Embed Size (px)
Citation preview
Developing Analytical Approaches to Forecast Wind Farm Production: Phase II
Kate Geschwind, 10
th Grade
Mayo High School
1420 11th Avenue Southeast
Rochester, MN 55904
Research Category: Mathematics
Acknowledgement
I would like to express my sincere appreciation to NeuroDimension, whose NeuroSolutions for
Excel software allowed me to efficiently create and test a variety of neural network models.
2
Introduction
The importance of wind-generated electricity continues to grow in our society as wind and other forms of renewable
energy offer chances for a cleaner environment. Wind energy promises clean and renewable electricity, but it also is
an intermittent form of energy, with the output of a wind farm constantly changing from hour to hour.
Consequently, it is difficult to predict the energy output of a wind farm in advance. This makes it difficult for
utilities and transmission grid operators who are required to maintain the reliability of the electrical system. They
must have other non-intermittent power plants available to generate more or less energy, depending on the wind.
Predicting incorrectly not only can be costly for electric utilities, but it can also lead to power outages or shortages.
Because wind generation is still a developing technology, much ongoing research is focusing on predicting the
intermittent output of wind farms.
The goal of this project is to develop an analytical approach for forecasting wind farm production over different time
periods using artificial neural networks and regression analysis. Being able to more accurately forecast hourly wind
farm production will not only save money and help maintain reliability for electric utilities, but it will also likely
encourage the use of more wind farms as their output patterns become better understood. This project is a
continuation of a project from last year. The purpose of last year's project was to explain the historical hourly output
of a Minnesota wind farm using regression analysis. That project did not attempt to forecast wind farm output, and
the method used was limited to regression analysis. This year’s project continues last year’s research and moves
from explaining the output to predicting the output – a move that is required in order for this research to have
practical applications. This year’s project also introduces the use of artificial neural networks for the model
development process to determine if neural networks can produce models that outperform regression-based models.
Finally, this year's project applies the developed forecasting approach to multi-turbine wind farms in Minnesota and
Oklahoma and a wind turbine in Vermont to evaluate the robustness of the approach.
My hypothesis is that by using regression analysis, artificial intelligence systems, and certain variables that have a
high correlation to wind farm production such as wind speed, wind speed squared, wind speed cubed, a one hour lag
of the actual wind farm production, and the change in the one hour lag from the prior hour, a mathematical model
3
can be made that can accurately forecast wind farm production for various lengths of time for wind farms of
different sizes and locations.
Materials and Procedures
The following materials and data were used in this project:
Hourly electrical production data from wind farms of different locations and sizes, including:
o The WAPSI wind farm near Dexter, Minnesota, with 67 wind turbines and a 100.5 MW capacity.
o The Oklahoma Municipal Power Authority (OMPA) Wind farm near Woodward, Oklahoma, with
34 wind turbines and a 50 MW capacity.
o A single 10 kW wind turbine at Middlebury College in Middlebury, VT.
Weather data (wind speed, temperature, relative humidity, dew point, wind direction, cloud cover) from the
national weather station with the nearest location to the wind turbines.
A standard spreadsheet software program with regression analysis.
Neural network analysis software
The controlled variables in the project were the wind farms that were used (WAPSI, OMPA, Vermont turbine), and
the inputs to the software programs. The independent variables to the project were the temperature, dew point,
relative humidity, wind speed, wind speed squared, wind speed cubed, wind direction, cloud cover, turbine
availability, maximum wind cutoff, minimum wind cutoff, a one hour lag in the actual wind farm production, the
change in the one hour lag, and the actual wind farm production. The dependent variable in the project was the
estimated energy output of the given wind farm (Minnesota, Oklahoma, Vermont) as determined by the various
mathematical models created.
Hourly observed weather data from Rochester, Minnesota; Tulsa, Oklahoma; and Burlington, Vermont was obtained
for the months of December 2009 through May 2010. Hourly forecasted weather data for Rochester, Minnesota was
also obtained from a commercial weather forecasting service for the months of December 2009 through May 2010.
The weather data for Rochester included temperature, dew point, relative humidity, wind speed, wind direction, and
4
cloud cover; and the weather information for Tulsa and Burlington was the wind speed. The hourly wind farm
output was also obtained for the same months.
The hourly information was then divided into two sections: December 2009 through February 2010 was used for
training data, and March 2010 through May 2010 was used for testing data. Hours with incomplete data were
excluded. Each training and testing data set consisted of data for over 2000 hours. The list of potential explanatory
variables was supplemented with derived explanatory variables: wind speed squared, wind speed cubed, a one hour
lag of the actual wind farm production, which is the actual wind farm production from the previous hour, and the
change in the one hour lag from the previous hour. The reasons for using these derived variables vary. For
example, the energy content of the wind varies with the cube of the wind speed, so the wind speed cubed was
calculated. The power extracted from the wind by a wind turbine is proportional to the drop in the wind speed
squared, so wind speed squared was derived. The one hour lag was calculated because the output of the wind farm
from one hour to the next does not appear to be completely random and will typically be related to the prior hour’s
output. Finally, the change in the one hour lag was used to evaluate if a “momentum” effect exists in the wind farm
output that could be explained through the use of a change variable.
The first step in the modeling was to use regression analysis on each set of training data to create different
explanatory models for each wind farm location. Different combinations of variables were used to create different
models. Each model was then applied to the testing data for its respective wind farm to create forecasts of varying
lengths into the future - one hour, six hours, 12 hours, and 24 hours. Model forecast output was compared to actual
observed output to calculate the root mean square error (RMSE) of a particular model. This was done by squaring
the difference between the models’ estimated hourly output and the actual production of the wind farm, and then
taking the square root of the mean of these hourly squared differences. RMSE was the primary metric used during
this project to compare the performance of the various models.
Next, artificial intelligence, or neural network models, were developed using the training data sets for each wind
farm. The types of neural networks tested were: the multilayer perceptron, the generalized feed forward network,
the CANFIS (Fuzzy Logic) network, the time-lag recurrent network, the support vector machine, and the function
5
approximation network. For most of the models, the input data was standardized so that no one variable
disproportionately influenced the training of the models. Each network model was then used with the testing data
for its respective wind farm to find the RMSE. During the development and training of the neural network models,
steps were taken to make sure that the models were not over-trained on the training data. Overtraining would
produce a model that performs well with the specific training data but poorly with other data, such as the testing
data.
Training data sets from the different wind farms were combined to test to see if it was possible to create a single
model applicable to multiple wind farms. Data sets from two wind farms were assembled in different combinations
to form models. The combined data sets were then trained for both regression models and neural network models,
and these models were then used to calculate RMSE values on the testing data for each wind farm from which the
model had been derived.
Models were evaluated and ranked based on the value of their RMSE; the lower the RMSE, the more accurate the
model is in predicting the actual output of the wind farm. Because each of the three wind farms used for this project
is a different size, each RMSE was specific to the wind farm. In order to standardize the results and allow for model
performance to be compared across the wind farms, the RMSE for each wind farm was divided by the average wind
farm output to create an RMSE percentage value. The initial model results were determined for the one-hour
forecast period. Six-hour, 12-hour, and 24-hour forecasts were then developed for each artificial intelligence and
regression model, and RMSE values and RMSE percentage values were determined and compared.
The different regression and neural network models were not only compared against each other, but they were also
compared against the general persistence model and also the power curve model of the wind farm from which they
were derived. A common method of wind farm forecasting is the persistence method, which is often used as a
forecasting model for short time periods. The persistence model assumes that the output for the current hour will
equal the output from the previous hour. Prior research has generally shown that the persistence model is relatively
accurate for short-term forecasts, but the model loses this accuracy at a high rate as the forecast periods lengthen in
6
time. The power curve model is a basic technique that uses manufacturer’s data to estimate the output of a wind
turbine based on wind speed.
Results and Discussion
As described above, a variety of neural network and regression models were developed in an effort to develop an
accurate prediction model. Table 1 shows the RMSE values for the models developed for the Minnesota WAPSI
wind farm. Figure 1 shows the RMSE values for the top models for the Minnesota WAPSI wind farm expressed as
a bar graph by forecast time period.
Figure 1 and Table 1 illustrate that the neural network models generally perform the best over the different forecast
time periods for the Minnesota wind farm. The neural models, in particular the neural persistence model and the
model developed using wind speed, wind speed squared, wind speed cubed, and the two lag variables, perform well
for the forecast periods beyond one hour. In order to demonstrate performance comparable to the persistence model
for the shorter time periods (i.e., one hour), the models, whether regression models or neural models, needed a lag
variable. Without a lag variable, a model typically performed poorly until forecast periods of 12 and 24 hours were
considered. As the forecast period increased, the benefit of the lag variable typically decreased, and model
performance became more dependent on the wind speed variables.
Table 2 shows the RMSE values for the models developed for the Oklahoma wind farm, and Table 3 shows the
RMSE values for the Vermont wind farm models. Figures 2 and 3 show the RMSE values for the top models for the
Oklahoma and Vermont wind farm, respectively, expressed as a bar graph by forecast time period.
The results of modeling the Oklahoma wind farm were somewhat different than the Minnesota results. As shown in
Figure 2, regression models typically outperformed neural network models. Consistent with the Minnesota
modeling results, the lack of a lag variable in a model disadvantaged that model for short-term forecasts compared to
models that incorporated a lag variable. Using a lag variable and change-in-lag variable proved to be beneficial
even in longer-term forecasts.
7
The Vermont modeling results continue to show the benefit of using a lag variable to provide the most accurate
short-term forecasts of wind farm output. Similar to Minnesota’s results, neural networks were able to outperform
regression, with the neural model that used the wind variables and lag variable being the best or near-best
performing model for all forecast time periods. However, as the forecast time period increases, the performance
results for all of the top-performing, non-persistence Vermont models converge, with the neural models
demonstrating a slight advantage over the regression models.
Finally, Figure 4 and Table 4 show a comparison of the RMSE percentage values for the top performing models for
each of the three wind farm locations considered in this analysis. The RMSE percentage metric allows for an
apples-to-apples comparison of the model performance at the different wind farm locations. Figure 4 demonstrates
that the models created for the Minnesota wind farm are the best performing models with the lowest RMSE
percentage values. The Oklahoma models have moderately high RMSE percentage values, and the Vermont models
have the highest RMSE percentage values. This is likely due to the greater spatial diversity provided by larger wind
farms.
All of the top models created for this project were able to perform better than the basic forecasting techniques of the
power curve model and the persistence model, both of which proved to be inaccurate in longer-term forecasting.
Conclusions
This project included a significant amount of modeling of the electrical output of three different wind farms – one in
Minnesota, Oklahoma, and Vermont. Each wind farm differed substantially in size and location and was chosen
specifically to determine how wind farm size might affect the overall results. The modeling used different
mathematical techniques, with an emphasis on artificial neural networks, to determine the best performing modeling
approach for each wind farm for forecast periods ranging from one hour to 24 hours.
My hypothesis for this project is that by using regression analysis, artificial intelligence systems, and certain
variables that have a high correlation to wind farm production, a mathematical model can be made that can
accurately forecast wind farm production for various lengths of time for wind farms of different sizes and locations.
8
This hypothesis was shown to be partially true. Mathematical models can be made to accurately predict wind farm
production, but no one mathematical model or technique is best for all wind farms or for all time periods. Both
neural network and regression models were top performers, depending on the location and forecast time period.
For the Minnesota and Vermont wind farms, the neural network models performed best. For the Oklahoma wind
farm, although the neural network models performed well, the regression models performed slightly better for most
of the forecast time periods.
Electric utility grid operators and wind farm owners desiring to accurately forecast the output of their wind farms
should consider a variety of forecasting techniques to determine which technique works best for their particular
circumstance. However, this project did identify key factors that should be considered:
1. For short-term forecasts (one to six hours), using a minimal number of explanatory variables is most
effective. In particular, using a lag variable that reflects the prior hour’s output or change in output is
critical for short-term forecast accuracy.
2. The accuracy benefits of a lag variable diminish for forecast periods approaching 12 to 24 hours and likely
beyond. For these longer forecast time periods, explanatory input variables should include forecasts of
wind speed-related variables (wind speed, wind speed squared, and wind speed cubed).
3. Forecast accuracy will be higher as wind farm size increases. In this analysis, the RMSE values for the
Minnesota wind farm forecasts approximately doubled between one and 24 hours. For the smaller
Oklahoma wind farm, the RMSE values nearly tripled between the one and 24-hour forecasts, and the
RMSE values for the very small Vermont wind turbine increased by nearly a factor of nine between the one
and 24-hour forecasts.
This project showed that relatively straightforward models can be developed and trained to accurately forecast
hourly wind farm output, regardless of the size and location of that wind farm. Accurate predictions of wind farm
output can help minimize operational concerns created by wind farms and improve utility system reliability and
economics. This, in turn, will likely encourage renewable energy development using wind energy.
9
References/Bibliography Akilimali, Jean S.; Richardo Bessa; Audun Botterud; Hrvoje Keko; Vladmimiro Miranda; and Jianhui
Wang. Wind Power Forecasting and Electricity Market Operations. Argonne National Laboratory. April
6, 2010. Web.
Berry, Michael J. A. and Gordon S Linoff. Data Mining Techniques. Wiley Computer Publishing. 2004.
Print.
Butler, Charles and Caudill, Maureen. Naturally Intelligent Systems. Massachusetts Institute of
Technology. 1990. Print.
Cataloa, J.P.S.; V.M.F. Mendes; and H.M.I. Pousinho. An Artificial Neural Network Approach for Short-
Term Wind Power Forecasting in Portugal. November 2009. Web.
Chuanwen, Jiang; Liu Hongling; Ma Lei; Zhang Yan. A Review on the Forecasting of Wind Speed and
Generated Power. Science Direct. Volume 13, Issue 4. May 2009.
Crichton, Nicola. Regression Analysis. Blackwell Science. January 10, 2010. Web.
Giebel, Gregor and George Kariniotakis. Best Practice in Short-Term Forecasting. A Users Guide. Riso
National Laboratory for Sustainable Energy, DTU. June 2009. Web.
Giesselmann, Michael G.; Shuhui Li; Edgar O’Hair; and Donald C. Wunsch. Comparative Analysis of
Regression and Artifical Neural Network Models for Wind Turbine Power Curve Estimation. Journal of
Solar Energy Engineering. November 2001, Volume 123.
Kandel, Eric; Thomas Jessell, and James Schwartz. Principles of Neural Science. McGraw-Hill
Medical; 4 Edition. 2000. Print.
Li, Lingling; Chengshan Wang; Minghui Wang; and Fenfen Zhu. Wind Power Forecasting Based on
Time Series and Neural Network. December 2009. Web.
Smith, Murray. Neural Networks for Statistical Modeling. Van Nostrand Reinhold Publishing. 1993.
Print.
Wind Power Forecasting: State-of-the-Art 2009. Argonne National Laboratory. 2009. Web.
10
Figures and Tables
11
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
1-Hour Forecast 6-Hour Forecast 12-Hour Forecast 24-Hour Forecast
RM
SE
Figure 1 - Selected Minnesota Models
Power Curve Model
Persistence Model
Full Input Regression (no lag)
Regression Model (Wind Speed and 1-hour Lag)
Neural FA Inputs: Wind, Wind^2,Wind^3 Non-Std.
Neural FA Inputs: Wind, Wind^2,Wind^3 Lag and Change in Lag
Neural FA: Persistence
12
0
5000
10000
15000
20000
25000
1-Hour Forecast 6-Hour Forecast 12-Hour Forecast 24-Hour Forecast
RM
SEFigure 2 - Selected Oklahoma Models
Power Curve Model
Persistence Model
Regression: MN and OMPA Lag and Change in Lag
Persistence Regression
Regression: Wind,
Wind^2, Wind^3, Lag, Change in Lag
Neural FA, Tulsa
Weather: Wind, Wind^2,Wind^3, Lag and Change in Lag
Time-Series Network: Wind, Wind^2, Wind^3 15 PE
13
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1-Hour Forecast 6-Hour Forecast 12-Hour Forecast 24-Hour Forecast
RM
SEFigure 3 - Selected Vermont Models
Power Curve Model
Persistence Model
Regression: Wind, Wind^2, Wind^3, Lag, Change in Lag
Regression: Lag and Change in Lag
Neural FA Burlington Weather: Wind, Wind^2, Wind^3
Neural Persistence
Neural FA: Wind, Wind^2, Wind^3, Lag
14
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
1-Hour Forecast 6-Hour Forecast 12-Hour Forecast 24-Hour Forecast
RM
SE/A
vera
ge F
arm
Ou
tpu
tFigure 4 - RMSE Percentage Values for Selected MN, OK, and VT
Models
MN: Neural FA: Persistence
MN: Neural GFF MN and OMPA applied to OMPA: Wind, Wind^2,Wind^3 Lag
and Change in Lag
OK: Persistence Regression
OK: Regression: MN and OMPA Lag and Change in Lag
VT: Neural FA: Wind, Wind^2, Wind^3, Lag
VT: Neural Persistence
15
1-Hour
Forecast
6-Hour
Forecast
12-Hour
Forecast
24-Hour
Forecast
Power Curve Model 34,198 34,198 34,198 34,198
Persistence Model 10,457 24,568 29,444 37,044
Regression ModelsRegression: Roch, OMPA Lag and Change in Lag Combined 10,185 19,271 23,476 29,122
Regression Model (1-hour Lag and Change in Lag) 10,196 22,071 25,813 30,284
Regression: Roch, OMPA Wind, Wind^2, Wind^3, Lag, Change in Lag Combined 10,205 18,278 21,705 24,081
Regression Persistence 10,327 19,365 24,230 29,604
Regression Model (Wind Speed and 1-hour Lag) 10,473 18,018 20,726 22,103
Full Input Regression (1-Hour Lag) 11,403 25,337 27,251 32,113
Regression: Wind Speed, Wind Speed^2, Wind Speed^3, Lag, Change in Lag 15,538 19,539 20,145 20,802
Full Input Regression (no lag) 42,175 42,175 42,175 42,175
Neural Network ModelsNeural FA: Persistence 10,268 14,719 17,078 19,547
Neural FA Inputs: Lag and Change in Lag 10,315 15,811 19,972 23,313
Neural FA Inputs: Wind, Wind^2,Wind^3 Lag and Change in Lag 10,356 15,166 18,431 20,520
Neural GFF MN and OMPA applied to OMPA: Wind, Wind^2,Wind^3 Lag and Change in Lag 10,368 14,895 17,977 20,303
Neural FA Inputs: Wind, Wind^2,Wind^3, and Lag 10,574 19,438 20,285 21,454
Neural GFF rom MN and OMPA applied to MN: Lag and Change in Lag 15 PE 11,802 19,431 25,115 29,916
Neural FA Inputs: Wind, Wind^2,Wind^3 Non-Std. 20,367 20,367 20,367 20,367
Neural FA: Wind, Wind^2, Wind^3 20,395 20,395 20,395 20,395
Neural FA Inputs: Wind, Wind^2,Wind^3 20,419 20,419 20,419 20,419
Neural Function Approximation, no lag, minimal independent variables, standardized 21,678 21,678 21,678 21,678
Time-Series Network: Wind, Wind^2, Wind^3 15 PE 22,029 22,029 22,029 22,029
Multilayer perceptron, 1 hidden layer, no lag, standardized 23,132 23,132 23,132 23,132
Neural Function Approximation, no lag, non-standardized 25,782 25,782 25,782 25,782
Fuzzy, no lag, standardized 26,388 26,388 26,388 26,388
Generalized Feed Forward, 2 hidden layers, no lag, standardized 27,479 27,479 27,479 27,479
Time Series Neural, no lag, non-standardized 29,296 29,296 29,296 29,296
Recurrent, no lag, non-standardized 37,746 37,746 37,746 37,746
Neural Function Approximation, (Not minimized on cross validation), no lag, non-standardized 40,580 40,580 40,580 40,580
Fuzzy, no lag, non-standardized 55,990 55,990 55,990 55,990
Multilayer Perceptron, 9 PE: Wind, Wind^2, Wind^3 20,311 20,311 20,311 20,311
Minnesota Model RMSE Values on Testing Data Using Observed Weather
Table 1
16
1-Hour
Forecast
6-Hour
Forecast
12-Hour
Forecast
24-Hour
Forecast
Power Curve Model 21,477 21,477 21,477 21,477
Persistence Model 5,721 11,324 14,756 17,329
Regression ModelsRegression: MN and OMPA Lag and Change in Lag 5,498 13,447 15,152 16,291
Regression: Lag and Change in Lag 5,510 10,507 13,315 15,400
Regression: Wind, Wind^2, Wind^3, Lag, Change in Lag 5,519 10,524 13,284 15,347
Persistence Regression 5,658 10,560 13,230 15,163
Regression: MN and OMPA Wind, Wind^2, Wind^3, Lag, Change in Lag 5,724 11,874 15,472 17,778
Neural Network ModelsNeural FA, Tulsa Weather: Wind, Wind^2,Wind^3, Lag and Change in Lag 5,573 10,008 14,030 17,535
Neural GFF, Tulsa Weather: Lag and Change in Lag with 10 PE 5,586 10,084 14,102 17,796
Neural GFF, Tulsa Weather: Wind, Wind^2, Wind^3, 15 PE 16,770 16,770 16,770 16,770
Neural GFF MN and OMPA applied to OMPA: Wind, Wind^2,Wind^3 Lag and Change in Lag 6,196 24,530 25,845 26,423
Neural GFF, MN and OMPA applied to OMPA: Lag and Change in Lag 15 PE 6,424 24,981 26,185 26,715
Time-Series Network, Tulsa Weather: Wind, Wind^2, Wind^3 15 PE 17,630 17,630 17,630 17,630
Neural FA, Tulsa Weather: Wind, Wind^2, Wind^3 16,711 16,711 16,711 16,711
Neural Persistence, Tulsa Weather 5,634.1 10,246.1 14,309.8 17,917.7
Neural FA, Tulsa Weather: Lag and Change in Lag 5,540.4 9,868.7 13,885.0 17,661.5
Neural FA, Tulsa Weather: Wind, Wind^2, Wind^3, Lag 5,629.9 10,300.3 14,781.6 19,032.0
Oklahoma Model RMSE Values on Testing Data Using Observed Weather
Table 2
17
1-Hour
Forecast
6-Hour
Forecast
12-Hour
Forecast
24-Hour
Forecast
Power Curve Model 1.090 1.090 1.090 1.090
Persistence Model 0.207 0.815 1.102 1.237
Regression ModelsRegression: Wind, Wind^2, Wind^3, Lag, Change in Lag 0.404 0.709 0.822 0.918
Regression: Lag and Change in Lag 0.407 0.702 0.822 0.928
Regression: Persistence 0.442 0.712 0.841 0.939
Regression: Wind Speed and Lag 0.444 0.713 0.834 0.927
Neural Network ModelsNeural GFF, Burlington Weather: Lag and Change in Lag with 5 PEs 0.133 0.544 0.759 0.893
Neural FA, Burlington Weather: Lag and Change in Lag with 10 PEs 0.146 0.522 0.745 0.916
Neural GFF, Burlington Weather: Wind, Wind^2, Wind^3, Lag and Change in Lag with 5 PE 0.168 0.572 0.789 0.920
Neural FA, Burlington Weather: Wind, Wind^2, Wind^3 0.917 0.917 0.917 0.917
Time-Series Network, Burlington Weather: Wind, Wind^2, Wind^3 15 PE 0.998 0.998 0.998 0.998
Neural Persistence, Burlington Weather 0.099 0.505 0.725 0.880
Neural FA, Burlington Weather: Wind, Wind^2, Wind^3, Lag 0.124 0.483 0.695 0.852
Vermont Model RMSE Values on Testing Data Using Observed Weather
Table 3
18
1-Hour
Forecast
6-Hour
Forecast
12-Hour
Forecast
24-Hour
Forecast
Power Curve ModelsPower Curve Model - MN 0.91 0.91 0.91 0.91
Power Curve Model - OK 1.03 1.03 1.03 1.03
Power Curve Model - VT 1.95 1.95 1.95 1.95
Persistence ModelsPersistence Model - MN 0.2774 0.6518 0.7812 0.9828
Persistence Model - OK 0.2741 0.5425 0.7069 0.8302
Persistence Model - VT 0.3696 1.4551 1.9667 2.2081
Top Regression ModelsMN: Regression: Roch, OMPA Lag and Change in Lag Combined 0.2702 0.5113 0.6228 0.7726
MN: Regression: Wind Speed, Wind Speed^2, Wind Speed^3, Lag, Change in Lag 0.4122 0.5184 0.5345 0.5519
OK: Regression: MN and OMPA Lag and Change in Lag 0.2634 0.6442 0.7259 0.7804
OK: Persistence Regression 0.2711 0.5059 0.6338 0.7264
VT: Regression: Wind, Wind^2, Wind^3, Lag, Change in Lag 0.7221 1.2650 1.4674 1.6397
VT: Regression: Wind Speed and Lag 0.7922 1.2734 1.4891 1.6542
Top Neural Network ModelsMN: Neural FA: Persistence 0.2724 0.3905 0.4531 0.5186
MN: Neural GFF MN and OMPA applied to OMPA: Wind, Wind^2,Wind^3 Lag and Change in Lag 0.2751 0.3952 0.4769 0.5387
OK: Neural FA: Lag and Change in Lag 0.2654 0.4728 0.6652 0.8461
OK: Neural FA, Tulsa Weather: Wind, Wind^2,Wind^3, Lag and Change in Lag 0.2670 0.4795 0.6721 0.8401
VT: Neural Persistence 0.1772 0.9025 1.2951 1.5706
VT: Neural FA: Wind, Wind^2, Wind^3, Lag 0.2205 0.8616 1.2416 1.5210
RMSE Values on Testing Data Using Observed Weather - RMSE/Mean Farm Output
Table 4
