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The Effect of Markov Chain State Size for Synthetic Wind Speed Generation Fatih O. Hocaoğlu, Ömer N. Gerek and Mehmet Kurban

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Presentation Plan Wind speed time series Markov chains Syntetic generation of wind speed Effect of Markov state size on wind speed data generation Results

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Wind speed time series

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Markov chains

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Syntetic generation of wind speed data 0.610.290.080.020.00 0.180.470.280.060.020.00 0.040.200.460.230.060.01 0.00 0.010.050.200.450.220.060.010.00 0.060.260.420.200.040.010.00 0.010.070.280.410.180.040.00 0.01 0.070.290.390.210.020.010.00 0.010.020.090.300.380.170.020.00 0.010.040.120.330.390.080.020.00 0.010.030.180.270.370.080.050.00 0.180.090.230.410.090.00 0.08 0.00 0.150.310.080.310.00 1.000.00

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Syntetic generation of wind speed data

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0.00...... 0.000.610.180.100.050.030.020.00...... 0.000.250.24 0.140.060.040.010.00...... 0.000.120.180.280.230.110.050.030.01 0.00...... 0.000.050.110.150.230.190.120.070.020.030.00...... 0.000.020.040.100.180.300.160.100.040.020.010.00...... 0.000.010.030.050.100.170.280.170.100.040.020.01...... 0.00 0.020.040.100.200.250.180.110.050.02...... 0.00 0.020.060.120.230.250.130.100.05...... 0.00 0.010.020.050.120.220.250.180.07...... 0.00 0.010.030.050.130.220.230.16...... 0.00 0.020.040.050.150.220.21......

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Syntetic generation of wind speed data is transition probability in the i th row at the k th state

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Syntetic generation of wind speed data 0.610.900.981.00 0.180.640.920.981.00 0.040.230.690.920.980.991.00 0.010.060.260.720.930.991.00 0.00 0.060.320.750.950.991.00 0.00 0.010.080.360.770.950.991.00 0.00 0.010.020.090.380.760.970.991.00 0.00 0.010.030.120.420.800.981.00 0.00 0.020.050.170.500.890.971.00 0.00 0.010.040.220.490.860.951.00 0.00 0.180.270.500.911.00 0.00 0.080.15 0.310.620.691.00 0.00 1.00

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Syntetic wind speed data generation algorithm An initial state is determined randomly and then by using a uniform random number generator, a random value is produced between 0 and 1. The next state is found where this random value is greater than the cumulative probability of the previous state but less than or equal to the cumulative probability of the following state. The actual wind speed value in each state is determined by another uniform random number generator for intermediate states.

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Syntetic wind speed data generation algorithm

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Results

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Observed Data Generated Data from Model-1 Generated Data from Model-2 Min0.000.020.00 Max12.4711.4412.77 Mean3.523.163.61 Median3.352.953.47 Std2.111.912.02

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Results

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Thank You Fatih Onur Hocaoglu

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