.975.559 213.234.800 3.173.901.049 357.432.680 127.758.120.910.699.000 2012 4.159.259.769 3.694.000.264 3.354.753.112 4.033.247.416 339.247.152 3.655.210.359 504.049.411 254.065.808.225.398.000 2013 4.360.477.994 4.027.239.129 3.690.996.121 4.363.482.138 336.243.009 4.372.494.569 -12.016.575 144.398.064.216.122 2014 4.388.722.350 4.207.980.740 3.949.488.430 4.466.473.049 258.492.310 4.699.725.146 -311.002.796 96.722.739.236.443.700 2015 4.556.602.274 4.382.291.507 4.165.889.968 4.598.693.045 216.401.538 4.724.965.359 -168.363.085 28.346.128.238.138.200 2016 4.776.380.310 4.579.335.908 4.372.612.938 4.786.058.878 206.722.970 4.815.094.584 -38.714.274 1.498.794.972.632.800
534.168.604.375.283.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,5 dan N = 8
SE = �et2 N
N
i=1
MSE = 534.168.604.375.283.000 MSE = 66.771.075.546.910.400 8
Tabel 4.7 Perhitungan Peramalan Banyaknya Energi Listrik yang Disalurkan PT. P LN (Persero) Ca bang Medan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,6
Tahun Xt St' St" at bt Ft et et2
2007 2.381.693.000 2.381.693.000 2.381.693.000 - - - - -
2008 2.934.732.684 2.713.516.810 2.580.787.286 2.846.246.335 199.094.286 - - -
2009 3.015.459.439 2.894.682.388 2.769.124.347 3.020.240.428 188.337.061 3.045.340.621 -29.881.182 892.885.025.764.606 2010 3.015.459.439 2.967.148.618 2.887.938.910 3.046.358.327 118.814.563 3.208.577.489 -193.118.050 37.294.581.189.453.800 2011 3.531.333.729 3.305.659.685 3.138.571.375 3.472.747.995 250.632.465 3.165.172.890 366.160.839 134.073.760.151.931.000 2012 4.159.259.769 3.817.819.735 3.546.120.391 4.089.519.080 407.549.016 3.723.380.460 435.879.309 189.990.772.300.255.000 2013 4.360.477.994 4.143.414.691 3.904.496.971 4.382.332.410 358.376.580 4.497.068.096 -136.590.102 18.656.855.911.657.900 2014 4.388.722.350 4.290.599.286 4.136.158.360 4.445.040.212 231.661.389 4.740.708.990 -351.986.640 123.894.594.694.923.000 2015 4.556.602.274 4.450.201.079 4.324.583.991 4.575.818.166 188.425.631 4.676.701.602 -120.099.328 14.423.848.504.711.300 2016 4.776.380.310 4.645.908.618 4.517.378.767 4.774.438.468 192.794.776 4.764.243.798 12.136.512 147.294.929.861.604
519.374.592.708.558.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,6 dan N = 8 SE = �et2
N
N
i=1
MSE = 519.374.592.708.558.000 MSE = 64.921.824.088.569.800 8
Tabel 4.8 Perhitungan Peramalan Banyaknya Energi Listrik yang Disalurkan PT. P LN (Persero) Ca bang Medan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,7
Tahun Xt St' St" at bt Ft et et2
2007 2.381.693.000 2.381.693.000 2.381.693.000 - - - - -
2008 2.934.732.684 2.768.820.779 2.652.682.445 2.884.959.112 270.989.445 - - -
2009 3.015.459.439 2.941.467.841 2.854.832.222 3.028.103.460 202.149.777 3.155.948.558 -140.489.119 19.737.192.445.004.800 2010 3.015.459.439 2.993.261.960 2.951.733.038 3.034.790.881 96.900.816 3.230.253.237 -214.793.798 46.136.375.538.980.000 2011 3.531.333.729 3.369.912.198 3.244.458.450 3.495.365.946 292.725.412 3.131.691.697 399.642.032 159.713.753.774.659.000 2012 4.159.259.769 3.922.455.498 3.719.056.383 4.125.854.612 474.597.933 3.788.091.358 371.168.411 137.765.989.339.112.000 2013 4.360.477.994 4.229.071.245 4.076.066.787 4.382.075.704 357.010.403 4.600.452.545 -239.974.551 57.587.785.258.091.700 2014 4.388.722.350 4.340.827.019 4.261.398.949 4.420.255.088 185.332.162 4.739.086.107 -350.363.757 122.754.762.047.384.000 2015 4.556.602.274 4.491.869.697 4.422.728.473 4.561.010.922 161.329.524 4.605.587.250 -48.984.976 2.399.527.916.676.520 2016 4.776.380.310 4.691.027.126 4.610.537.530 4.771.516.722 187.809.057 4.722.340.446 54.039.864 2.920.306.927.603.070 549.015.693.247.511.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,7 dan N = 8 SE = �et2
N
N
i=1
MSE = 549.015.693.247.511.000 MSE = 68.626.961.655.938.900 8
Tabel 4.9 Perhitungan Peramalan Banyaknya Energi Listrik yang Disalurkan PT. P LN (Persero) Ca bang Medan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,8
Tahun Xt St' St" at bt Ft et et2
2007 2.381.693.000 2.381.693.000 2.381.693.000 - - - - -
2008 2.934.732.684 2.824.124.747 2.735.638.398 2.912.611.097 353.945.398 - - -
2009 3.015.459.439 2.977.192.501 2.928.881.680 3.025.503.321 193.243.282 3.266.556.494 -251.097.055 63.049.731.230.551.000 2010 3.015.459.439 3.007.806.051 2.992.021.177 3.023.590.926 63.139.497 3.218.746.604 -203.287.165 41.325.671.258.581.200 2011 3.531.333.729 3.426.628.193 3.339.706.790 3.513.549.597 347.685.613 3.086.730.423 444.603.306 197.672.100.068.926.000 2012 4.159.259.769 4.012.733.454 3.878.128.121 4.147.338.787 538.421.331 3.861.235.210 298.024.559 88.818.637.852.975.600 2013 4.360.477.994 4.290.929.086 4.208.368.893 4.373.489.279 330.240.772 4.685.760.118 -325.282.124 105.808.459.932.895.000 2014 4.388.722.350 4.369.163.697 4.337.004.736 4.401.322.658 128.635.843 4.703.730.051 -315.007.701 99.229.851.566.607.600 2015 4.556.602.274 4.519.114.559 4.482.692.594 4.555.536.523 145.687.858 4.529.958.501 26.643.773 709.890.619.524.895 2016 4.776.380.310 4.724.927.160 4.676.480.247 4.773.374.073 193.787.652 4.701.224.381 75.155.929 5.648.413.676.020.610
602.262.756.206.081.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,8 dan N = 8 SE = �et2
N
N
i=1
MSE = 602.262.756.206.081.000 MSE = 75.282.844.525.760.200 8
Tabel 4.10 Perhitungan Peramalan Banyaknya Energi Listrik yang Disalurkan PT. PLN (Persero) Cabang Medan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,9
Tahun Xt St' St" at bt Ft et et2
2007 2.381.693.000 2.381.693.000 2.381.693.000 - - - - -
2008 2.934.732.684 2.879.428.716 2.829.655.144 2.929.202.287 447.962.144 - - -
2009 3.015.459.439 3.001.856.367 2.984.636.244 3.019.076.489 154.981.100 3.377.164.431 -361.704.992 130.830.501.382.402.000 2010 3.015.459.439 3.014.099.132 3.011.152.843 3.017.045.421 26.516.599 3.174.057.589 -158.598.150 25.153.373.272.237.700 2011 3.531.333.729 3.479.610.269 3.432.764.527 3.526.456.012 421.611.684 3.043.562.019 487.771.710 237.921.240.945.600.000 2012 4.159.259.769 4.091.294.819 4.025.441.790 4.157.147.848 592.677.263 3.948.067.696 211.192.073 44.602.091.899.091.700 2013 4.360.477.994 4.333.559.677 4.302.747.888 4.364.371.465 277.306.098 4.749.825.111 -389.347.117 151.591.177.830.383.000 2014 4.388.722.350 4.383.206.083 4.375.160.263 4.391.251.902 72.412.375 4.641.677.563 -252.955.213 63.986.339.892.873.900 2015 4.556.602.274 4.539.262.655 4.522.852.416 4.555.672.894 147.692.153 4.463.664.277 92.937.997 8.637.471.199.185.200 2016 4.776.380.310 4.752.668.544 4.729.686.932 4.775.650.157 206.834.516 4.703.365.047 73.015.263 5.331.228.694.969.940 668.053.425.116.742.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,9 dan N = 8 SE = �et2
N
N
i=1
MSE = 668.053.425.16.742.000 MSE = 83.506.678.139.592.800 8
Tabel 4.11 Perhitungan P eramalan B anyaknya Energi L istrik yang D ijual P T. P LN ( Persero) C abang M edan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,1
Tahun Xt St′ St" at bt Ft et et2
2007 2.686.768.353 2.686.768.353 2.686.768.353 - - - - -
2008 2.637.320.236 2.681.823.541 2.686.273.872 2.677.373.211 -494.481 - - -
2009 2.728.410.791 2.686.482.266 2.686.294.711 2.686.669.821 20.839 2.676.878.730 51.532.061 2.655.553.352.133.380 2010 2.924.924.483 2.710.326.488 2.688.697.889 2.731.955.087 2.403.178 2.686.690.661 238.233.822 56.755.354.082.903.500 2011 3.115.760.256 2.750.869.865 2.694.915.087 2.806.824.643 6.217.198 2.734.358.265 381.401.991 145.467.479.034.732.000 2012 3.366.189.669 2.812.401.845 2.706.663.762 2.918.139.928 11.748.676 2.813.041.841 553.147.828 305.972.520.111.760.000 2013 3.386.435.530 2.869.805.214 2.722.977.908 3.016.632.520 16.314.145 2.929.888.604 456.546.926 208.435.095.798.946.000 2014 3.427.157.045 2.925.540.397 2.743.234.156 3.107.846.637 20.256.249 3.032.946.665 394.210.380 155.401.823.758.089.000 2015 3.473.772.983 2.980.363.655 2.766.947.106 3.193.780.204 23.712.950 3.128.102.886 345.670.097 119.487.815.913.148.000 2016 3.653.601.000 3.047.687.390 2.795.021.135 3.300.353.645 28.074.028 3.217.493.154 436.107.846 190.190.053.009.661.000 1.184.365.695.061.370.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,1 dan N = 8
MSE = �et2 N
N
i=1
MSE = 1.184.365.695.370.000 MSE = 148.045.711.882.671.000 8
Tabel 4.12 Perhitungan P eramalan B anyaknya Energi L istrik yang D ijual P T. P LN ( Persero) C abang M edan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,2
Tahun Xt St′ St" at bt Ft et et2
2007 2.686.768.353 2.686.768.353 2.686.768.353 - - - - -
2008 2.637.320.236 2.676.878.730 2.684.790.428 2.668.967.031 -1.977.925 - - -
2009 2.728.410.791 2.687.185.142 2.685.269.371 2.689.100.913 478.943 2.666.989.106 61.421.685 3.772.623.363.670.460 2010 2.924.924.483 2.734.733.010 2.695.162.099 2.774.303.921 9.892.728 2.689.579.855 235.344.628 55.387.093.721.355.100 2011 3.115.760.256 2.810.938.459 2.718.317.371 2.903.559.548 23.155.272 2.784.196.649 331.563.607 109.934.425.370.140.000 2012 3.366.189.669 2.921.988.701 2.759.051.637 3.084.925.765 40.734.266 2.926.714.820 439.474.849 193.138.143.149.679.000 2013 3.386.435.530 3.014.878.067 2.810.216.923 3.219.539.211 51.165.286 3.125.660.032 260.775.498 68.003.860.607.826.200 2014 3.427.157.045 3.097.333.863 2.867.640.311 3.327.027.414 57.423.388 3.270.704.497 156.452.548 24.477.399.785.024.500 2015 3.473.772.983 3.172.621.687 2.928.636.586 3.416.606.787 60.996.275 3.384.450.802 89.322.181 7.978.451.986.460.400 2016 3.653.601.000 3.268.817.549 2.996.672.779 3.540.962.320 68.036.193 3.477.603.062 175.997.938 30.975.274.029.980.600
493.667.272.014.137.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,2 dan N = 8 MSE = �et2
N
N
i=1
MSE = 493.667.272.014.137.000 MSE = 61.708.409.001.767.100 8
Tabel 4.13 Perhitungan P eramalan B anyaknya Energi L istrik yang D ijual P T. P LN ( Persero) C abang M edan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,3
Tahun Xt St′ St" at bt Ft et et2
2007 2.686.768.353 2.686.768.353 2.686.768.353 - - - - -
2008 2.637.320.236 2.671.933.918 2.682.318.022 2.661.549.813 -4.450.331 - - -
2009 2.728.410.791 2.688.876.980 2.684.285.710 2.693.468.250 1.967.687 2.657.099.483 71.311.308 5.085.302.677.195.500 2010 2.924.924.483 2.759.691.231 2.706.907.366 2.812.475.096 22.621.656 2.695.435.937 229.488.546 52.664.992.657.988.400 2011 3.115.760.256 2.866.511.938 2.754.788.738 2.978.235.139 47.881.372 2.835.096.752 280.663.504 78.772.002.542.672.000 2012 3.366.189.669 3.016.415.258 2.833.276.694 3.199.553.821 78.487.956 3.026.116.511 340.073.158 115.649.753.006.679.000 2013 3.386.435.530 3.127.421.339 2.921.520.087 3.333.322.591 88.243.394 3.278.041.777 108.393.753 11.749.205.608.099.200 2014 3.427.157.045 3.217.342.051 3.010.266.676 3.424.417.426 88.746.589 3.421.565.985 5.591.060 31.259.953.044.146 2015 3.473.772.983 3.294.271.331 3.095.468.073 3.493.074.589 85.201.396 3.513.164.015 -39.391.032 1.551.653.374.127.490 2016 3.653.601.000 3.402.070.231 3.187.448.720 3.616.691.743 91.980.648 3.578.275.985 75.325.015 5.673.857.921.908.450 271.178.027.741.714.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,3 dan N = 8 MSE = �et2
N
N
i=1
MSE = 271.178.027.714.000 MSE = 33.897.253.467.714.300 8
Tabel 4.14 Perhitungan P eramalan B anyaknya Energi L istrik yang D ijual P T. P LN ( Persero) C abang M edan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,4
Tahun Xt St′ St" at bt Ft et et2
2007 2.686.768.353 2.686.768.353 2.686.768.353 - - - - -
2008 2.637.320.236 2.666.989.106 2.678.856.654 2.655.121.558 -7.911.699 - - -
2009 2.728.410.791 2.691.557.780 2.683.937.105 2.699.178.456 5.080.450 2.647.209.859 81.200.932 6.593.591.292.707.860 2010 2.924.924.483 2.784.904.461 2.724.324.047 2.845.484.875 40.386.943 2.704.258.906 220.665.577 48.693.296.890.396.400 2011 3.115.760.256 2.917.246.779 2.801.493.140 3.033.000.418 77.169.093 2.885.871.818 229.888.438 52.848.693.959.184.200 2012 3.366.189.669 3.096.823.935 2.919.625.458 3.274.022.412 118.132.318 3.110.169.511 256.020.158 65.546.321.277.767.100 2013 3.386.435.530 3.212.668.573 3.036.842.704 3.388.494.442 117.217.246 3.392.154.730 -5.719.200 32.709.250.510.400 2014 3.427.157.045 3.298.463.962 3.141.491.207 3.455.436.717 104.648.503 3.505.711.688 -78.554.643 6.170.831.946.118.060 2015 3.473.772.983 3.368.587.570 3.232.329.752 3.504.845.388 90.838.545 3.560.085.220 -86.312.237 7.449.802.188.942.410 2016 3.653.601.000 3.482.592.942 3.332.435.028 3.632.750.856 100.105.276 3.595.683.933 57.917.067 3.354.386.599.724.260 190.689.633.405.351.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,4 dan N = 8 MSE = �et2
N
N
i=1
MSE = 190.689.633.405.351.000 MSE = 23.836.204.175.668.800 8
Tabel 4.15 Perhitungan P eramalan B anyaknya Energi L istrik yang D ijual P T. P LN ( Persero) C abang M edan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,5
Tahun Xt St′ St" at bt Ft et et2
2007 2.686.768.353 2.686.768.353 2.686.768.353 - - - - -
2008 2.637.320.236 2.662.044.295 2.674.406.324 2.649.682.265 - 12.362.029 - - -
2009 2.728.410.791 2.695.227.543 2.684.816.933 2.705.638.152 10.410.610 2.637.320.236 91.090.555 8.297.489.210.208.020 2010 2.924.924.483 2.810.076.013 2.747.446.473 2.872.705.553 62.629.540 2.716.048.762 208.875.721 43.629.066.927.707.700 2011 3.115.760.256 2.962.918.134 2.855.182.304 3.070.653.965 107.735.831 2.935.335.093 180.425.164 32.553.239.624.001.700 2012 3.366.189.669 3.164.553.902 3.009.868.103 3.319.239.701 154.685.799 3.178.389.796 187.799.873 35.268.792.369.241.100 2013 3.386.435.530 3.275.494.716 3.142.681.409 3.408.308.022 132.813.307 3.473.925.500 - 87.489.970 7.654.494.795.919.670 2014 3.427.157.045 3.351.325.880 3.247.003.645 3.455.648.116 104.322.236 3.541.121.329 - 113.964.284 12.987.858.024.071.300 2015 3.473.772.983 3.412.549.432 3.329.776.538 3.495.322.325 82.772.893 3.559.970.352 - 86.197.369 7.429.986.347.099.460 2016 3.653.601.000 3.533.075.216 3.431.425.877 3.634.724.555 101.649.339 3.578.095.219 75.505.781 5.701.123.029.897.630 153.522.050.328.147.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,5 dan N = 8 MSE = �et2
N
N
i=1
MSE = 153.522.050328.147.000 MSE = 19.190.256.291.018.300 8
Tabel 4.16 Perhitungan P eramalan B anyaknya Energi L istrik yang D ijual P T. P LN ( Persero) C abang M edan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,6
Tahun Xt St' St" at bt Ft et et2
2007 2.686.768.353 2.686.768.353 2.686.768.353 - - - - -
2008 2.637.320.236 2.657.099.483 2.668.967.031 2.645.231.935 -17.801.322 - - -
2009 2.728.410.791 2.699.886.268 2.687.518.573 2.712.253.962 18.551.542 2.627.430.613 100.980.178 10.196.996.429.695.700 2010 2.924.924.483 2.834.909.197 2.775.952.947 2.893.865.446 88.434.374 2.730.805.505 194.118.978 37.682.177.790.589.000 2011 3.115.760.256 3.003.419.832 2.912.433.078 3.094.406.586 136.480.131 2.982.299.821 133.460.435 17.811.687.765.908.700 2012 3.366.189.669 3.221.081.734 3.097.622.272 3.344.541.197 185.189.194 3.230.886.717 135.302.952 18.306.888.716.001.400 2013 3.386.435.530 3.320.294.012 3.231.225.316 3.409.362.708 133.603.044 3.529.730.390 -143.294.860 20.533.416.999.998.200 2014 3.427.157.045 3.384.411.832 3.323.137.225 3.445.686.438 91.911.910 3.542.965.752 -115.808.707 13.411.656.508.370.400 2015 3.473.772.983 3.438.028.522 3.392.072.004 3.483.985.041 68.934.778 3.537.598.348 -63.825.365 4.073.677.162.528.920 2016 3.653.601.000 3.567.372.009 3.497.252.007 3.637.492.011 105.180.003 3.552.919.820 100.681.180 10.136.700.084.467.600
132.153.201.457.560.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,6 dan N = 8 MSE = �et2
N
N
i=1
MSE = 132.153.210.457.560.000 MSE = 16.519.150.182.195.000 8
Tabel 4.17 Perhitungan P eramalan B anyaknya Energi L istrik yang D ijual P T. P LN ( Persero) C abang M edan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,7
Tahun Xt St' St" at bt Ft et et2
2007 2.686.768.353 2.686.768.353 2.686.768.353 - - - - -
2008 2.637.320.236 2.652.154.671 2.662.538.776 2.641.770.567 -24.229.577 - - -
2009 2.728.410.791 2.705.533.955 2.692.635.401 2.718.432.509 30.096.626 2.617.540.989 110.869.802 12.292.112.951.171.400 2010 2.924.924.483 2.859.107.325 2.809.165.748 2.909.048.902 116.530.346 2.748.529.134 176.395.349 31.115.319.011.243.500 2011 3.115.760.256 3.038.764.377 2.969.884.788 3.107.643.965 160.719.040 3.025.579.248 90.181.008 8.132.614.204.617.550 2012 3.366.189.669 3.267.962.081 3.178.538.893 3.357.385.269 208.654.105 3.268.363.006 97.826.663 9.570.056.077.357.410 2013 3.386.435.530 3.350.893.495 3.299.187.115 3.402.599.876 120.648.221 3.566.039.375 -179.603.845 32.257.541.018.039.900 2014 3.427.157.045 3.404.277.980 3.372.750.721 3.435.805.240 73.563.606 3.523.248.098 -96.091.053 9.233.490.371.863.070 2015 3.473.772.983 3.452.924.482 3.428.872.354 3.476.976.611 56.121.633 3.509.368.845 -35.595.862 1.267.065.426.003.170 2016 3.653.601.000 3.593.398.045 3.544.040.337 3.642.755.752 115.167.984 3.533.098.244 120.502.756 14.520.914.260.235.400
118.389.113.320.531.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,7 dan N = 8 MSE = �et2
N
N
i=1
MSE = 118.389.113.320.531.000 MSE = 14.798.639.165.066.400 8
Tabel 4.18 Perhitungan P eramalan B anyaknya Energi L istrik yang D ijual P T. P LN ( Persero) C abang M edan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,8
Tahun Xt St′ St" at bt Ft et et2
2007 2.686.768.353 2.686.768.353 2.686.768.353 - - - - -
2008 2.637.320.236 2.647.209.859 2.655.121.558 2.639.298.161 -31.646.795 - - -
2009 2.728.410.791 2.712.170.605 2.700.760.795 2.723.580.414 45.639.237 2.607.651.366 120.759.425 14.582.838.774.634.100 2010 2.924.924.483 2.882.373.707 2.846.051.125 2.918.696.290 145.290.330 2.769.219.651 155.704.832 24.243.994.633.409.400 2011 3.115.760.256 3.069.082.946 3.024.476.582 3.113.689.311 178.425.457 3.063.986.619 51.773.637 2.680.509.456.729.410 2012 3.366.189.669 3.306.768.324 3.250.309.976 3.363.226.673 225.833.394 3.292.114.768 74.074.901 5.487.091.018.605.060 2013 3.386.435.530 3.370.502.089 3.346.463.666 3.394.540.511 96.153.690 3.589.060.067 -202.624.537 41.056.702.955.820.100 2014 3.427.157.045 3.415.826.054 3.401.953.576 3.429.698.531 55.489.910 3.490.694.202 -63.537.157 4.036.970.296.537.340 2015 3.473.772.983 3.462.183.597 3.450.137.593 3.474.229.601 48.184.017 3.485.188.441 -11.415.458 130.312.687.082.238 2016 3.653.601.000 3.615.317.519 3.582.281.534 3.648.353.505 132.143.941 3.522.413.618 131.187.382 17.210.129.188.744.800
109.428.549.011.562.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,8 dan N = 8 MSE = �et2
N
N
i=1
MSE = 109.428.549.011.562.000 MSE = 13.678.568.626.445.300 8
Tabel 4.19 Perhitungan P eramalan B anyaknya Energi L istrik yang D ijual P T. P LN ( Persero) C abang M edan dengan Smoothing Eksponensial Ganda Linier dari Brown dengan α = 0,9
Tahun Xt St′ St" at bt Ft et et2
2007 2.686.768.353 2.686.768.353 2.686.768.353 - - - - -
2008 2.637.320.236 2.642.265.048 2.646.715.378 2.637.814.717 -40.052.975 - - -
2009 2.728.410.791 2.719.796.217 2.712.488.133 2.727.104.301 65.772.755 2.597.761.742 130.649.049 17.069.173.900.084.500 2010 2.924.924.483 2.904.411.656 2.885.219.304 2.923.604.009 172.731.171 2.792.877.055 132.047.428 17.436.523.212.365.100 2011 3.115.760.256 3.094.625.396 3.073.684.787 3.115.566.005 188.465.483 3.096.335.180 19.425.076 377.333.581.179.898 2012 3.366.189.669 3.339.033.242 3.312.498.396 3.365.568.087 238.813.609 3.304.031.488 62.158.181 3.863.639.457.707.370 2013 3.386.435.530 3.381.695.301 3.374.775.611 3.388.614.992 62.277.214 3.604.381.697 -217.946.167 47.500.531.523.873.100 2014 3.427.157.045 3.422.610.871 3.417.827.345 3.427.394.397 43.051.734 3.450.892.206 -23.735.161 563.357.873.582.199 2015 3.473.772.983 3.468.656.772 3.463.573.829 3.473.739.714 45.746.484 3.470.446.131 3.326.852 11.067.947.163.705 2016 3.653.601.000 3.635.106.577 3.617.953.302 3.652.259.852 154.379.473 3.519.486.199 134.114.801 17.986.779.873.938.000
104.808.407.369.894.000 Sumber Hasil : Perhitungan
Untuk mendapatkan nilai MSE digunakan Persamaan (2.9) dengan α = 0,9 dan N = 8 MSE = �et2
N
N
i=1
MSE = 104.808.407.369.894.000 MSE = 13.101.050.921.236.700 8
4.2 Pembahasan
Selanjutnya dari n ilai-nilai M SE y ang t elah d iperoleh d apat d ilihat n ilai 𝛼 (parameter smoothing) yang memberikan nilai MSE yang paling kecil. Perbandingan ukuran ke tepatan m etode pe ramalan banyaknya en ergi l istrik yang d isalurkan d an banyaknya energi listrik yang dijual dengan melihat MSE adalah sebagai berikut:
Tabel 4.20 Perbandingan Ukuran Ketepatan Metode Peramalan
α MSE Energi Listrik yang
Disalurkan MSE Energi Listrik yang Dijual 0,1 834.886.003.660.482.000 148.045.711.882.671.000 0,2 273.960.447.912.202.000 61.708.409.001.767.100 0,3 123.805.982.760.383.000 33.897.253.467.714.300 0,4 80.026.673.474.317.300 23.836.204.175.668.800 0,5 66.771.075.546.910.400 19.190.256.291.018.300 0,6 64.921.824.088.569.800 16.519.150.182.195.000 0,7 68.626.961.655.938.900 14.798.639.165.066.400 0,8 75.282.844.525.760.200 13.678.568.626.445.300 0,9 83.506.678.139.592.800 13.101.050.921.236.700 Sumber : Hasil Perhitungan
Dari tabel 4.20 diatas didapat bahwa yang menghasilkan nilai MSE yang paling kecil yaitu:
1. MSE pada Energi Listrik yang Disalurkan pada α = 0,6 yaitu dengan nilai MSE
= 64.921.824.088.569.800
2. MSE Energi Listrik yang Dijual pada p ada α = 0,9 yaitu dengan nilai MSE = 13.101.050.921.236.700
Melalui cara trial and error dengan 0 < α < 1, telah diperoleh perhitungan peramalan pemulusan eksponensial linier satu – parameter dari Brown dengan α = 0,1, sehingga d apat ditentukan bentuk persamaan peramalan untuk periode-periode berikutnya.
Berdasarkan perhitungan pada α = 0,1 dapat diperoleh persamaan peramalan untuk periode berikutnya yaitu dengan menggunakan persamaan sebagai berikut:
1. Bentuk persamaan untuk peramalan banyaknya energi listrik yang disalurkan 𝐹𝑡+𝑚 = 𝑎𝑡 + 𝑏𝑡𝑚
𝐹𝑡+𝑚 = 4.774.438.468 + 192.794.776 (m)
2. Bentuk persamaan untuk peramalan banyaknya energi listrik yang dijual 𝐹𝑡+𝑚 = 𝑎𝑡 + 𝑏𝑡𝑚
𝐹𝑡+𝑚 = 3.652.259.852 + 154.379.473 (m)
Setelah diperoleh bentuk persamaan peramalan banyaknya energi listrik yang disalurkan dan dijual diatas, maka dapat dihitung peramalan banyaknya energi listrik yang disalurkan dan dijual oleh PT.PLN (Persero) untuk m periode kedepan.
1. Peramalan banyaknya energi listrik yang yang disalurkan Perhitungannya adalah:
F27 = 5.545.617.571
2. Peramalan banyaknya energi listrik yang yang dijual Perhitungannya adalah: F26+1 = 3.652.259.852+ 154.379.473 (4) F27 = 4.269.777.745
Tabel 4.21 Peramalan Banyaknya Energi Listrik yang Disalurkan dan Dijual di PT.PLN (Perserp)Cabang Medan 2017, 2018, 2019, dan 2020
Tahun Periode Banyaknya Energi Listrik
Disalurkan Dijual
2017 11 4.967.233.244 3.806.639.325
2018 12 5.160.028.019 3.961.018.799
2019 13 5.352.822.795 4.115.398.272
2020 14 5.545.617.571 4.269.777.745
Sumber : Hasil Perhitungan
BAB 5