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J. McCalley

J. McCalley. Wind Power Variability in the Grid: Regulation. Summary of power balance control levels. Completed. Completed. Topic of these slides. =. +. Load Following. Regulation. Obtaining regulation component. How to get the time series of the regulation component?.

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J. McCalley

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  1. J. McCalley Wind Power Variability in the Grid: Regulation

  2. Summary of power balance control levels Completed. Completed. Topic of these slides.

  3. = + Load Following Regulation Obtaining regulation component How to get the time series of the regulation component? Steve Enyeart, “Large Wind Integration Challenges for Operations / System Reliability,” presentation by Bonneville Power Administration, Feb 12, 2008, available at http://cialab.ee.washington.edu/nwess/2008/presentations/stephen.ppt. 3

  4. Obtaining regulation component Define Lk, LFk, and LRk as the load, load following component, and regulation component, respectively, at time k∆t. Assume that the load, Lk, is given for k=1,…,N. The load-following component is given by a moving average of length 2T time intervals, i.e., Example: Load data taken at ∆t=2 minute intervals, and compute LFk based on a 28 minute rolling average. So T was chosen as 7, resulting in When k=20 (the 20th time point), then B. Kirby and E. Hirst, “Customer-Specific Metrics for The Regulation and Load-Following Ancillary Services,” Report ORNL/CON-474, Oak Ridge National Laboratories, Energy Division, January 2000... 4

  5. Obtaining regulation component A result of this computation, where it is clear that the moving average tends to smooth the function. Once the load following component is obtained, then the regulation component can be computed from Then you can compute the deviations for a desired time interval, e.g., 2, 5, 10 minutes, and then obtain the corresponding standard deviation of the resulting distribution. R. Hudson, B. Kirby, and Y. Wan, “Regulation Requirements for Wind Generation Facilities,” available at http://www.consultkirby.com/files/AWEA_Wind_Regulation.pdf. 5

  6. Temporal variability of wind power • For fixed speed machines, because the mechanical power into a turbine depends on the wind speed, and because electric power out of the wind generator depends on the mechanical power in to the turbine, variations in wind speed from t1 to t2 cause variations in electric power out of the wind generator. • Double-fed induction generators (DFIGs) also produce power that varies with wind speed, although the torque-speed controller provides that this variability is less volatile than fixed-speed machines. • For a single turbine, this variability depends on three features: (1) time interval; (2) location; (3) terrain. 6

  7. Temporal variability of wind power – time interval Source: Task 25 of the International Energy Agency (IEA), “Design and operation of power systems with large amounts of wind power: State-of-the-art report,” available at www.vtt.fi/inf/pdf/workingpapers/2007/W82.pdf. 7

  8. Temporal variability of wind power – location and terrain “In medium continental latitudes, the wind fluctuates greatly as the low-pressure regions move through. In these regions, the mean wind speed is higher in winter than in the summer months. The proximity of water and of land areas also has a considerable influence. For example, higher wind speeds can occur in summer in mountain passes or in river valleys close to the coast because the cool sea air flows into the warmer land regions due to thermal effects. A particularly spectacular example are the regions of the passes in the coastal mountains in California through to the lower lying desert-like hot land areas in California and Arizona.” 8 Reference: E. Hau, “Wind turbines: fundamentals, technologies, applications, economics,” 2nd edition, Springer, 2006.

  9. Spatial variability of wind power – geographical smooting from geo-diversity 1 turbine. 1 wind plant. All turbines in region. Variability of single turbine, as percentage of capacity, is significantly greater than the variability of wind plant, which is significantly greater than variability of the region. Source: Task 25 of the International Energy Agency (IEA), “Design and operation of power systems with large amounts of wind power: State-of-the-art report,” available at www.vtt.fi/inf/pdf/workingpapers/2007/W82.pdf. 9

  10. Spatial variability of wind power – geographical smoothing from geo-diversity Single turbine reaches or exceeds 100% of its capacity for ~100 hours per year, the area called “Denmark” has a maximum power production of only about 90% throughout the year, and the overall Nordic system has maximum power production of only about 80%.  At other extreme, single turbine output exceeds 0 for about 7200 hours per year, leaving 8760-7200=1560 hours it is at 0. The area wind output rarely goes to 0, and the system wind output never does. Duration curve: provides number of hours on horizontal axis for which wind power production exceeds the percent capacity on the vertical axis. You can divide the horizontal by 8760 hours and then switch the axes to obtain a cumulative distribution function. H. Holttinen, “The impact of large-scale power production on the Nordic electricity system,” VTT Publications 554, PhD Dissertation, Helsinki University of Technology, 2004. 10

  11. Spatial variability of wind power – geographical smoothing from geo-diversity 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 The cumulative distribution function (CDF) can be used to characterize the past and provide predictions of the future in regards to the percentage of time the wind output of a given turbine, plant, or region will exceed a given level. This can be useful in making decisions about building other plants and/or building transmission. 0 10 20 30 40 50 60 70 80 90 100 H. Holttinen, “The impact of large-scale power production on the Nordic electricity system,” VTT Publications 554, PhD Dissertation, Helsinki University of Technology, 2004. 11

  12. Temporal & spatial variability of wind power Correlation coefficient between time series of intervals taking averages of T=5 min, 30 min, 1 hr, 2 hr, 4 hr, 12 hr, for multiple locations, as a function of distance between those locations. For example, this point indicates that the time series for two points 100 miles apart, when taking 2 hour averages, is correlated at 0.35. The correlation coefficient indicates how well 2 time series follow each other. It will be near 1.0 if the 2 time series follow each other very well, it will be 0 if they do not follow each other at all. For 5min averages, there is almost no correlation for locations separated by more than ~20 km, since wind gusts tend to occur for only relatively small regions. This suggests that that even small regions experience geographical smoothing at 5min averages. For 12hr averages, wind power production is correlated even for very large regions, since these averages are closely linked to overall weather patterns that can be similar for very large regions. H. Holttinen and Ritva Hirvonen, “Power System Requirements for Wind Power,” in “Wind Power in Power Systems,” editor, T. Ackermann, Wiley, 2005. 12

  13. Spatial variability of wind power – geographical smoothing from geo-diversity The variability of the 1 farm, given as a percentage of its capacity, is significantly greater than that of the entire region of Western Denmark. International Energy Agency,”VARIABILITY OFWIND POWER AND OTHER RENEWABLES: Management options and strategies,” June 2005, at http://www.iea.org/textbase/papers/2005/variability.pdf. 13

  14. Temporal & spatial variability of wind power If data used to develop the fig on the last slide is captured for a large number of wind farms and regions, the standard deviation may be computed for each farm or region. This standard deviation may then be plotted against the approximate diameter of the farm’s or region’s geographical area. Above indicates that hourly variation, as measured by standard deviation, decreases with the wind farm’s or region’s diameter. Task 25 of the International Energy Agency (IEA), “Design and operation of power systems with large amounts of wind power: State-of-the-art report,” available at www.vtt.fi/inf/pdf/workingpapers/2007/W82.pdf. 14

  15. Variability of load These plots show that the particular control area responsible for balancing this load must have capability to ramp 400 MW in one hour (6.7 MW/min), 80 MW in 10 minutes (8 MW/min), and 10 MW in one minute (10 MW/min) in order to meet all MW variations seen in the system. 15

  16. Net load What happens to these requirements if wind is added to the generation portfolio? Because wind is not controllable the non-wind generation must also meet its variability. The composite variability that needs to be met by the wind is called the net load. If we plot the distribution (histogram) for net load variation, we will find it is wider than the distribution for load alone. 16

  17. Variability of net load Net load is red. Load is blue. These plots show that if the particular control area is responsible for balancing only this load, then it must have capability to ramp 300 MW in one hour (5 MW/min), but…. If the control area is responsible for balancing the net load, it must have capability to ramp 500 MW is one hour (8.33MW/min). 17

  18. Variability of net load The net load relationship must treat PL and Pw (or their deviations) as random variables. So the real question is this: Given two random variables x (load deviation) and y (wind power deviation) for which we know the distributions fx(x) and fY(y), respectively, how do we obtain the distribution of the net-load random variable z=x-y, fz(z)? Answer: For the means, μz=μx-μy, and, if these random variables are independent, then for the variances, σz2= σx2+σy2. 18

  19. Variability of net load μz=μx-μy, σz2= σx2+σy2. The impact on the means is of little interest since the variability means, for both load and wind, will be ~0. On the other hand, the impact on the variance is of great interest, since it implies the distribution of the difference will always be wider than either individual distribution. Therefore we expect that when wind generation is added to a system, the maximum MW variation seen in the control area will increase, as seen on slide 20. 19

  20. Correlation between ΔPL and ΔPw It may be that load variation and wind variation are not independent, but rather, that they may tend to change in phase (both increase or decrease together) or in antiphase (one increases when the other decreases). We capture this with Pearson’s correlation coefficient: where N is the number of points in the time series, and μx, μy and σx, σy are the means and standard deviations, respectively, of the two time series. 20

  21. Correlation between ΔPL and ΔPw The correlation coefficient measures strength and direction of a linear relationship between two random variables. It indicates how well two time series, x and y, follow each other. It will be near 1.0 if the two time series follow each other very well, it will be 0 if they do not follow each other at all, and it will be near -1 if increases in one occur with decreases in another. 21

  22. Correlation between ΔPL and ΔPw • If two variables are independent, they are uncorrelated and rxy=0. • If rxy=0, then the two variables are uncorrelated but not necessarily independent, because rxy­ detects only linear dependence between variables. • A special case exists if X and Y are jointly normal, i.e., that aX+bY is normal for any chosen scalars a and b. In this case, rxy=0 implies independence. We assume this is the case for our regulation data, i.e., that if X is load deviation and Y is wind deviation, that aX+bY is normal. • If rxy=1 or if rxy=-1, then X and Y are dependent. • If X and Y are jointly normal, then for values of rxy such that 0<|rxy|<1, the correlation coefficient reflects the degree of dependence between the two variables, or conversely, the departure of the two random variables from independence. 22

  23. Using variance and correlation to measure regulation coincidence We will use four ideas in what follows: We assume that load and wind variations are jointly normal. In this case, rxy can be used to measure independence. Three standard deviations (3σ) of the net load is our measure of “regulation burden.” 4. We assign angles to the standard deviation of each component comprising the net load, so we can treat them as vectors. 23

  24. σz σy σz σz σy σy σx σx σx Using variance and correlation to measure regulation coincidence If two random variables (wind & load variation) are independent, then the variance of their sum (or their difference) is Positive variations in wind MW and load MW are assumed to represent increases. Thus, positive correlation implies that wind variation tends to offset load variation. Fig 1 Consider if time series for wind and load are perfectly correlated, i.e., rxy=1, implying X and Y follow each other perfectly: Consider if time series for wind and load are perfectly anti-correlated, i.e., rxy=-1, implying X and Y change in perfect anti-phase: Fig 3 Fig 2 24

  25. σz σy θ σx Using variance and correlation to measure regulation coincidence Define an angle θ: where rxy ranges from -1 to 0 to 1, θ ranges from 0 to π/2 to π, (as in the three cases illustrated on slide 27), per the below table. What have we done? The figure to the right fits conforms to the three figures on the previous page and the corresponding values of rxy when Then, from Law of cosines: θ=0 (Fig. 3)σZ2=(σX+σY)2 θ=180 (Fig. 2)σZ2=(σX-σY)2 and θ=90 (Fig. 1)σZ2=σX2+ σY2 25

  26. Alternative expression for theta We can also derive the angle θ, as follows… Let random variables Z, X, and Y, not necessarily independent, be related by Z=X-Y. We can obtain from statistics that * where σZ2, σX2, and σY2 are the variances of Z, X, Y, respectively, and σXY is the covariance of X and Y. From slide 20, we have ** Substituting (**) into (*) results in From law of cosines: The above expressions are the same, so This is an exact expression; the previous expression given for theta is a linearized version of this, as illustrated on the next slide. 26

  27. Alternative expression for theta 27

  28. What can you do with it? Consider that a particular ISO projects 10 GW of additional wind in the coming 5 years, and wind data together with knowledge of where the wind farms will be located are available. Then σw and rLw can be estimated, and since we know σL, we may compute σT as: where or Our new “regulation burden” will therefore be 3σT, and we will need to have a generation portfolio to handle this. 28

  29. Example Several very large wind farms in close proximity to one another and within the service area of a certain balancing authority (BA) have 10-minute variability characterized by 3 standard deviations equal to 75 MW. The BA net load previous to interconnection of these wind farms has 10-minute variability characterized by 3 standard deviations equal to 300 MW. The correlation coefficient between the 10-minute variation of the wind farms and that of the BA net load previous to interconnection is -0.5. • Determine the regulation burden of the BA net load after interconnection of the new wind farms. We observe that σw=25, σL=100, and rLw=-0.5. 29

  30. σT σw θ σL Using variance and correlation to measure regulation coincidence Problem: Given the load has a standard deviation of σL and the wind generation has a standard deviation of σw, and the composite of the two (net load) has a standard deviation of σT, then what component of σT can we attribute to the wind generation? To solve this problem, we redraw our figure, where the only change we have made is to re-label according to the nomenclature of this problem. • Should we say that the wind has contributed • an amount of variability equal to σw? • i.e., a regulation burden equal to 3σw? Let’s provide an answer to this question. 30

  31. σT σw X σT - X Y θ σL Using variance and correlation to measure regulation coincidence The contribution of σw to σT will be the projection of the σw vector onto the σT vector, i.e., it will be the component of σw in the σT direction. In the below figure, we have denoted this component as X (we have also defined some additional features in the figure to facilitate analytic development). 31

  32. σT σw X σT - X Y θ σL Using variance and correlation to measure regulation coincidence The smaller right-triangle to the right provides * The larger right-triangle to the left provides: ** Subtracting (**) from (*) results in: Expanding the right-hand-side: which simplifies to: Solving for X results in: X is the “regulation share” of the “generator of interest.” It was applied in [A,B] to different kinds of resources, including wind & solar. It can also be applied to different kinds of loads. [A] B. Kirby, M. Milligan, Y. Makarov, D. Hawkins, K. Jackson, H. Shiu “California Renewables Portfolio Standard Renewable Generation Integration Cost Analysis, Phase I: One Year Analysis Of Existing Resources, Results And Recommendations, Final Report,” Dec. 10, 2003, available at http://www.consultkirby.com/files/RPS_Int_Cost_PhaseI_Final.pdf. [B] H. Shiu, M. Milligan, B. Kirby, and K. Jackson, “California Renewables Portfolio Standard Renewable Generation Integration Cost Analaysis,” May 2006, at http://s3.amazonaws.com/academia.edu.documents/45528680/California_Renewables_Portfolio_Standard20160510-3122-16m0gl0.pdf?AWSAccessKeyId=AKIAJ56TQJRTWSMTNPEA&Expires=1478797127&Signature=Hub3UPS18ILUqXPmGiHUieCYW6Y%3D&response-content-disposition=inline%3B%20filename%3DCalifornia_Renewables_Portfolio_Standard.pdf 32

  33. Example Several very large wind farms in close proximity to one another and within the service area of a certain balancing authority (BA) have 10-minute variability characterized by 3 standard deviations equal to 75 MW. The BA net load previous to interconnection of these wind farms has 10-minute variability characterized by 3 standard deviations equal to 300 MW. The correlation coefficient between the 10-minute variation of the wind farms and that of the BA net load previous to interconnection is -0.5. • Determine the regulation burden of the BA net load after interconnection of the new wind farms. • Determine the regulation share of the new wind farm. 33

  34. How to determine the generation portfolio necessary to handle a given σT ? You should also know the typical operating conditions you expect, and the committed units throughout those operating conditions (from historical data or a production cost simulation). This information will be highly influenced by the spinning reserve requirement. Then a guiding criteria is that for all operating conditions, we would like to satisfy the following relation: SRj is up (or down) “headroom” for unit j, RR is ramp rate of unit j, ΔT is time interval over which σT is computed. Need to update this slide based on [A]. [A] *V. Krishnan, *T. Das, *E. Ibanez, *C. Lopez, and J. McCalley, “Modeling Operational Effects of Variable Generation within National Long-term Infrastructure Planning Software,” Vol. 28, Issue 2, IEEE Transactions on Power Systems, 2013, pp. 1308-1317. 34

  35. How is variability handled in the grid? 35

  36. ECCs: SCADA, Telemetry, EMS, RT, DA Markets EMS Day-ahead market Real-time market Automatic Generation Control (AGC) is a feedback control system that regulates the power output of electric generators to maintain a specified system frequency and/or scheduled interchange. Intra-day & day-ahead reliability unit commitment (RAC) 36

  37. ECCs: SCADA, Telemetry, EMS, RT, DA Markets SCED1, SCED2 dispatch signals provided as “base-points” to AGC which communicates them to gens. SCED1 computes LMPs. Automatic Generation Control (AGC) is a feedback control system that regulates the power output of electric generators to maintain a specified system frequency and/or scheduled interchange. • EMS performs contingency & loss analysis for • SCED1 to perform 5 min RTM solutions to get dispatch and LMPs. • SCED2 to perform redispatch in case RAC changes commitment. Ref: Xingwang Ma, Haili Song, Mingguo Hong, Jie Wan, Yonghong Chen, Eugene Zak, “The Security-constrained Commitment and Dispatch For Midwest ISO Day-ahead Co-optimized Energy and Ancillary Service Market,” Proc. of the 2009 IEEE PES General Meeting. A SCADA scan rate of 2 sec is typical. AGC sends pulses to units every 4 seconds. 37

  38. Balancing Systems ENERGY BUY BIDS DAY-AHEAD MARKET 1 sol/day gives 24 oprtingcdtns min ΣΣ zit{Cost(GENit)+Cost(RSRVit)} sbjct to ntwrk+statuscnstraints ENERGY & RESERVE SELL OFFERS REQUIRED RESERVES LARGE MIXED INTEGER PROGRAM BOTH CO-OPTIMIZE: energy & reserves ENERGY BUY BIDS REAL-TIME MARKET 1 sol/5min gives 1 oprtngcdtn min ΣΣ {Cost(GENit)+Cost(RSRVit)} sbjct to ntwrkcnstraints ENERGY & RESERVE SELL OFFERS REQUIRED RESERVES LARGE LINEAR PROGRAM NETWORK AUTOMATIC GENERATION CONTROL SYSTEM ACE=TIE LINE EXPORT DEVIATIONS FROM SCHEDULE +10B×[FREQUENCY DEVIATION FROM 60 HZ] 38

  39. Summary of power balance control levels WHAT WE ARE STUDYING The real-time market has a secondary influence on the system’s ability to control steady-state frequency because it computes base points based on a net load forecast. The accuracy of this forecast determines how much the units will be moved by AGC and as a result, how much frequency variability is present. We study #3, #4, and #5 of the above table, in this order..

  40. = Regulation & Load Following + #4 Load Following (handled using Real-Time Market) #3 Regulation (handled using AGC) Chart from previous slide Steve Enyeart, “Large Wind Integration Challenges for Operations / System Reliability,” presentation by Bonneville Power Administration, Feb 12, 2008, available at http://cialab.ee.washington.edu/nwess/2008/presentations/stephen.ppt.

  41. 1. “Small” due to “normal” variation (occurring continuously); response is via AGC and not governors (due to gov deadband). Frequency Variation 2. “Large” due to contingencies Response is via governors and then AGC. Eastern Interconnection Frequency – 2/1/11; (1-min values) Extreme cold caused instrumentation freezing, resulting in large number of unit trips around the nation. “Analysis of power system impacts and frequency response performance: Feb 1-4, 2011 Texas & Southwestern U.S. Cold Snap,” September, 2011. http://www.nerc.com/files/RISA%20cold%20Snap%20report%20September%202011.pdf

  42. Frequency Variation Western Interconnection Frequency – 2/2/11; (1-min values) Extreme cold caused instrumentation freezing, resulting in large number of unit trips around the nation. “Analysis of power system impacts and frequency response performance: Feb 1-4, 2011 Texas & Southwestern U.S. Cold Snap,” September, 2011. http://www.nerc.com/files/RISA%20cold%20Snap%20report%20September%202011.pdf

  43. Area Control Error (ACE) We saw on slide 12 that: ACE=TIE LINE FLOW DEVIATIONS FROM SCHEDULE +10B×[FREQUENCY DEVIATION FROM 60 HZ] Let’s characterize “Tie Line Flow Deviations from Schedule” as “Deviation from Scheduled Export,” denoted ΔPexp=Pexp,A-Pexp,S. Then: ACE= ∆Pexp + 10B∆f REST OF THE INTERCONNECTION BA P3 P1 P2 Pexp=P1+P2+P3 43

  44. Six Questions • What is net load? • AGC: what is it? How does it use ACE? • Why are ACE excursions undesirable? • What causes ACE excursions? • How does wind affect ACE excursions? • How to decrease ACE excursions? 44

  45. 1. What is net load? NETLOAD =LOAD+LOSSES-WIND-SOLAR (Units are MW) More simply, NETLOAD=LOAD-VG (Units are MW) where VG is “variable generation.” That is, Z=X-Y. Before wind & solar, we did not use this term. We wil be interested in the variation in net load: ΔZ= ΔX- ΔY 45

  46. 2. Automatic Generation Control: What is it? Turbine-Gen N Turbine-Gen … Turbine-Gen 2 Turbine-Gen 1 ACE= ∆Pexport + 10B∆f Primary control controls output in response to transient frequency deviations but deadband prevents response under normal) Secondary control provides regulation ∆Pexport ∆f 46

  47. ACE= (ΔPexport) + 10B (Δf) • It means either • 1. Pexp is deviated from scheduled value: • There are economic implications and there are flow implications • 2. f is deviated from 60 Hz: • This risks increased frequency deviations after contingencies. • Gens providing AGC must move in order to correct. 3. Why are ACE excursions undesirable? Deployed Regulation >0 ACE<0

  48. ACE= (ΔPexp) + 10B (Δf) • It means either • 1. Pexp is deviated from scheduled value: • There are economic implications and there are flow implications • 2. f is deviated from 60 Hz: • This risks increased frequency deviations after contingencies. • Gens providing AGC must move in order to correct. • AND THIS COST MONEY! 3. Why are ACE excursions undesirable? Similar data from another source [A] Start-up time Max ramp rate • Nuclear plants [A] Source: A. Vuorinen, “Fundamentals of power plants,” available at http://www.idmeb.org/contents/resource/fundamentals_of_power_plants_33_42.pdf. Also in: A. Vuorinen, “Planning of optimal power systems,” Ekoenergo Oy, 2007 (see www.optimalpowersystems.com).

  49. How to determine the generation portfolio necessary to handle a given σT ? First, you should know ramp rates (RR) of gens in your existing portfolio. You should also know RR of gens that can be added to your portfolio.  Diesel engines 40 %/min  Industrial GT 20 %/min  GT Combined Cycle 5 -10 %/min  Steam turbine plants 1- 5 %/min  Nuclear plants 1- 5 %/min 49

  50. ACE= (ΔPexp) + 10B (Δf) Therefore the North American Electric Reliability Corporation (NERC) has control performance measures on ACE that must be reported by balancing authorities (ISOs). Penalties are imposed if the corresponding standards are not met. See next slide. 3. Why are ACE excursions undesirable?

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