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J. McCalley

J. McCalley. Wind Power Variability in the Grid: Regulation. Outline. Power production: wind power equation Variability: time and space Governor response. 2. Power production Wind power equation. Mass flow rate is the mass of substance which passes through a given surface per unit time.

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J. McCalley

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

  2. Outline Power production: wind power equation Variability: time and space Governor response 2

  3. Power production Wind power equation Mass flow rate is the mass of substance which passes through a given surface per unit time. Swept area At of turbine blades: • The disks have larger cross sectional area from left to right because • v1 > vt > v2 and • the mass flow rate must be the same everywhere within the streamtube (conservation of mass): • ρ=air density (kg/m3) • Therefore, A 1 < At < A 2 v1 vt v2 v x 3 Reference: E. Hau, “Wind turbines: fundamentals, technologies, applications, economics,” 2nd edition, Springer, 2006.

  4. Power production Wind power equation 2. Air mass flowing: 1. Wind velocity: 3. Mass flow rate at swept area: 4b. Force on turbine blades: 4a. Kinetic energy change: 5b. Power extracted: 5a. Power extracted: 6b. Substitute (3) into (5b): 6a. Substitute (3) into (5a): 7. Equate 8. Substitute (7) into (6b): 9. Factor out v13: 4

  5. Power production Wind power equation 10. Define wind stream speed ratio, a: This ratio is fixed for a given turbine & control condition. 11. Substitute a into power expression of (9): 12. Differentiate and find a which maximizes function: (we hold v1 constant here) 13. Find the maximum power by substituting a=1/3 into (11): 5

  6. Power production Wind power equation 14. Define Cp, the power (or performance) coefficient, which gives the ratio of the power extracted by the converter, P, to the power of the air stream, Pin. power extracted by the converter power of the air stream 15. For a given v1, the maximum value of Cp occurs when its numerator is maximum, i.e., when a=1/3: The Betz Limit! 16. Cp depends on a=v2/v1. For a given v1, v2 depends on how much energy is extracted by the converter, which depends on pitch, θ, and rotational speed, ω. 6

  7. Power production Wind power equation 17. At the condition of maximum energy extraction, where a=v2/v1=1/3, we have the reduce downstream speed is From slide 4, we know that Substituting the downstream speed at maximum energy extraction, the speed at the converter is: Recall Some points of interest: a=1v2=v1=vt, and P=0; a=1/3v2=v1/3, vt=2v1/3, and P=(ρAtv13/4)(32/27) a=0v2=0, vt=v1/2, and P=ρAtv13/4 a=-1/3, v2=-v1/3, vt=v1/3, and P=(ρAtv13/4)(16/27) a=-1v2=-v1, vt=0, and P=0 7

  8. Power production Cp vs. λ and θ u: tangential velocity of blade tip Tip-speed ratio: ω: rotational velocity of blade R: rotor radius v1: wind speed Pitch: θ GE SLE 1.5 MW 8

  9. Power production Wind Power Equation • So power extracted depends on • Design factors: • Swept area, At • Environmental factors: • Air density, ρ (~1.225kg/m3 at sea level) • Wind speed v13 • 3. Control factors affecting performance coefficient CP: • Tip speed ratio through the rotor speed ω • Pitch θ 9

  10. Power production Cp vs. λ and θ One may plot P vs ω, for different wind speeds v1, as shown below [*]. MPP is the maximum power point. • Important concept #1: The control strategy of all US turbines today is to operate turbine at point of maximum energy extraction, as indicated by the locus of points in the figure. • Important concept #2: This strategy maximizes energy produced. Any other strategy “spills” wind. • Important concepts #3: • Cut-in speed>0 because for lower speeds, turbine generates less power than it’s internal consumption. • Generator should not exceed rated power • Cut-out speed protects turbine in high winds • Important concepts #4: • Pitch control used to limit power only if max pwr exceeds rated; otherwise, blades fully pitched. • Generator (rotor) control used to control speed. For a given v1 and θ, one can control ω and thus λ (using direct speed control or indirect speed control [**]). [*] B. Wu, et al., “Power conversion and control of wind energy systems,” Wiley, 2011. [**] G. Abad, et al., “Doubly fed induction machine: modeling & control for wind energy generation,” Wiley, 2011. 10

  11. Power production Typical power curve Cut-in speed (6.7 mph) Cut-out speed (55 mph) 11

  12. Wind Power Temporal & Spatial Variability JULY2006 JANUARY2006 Blue~VERY LOW POWER; Red~VERY HIGH POWER • Notice the temporal variability: • lots of cycling between blue and red; • January has a lot more high-wind power (red) than July; • Notice the spatial variability • “waves” of wind power move through the entire Eastern Interconnection; • red occurs more in the Midwest than in the East 12

  13. 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. 13

  14. 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. 14

  15. Temporal variability of wind power – time interval • Extreme weather events: • Denmark: 2000 MW (83% of capacity) decrease in 6 hours or 12 MW (0.5% of capacity) in a minute on 8th January, 2005. • North Germany: over 4000 MW (58% of capacity) decrease within 10 hours, extreme negative ramp rate of 16 MW/min (0.2% of capacity) on 24th December, 2004 • Ireland: 63 MW in 15 mins (approx 12% of capacity at the time), 144 MW in 1 hour (approx 29% of capacity) and 338 MW in 12 hours (approx 68% of capacity) • Portugal: 700 MW (60% of capacity) decrease in 8 hours on 1st June, 2006 • Spain: Large ramp rates recorded for about 11 GW of wind power: 800 MW (7%) increase in 45 minutes (ramp rate of 1067 MW/h, 9% of capacity), and 1000 MW (9%) decrease in 1 hour and 45 minutes (ramp rate -570 MW/h, 5% of capacity). Generated wind power between 25 MW and 8375 MW have occurred (0.2%-72% of capacity). • Texas, US: loss of 1550 MW of wind capacity at the rate of approximately 600 MW/hr over a 2½ hour period on February 24, 2007. 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. 15

  16. 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.” 16 Reference: E. Hau, “Wind turbines: fundamentals, technologies, applications, economics,” 2nd edition, Springer, 2006.

  17. 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. 17

  18. Spatial variability of wind power – geographical smooting from geo-diversity Single turbine reaches or exceeds 100% of its capacity for ~100 hours per year, the area called “Denmark West” 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. H. Holttinen, “The impact of large-scale power production on the Nordic electricity system,” VTT Publications 554, PhD Dissertation, Helsinki University of Technology, 2004. 18

  19. Temporal & spatial variability of wind power Correlation coefficient between time series of intervals T=5 min, 30 min, 1 hr, 2 hr, 4 hr, 12 hr, for multiple locations, as a function of distance between those locations. 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 5 min intervals, 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 intervals. For 12hr intervals, 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. 19

  20. Spatial variability of wind power – geographical smooting 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. 20

  21. 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. 21

  22. Generation portfolio design to meet load variability A control area’s portfolio of conventional generation is designed to meet that load variability. This is done by ensuring there are enough generators that are on governor control, and that there are enough generators having ramp rates sufficient to meet the largest likely load ramp. Typical ramp rates for different kinds of units are listed below (given as a percentage of capacity):  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 22

  23. 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. 23

  24. 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. 24

  25. 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). 25

  26. 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: If these random variables are independent, then for the means, μz=μx-μy, and for the variances, σz2= σx2+σy2. 26

  27. 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 25. 27

  28. 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 the 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. 28

  29. 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. 29

  30. 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 both normally distributed, then rxy=0 implies independence. This will be the case for our regulation data since it is comprised of variations. • If rxy=1 or if rxy=-1, then x and y are dependent. • 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. 30

  31. Using variance and correlation to measure regulation coincidence • We will use four ideas in what follows: • We assume the regulation component of load is normal. • For normally distributed random variables, rxy can be used to measure independence. • Three standard deviations (3σ) of the net load is our measure of “regulation burden.” • We assign angles to the standard deviation of each component comprising the net load, so we can treat them as vectors. 31

  32. σz σy σz σz σy σy σx σx σx Using variance and correlation to measure regulation coincidence If two random variables are independent, then the variance of their sum (or their difference) is Fig 1 Consider if two time series are perfectly anti-correlated, i.e., rxy=-1, implying x and y changes in anti-phase: Consider if two time series are perfectly correlated, i.e., rxy=1, implying x and y follow each other perfectly: Fig 3 Fig 2 32

  33. 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 π to π/2 to 0, (as in the three cases illustrated on slide 32), as summarized below. The figure to the right illustrates the situation for an angle θ, in this case corresponding to a value rxy such that 0<rxy<1. Because wind is gen and netload is load, we should use 33

  34. 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 newly-stated problem. 34

  35. 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 enhanced the figure to facilitate analytic development). 35

  36. 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: Also, from law of cosines: Solving for X results in: X is the “regulation share” of the “generator of interest.” It was applied in [#] to different kinds of resources, including wind and solar. It can also be applied to different kinds of loads. [#] 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. 36

  37. 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 Our new “regulation burden” will therefore be 3σT, and we will have to have a generation portfolio to handle this. 37

  38. 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. 38

  39. What can you do with it? How to determine the generation portfolio necessary to handle it? First, you should 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 You should also know the typical operating conditions you expect, and the committed units at throughout those operating conditions (from historical data or a production cost simulation) spinning reserve criteria. 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. 39

  40. = + 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. 40

  41. 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... 41

  42. 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. 42

  43. Governor response A conventional synchronous generator, for both steam-turbines and hydro turbines, can control the mechanical power seen by the generator in response to either a change in set-point, ∆PC, or in response to change in frequency, ∆ω. The dynamics of this feedback control system are derived in EE 457 and EE 553, the conclusion of which is: where TT is the time constant of the turbine, and TG is the time constant of the speed-governor, and the circumflex indicates Laplace domain. Now consider a step-change in power of ΔPC and in frequency of Δω, which in the LaPlace domain is: 43

  44. Governor response Consider ΔPM(t) for very large values of t, i.e., for the steady-state, using the final value theorem: Applying FVT • Some important cautions: • Δ PM, ΔPC, and Δω in the above are time-domain variables (not Laplace) • Δ PM, ΔPC, and Δω are steady-state values of the time-domain variables (the values after you wait a long time) • Δ PM, ΔPC, and Δω are not the cause of the condition but rather the result of a ΔPL somewhere in the network, and the above shows how they are related in the steady-state. 44

  45. Governor response Assuming that the local behavior as characterized by previous equation can be extrapolated to a larger domain, we can draw the below figure: “Droop” characteristic: Primary control system acts in such a way so that steady-state frequency “droops” with increasing mechanical power. The R constant, previously called the regulation constant, is also referred to as the droop setting. When power is specified in units of MW and frequency in units of rad/sec, then R has units of rad/sec/MW. When power and frequency are specified in pu, then R is dimensionless and relates fractional changes in ω to fractional changes in PM. In North America, governors are set with Rpu­=0.05, i.e., if a disturbance occurs which causes a 5% increase in steady-state frequency (from 60 to 57 Hz), the corresponding change in unit output will be 1 pu (100%). 45

  46. Governor response Now consider a general multimachine system having K generators. From eq. (6), for a load change of ΔP MW, the ith generator will respond according to: The total change in generation will equal ΔP, so Solving for Δf results in Substitute previous expression into top expression for ΔPMi results in If all units have the same per-unit droop constant, i.e., Rpui=R1pu=…=RKpu, then 46

  47. Governor response Conclusion of previous slide is that, for a MW imbalance of ΔP (caused by, for example, a generation trip), following the action of primary control (but before action of AGC), units “pick up” in proportion to their MVA ratings. So full primary control action generally occurs within about 30 seconds following an outage. AGC will generally not have too much influence until about 1-2 minutes following an outage. So the above relation may be thought of as characterizing the state of the power system in the 30 second to 2 minute time frame. 47

  48. Governor response I performed a brief review of the websites from TSOs (in Europe), reliability councils (i.e., NERC and regional organizations) and ISOs (in North America) in 2009 and concluded that there are no requirements regarding use of primary frequency control in wind turbines. I did a little more searching this past week and conclude that the situation in the US has not yet changed much, but it is possible I may have missed something. Please let me know if you come across any North American requirements for wind turbines to have primary control capability. The technology for implementing primary control is available from most utility-scale turbine manufacturers, however. 48

  49. Generator control view of a standard DFIG G. Ramtharan, J.B. Ekanayake and N. Jenkins, “Frequency support from double fed induction wind turbines,” IET Renew. Power Gener., 2007, 1, (1), pp. 3–9 49

  50. Generator control view of a standard DFIG for maximum power extraction from the wind A torque set point, TSP, is det-ermined by the rotor charac-teristic curve for max power extraction. A reference rotor current iqrref is derived from the electromagnetic torque equation & then compared with the measured current iqr. A proportional integral (PI) controller is used to determine the required rotor voltage, vqr. 50

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