A static analysis method to determine the availability of kinetic energy from wind turbines Rawn, B.G.; Gibescu, M.; Kling, W.L.

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1 A static analysis method to determine the aailability of kinetic energy from wind turbines Rawn, B.G.; Gibescu, M.; Kling, W.L. Published in: Proceedings of the IEEE Power and Energy Society (PES) general meeting, 5-9 July, Minneapolis USA Published: // Document Version Publisher s PDF, also known as Version of Record (includes final page, issue and olume numbers) Please check the document ersion of this publication: A submitted manuscript is the author's ersion of the article upon submission and before peer-reiew. There can be important differences between the submitted ersion and the official published ersion of record. People interested in the research are adised to contact the author for the final ersion of the publication, or isit the DOI to the publisher's website. The final author ersion and the galley proof are ersions of the publication after peer reiew. The final published ersion features the final layout of the paper including the olume, issue and page numbers. Link to publication Citation for published ersion (APA): Rawn, B. G., Gibescu, M., & Kling, W. L. (). A static analysis method to determine the aailability of kinetic energy from wind turbines. In Proceedings of the IEEE Power and Energy Society (PES) general meeting, 5-9 July, Minneapolis USA (pp. -8). Piscataway: USA. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of priate study or research. You may not further distribute the material or use it for any profit-making actiity or commercial gain You may freely distribute the URL identifying the publication in the public portal? Take down policy If you beliee that this document breaches copyright please contact us proiding details, and we will remoe access to the work immediately and inestigate your claim. Download date: 3. Sep. 8

2 A Static Analysis Method to Determine the Aailability of Kinetic Energy from Wind Turbines Barry G. Rawn, Student Member, IEEE, Madeleine Gibescu, Member, IEEE, Wil L. Kling, Member, IEEE Abstract This paper introduces definitions and an analysis method for estimating how much kinetic energy can be made aailable for inertial response from a wind turbine oer a year, and how much energy capture must be sacrificed to do so. The analysis is based on the static characteristics of wind turbines, Weibull distributions of wind speed, and standard definitions of turbulence intensity. A control scheme is presented that extracts an appropriate amount of kinetic energy based on operating point. The tradeoff of wholesale energy reenue for potential kinetic energy reenue is explored. The break-een point is compared with marginal prices for kinetic energy obtained in the literature, and found to be faourable for one example of a full-conerter interface wind turbine haing a wide speed range. Index Terms wind power generation, inertia, real-time markets I. INTRODUCTION A. Background Wind turbines and farms are expected to be a signifcant fraction of installed generation capacity in the future, and their current fraction is increasing rapidly. In addition to supplying energy to the power system, wind farms are also required to proide ancillary serices such as oltage control, and een the regulation of actie power to support the frequency of the power system [6]. One important aspect of power system frequency stability that is not usually classified as an ancillary serice is the inertial response of generating units to changes in frequency. In an inertial response to a sudden loss of generation, for example, synchronous generators are physically forced to inject energy into the power grid. That is not the case with conerter-interfaced wind turbines [5], [8],[6]. Typical conerter controls make the machine appear as a current source in the network with no frequency dependence. Yet, the conerter controls can easily be altered to produce any desired dependence on frequency, in particular to cause the injection of rotational kinetic energy into the grid during a frequency eent [4], [], [5]. It has been obsered [3],[5] that some of these schemes only temporarily contribute energy This research is part of the project RegelDuurzaam, which is funded under the SenterNoem program EOS-LT. SenterNoem is an agency of the Dutch Ministry of Economic Affairs Barry Rawn, Madeleine Gibescu and Wil Kling are with the Department of Electrical Sustainable Energy, Delft Uniersity of Technology, 6 CD Delft, The Netherlands ( s:b.g.rawn@tudelft.nl, m.gibescu@tudelft.nl, w.l.kling@tudelft.nl). Wil Kling is also with the Electrical Power Systems Group, Eindhoen Uniersity of Technology, 56 AZ Eindhoen, The Netherlands ( w.l.kling@tue.nl). into a frequency drop and mostly affect rate of change of frequency. Howeer, other schemes can be arranged whereby a net contribution of energy is made [4]. This comes at the expense of operating the turbine away from the optimal point, which results in a reduced capture of energy. The contribution possible from a wind turbine can exceed that of a synchronous machine [7]. Howeer, like the actie power of a wind farm, it is not always aailable, and the potential contribution depends on the operating point. In small power systems found on islands, concerns oer frequency stability during contingencies could result on limits to the percentage of installed wind power capacity. It has been proposed to include frequency-related constraints in market dispatch algorithms, and derie a price signal for proiding inertial resere []. If a market for kinetic energy were established, this could represent another stream of reenue for wind farm operators. Another scenario is that system operators will mandate the proision of inertial response from all generators. Therefore, it will become important to characterize the capability of inertial response in wind farms in order to exploit the potential of wind farms fully, and to foster further deelopment of wind farms. B. Contribution Inertial response proofs of concept [4],[8] and some analysis of their physical limitations on such schemes appear in the literature. Some of these works inestigate operating range and maximum aailable size [], [] or examine how the bound on wind ariations constrains safe operation [3]. They do not explore how the longer term ariations of the wind resource constrain the aailability of kinetic energy. It would be helpful to quantify the magnitude of this energy, how often it can be made aailable, and what the tradeoff is of proiding such a serice. The significance of operating point changes must be acknowledged. This paper addresses these issues starting with Section II, which presents an inertial response control scheme that extracts a kinetic energy dependent upon operating point. Section III presents definitions and an analysis method to estimate quantity and aailability of kinetic energy resere, and the sacrifice of energy capture. Section IV presents numerical results, explores the possible tradeoff of wholesale energy reenue for potential kinetic energy reenue is explored, and examines the sensitiity of the results to a site s wind characteristics is presented, based on IEC standard ranges //$6. IEEE

3 ω C.45 p opt.4 Cp.35.3 P +ΔP ω H C p (λ,).5. Power λ L λ opt λ H Fig.. De-rated operating philosophy, shown on power conersion efficiency cure C p(λ). Operation occurs not around optimal tip-speed ratio λ opt, but around λ H at a de-rated efficiency Cp. A resere of kinetic energy is made aailble between λ H and λ L. λ t Time (a) Power t + τ P opt P t Time (b) Rotational speed t + τ Fig.. Illustration of kinetic energy resere due to de-rating. Resere is tapped to proide an power pulse ΔP oer duration τ without dipping below leel P. ω L II. MODELING AND ASSUMPTIONS A. Resere Capability and De-rating A wind turbine conerts the power in flowing mass of air to mechanical power with a ariable efficiency using its bladed rotor. The aerodynamic characteristics of the blades result in an efficiency that aries with tip-speed ratio λ λ = Rω () where the windspeed is, and the speed of the blade tip is determined by the turbine radius R and rotational speed ω. The power conersion efficiency C p (λ), depicted in Fig. is nonlinear, with a peak alue Cp opt at an optimal tip-speed ratio λ opt. The wind turbine power is gien by P (,λ) = πρπr C p (λ) 3 () A de-rated efficiency occurs for λ λ opt, and a chosen derating can be obtained oer a wider speed range. For example, in Fig., a derated efficiency of C p has been chosen. If, for a gien wind speed, the tip-speed ratio λ opt produces a power P opt, then operating at either λ L or λ H would yield a power P <P opt. For tip speed ratios in the interal [ λ l λ h], the efficiency of conersion is at least C p or greater. A de-rating α in percent is defined as follows: α = ( C p ) (3) C p opt For a gien constant wind speed and de-rating α, the rotational speed of the wind turbine can be reduced from a speed ω H to as low a speed as ω L implied by (): [ω L,ω H ]= R [λ L,λ H ]. (4) The effect of such a reduction is depicted in Fig.. The difference in kinetic energy can be extracted to make a change in power ΔP for a duration τ. De-rating to the non-optimal efficiency Cp thus makes a resere of kinetic energy aailable. The quantity of energy aailable will depend on the operating wind speed and the turbine s rotor inerta J, as follows ΔE K (,λ H )= ( ) J ( λ H R ) λ L (5) where λ L is the alue of λ such that C p (λ L )=C p (λ H ),asin Fig.. A small resere of power is made aailable through derating. Power resere can also be obtained be altering the pitch of the wind turbine blades. Neither capability is of interest for this work. B. Generator Torque Control and Operating Ranges To maximize energy capture, turbine controls are usually set to cause changes in ω so as to maintain λ at λ opt when changes in wind speed occur [4]. This is possible only in the ariable speed range of a wind turbine, and can achieed by setting a generator torque that has appropriate intersections with the wind-dependent aerodynamic torque cures. This is achieed by setting the following torque with λ = λ opt : T gen = πρc p(λ ) R5 }{{ λ 3 ω (6) } k load (λ ) Such a torque is depicted in Fig. 3 as a thick solid line. The aerodynamic torque is deried by diiding () by ω and is depicted using thin solid lines for a number of threshold wind speeds. There are a number of different operating modes of a wind turbine that are partly enforced by generator torque, and by blade pitch []. These modes occur at the speeds 6, which are described in Table I and shown in Fig. 3 for a particular model of turbine. The limits on ariable speed range are imposed by the power electronic frequency conerter at low speed [], and the maximum allowable speed of the wind turbine at high speed [9]. The optimal generator torque is not permitted to intersect these limiting speeds discontinuously. Instead it is set to ramp towards these operational endpoints starting aboe ω lower and below ω upper [4]. This reduces fluctations in power as the

4 3 aerodynamic torque cures 5.9 T rated.8 Trated T (p.u.) T (p.u.) generator torque cures ω lower 3 λ L λ opt λ H ω(p.u.) ω upper torque ω L ω H ω lower ω upper ω(p.u.) Fig. 4. Transient in torque-speed plane for constant power pulse and limiting alue of wind speed torque. Fig. 3. De-rated load cures for λ opt and λ corresponding to α =% intersecting with aerodynamic torque cures for threshold wind speeds of Table. turbine transitions between zero and full rated power, and also eases the task of the pitch control at high speeds, which actiates to limit the rotational speed of the wind turbine by spilling aerodynamic power [9]. For an optimal generator torque, the wind speeds at which all of these transitions occur are marked in Fig. 3 and listed in Table. I. These wind speeds denote the different operating modes of the windturbine. It is also possible to set the generator torque cure to produce intersections that presere a different tip-speed ratio λ (for example, λ H or λ L instead of λ opt ). This is achieed by replacing the parameter λ opt with λ in the gain k load (λ) in (6). Wind speeds corresponding to operation at the tip-speed ratios λ L and λ H are also marked in the figure and listed in Table. I. Wind Speed Threshold Value (m/s) cut-in, optimal.5 cut-in, resere depleted (λ L ) transition zone, de-rated(λ R ) transition zone, optimal (λ opt) 5 rated speed and power reached cut-out wind speed reached 3 TABLE I TABLE OF WIND SPEED THRESHOLDS DEMARCATING DIFFERENT OPERATING MODES, ENERCON E-7 WIND TURBINE. C. Kinetic Energy Extraction Most works in the literature that address exploitation of wind turbine kinetic energy consider its application to inertial response. There are a ariety of controllers that may be applied to produce an injection of power that reduces the rotational speed of the turbine [4],[8], [],[7]. These controllers must be designed not to cause iolations of rotational speed limits or conerter current limits. This paper aims only to introduce basic concepts about aailability and produce a basic ealuation of the aailable energy, and so some simplifying assumptions are employed. It is assumed that during the short period that kinetic energy is proided, the wind speed is constant. A control for extracting kinetic energy as a constant power pulse of limited duration [], [7] is selected because it is simplest. An enhancement of such methods is presented here to allow an analysis oer all operating points. The control is a ΔT that is added to the generator torque cure: { ΔP (t) ΔT (ω, t) = ω, t <t<t + τ (7) T op, t > t + τ where the quantity ΔP is the constant power pulse used to delier the aailable energy resere, as shown in Fig., the time τ is a chosen duration, t is the time of actiation and the constant quantity T op ( (λh ) 3 T op (t )=k load (λ H ) ) ω(t ) (8) is a torque added to the generator load torque to maintain the new operating point at ω L. The ΔP (t ) chosen in this control strategy would hae to be based instead on rotational speed ω, the only measurement reliably aailable. By assuming that the current speed is indeed tracking the desired λ H, the wind speed would be estimated as ˆ w = R λ H ω (9) and the estimate of aailable energy would be obtained by substituting into (5): ΔÊK(t )= ( ) ) Jω(t ) ( λl () This resere of kinetic energy will be depleted for any ΔP that exceeds maximum power aailable. Any combination of ΔP and τ will achiee this according to the formula: ΔP (t )= ΔÊK(t ) () τ Typically kinetic energy is of alue when deliered quickly during a frequency drop; a reasonable amount for τ might be -5 seconds. λ L λ H

5 4 f()..5 c=8.47 c=9.6 c=.3 3 (m/s) (a) c parameter of IEC I, II, and III. k = f()..5 k=3 k= k=. 3 (m/s) (b) k parameter oer typical range, for IEC II (c =9.6) Fig. 5. Effect on probability distribution function f() of arying shape k and scale c parameters oer ranges specified by the IEC. The resulting type of transient is shown on the torquespeed plane in Fig. 4. The limits on such a response due to speed limits and torque limits will be ealuated in the Analysis section. D. Wind Resource Ten minute aerages of wind speed measurements are frequently used to determine the statistics of a wind turbine site s resource. Such statistics are used to assess the yearly production of wind farms. The probability distribution of wind speeds is widely recognized to be well-fit by a Weibull distribution f() = k ( ) k e ( c ) k () c c where is the ten minute aerage alue, c is called a scale parameter and k is called a shape parameter. Fig. 5 shows a set of probability distribution functions that result from typical alues of these parameters [],[]. Substantial fluctuation in wind speed can occur within a minute period, with periods of minutes to second. These fluctuations cause significant changes in wind turbine operating point. The distribution of wind speeds around a minute aerage alue can be iewed as Gaussian, and therefore characterized by a standard deiation σ dependent on the mean oer a minute interal. The turbulence intensity T.I. is the ratio of these two quantities. T.I = σ (3) The turbulence intensity aries in general with the mean alue. In calculations of energy yield, the effect of turbulence is usually neglected, possibly due to cancelation []. Howeer, in this paper, normally distributed turbulent ariations will be accounted for along with the Weibull distribution to understand ariations in wind turbine operating point. III. ANALYSIS METHOD As is well known in the field, the energy capture of a wind turbine can be estimated using the probability distribution of wind speeds. The distribution f() is gien by () and the power at a gien wind speed can be obtained from () by assuming λ = λ, where λ corresponds to a desired α. The yearly capture in MWh of a wind turbine eligible for sale on f() (m/s) 6 (a) Probability density f() of minute aerage wind speed P (, λ ) (MW) f() P (, λ ) MWh/(m/s) (m/s) 6 (b) Power cure P (, λ ) E WH (m/s) (c) Wholesale energy capture density. Fig. 6. Illustration of computation of energy capture for wholesale market. Turbine produces between wind speeds and 6 (dashed lines). the wholesale energy market is referred in this paper to as a quantity E WH and gien by integrating the product: E WH = seconds/year J/MWh 6 f()p (, λ opt )d (4) where and 6 are the cut-in and cut-out speeds gien in Table I. This paper uses a similar approach to analyze the proision of kinetic energy and its consequences for energy capture. It is illustrated in Fig. 7. A cure E KR (, λ ) giing the dependence of kinetic energy resere on wind speed (Fig. 7(b) is deried in analogy to P (, λ ), so that a cummulatie kinetic energy resere E CKR (area in Fig. 7(c)) aailable oer a year can be determined by integrating the product: E CKR = N int H L f()e KR (,λ )d (5) where N int is the number of minute interals in a year, L and H denote the lowest and highest wind speeds for which a kinetic energy resere can be reliably made aailable, and E KR is the magnitude of that resere. The calculation of the speeds and magnitude is detailed in sections III.A and III.B. When de-rating is applied oer the range [ L, H ], a quantity of energy capture ΔE WH is sacrificed: ΔE WH = seconds/year J/MWh ( ) C H p Cp opt f()p (,λ )d L (6) This quantity can be computed to ealuate the economic tradeoff of proiding resere.

6 MJ/(m/s) 5 f() EKR(, λ ) (MJ) f() EKR(, λ ) L H (m/s) (a) Probability density f() of minute aerage wind speed L H (m/s) (b) Minimum aailable kinetic energy E KR (λ, ) E CKR (m/s) (c) Kinetic energy resere density. Fig. 7. Illustration of analysis method. Within the range of wind speeds [ L, H ] (dashed lines) whose computation is outlined by the paper, kinetic energy resere can be made aailable by sacrificing energy capture by derating. α =% c =9.6,k = A. Calculation of Wind Speed Range [ L, H ] Corresponding to Kinetic Energy Aailability The wind turbine dynamics due to the rotor s inertia and spatial filtering of windspeed will be neglected. Including such effects requires a more sophisticated analysis, additional assumptions, and a proper model of wind speed spectral content. It is be assumed that the speeds ω L and ω H can be algebraically associated with wind speed inputs through the relation (). Thus, the limits ω lower and ω upper translate directly into a range of wind speeds outside of which kinetic energy can not be extracted. The maximum limit on generator torque can in some cases further resrict the iable range of wind speeds. Also, the actual range of windspeeds used in the analysis must be adjusted for turbulence. ) Torque Constraint: A constant power cure in the torque speed plane implies an increasing torque as speed decreases, as shown in Fig. 4, and this means that the maximum torque of the transient will be reached at the speed ω L. The condition that generator torque reaches the rated alue T rated at ω L corresponds to a worst case wind speed torque. This worst case speed depends on the de-rating α, which determines ω L, and the discharge duration τ, which determines the height of ΔT through () and (5). An expression determining torque can be found as follows. The total generator torque during a transient is obtained by adding (6) and (7) at t = t + τ. Substituting in () to eliminate ω, the critical condition depicted in Fig.4 is: ( ) λl T rated k load (λ H ) torque R ( ) R R +ΔP λ L torque torque λ L (7) where ω has been set to ω L and expressed in terms of wind speed and tip-speed ratio λ L ia (). Substituting (),(), and (9), and setting ˆ w = torque, one obtains this equation for torque : ( λl T rated k load (λ) R ( + J τ ) torque ( λl λ R ) ) λ H Rλ L torque (8) Whether this torque-limit induced limit on wind speed is more restrictie than that caused by upper rotor speed depends on the characteristic C p (λ) of the turbine, the amount of derating α, and the desired duration of discharge τ. For smaller de-ratings and longer durations of discharge, (e.g. for the model studied, % or less and longer than 3 seconds), the wind speed torque is lower than the wind speed 3 associated with upper rotational speed limit ω upper. In other cases, the aailability is further reduced. ) Accounting for Turbulence: It is important to account for how turbulent ariations in wind speed will affect the occurence of different operating points. Within a ten minute interal the wind speed, and hence the operating rotational speed, will ary significantly. Two standard deiations are taken as the likely range of wind ariations around the interal s mean alue, representing a probability of 95%. An IEC standard gies guidelines for turbulence intensity [] and through (3) the magnitude of the standard deiation σ(). The range of possible wind speeds can be computed as: ± σ() = ( ± I 5 a + 5 +a ) (9) where I 5 has high and low alues of. and.6, and a has alues between and 3 [], corresponding to the IEC turbulence classes C-A respectiely. The alues L and H to be used in this analysis are obtained by equating (9) to critical alues of wind speed and soling: L = + I5 +a I5 +a a () H = min( 3, torque ) I5 +a + I5 +a a () where and 3 are gien in Table I and torque is implicity defined in (8). In this work it is assumed that τ and α hae been chosen such that torque > 3. B. Probable Quantity of Kinetic Energy It must be assumed that during a minute interal, any wind ariation within standard deiations σ can occur.

7 6 (MJ) E KR E CKR synchronous machine A interals per year (%) Fig. 8. Duration cure of kinetic energy reseres E KR (, λ ) oer a year of ten-minute interals, for a wind turbine (solid) and synchronous generator (dashed). The aailability A, mean resere E KR, and cummulatie kinetic energy resere E CKR (shaded area), are marked on the figure Thereis thus a range of possible kinetic energy resere. It is conseratie to use the lower bound in the calculation of kinetic energy resere E KR, so that it can then be interpreted as a quantity that can be guaranteed oer the minute interal. Thus, E KR (, λ )) = J ( σ() R ) ( λ ) λ L () where is ten-minute mean, σ() is the standard deiation for that mean alue, J is the turbine inertia, and λ L is such that C p (λ )=C p (λ L ). IV. RESULTS Computations are based on a diision of the year into minute interals, where the interals hae mean wind speeds that hae a Weibull distribution corresponding to an IEC site of class II B (alues k =, c =9.6, and T.I. =.4)The sensitiity of the results to k, c, and T.I is examined at the end of the section. For all of those interals haing a windspeed that lies within [ L, H ], the kinetic energy resere E KR (, λ ) can be computed. In Fig. 8, the alues hae been computed for a de-rating α =%and sorted from highest to lowest, forming a duration cure for kinetic energy resere. This cure can be used to make seeral obserations and definitions. The percentage of interals when kinetic energy is aailable is denoted by A. The mean alue of resere aailable is denoted as E KR. The cumulatie quantity of kinetic energy resere E CKR defined earlier as (5) corresponds to the shaded area. This area clearly depends on the quantities A and E KR. For comparison, a horizontal line in Fig. 8 shows the energy that would be aailable from a synchronous generator haing the same physical inertia as a wind turbine. The quantity released in a relatiely large frequency deiation of % has been chosen for comparison. Because of its ability to run asynchronously, the wind turbine is capable of deliering twice this amount (and as much as fie times at higher de-ratings, see Fig. 9). Howeer, during some ten-minute interals of the year, proiding such an amount may be either impossible or A (%) A E KE α (%) Fig. 9. Dependence on de-rating α of mean kinetic energy resere E KE and its aailability A. Increasing quantity of resere is countered by a decreased number of aailable interals. uncertain. The shaded area E CKR would be proportional to profit in a kinetic energy resere market. It is eident that a wind turbine would hae to hae a larger inertia to hae the same potential for profit. Also, for the example shown, kinetic energy resere would be unaailable 85% of the time. A. Dependence of Kinetic Energy Aailability and Quantity on De-rating While adjusting the de-rating of the generator torque makes a greater resere of energy possible, such a resere is aailable for a smaller fraction of time. This can be obsered from in Fig 9. For this case of a full-conerter interfaced wind turbine with a wide speed range, it appears that the aerage kinetic energy offered could range from 3 MJ, offered % of the time, to. MJ, offered % of the time. It must be mentioned that the model of turbine studied has a wide rotational speed range and thus other models would hae both a lower aailability. The conflicting trends of Fig 9 suggest that the cumulatie amount of kinetic energy aailable from the turbine is maximized by some particular alue of de-rating. In Fig, the cumulatie quantity of resere aailable oer the year E CKR is plotted. This quantity is maximized for this example around α =%. The quantity that could be expected from a synchronous machine with equal inertia, during a % frequency drop, is also plotted as a dashed line. The aailable resere oer a long period from the wind turbine is less than that expected from a synchronous machine of the same inertia, een though for a gien interal it may be able to supply much more kinetic energy than a synchronous machine. B. Dependence of Energy Capture on De-rating The penalty of offering kinetic energy is reduced energy capture. Ideally, as assumed by (6), de-rating would not be used except during ten-minute interals when mean wind speed was expected to fall in the interal [ L, H ]. In Fig, the quantity of energy sacrificed to proide kinetic energy resere is plotted. Due to the low energy density in the range [ L, H ] and limited aailability, the reduction in energy capture is small. For example, at a de-rating of %, the change ΔE WH in energy capture is only.8% E KR (MJ)

8 % 7 x 4.5 ECKR (MJ/year).5 r BE α (%) α (%) Fig.. Yearly E CKR, as function of de-rating α for wind turbine (solid) and synchronous machine of equal inertia (dashed). A maximum occurs close to α =%for the wind turbine chosen. (MJ/year) ΔEWH.5 x α (%) Fig.. Sacrifice of energy capture traded for kinetic energy resere, oer year, as a function of de-rating. Total capture is 9. 6 MJ (89 MWh) C. Break-een Analysis It may be that in systems with a high amount of wind power, the proision of kinetic energy from wind farms would be mandated by grid code. In that case, the economic burden of doing so is of interest, and this can be inferred from Fig.. In the eent that some compensation is proided for such a serice, it also becomes of interest to know what price would make the serice iable or een profitable for a wind farm operator. Let the price offered for a unit of energy on the wholesale market be p WH, and that offered for kinetic energy resere be p KR. If the quantities of energy sacrificed and deliered into these two markets oer the course of year are ΔE WH and E CKR respectiely, then the condition of breaking een is EWH p KR E CKR p WH ΔE WH = (3) and a break-een ratio r BE can be identified: r BE = p KR = ΔE WH (4) p WH E CKR In Fig, r BE is plotted. It appears that that short-term kinetic energy resere would hae to be alued significantly higher than wholesale energy if the offering of kinetic energy resere were to be economically neutral. If the de-rating α is chosen in the range.5% 3% so as to yield a useful aailability, then the break-een ratio r BE ranges from about Fig.. Break-een price ratio r BE of the kinetic energy resere price to the wholesale price, as a function of de-rating. Aailability A (%) 5 5 Weibull c Weibull k Turbulence Intensity 4 4 % change in parameter (a) Aailability (as percentage of total # minute interals) r BE Weibull c Weibull k Turbulence Intensity 4 4 % change in parameter (b) Break-een price ratio r BE Fig. 3. Sensitiity to site wind resource parameters for de-rating of %; plot ranges oer IEC standard classes IEC I-IV, turbulence A-C, k to 8. A marginal price for kinetic energy has been inferred in one literature study of a power system dispatch model and its security constraints []. The breakeen ratio r BE can be compared with the ratio of prices obsered in that work. For illustration, α =%will be chosen, with a break-een ratio of 7. Assuming a spot price of 3 euro/mwh as in [], this would translate to a alue of.6 euro/mj for resere kinetic energy. This outcome is promising, as the marginal price for kinetic energy inferred in [] was at least this amount, and sometimes as much as 4-5 times as much. D. Sensitiity Analysis The sensitiity of the preceeding results to the characteristics of the wind resource has been studied by taking IEC classes as a reasonable range of possible alues. The c and k parameters ary oer the IEC classes I-III as indicated in Fig. 5, and three turbulence intensity classes A-C are identified by the IEC []. The sensitiity of the aailability A and the break-een price ratio r BE, are shown in the so-called spider plots of Fig. 3(a) and 3(b). For the model wind turbine studied, aailability aried as much as ±5% with site parameters, but did not reduce to zero for any of the IEC classes. Higher aailability corresponded to site parameters corresponding to low mean wind speed, high shape factors, and low turbulence intensity. Break-een ratio was relatiely insensitie to site parameters, except for turbulence intensity. This may be due to the tradeoff between A and E k.

9 8 V. CONCLUSIONS The kinetic energy resere aailable from wind turbines using a de-rating philosophy was studied. De-rating increases the size of the resere but decreases its aailability, and there is thus an optimal de-rating from the perspectie of yearly cummulatie kinetic energy resere. For the wind turbine chosen and an IEC II B wind resource, the kinetic energy resere made aailable was maximized by a de-rating of about %. For this de-rating, a resere of energy.3 MJ could be made aailable 5% of the time. A synchronous machine offers a similar quantity of resere during a major frequency drop, but does so continuously. The yearly quantity of kinetic energy made aailable for a de-rating of % was 3MJ, which is about one-fifth the quantity that would be aailable from a synchronous machine oer the same period. To obtain this quantity, about.8% of total yearly capture would be sacrificed from sales on the wholesale market. It was found that the market alue of kinetic energy resere per unit of energy would hae to be seen times that of wholesale energy in order for economic break-een. This analysis has been based on probability distributions, which offer easy computation of cumulatie results based on analytical expressions, but cannot describe the consequences of time ariations. Also, the sensitiity of the results to wind turbine model should be inestigated. Approximations were necessary that gie a pessimistic estimate of the kinetic energy resere. In order to more accurately assess the aailability of kinetic energy from wind turbines, an analysis method should account for the spectral content of wind speed and wind turbine dynamics in the minute to second range time scale. In addition, allowing shorter market interals might allow a better exploitation of the kinetic energy resere. REFERENCES [] T. Burton, D. Sharpe, N. Jenkins, and E. Bossanyi. Wind Energy Handbook. Wiley,. [] International Electrotechnical Commission. IEC 64-, Wind Turbines - Part : Design Requirements. Wiley,. [3] J. Conroy and R. Watson. Frequency response capability of full conerter wind turbine generators in comparison to conentional generation. IEEE Transactions on Power Systems, 3(), May 8. [4] J. Ekanayake and N. Jenkins. Comparison of the response of doubly fed and fixed-speed induction generator wind turbines to changes in network frequency. IEEE Transactions on Energy Conersion, 9(4):8 8, 4. [5] M. O Malley G. Lalor, A. Mullane. Frequency control and wind turbine technologies. IEEE Transactions on Power Systems, (4):95 93, Noember 5. [6] C. Jauch, J. Mateosyan, T. Ackermann, and S. Bolik. International comparison of requirements for connection of wind turbines to power systems. Wind Energy, 8:95 36, 5. [7] P.K. Keung, P. Lei, H. Banakar, and B.T. Ooi. Kinetic energy of windturbine generators for system frequency support. IEEE Transactions on Power Systems, 4():79 87, 9. [8] J. 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In Nordic Wind Power Conference 9, Sept - 9. [4] J. G. Slootweg, H. Polinder, W. L. Kling, and J.A Ferreira. Representing wind turbine electrical generating systems in fundamental frequency simulation. IEEE Transactions on Energy Conersion, 8(4):56 54, December 3. [5] G. Tarnowski, P. Kjaer, P. Sørensen, and J. Østergard. Study on ariable speed wind turbines capability for frequency response. In Proceedings of the 9 European Wind Energy Conference, 9. [6] E. Vittal, J.D McCalley, V. Ajarapu, and T. Harbour. Wind penetration limited by thermal constraints and frequency stability. Power Symposium, 7. NAPS 7. 39th North American, pages , 7. Barry G. Rawn (S3) receied the PhD degree in electrical engineering from the Department of Electrical & Computer Engineering at the Uniersity of Toronto in March, where he receied the BASc and MASc degrees in Engineering Science and Electrical Engineering respectiely from the Uniersity of Toronto in and 4. He is currently a postdoctoral researcher in the Department of Electrical Sustainable Energy at the Delft Uniersity of Technology, The Netherlands. Madeleine Gibescu (M5) receied the Dipl.Eng. in power engineering from the Uniersity Politehnica, Bucharest, Romania in 993 and her MSEE and Ph.D. degrees from the Uniersity of Washington, Seattle,WA, U.S. in 995 and 3, respectiely. She has worked as a Research Engineer for Clear- Sight Systems and as a Power Systems Engineer for the AREVA T&D Corporation. She is currently an Assistant Professor in the Department of Electrical Sustainable Energy at the Delft Uniersity of Technology, The Netherlands. Wil L. Kling (M95) receied the M.Sc. degree in electrical engineering from the Eindhoen Uniersity of Technology, the Netherlands, in 978. From 978 to 983 he worked with Kema, from 983 to 998 with Sep and since then up till the end of 8 he was with TenneT, the Dutch Transmission System Operator, as senior engineer for network planning and network strategy. Since 993 he is a part-time Professor at the Delft Uniersity of Technology, and from December 8 he is appointed as a full Professor and chair of Electrical Power Systems group at the Eindhoen Uniersity of Technology. He is leading research programs on distributed generation, integration of wind power, network concepts and reliability issues. Prof. Kling is inoled in scientific organisations such as Cigré and IEEE. He is the Dutch representatie in Study Committee C6 Distribution Systems and Dispersed Generation and the Administratie Council of Cigré.