Simulation in Wind Turbine Vibrations: A Data Driven Analysis Graduate Students: Zijun Zhang PI: Andrew Kusiak Intelligent Systems Laboratory The University of Iowa

Outline Modeling wind turbine vibrations Multi-objective optimization model Evolutionary strategy algorithm Simulation results and discussion

Modeling wind turbine vibrations

Parameter description ParameterDescription y1(t)y1(t)Average Drive Train Acceleration at time t y2(t)y2(t)Tower Acceleration at time t y3(t)y3(t)Generated Power at time t y 1 (t-1)Average Drive Train Acceleration at time t-1 y 2 (t-1)Tower Acceleration at time t-1 x1(t)x1(t)Generator Torque at time t x 1 (t-1)Generator Torque at time t-1 x2(t)x2(t)Average Blade Pitch Angle at time t x 2 (t-1)Average Blade Pitch Angle at time t-1 v1(t)v1(t)Wind Speed at time t v 1 (t-1)Wind Speed at time t-1

Models of wind turbine vibrations Wind turbine vibration models: Data-derived model to predict drive train acceleration Data-derived model to predict tower acceleration

Models of wind turbine vibrations Parametric model of power output: Data-derived model of power output:

Power Curve Power curve of a 1.5 MW turbine

Sample datasets 10-s dataset 1-min dataset TimeTorque value Torque Value(T-1) Wind Speed Wind Speed(T- 1) …….Drive Train Acc Drive Train Acc(T-1) 19/10/08 3:01:10 PM …… /10/08 3:01:20 PM …… ……. TimeTorque value Torque Value(T-1) Wind Speed Wind Speed(T- 1) …….Drive Train Acc Drive Train Acc(T-1) 10/19/08 3:01 PM …… /19/08 3:02 PM …… …….

Validation of data-driven models Four metrics to assess the performance of data driven models: Mean absolute error: Standard deviation of the mean absolute error: Mean absolute percentage error: Standard deviation of Mean absolute percentage error:

Validation of data-driven models in 10-s dataset Test results of the NN models for 10-s data Predicted ParameterMAEStd of MAEMAPEStd of MAPE Drive train acceleration Tower acceleration Generated power

Validation of data-driven models in 10-s dataset The first 50 test points of the drive train acceleration for 10-s data

Validation of data-driven models in 10-s dataset The first 50 test points of the tower accelerations for 10-s data

Validation of data-driven models in 10-s dataset The first 50 test points of the power output for 10-s data

Validation of data-driven models in 1-min dataset Test results of the NN models for 1-min data Predicted ParameterMAEStd of MAEMAPEStd of MAPE Drive train acceleration Tower acceleration Generated power

Validation of data-driven models in 1-min dataset The first 50 test points of the drive train accelerations for 1-min data

Validation of data-driven models in 1-min dataset The first 50 test points of the tower acceleration for 1-min data

Validation of data driven models in 1-min dataset The first 50 test points of the power output 1-min data

Multi-objective optimization model

Multi-objective optimization

Evolutionary strategy algorithm

Strength Pareto Evolutionary Algorithm 1. Initialize three sets, parent set (Sp ), offspring set ( So) and elite set (Se ). Generate u individuals (solutions) randomly to conduct the first generation of population. 2. Repeat until the stopping criteria (number of generation, N) is satisfied 2.1. Search the best non-dominated solutions in So. Copy all non-dominated solutions to Se Search and delete all dominated solutions in Se A clustering technique is applied to reduce size of Se if the size of Se is too large Assign fitness to solutions in Se and So Apply a binary tournament selection to select u parents from the SoUSe to form the population of parents and this population is stored in Sp Recombine two parents from Sp to generate a new population Mutate individuals in So by the mutation operator and assign fitness values to them. 3. Check number of generation, if it is equal to N, then stop.

Strength Pareto Evolutionary Algorithm Recombination of parents in SPEA Mutation operator

Tuning parameters of SPEA Experiment No. Description 1 Select an instance from the 10-s data set to tune the selection pressure and population size of the ES algorithm that will be implemented in the model extracted from 10-s data set 2 Select an instance from the 1-min data set to tune the selection pressure and population size of the ES algorithm that will be implemented in the model extracted from 1-min data set One instance selected from the 10-s data set for experiment 1 TimeTVTV(t-1)WSWS(t-1)PowerTATA(t-1)BPABPA(t-1)DTADTA(t-1) 10/18/08 10:55:10 PM One instance selected from the 1-min data set for experiment 2 TimeTVTV(t-1)WSWS(t-1)PowerTATA(t-1)BPABPA(t-1)DTADTA(t-1) 10/18/08 10:55 PM Two experiments for tuning selection pressure and population size

Tuning parameters of SPEA Convergence for 10 values of the selection pressure in experiment 1 Combinations of selection pressure Converge speed of average drive train acceleration (generations) Converge speed of inverse of power output (generations) Converge speed of tower acceleration (generations) Average converge speed (generations) Ratio1 (2parents/2offsprings) Ratio2 (2parents/4offsprings) Ratio3 (2parents/6offsprings) Ratio4 (2parents/8offsprings) Ratio5 (2parents/10offsprings) Ratio6 (2parents/12offsprings) Ratio7 (2parents/14offsprings) Ratio8 (2parents/16offsprings) Ratio9 (2parents/18offsprings) Ratio10 (2parents/20offsprings)

Tuning parameters of SPEA Convergence for 10 values of the selection pressure in experiment 2 Combinations of selection pressure Converge speed of average drive train acceleration (generations) Converge speed of inverse of power output (generations) Converge speed of tower acceleration (generations) Average converge speed (generations) Ratio1 (2parents/2offsprings) Ratio2 (2parents/4offsprings) Ratio3 (2parents/6offsprings) Ratio4 (2parents/8offsprings) Ratio5 (2parents/10offsprings) Ratio6 (2parents/12offsprings) Ratio7 (2parents/14offsprings) Ratio8 (2parents/16offsprings) Ratio9 (2parents/18offsprings) Ratio10 (2parents/20offsprings)

Tuning parameters of SPEA Convergence of the ES algorithm for two populations of experiment 1 Population Sizes Converge speed of average drive train acceleration (generations) Converge speed of inverse of power output (generations) Converge speed of tower acceleration (generations) Average converge speed (generations) PS1(2parents/18offsprings) PS2(10parents/90offsprings ) Convergence of the ES algorithm for two populations of experiment 2 Population Size Converge speed of average drive train acceleration (generations) Converge speed of inverse of power output (generations) Converge speed of tower acceleration (generations) Average converge speed (generations) PS1(2parents/20offsp rings) PS2(10parents/100of fsprings)

Simulation results and discussion

Simulation Results of Single Point Optimization Partial solution set generated by the evolutionary strategy algorithm Solution No. Solution (TV, BPA) Drive Train Acceleration Gain in Drive Train Acceleration Tower Acceleration Gain in Tower Acceleration Power Gain in Power 1(90.0, 8.81) % % % 2(90.0, 7.34) % % % 3(63.9, 15.00) % % % 4(67.6, 15.00) % % % 5(50.9, -3.23) % % % 6(90.0, 8.09) % % % 7(63.4, 15.00) % % %

Simulation Results of Single Point Optimization Solution of the elite set in a 3-dimensional space

Multi-points Optimization Simulation Results Gains in vibration reductions of the drive train for Case 1 (10/19/2008 2:43:00 AM - 10/19/2008 2:54:00 AM) Case 1 (Minimize average drive train acceleration) Minimum value (mean)Original value (mean)Gain (mean) Average drive train acceleration %

Simulation Results The optimized and original drive train acceleration of Case 1 for 10-s data (10/19/2008 2:43:00 AM - 10/19/2008 2:54:00 AM)

Simulation Results The computed and original torque value of Case 1 for 10-s data (10/19/2008 2:43:00 AM - 10/19/2008 2:54:00 AM)

Simulation Results The computed and original average blade pitch angle of Case 1 for 10-s data (10/19/2008 2:43:00 AM - 10/19/2008 2:54:00 AM)

Simulation Results Comparison of computational results for 10-s data set and 1-min data set over 10 min horizon Mean Value Minimize Drive Train Acceleration Optimized Drive Train Acceleration Original Drive Train Acceleration Gain 10-s data set % 1-min data set % Minimize Tower Acceleration Optimized Tower Acceleration Acceleration Gain 10-s data set % 1-min data set % Maximize Power Output Optimized Power Output Original Power OutputGain 10-s data set % 1-min data set %

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