A simplified wind power generation model for reliability evaluation

A Simplified Wind Power Generation Modelfor Reliability EvaluationRajesh Karki,Senior Member,IEEE,Po Hu,Student Member,IEEE,and Roy Billinton,Life Fellow,IEEEAbstract—Renewable energy sources,especially wind turbine generators,are considered as important generation alternatives in electric power systems due to their nonexhausted nature and benign environmental effects.The fact that wind power penetra-tion continues to increase has motivated a need to develop more widely applicable methodologies for evaluating the actual benefits of adding wind turbines to conventional generating systems.Relia-bility evaluation of generating systems with wind energy sources is a complex process.It requires an accurate wind speed forecasting technique for the wind farm site.The method requires historical wind speed data collected over many years for the wind farm lo-cation to determine the necessary parameters of the wind speed models for the particular site.The evaluation process should also accurately model the intermittent nature of power output from the wind farm.A sequential Monte Carlo simulation or a multi-state wind farm representation approach is often used.This paper presents a simplified method for reliability evaluation of power systems with wind power.The development of a common wind speed model applicable to multiple wind farm locations is pre-sented and illustrated with an example.The method is further simplified by determining the minimum multistate representation for a wind farm generation model in reliability evaluation.The paper presents a six-step common wind speed model applicable to multiple geographic locations and adequate for reliability eval-uation of power systems containing significant wind penetration. Case studies on a test system are presented using wind data from Canadian geographic locations.Index Terms—Generation system,reliability evaluation,time-series model,wind power.I.I NTRODUCTIONW IND is one of the fastest growing energy sources,and is regarded as an important alternative to traditional power generating sources.Enhanced public awareness of the environ-ment has led to rapid wind power growth throughout the world to reduce greenhouse gas emissions associated with conventional energy generation.An energy policy known as the renewable portfolio standard(RPS)is being widely accepted around the world.Acceptance of the RPS is a commitment to produce a specified percentage of the total power generation from renew-able sources within a certain date.In the North America,many US states and Canadian provinces have agreed to generate be-tween5%and25%of electrical power from renewable energy resources by2010–2015.Most of this renewable energy willManuscript received September15,2005;revised September15,2005.Paper no.TEC-00177-2005.The authors are with the Power System Research Group,Department of Electrical Engineering,University of Saskatchewan,Saskatoon,SK S7N5A9Canada(e-mail:Rajesh.Karki@usask.ca,poh591@ask.ca, Roy Billinton@ask.ca).Digital Object Identifier10.1109/TEC.2006.874233come from wind as other renewable sources are not suitable for bulk power generation.The development of comprehensive reliability and cost-evaluation techniques becomes more important as wind power penetration levels in traditional power systems continue to in-crease in the near future.Both Monte Carlo simulation[1],[2] and analytical methods[3]–[5]have been utilized in adequacy assessment of generation systems containing wind power. Simulation methods can recognize the chronology of wind variation and its impact on a power system.Reference[6] presents an algorithm to simulate the hourly wind speed us-ing a time-series auto regressive and moving average(ARMA) model.The method requires actual hourly wind speed data col-lected over a long period of time for the particular geographic location to construct a wind speed simulation model for the specific site.This model can reflect the true probabilistic char-acteristics of wind speed for the wind site.The process for obtaining the proper ARMA model is quite complex,and is specific to the geographic location of the wind plex techniques are not readily applied in a practical world.It would be very useful from a practical application point of view if a common ARMA model could be developed that would work for multiple wind farm locations[7].It should also be noted that historical wind data are not available for all poten-tial wind farm locations.This paper presents the development of a common wind speed model that can generate wind speed prob-ability distributions for multiple wind farm sites if their annual mean wind speed and standard deviation are known.Histori-cal wind speed data from three Canadian sites(Swift Current, North Battleford,and Toronto,which have different geographic characteristics),are used in this paper to obtain the common wind speed model.The wind speed distribution obtained from the common wind speed model can then be used in an analytical method for reliability evaluation of power systems containing wind farms.A wind turbine generator(WTG)is modeled as a multistate unit in reliability evaluation using an analytical method[3]–[5]. The multistate model represents a WTG by a number of derated power output states using the wind speed model for the wind farm location and the power curve of the WTG.The model appropriately reflects thefluctuating characteristics of the site-specific wind.Reliability studies using the Roy Billinton Test System (RBTS)[8]are presented to determine the appropriate number of states in the multistate WTG model,and develop a simpli-fied model applicable to any wind farm connected to a power system.The development of a simplified6-step common wind speed model that can be applied to any wind farm in power0885-8969/$20.00©2006IEEEsystem reliability evaluation is presented.The validity of the developed method and its practicality is illustrated by evaluat-ing wind power penetration in the RBTS.II.S ITE-S PECIFIC W IND D A TA S IMULA TIONWind resource at a geographic location is highly variable. Power generated from WTG depends on the wind speed,which fluctuates randomly with time.Wind power studies,therefore, require accurate models to forecast wind speed variation for wind farm locations of interest.Wind speed distributions are often characterized by Weibull distributions,and methods using Weibull distributions[5]have been previously used to estimate wind speed data in wind power studies.Historical hourly data for the wind farm site collected over significant time are normally required to obtain the shaping parameters.An ARMA time-series model has been used by researchers [1],[2],[6]as an accurate method to forecast wind speed data at any particular location.The wind speed at any given time for a particular geographic location can be simulated using(1)SW t=µt+σt...y t(1) where SW t is the simulated wind speed for hour t from his-torical mean wind speedµt and standard deviationσt.Time-series values of y t can be obtained sequentially using(2),where ϕi(i=1,...,n)andθj(j=1,...,m)are the auto-regressive and moving average parameters of the model,respectively y t=φ1y t−1+φ2y t−2+...+φn y t−n+αt−αt−1θ1−αt−2θ2−...−αt−mθm(2) where{αt}is a normal white noise process with zero mean and a variance ofσ2a(i.e.,αt∈NID(0,σ2a),where NID denotes normally independently distributed.The order[n,m]and the values of the auto-regressive and moving average parameters shown in(2)can be obtained from many years of collected wind speed data using nonlinear least-square methods[9].A computer program was developed to estimate the parameters of ARMA(n,m)models for geographic wind farm sites using the algorithm provided in[9].Historical wind data was obtained for three different locations in Canada:Swift Current,North Battleford,and Toronto.Swift Current lies in the southern part of the Saskatchewan province and is home to one of the largest wind farms in Canada.North Battleford lies to the north in the same province,but does not have a good wind resource.Toronto lies at the great lakes and has a coastal wind regime.These three locations have diverse wind variation patterns and are therefore selected in the study. Historical data on hourly wind speeds for three years(from January1,2001to December31,2003),and the hourly mean and standard deviation of wind speeds from a15-year database (from January1,1989to December31,2003)were obtained from Environment Canada to determine the ARMA model for the Swift Current location.The parameters are shown in(3) y t=0.8782y t−1−0.0066y t−2+0.0265y t−3+αt−0.2162αt−1+0.0091αt−2(3)αt∈NID(0,0.557922).TABLE IM AIN S TA TISTICAL C HARACTERISTICS OF S IMULA TEDAND A CTUAL W IND S PEED D ATAEquations(4)and(5)show the time-series ARMA models obtained similarly for North Battleford and Toronto locations respectivelyy t=1.7901y t−1−0.9087y t−2+0.0948y t−3+αt−1.0929αt−1+0.2892αt−2(4)αt∈NID(0,0.4747622)y t=0.4709y t−1+0.5017y t−2−0.0822y t−3+αt+0.1876αt−1−0.2274αt−2(5)αt∈NID(0,0.55082).Hourly wind speeds were repeatedly simulated for a large number of yearly samples to obtain annual wind speed data for the three sites.Table I shows the mean value and standard de-viation of20years’average actual collected data and simulated wind speed data for a year for these sites.It can be seen that the simulated values are very close to those obtained from the actual data.The entire range of the simulated data is equally divided into N a intervals,and the SW ai(i=1,...,N a)is the midpoint of each interval.The probability P ai of a wind speed in an interval SW ai(i=1,...,N a)can be obtained using(6)by counting the number N ai(i=1,...,N a)of simulated wind speed data in the intervalP ai=N ai/(8760×N y)(6) where N y is the number of sample years simulated.The wind speeds SW ai at each of the N a intervals and their corresponding probabilities of occurrence P ai were calculated for the three sites.Fig.1shows the probability distributions of simulated wind speed data for these three sites.Wind speed probability distributions are often represented by Weibull distributions.Weibull distribution in general can have various shapes depending on the shaping parameters.The wind speed probability distributions obtained for the three diverse geographic locations,however,are close to normal distribution as shown in Fig.1.It can however be seen that the three curves are quite different,as the three selected sites have different types of wind regimes.Time-series ARMA model generate both positive and negative values of wind speeds as seen in Fig.1. Negative values have no physical meaning in this study,and are set to zeros as recommended in[7].KARKI et al.:A SIMPLIFIED WIND POWER GENERATION MODEL FOR RELIABILITY EV ALUATION535Fig.1.Probability distributions of simulated wind data.III.C OMMON W IND S PEED M ODEL FORM ULTIPLE W IND S ITESThe determination of a proper wind speed model for a wind farm location is a complicated process as described in Section II.The process also requires historical wind speed data collected over a significant period of time.It would be very useful for prac-tical applications,if a common wind speed model could be used for benefit analysis of wind power sources located at different geographic sites.This approach will prove useful for prospec-tive wind farm locations lacking adequate historical data.The objective is to determine a general model that can be used to obtain power output from wind turbines located at different sites with reasonable accuracy.The probability distributions of wind speeds at the three se-lected geographic sites are shown in Fig.1in Section II.In this section,the probability distributions are plotted in terms of the annual mean wind speed valueµ,and the standard de-viationσfor the selected locations.The distribution consid-ers wind speeds up to10σto include extreme values despite their low probability of occurrences.The distribution is di-vided into N b number of interval steps,and each step has a length of10σ/N b,where the midpoint values of these steps are SW b i(i=1,...,N b),and one of the steps has a midpoint value ofµ.The steps SW b i are defined as in(7).For example,for a 100-step model,the midpoint values SW b i of the wind speed steps will be as follows:µ–4.9σ,µ–4.8σ,...,µ–0.1σ,µ,µ+ 0.1σ,µ+0.2σ,...,µ+5σ.The probability of each step P b i(i=1,...,N b)can be calculated by(8)SW b i=µ+(10σ/N b)×(i−0.5×N b)for even N b,and =µ+(10σ/N b)×(i−0.5×(N b+1))for odd N b(7) P b i=N b i/(8760×N y)(8) where N b i is the number of simulated wind speed data in the step SW b i(=1...,N b)bining wind speed models for different sites.The probability distributions plotted in terms ofµandσas discussed above are shown in Fig.2for the three locations.It can be seen that the three curves are very close.The three curves for the three different wind regimes can be combined to obtain a common wind speed model.The probability P c i(i=1,...,N b) for each step in the common wind speed model is obtained by taking the average value of P b i(i=1,...,N b)for these three wind sites.Fig.2also shows the curve for the common wind speed model.The common wind speed model can be used to obtain the wind speed probability distribution for any geographic location with wind speed characteristics close to the selected Canadian sites.The only data required are the annual mean wind speedµand the standard deviationσfor that site.Negative wind speed values are converted to zeroes in this process.It is shown in Section VI that the wind speeds and their probabilities obtained for a specific site using the common wind speed model can be used with reasonable accuracy in the reliability evaluation of power systems containing wind power.Fig.3shows a common wind speed model that can be used for multiple geographic locations.The application of the common wind speed model in Fig.3 is illustrated in this paper by applying it to a site in Regina, Saskatchewan.Theµandσvalues for Regina wind data are 19.53and10.06km/h,respectively.The common wind speed model is used to obtain the wind speeds and their corresponding probabilities for the example site.Table II shows the wind speeds in km/h and their corresponding probabilities.Only5out of the 100steps in the wind speed model are shown.It should be noted that the negative values are converted to zeroes in Table II.IV.C OMMON WTG P OWER G ENERA TION M ODEL FORR ELIABILITY E V ALUA TIONIt is important to accurately assess the electric power gen-erated by a WTG located at a particular geographic site in re-liability analysis.The generated power varies with the wind536IEEE TRANSACTIONS ON ENERGY CONVERSION,VOL.21,NO.2,JUNE2006mon wind speed model.TABLE IIW IND M ODEL FOR R EGINA S ASKA TCHEWANFig.4.Power curve of a WTG.speed at the wind farm site.The power output of a WTG canbe determined from its power curve,which is a plot of output power against wind speed.Fig.4shows a typical power curve of a WTG.A WTG is designed to start generating at the cut-in speed V ci (V c )and is shut down for safety reasons at the cut-out speed V co .Rated power P r is generated when the wind speed is between the rated speed V r and the cut-out speed V co .There is a nonlinear relationship between the power output and the wind speed when the wind speed lies within the cut-in speed V ci and the rated speed V r as shown in Fig.4.Fig.5.Development of a WTG model.Fig.5shows the development of the power generation model of a WTG located at a particular geographic site.The annual µand σwind speed data for the wind farm site is used in the common wind speed model shown in Fig.3to obtain the site-specific wind speed model.This site-specific wind speed model is then combined with the WTG power curve to obtain the WTG power generation model.Equation (9)is the mathematical expression for the power curve.The power generated P i (i =1,...,N b )corresponding to a given wind speed SW b i (i =1,...,N b )can therefore be obtained from (9)P i =0,0≤SW b i <V ci=P r (A +B ×SW b i +C ×SW 2b i ),V ci ≤SW b i <V r=P r ,V r ≤SW b i ≤V co =0,V co <SW b i(9)where the constants A,B ,and C are presented in [3].Wind speeds less than V ci and greater than V co produce zero output power from the WTG.The wind speed model steps cor-responding to these values can,therefore,be combined into a cumulative step,and the zero output probability P p0can be ob-tained from (10).Similarly,wind speed steps between V r and V co can be combined,and the probability of rated power output P pr can be obtained from (11)P p0=P ci for 0≤SW b i <V ci or V co <SW b i (10)P pr =P cifor V r ≤SW b i ≤V co(11)The application of the common WTG power generation model is illustrated in this paper by applying it to a WTG installed in Regina.WTG rated at 1.5MW,and with cut-in,rated,and cut-out wind speeds of 14.4,45,and 90km/h,re-spectively,are used in the studies.The site-specific wind speed model shown in Table II is combined with the power curve to obtain the WTG generation model.Table III shows the power output levels and their corresponding probabilities.The 100-step wind speed model in Table II is reduced to 33steps in the power generation model in Table III as different wind speeds producing the same power level are aggregated into single steps.KARKI et al.:A SIMPLIFIED WIND POWER GENERATION MODEL FOR RELIABILITY EV ALUATION 537TABLE IIIP OWER G ENERA TION M ODEL FOR A WTG IN REGINATABLE IVT RADITIONAL G ENERA TING U NIT R ELIABILITY D A TA(RBTS)A wind farm usually consists of many WTG units subjected to the same wind regime characterized by the geographic loca-tion.The total power generation model for the wind farm can be obtained by summing up the individual WTG power levels corresponding to each wind speed interval in the common wind speed model.V .V ALIDITY OF THE C OMMON W IND S PEED M ODEL FORR ELIABILITY S TUDIES The power generation model for a wind farm can be easily obtained from the common wind speed model shown in Fig.3using only the site-specific µand σdata and the WTG power curve.The validity of this common model for practical reliability applications is analyzed using a test system.Reliability studies using analytical techniques were conducted on the RBTS [8]to illustrate the practicality of a common wind speed model for different sites.The RBTS is a basic reliability test system that evolved from the research and teaching program conducted at the University of Saskatchewan.The RBTS consists of 11traditional generating units with a total capacity of 240MW.The generating unit ratings and reliability data are shown in Table IV.The system peak load is 185MW [8].A wind farm with 18WTG units was added to the RBTS.WTG rated at 1.5MW,and with cut-in,rated,and cut-out wind speeds of 14.4,45,and 90km/h,respectively,was used in the studies.The added wind capacity is 27MW,which is almost 10%of the total installed system capacity.The generating system adequacy of the test system was eval-uated for three different cases,in which the wind farm was considered at separate locations with North Battleford,Toronto,and Swift Current wind regimes.Table I shows the mean wind speed and the standard deviation for the three sites.Table V shows the loss of load expectation (LOLE)[10]for the RBTS before and after adding WTG at the different locations.The LOLE results were obtained by convolving theTABLE VLOLE C OMPARISON OF RBTS I NCLUDING WECS L OCA TEDA T D IFFERENT W IND SITESFig.6.LOLE comparison for North Battleford using its ARMA model and the common wind speed model.system generation model with the load model using an analytical technique.The conventional generating units were represented by a two-state model,in which the unit is either operating at rated power output or on forced outage.To account for the randomly varying power output from WTG units,they were represented by 100-state model in the studies.The annual load duration curve for the RBTS was used as the load model,and the data are provided in [8].The second row of Table V shows the indices using the site-specific ARMA models shown in (3)–(5)for the three locations.The third row shows the results obtained using the common wind speed model in Fig.3.It can be seen that the results are very close.It can also be seen from Table V that the adequacy of the RBTS is improved by adding the 27-MW wind farm.The improvement with the Swift Current site is more significant than that of the other two locations,as Swift Current has a higher mean wind speed,and therefore,provides a better wind resource.Table V shows that the common wind speed model produces accurate results for wind farm locations with different wind regimes.Power system reliability is very sensitive to changes in the system peak load.The accuracy of the common wind speed model is therefore analyzed for different peak load levels at the three geographic wind farm locations.Fig.6shows the system LOLE for different peak load levels with the wind farm located in North Battleford.The results obtained using the common wind speed model is compared with those obtained using the North Battleford ARMA model given in (4).Fig.6shows that the common wind speed model also produces very close results at different peak load levels.Fig.7shows similar results when the wind farm is considered to be in the Toronto location.The results show that the common wind speed model can be utilized in the reliability evaluation of power systems containing wind farms,538IEEE TRANSACTIONS ON ENERGY CONVERSION,VOL.21,NO.2,JUNE2006Fig.7.LOLE comparison for the Toronto Data using its ARMA model and the common wind speed model.and provide very close results compared to the site-specific ARMA models for the different sites.VI.S IMPLIFIED M ULTISTA TE WTG M ODELA conventional generating unit is usually represented by a two-state model in power system reliability evaluation.The two states are the unit-operating state with rated power output,and the unit-failure state with zero output.A WTG unit,however, cannot be represented by a two-state model since the power output can vary continuously and intermittently from zero to the rated value depending on the wind speed at the wind farm site. WTG units are therefore represented by multistate models in analytical methods used in power system reliability assessment. Accurate reliability assessment can be obtained by represent-ing a wind farm by a large number of discrete output states. This can be obtained from a wind speed model with a large number of discrete wind speed steps.The model can be simpli-fied by reducing the number of steps at the cost of accuracy.It is,therefore,important to determine the minimum number of steps that can be used in a simplified wind speed model to obtain reasonable accuracy for all practical purposes.Studies were done to evaluate the system LOLE with increas-ing peak load levels using different numbers of wind speed steps in the common wind speed model.The wind farm is assumed to be located in Swift Current.Fig.8shows the results of the study.It can be seen that using six or more steps in the wind speed model provides close results.The reliability contribution of a wind farm highly depends on the site wind regime.Studies similar to that shown in Fig.8were also conducted for a wind farm site with a different wind regime. Fig.9shows the system LOLE results for the case in which the wind farm is assumed to be located in Toronto.Fig.9also shows that a6-step wind speed model is adequate for reliability studies with reasonable accuracy.It should be noted that27MW of wind capacity is added to the RBTS in the above studies,which amounts to about a10%wind penetration.Since the reliability contribution of wind sources is highly dependent on the wind penetration level,it is important to determine the appropriate number of wind speed model steps at practical wind penetration levels.The existing wind penetration levels in most power systems are much lower than10%for Fig.8.Swift Current wind site with a10%wind power penetration level(18WTG).Fig.9.Toronto wind site with a10%wind power penetration level(18WTG). Fig.10.Swift Current wind site with a15%wind power penetration level(28WTG).which the above results are obtained.Studies conducted for wind penetration of1%showed that the number of steps had no impact on the system LOLE results.When the penetration level is insignificant,wind power has relatively little influence on the total system reliability performance.Reliability evaluation in power system planning should con-sider a long-term planning horizon.It is expected that wind power penetration will grow to10%–15%in the next10–15 years.Fig.10shows the results obtained when the wind farm added to the RBTS contains28WTG units,increasing the wind penetration to15%of the total installed system capacity.The results show that a six-step wind speed model is adequate for reliability studies with reasonable accuracy.KARKI et al.:A SIMPLIFIED WIND POWER GENERATION MODEL FOR RELIABILITY EV ALUATION539Fig.11.Six-step common wind speed model.TABLE VISix-S TEP W IND M ODEL FOR R EGINA SITETABLE VIIS IMPLIFIED P OWER G ENERA TION M ODEL FORTHE R EGINA W IND FARMThe 6-step common wind speed model that can be used for reliability studies of power systems with reasonable accuracy is shown in Fig.11.The model shows the six wind speed steps and the corresponding probabilities.The wind speeds for a ge-ographic site can be obtained from this model using (12),if µand σfor the site are known SW b i =µ+(i −3)×(5σ/3)for (i =1,...,6).(12)The application of the six-step common wind speed model is illustrated by applying it to a site in Regina.Table VI shows the wind speeds in km/h and their corresponding probabili-ties.It should be noted that the negative values are converted to zeroes.A simplified multistate power generation model for a WTG can be determined by combining the 6-step common wind speed model with the power curve equation (9).This method can be utilized to develop a simple but adequate multistate wind generation model.The only data required are the wind farm site annual µand σdata,and the power-curve data for the WTG units.For example,Table VII shows the simplified multistate power generation model for a wind farm consisting of 18WTG units in Regina.Fig.12shows the results of reliability assessment of the RBTS system with 10%wind penetration coming from the 27-MW Regina wind farm.The shaded bars show the LOLEresultsparison of different models for WTG power output by LOLEindex.using the simplified model in Table VII.The results obtained from the simplified model are compared with those obtained from a 100-step wind speed model derived from an accurate ARMA (4,3)model for Regina as shown in (13)y t =0.9336y t −1+0.4506y t −2−0.5545y t −3+0.1110y t −4+αt −0.2033αt −1−0.4684αt −2+0.2301αt −3(13)αt ∈NID(0,0.4094232)It can be seen from Fig.12that the simplified multistate WTG power generation model derived from the common 6-step wind speed model can provide very close results when compared with the 100-step model derived from the site-specific time-series ARMA wind speed model for Regina.The simplified model can therefore be used in the reliability evaluation of generating system including wind power with reasonable accuracy.VII.C ONCLUSIONIt becomes increasingly important to develop realistic reliabil-ity evaluation techniques that are practically useful for electric power industries that are expected to include a rapidly growing proportion of wind generation in the coming years.The bene-fits from wind sources are largely dictated by the wind regime at the wind farm site.It is,therefore,very important to obtain suitable wind speed simulation models and appropriate tech-niques to develop power generation model for WTG in reliability evaluation.It requires a significant amount of historical data and effort to develop a realistic wind speed model for a geographic site.Historical data from three Canadian sites with diverse wind regimes were used to obtain a common wind speed model in this paper.The common wind speed model can be applied to obtain a wind farm power generation model for any geographic location if the mean wind speed and standard deviation,and the WTG power curve parameters are known.Results from different analytical reliability studies are presented in this paper to show that a wind power generation model can be greatly simplified by using only 6steps in the common wind speed model.The technique to develop the simplified WTG multistate model for any geographic location is presented and illustrated with an example.The results show that the simplified method。