1. Simulation of Wind Generation in Resource Adequacy Assessments Mary Johannis, Bonneville Power Administration

2. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 2 Topics of Discussion Backcast of Wind Generation Correlation of Wind Generation and Temperature Creation of Synthetic Wind Generation Records –Correlated with temperature –Exhibiting observed persistence Do recent Extreme Temperature Events Capture Historical Variability?

3. Backcast of Wind Generation This topic and others investigated by Ben Kujala, BPA Student Intern

4. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 4 Backcast Prerequisites Borismetrics Contract identified problem with trying to backcast wind generation using off-site anemometer data:  no unique function In order to backcast, prerequisites include: –Long-term clean anemometer data record, on-site if possible –Good correlation between anemometer data & wind generation

5. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 5 Lack of Anemometer Data

6. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 6 Vansycle Backcast Case Study Vansycle has an anemometer on-site –½ mile from the nearest generator –6 miles from the furthest generator Wind speed data is available in 10 minute intervals for period Scada data is available in 5 minute intervals for period Vansycle Backcast should be doable –Relatively long-term Generation Record –Relatively clean Anemometer Record Wind Turbine Power Characteristics: –Cut-in wind speed 4 m/s (8.9 mph) –Nominal wind speed 15 m/s (33.6 mph) –Stop wind speed 25 m/s (55.9 mph)

7. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 7 Evaluating Correlation between Anemometer and Wind Generation Data R 2 may overstate model validity especially if there are a lot zero generation observations. Frequency of zero generation: –When anemometer measured speeds below cut-in there was zero (or less) generation 74.3% of the time. –From cut-in to nominal wind speed there was zero generation 12.42% of the time. –From nominal to stop wind speed there was zero generation 3.19% of the time. –Above stop wind speed there was zero generation 57.26% of the time. Residual Analysis is important

8. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 8 Developing the Model Model needs to respect wind turbine characteristics –If wind speed < 8.95 mph then adjusted wind capacity = 0 –If wind speed >= 8.95 and <= 33.6 then wind capacity (rolling average) is correlated with a function of (wind speed – 8.95)/(33.55-8.95) –If wind speed > 33.6 and <= 55.9 then adjusted wind capacity = 1 –If wind speed > 55.9 then adjusted wind capacity = 0 Cubic polynomial regression was applied to the adjusted wind speed (after centering) and used to predict the rolling capacity –Initial R 2 =.7266 after excluding zero generation –Residual analysis indicates problem with initial model

9. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 9 Residual Analysis Residuals are the difference between the observation and the proposed model (fits). –Ideally residuals should be evenly scattered about zero for any given wind speed. That is the model should pass through the “middle” of the observed data. –Rather than simply looking at the model, it is sometimes easier to examine a residual plot where residuals are plotted against various other variables. A good model will have evenly scattered residuals that are roughly in a rectangular region about the zero line in a residual plot.

10. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 10 Initial Regression Residuals Residuals all above or below zero

11. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 11 20 MPH Baseline Prediction Interval Adjusted Wind Capacity is (20 – 8.95)/(33.55-8.95)=.449 –Centered is.449 -.284 =.165 –The Fit is –Prediction interval is.721346 ±.147852 or (.573494,.869198) if parametric assumptions hold or are approximately close enough. Prediction interval formula is: –Where Putting R 2 in perspective – s 2 {pred}=.004616 is the variance with the regression model, without the regression model s 2 =.1521, thus there is significant reduction in variance based on the regression relation. However, that doesn’t necessarily mean the prediction interval is small enough to give useful extrapolations.

12. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 12 Revised Regression 1/ Analysis of Variance SourceDFSum of Squares Mean Square F ValuePr > F Model3125.2634741.754496781.78<.0001 Error15499.536980.00616 Corrected Total1552134.80045 Root MSE0.07847R-Square0.9293 Dependent Mean0.62331Adj R-Sq0.9291 Coeff Var12.58856 Parameter Estimates VariableDFParameter Estimate Standard Error t ValuePr > |t|Variance Inflation Intercept10.176500.0051234.51<.00010 AdjWind_3_co11.002970.0831912.06<.00011.98117 lagRollCap_co11.086670.0118891.51<.00012.01284 Freezing1-0.008530.00451-1.890.05851.03379 R-squared is fairly high and no issues with Variance Inflation Factors. This is without zero generation. 1/ multivariate regression after Cochran-Orcutt

13. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 13 Residual for Revised Regression Residuals vs. Wind SpeedResiduals vs. Predicted Capacity

14. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 14 20 MPH Prediction Interval Since this is a multivariate model to come up with a prediction interval we need to have lags for the model too, so it’s not exactly a 20 MPH Prediction Interval…. –Looking through the data we had close to 20 MPH wind with the following lag: Rolling Capacity: First Lag - 0.55872 Assuming temperature above freezing –The fit is.8698: That translates to sin(.8698)^2 =.5840 Rolling Capacity Prediction Interval is.8698 ±.1539 or (.7158, 1.0237) which translates to a Rolling Capacity interval of (.4306,.7294). –Parametric assumptions are now based on observed residual plots and variables that are transformed to eliminate autocorrelation. –Range is.2987925 which is a bit expanded after the model assumptions have been met.

15. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 15 Conclusions Lessons learned: –High R 2 of multivariate regression (without zeros) and residual analysis indicates that Persistence is an important feature in regression –Other regressions have artificially high R 2 by including zeros –Prediction interval of.3 is not sufficiently tight to backcast Backcasting Wind Generation for NW is NOT feasible –Even on-site wind anemometers can be miles from some wind turbines resulting in the LACK of a unique correlation –Due to the persistence feature of the regression cannot use other means to reflect randomness in the correlation –Insufficient on-site anemometer data to backcast the entire NW wind generation fleet

16. Correlation of Wind Generation and Temperature

17. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 17 Wind Speed/Temperature Correlations Cumulative probability graphs for wind speed vs. on- site temperature show decrease in wind speed for High and Low temperatures What about correlation between wind speed and load center temperatures? Minimum and Maximum Temperatures are averaged in each of the Load Centers then Averaged together Correlation in tact—see following graphs

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23. Recommendation to Create Synthetic Wind Generation Records Correlated with Historic Temperature

24. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 24 Creating Valid Long-term Synthetic Data Records Kennewick Presentation at 8/14/08 Forum Wind Assessment Team Meeting provides support that short-term wind attributes ~ long-term wind attributes  historical wind generation can be used to create synthetic data that mimics long-term record Synthetic data should have the same, or at least a very similar distribution as observed data. Synthetic data should preserve the structure of observed data. –For instance, with wind generation data it is important to maintain persistence. Purely Synthetic data should not lead to fundamentally different conclusions than the observed data would warrant.

25. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 25 Creating a Synthetic Historical Record with the Question in Mind What questions are the studies trying to answer? –Is wind generation related to hydro generation? –Is wind generation related to demand because both are correlated to temperature? –Is there seasonality in wind generation? –How can wind uncertainty be correctly modeled in the tails, i.e. when Loss of Load may occur? The problem with using something other than a time span as the selection criteria is that wind generation is a time series, so to break apart the observations and not maintain order means that there must be some other way to maintain the structure of the data

26. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 26 What is the Kth Nearest Neighbor Method? Given a time series of size N, a possible approach to creating synthetic data is to randomly select a single or two consecutive of the N observations then select the third based on how “close” the lag(s) for the selected observation are to the randomly selected observation(s). –For example, if we select two hours where the capacity is.3 the first and.4 the second, then look through the data and pull from observations that have capacities that are close to.3 for the observation 2 hours prior and.4 for the hour prior. –Creating a subset of the K “closest” observations to draw from maintains the structure that is expected in the time series.

27. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 27 Why Use Kth Nearest Neighbor? This methodology appears to complicated for no comprehensible gain; HOWEVER... –It does create a feasible data set –It allows us to leverage what we know about the past (e.g. historical temperatures) to create records that would be “closer” to what the reality would have been had the wind generation been there It requires serious computer power –using VB I to create a very basic synthetic data set for a single month (30 days) took 400 minutes (6 hours 40 minutes) to create. –To create a 30 year record would take approximately 400*12*30=144000 minutes (2400 hours or 100 days). –That said, there is certainly room for improvement in the software and hardware used. Also, I used 2 lags, one would take less time.

28. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 28 Comparability All synthetic data sets should be compared to one another. Creating data sets without some sort of baseline comparison is definitely not recommended. They should be consistent with actual observations and other synthetic data. The improvements should be seen in specific areas such as load comparison where there is a rational explanation for simulated effects.

29. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 29 Develop Proof of Concept of Kth Nearest Neighbor Synthetic Data Methodology BPA is pursuing Contract with contract with Portland State University to provide statistical review of methodology –Ben Kujala will develop proof of concept Long-term Alternatives –If Proof of Concept successful, create long-term Synthetic Wind Generation set that is correlated to temperature for partial or entire data set –Explore other Synthetic Data Alternatives

30. An Examination of Historical Temperature Extremes BPA Investigation by Peggy Miller 10/16/08

31. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 31 Do recent temperature extremes capture variations in historical record? Examine historical record –Daily minimum (min) and maximum (max) temperature readings (back to 1948) –Seattle, Portland, Spokane and weighted load center average (weights: 36%, 36%, and 28% respectively) –Search for ‘best fitting’ regression equations to model patterns in average annual min and max graphs Identify upper and lower 90 th %tiles of min and max historical distributions during winter and summer (ie. define seasonal extreme temps) –Examine seasonal extreme temp days each year

32. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 32 Historical Annual Ave Min Temps

33. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 33 Historical Annual Ave Max Temps

34. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 34 Cold Winter Nights Daily Minimums Below 90 th %tile

35. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 35 Cold Winter Days Daily Maximums Below 90 th %tile

36. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 36 Hot Summer Nights Daily Minimums Above 90 th %tile

37. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 37 Hot Summer Days Daily Maximums Above 90 th %tile

38. November 14, 2008PNW Resource Adequacy Technical Committee Meeting 38 Conclusions The data suggest that the average annual mins and maxes have significantly increased about 2.4 °F (~0.04 °F * 60 years) since 1948 in Portland, Seattle and on a weighted load center basis. (Note that these temp increases are not necessarily due to global warming. Variables such as population, urbanization, albedo, possible long term cyclical nature, etc. were not included in the model) Overall, temp extremes during recent years do capture historical variations in temp extremes, but are slightly warmer than the 60-year mean in keeping with the trend of increasing temperature