DECEMBER 2008 CASSOLAETAL. 3099

Optimization of the Regional Spatial Distribution of Wind Power Plants to Minimize the Variability of Wind Energy Input into Power Supply Systems

FEDERICO CASSOLA,MASSIMILIANO BURLANDO,MARTA ANTONELLI, AND CORRADO F. RATTO Department of Physics, University of Genoa, Genoa, Italy, and National Consortium of Universities for Physics of Atmospheres and Hydrospheres (CINFAI), Toronto, Ontario, Canada

(Manuscript received 1 October 2007, in final form 15 February 2008)

ABSTRACT

In contrast to conventional power generation, wind energy is not a controllable resource because of its stochastic nature, and the cumulative energy input of several wind power plants into the electric grid may cause undesired fluctuations in the power system. To mitigate this effect, the authors propose a procedure to calculate the optimal allocation of wind power plants over an extended territory to obtain a low temporal variability without penalizing too much the overall wind energy input into the power system. The procedure has been tested over Corsica (France), the fourth largest island in the Mediterranean Basin. The regional power supply system of Corsica could be sensitive to large fluctuations in power generation like wind power swings caused by the wind intermittency. The proposed methodology is based on the analysis of wind measurements from 10 anemometric stations located along the shoreline of the island, where most of the population resides, in a reasonably even distribution. First the territory of Corsica has been preliminarily subdivided into three anemological regions through a cluster analysis of the wind data, and the optimal spatial distribution of wind power plants among these regions has been calculated. Subsequently, the 10 areas around each station have been considered independent anemological regions, and the procedure to calculate the optimal distribution of wind power plants has been further refined to evaluate the improve- ments related to this more resolved spatial scale of analysis.

1. Introduction not without consequences for many power systems yet. In contrast to conventional power generation, where After the Kyoto conference on global climate change energy input can be scheduled and regulated to be con- in 1997, the worldwide on- and offshore capacity of sistent with the national power supply system (PSS), grid-connected wind power plants has increased expo- wind energy is indeed not a controllable resource be- nentially. According to the Global Wind Energy Coun- cause of its stochastic nature. cil Report (2006), 2006 was another record year for the On the local scale, the control system for a single wind energy market, with installations of 15 197 MW, wind power plant is usually designed just to regulate the which has brought the total installed wind energy energy output of both the overall wind farm and indi- capacity to 74 223 MW. In terms of new installed ca- vidual wind turbines to optimize the wind farm dynamic pacity in 2006, the United States continued to lead. performance (Steinbuch et al. 1988; Chinchilla et al. Nevertheless, Europe still remains the market leader 2005). At this scale, the interest is primarily focused on with 48 545 MW of installed capacity, representing 65% the evaluation of the maximum wind turbine efficiency of the global total. so as to extract as much energy as possible (Mosetti et From a technical point of view, at present, wind en- al. 1994; Milligan and Factor 2000). ergy is often conveniently integrated into regional elec- On the regional or national scale, the cumulative en- tricity supply systems, but its intermittent character is ergy input of the overall wind power plants may cause noticeable input fluctuations in the power system. In- deed, the intermittency of wind is directly transmitted Corresponding author address: Federico Cassola, Department of Physics, University of Genoa, Via Dodecaneso 33, 16146 into the power supply system and this dramatically re- Genoa, Italy. duces the marketing value of wind energy (Milligan and E-mail: [email protected] Porter 2005). At an operational level, the actual chal-

DOI: 10.1175/2008JAMC1886.1

© 2008 American Meteorological Society Unauthenticated | Downloaded 09/26/21 12:40 PM UTC

JAMC1886 3100 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 47 lenge is to develop accurate models to perform wind After stating the advantages of interconnected wind power forecasting to predict the overall energy input farms with respect to an individual wind farm in terms into the power system (Persaud et al. 2003). For ex- of base load power supply and reduction of the vari- ample, the “development of a next-generation wind re- ability of wind energy production (see also Kahn 1979; source forecasting system for the large-scale integration Archer and Jacobson 2003; Simonsen and Stevens of onshore and offshore wind farms” (ANEMOS) 2004), in the present paper we suggest a possible meth- project (Kariniotakis et al. 2006) focuses on forecasting odology to answer the specific question about which the wind resource available for wind power plants up to wind power distribution maximizes the base load and two days ahead through physical and statistical predic- minimizes the variability. Therefore, following the idea tion models (Giebel et al. 2006; Sánchez 2006; Madsen that the spatial distribution of wind power plants on a et al. 2005). The outcome of the ANEMOS project is regional scale could be optimized to guarantee the expected to increase the wind energy integration minimum temporal variability without penalizing too through an optimized management of the risk related much the overall wind energy input into the power sys- to the intermittent nature of wind generation. tem, we propose a procedure to calculate the optimal Provided that short-term wind power prediction is a allocation of fractions of wind power through the mini- primary requirement for the efficient integration of mization of either the wind energy variability or the wind energy in power systems and electricity markets, it ratio between energy variability and energy input into is also of particular interest to the wind power industry the PSS. On behalf of Agence De l’Environment et de to develop standard procedures to find the best way to la Maîtrise de l’Energie (ADEME) and Collectivité distribute wind-generating capacity among several Territorial de Corse, this procedure has been applied to sites, to control the stability of the overall wind energy Corsica (France), the fourth largest island in the Medi- input into the power system. For example, Pantaleo et terranean Basin, and is based on two steps: al. (2003) noted that the high concentration of the Ital- • wind measurements at 10 m above ground level ian wind energy resource in few areas of southern re- (AGL) are converted into wind power output at gions could cause grid integration difficulties, like over- higher levels; loading and regulation problems. Archer and Jacobson • the aforementioned minimization is performed to (2007) suggested interconnecting wind farms as a pos- calculate the optimal distribution of a fixed number sible solution to improve wind power reliability by re- of wind power plants among zones with different ducing wind energy fluctuations on the power system. anemological regimes. They show how by linking a certain number of wind farms together, the overall performance of intercon- We anticipate that, in the procedure, the definition of nected systems might improve substantially when com- zones similar from the wind climatology point of view is pared with that of any individual wind farm. The ad- essential to calculate the final optimal spatial distribu- vantages concern both supplying base load power as tion of power plants. These zones can be characterized well as reducing deliverable power swings caused by by individual anemological stations, if enough repre- wind intermittency. Their idea is that while wind speed sentative of the surrounding territory, as well as by clus- could be calm at a given location, it will be higher some- ters of stations. In this paper we shall analyze both where else, so that the wind energy production of the cases, first by considering three large regions and then interconnected system is more regular and constant as 10 smaller regions. the number of interconnected wind farms increases. In The present document is organized as follows: in sec- particular, Archer and Jacobson (2007), starting from tion 2 a short description of the territory under study 19 measurement sites, analyzed the performances of and of available wind measurements is reported. Re- all the possible combinations of k sites (with k 1, 3, 7, sults from a cluster analysis of these anemological 11, 15, 19). In so doing, more than 130 000 different data, performed to identify the different anemological spatial wind power distributions were taken into ac- regions of Corsica (Burlando et al. 2008) within which count, as each site is considered to have a single wind the total wind power should be distributed, are also turbine. For instance, when they analyzed the advan- briefly presented. In section 3, measurements are trans- tages of connecting 11 stations (k 11) over 19, they formed into wind power and the procedure is verified studied all the possible combinations (75 582) of 11 for one station through comparison with the wind en- sites among the 19 of interest. However, since they re- ergy produced by a wind farm already installed in the ported results averaged over all the combinations, the area under study. Section 4 focuses on the methodology question about which combination performs best still for the minimization of wind power variability onto the remains open. power system. Conclusions are drawn in section 5.

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC DECEMBER 2008 CASSOLAETAL. 3101

2. Territory, measurements, and anemology of eter of the island, they could induce fluctuations on Corsica the power supply system with a typical half-day cycle. Instead, synoptically driven regimes are usually charac- The present research has been developed for Cor- terized by winds stronger than breezes, so that they sica, a large island situated in the northwestern part of contribute more significantly to the wind energy budget the Mediterranean Basin. When this study was under- of the island. Contrary to breezes, they typically corre- taken, the island had an independent power supply sys- spond to surface wind patterns with higher winds up- tem because of the geographic isolation from the con- stream of the mountains and large sheltered areas on tinent: the distance from the nearest national coast, in their lee side. For example, during the northeast wind Côte d’Azur, is indeed as far as 90 n mi and the bathym- gregale, the wind mainly blows southward in the east- etry is as deep as about 2000 m. An interconnection ern part of the island and southwestward in the north- with the electrical network of the adjacent Sardinia Is- ern part, while the southern side is sheltered. The other land, that is part of Italy, has been operational since synoptically driven regimes are sirocco, libeccio, and February 2006. Nevertheless, the power supply system maestro, which correspond to the wind coming from of Corsica is still quite limited and sensitive to fluctua- southeast, southwest, and northwest, respectively. All tions in power generation. these wind regimes contribute to lowering the wind The island does not have very relevant industrial ac- speed correlation among their corresponding upstream tivities, and the electricity consumption is strongly de- and downstream areas, and consequently they contrib- pendent on tourism, while its wind energy potential is ute to make the wind energy input more regular and considerable. Therefore, unexpected energy inputs into constant during the year (see, e.g., Kahn 1979; Archer the power system can easily cause undesired fluctua- and Jacobson 2007). Moreover, the rapid succession of tions. The intermittency of wind energy is therefore different surface wind patterns is often brought about particularly critical for the regional power system, and by the advection of a single weather system so that a slowly variable wind energy input would be desirable exposed and sheltered areas interchange with each rather than a very high one. other, thus contributing to maintain more regular wind Following these considerations, the question that energy production for a longer time. This is the case, for arises is whether it is possible to distribute the overall instance, of the typical orographic cyclogenesis in the wind power over the territory in such a way that the Gulf of Genoa, just north of Corsica, induced by the wind power plants “switch on” in turn. We suggest that interaction of a major synoptic low pressure system the answer depends on the morphology and extension of the territory itself. Indeed, Corsica consists of a ter- over central or northern Europe with the Alps (Buzzi ritory about 175 km wide in latitude and 80 km in lon- and Tibaldi 1978; Egger 1988). During the deepening gitude and it is characterized by a very complex topog- phase of the cyclone, westerly regimes (libeccio and raphy, with one main mountain chain crossing the maestro) affect Corsica, thus sheltering the eastern side whole island from the northern to the southern edge of the island. When the cyclone moves away, following and more than 2000-m-high peaks (see Fig. 1). In this a typical southeastward route (Trigo et al. 1999), the geographical context, it is likely to expect that the to- opposite situation occurs: the wind blows mainly from pography strongly influences surface wind regimes, in the northeast (gregale), and the western and southern that when westerly winds blow the wind power plants in parts of Corsica are now the downstream areas. western Corsica are on while the power plants in the To catch the alternation of contributions of different eastern side should be almost off, and vice versa. areas to the wind energy production, we have based our This scheme is in fact a rough approximation of the analyses on measurements from 10 anemometric sta- actual situation. Burlando et al. (2008) identified the tions located along the shoreline of Corsica in a rea- main wind climate regimes of Corsica, showing that sonably even distribution along the whole perimeter of they can be separated into two distinct classes: ther- the island. All stations belong to the Météo France net- mally forced and synoptically driven wind regimes. work and record the horizontal wind intensity and di- Thermally forced regimes are usually low to medium rection at 10 m AGL. They are numbered counter- winds corresponding to sea and land breezes, and they clockwise from 1 (Solenzara) to 10 (Figari) in Fig. 1, consist of flows that converge toward or diverge from while Oletta, used in the previous work by Burlando et the inland areas. Their contribution to the total wind al. (2008), is not explicitly considered in the present energy budget of the island is quite relevant especially paper for the reasons discussed in the following. All during summer. However, as the onset of these circu- wind measurements are averages over the last 10 min of lations is almost synchronous along the whole perim- the hour. The datasets, available for a 3-yr period from

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC 3102 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 47

FIG. 1. Topography of Corsica. The locations of the 11 anemometric stations along the shoreline of the island used in the study are also shown. Stations are numbered counterclock- wise from 1 (Solenzara) to 10 (Figari), while Oletta is not numbered since it is not explicitly considered in the present paper.

1 October 1996 to 30 September 1999, have a sampling lated with respect to the coast and not very suitable for rate every hour (24 times per day from 0000 UTC to the installation of wind power plants because of the 2300 UTC), apart from the dataset of Cap Corse, which very complex topography as well as the presence of records every 3 h (8 times per day from 0000 to 2100 several national parks. UTC). A summary of the main characteristics of the Recently, Burlando et al. (2008) proposed a classifi- stations and of the corresponding datasets is reported cation of Corsica into distinct anemological regions in Table 1: columns 3–5 report geographical coordi- based on a cluster analysis of the aforementioned wind nates and elevation of the stations; average wind speeds measurements. As explained in that paper, the hierar- at 10 m AGL and wind calm percentages are shown in chical cluster analysis requires using synchronous columns 6 and 7; the shape and scale parameters of the datasets (see also Kaufmann and Whiteman 1999), so corresponding nondirectional Weibull probability den- that the analysis was performed only on measure- sity function (Weibull 1951), evaluated from the wind ments simultaneously collected at all stations, namely speed time series at 10 m AGL, are reported in columns for a maximum of N 8760 (3 years 365 days per 8 and 9; finally, column 10 provides average wind year 8 measurements per day). However, the number speeds at 50 m AGL calculated as discussed in section of available measurements per station was N7271, 3a. As suggested by ADEME, inland stations were not which is somewhat lower than N because of recording taken into account, since such areas are scarcely popu- interruptions for maintenance or damage, so that the

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC DECEMBER 2008 CASSOLAETAL. 3103

TABLE 1. Geographical and anemological characteristics of the considered anemometric stations.

Values at Geographical coordinates Values at 10 m AGL 50 m AGL Lon Lat Alt Avg Calms Shape Scale parameter Avg No. Station (°E) (°N) (m, MSL) (m s1) (%) parameter (m s1) (m s1) 1 Solenzara 9.41 41.93 17 3.1 2 2.1 3.4 4.5 2 Alistro 9.54 42.26 65 3.7 8 2.0 4.4 5.5 3 Bastia 9.48 42.55 10 3.1 2 1.9 3.5 5.5 4 Cap Corse 9.36 43.00 80 7.1 4 1.3 8.7 9.5 — Oletta 9.34 42.64 130 2.9 11 1.3 3.3 — 5 Ile Rousse 8.92 42.63 142 4.8 8 1.2 6.0 7.5 6 Calvi 8.79 42.52 57 3.8 3 1.6 4.3 6.5 7 Ajaccio 8.80 41.92 4 3.5 1 2.4 3.8 5.5 8 Pila Canale 8.91 41.82 408 2.3 22 1.5 3.0 4.0 9 Sartene 8.98 41.65 60 2.4 17 1.5 3.1 4.0 10 Figari 9.10 41.51 22 4.9 3 1.7 5.7 7.0 time series of contemporaneous measurements actually the height at which the turbine operates. A common consisted of about 83% of N. problem then arising is how to evaluate the wind speed The anemological regions were defined through the at the turbine hub height. Since in our study only tur- comparison of 15 different clustering techniques result- bines with hub height of h 50 m have been taken into ing from the combination of three distance measures account, we had first to convert, for each anemometric and five agglomerative methods. The results of this station j (j 1,...,10),thewindspeeddataat10m, 10 50 analysis identified the following three wind climate re- j , into the corresponding wind speeds at 50 m, j . gions: the eastern region (ER), the northwestern region The procedure adopted to perform this conversion is (NWR), and the southwestern region (SWR). In par- described in the following subsection. ticular, ER includes the cluster comprising stations 1, 2, a. Calculation of wind speed data at the hub height and 3, NWR includes the cluster comprising stations 4, 5, and 6, and the cluster containing stations 8, 9, and 10 Simple approaches to evaluate the wind speed at the identifies SWR. Station 7 (Ajaccio) showed to be a turbine hub height are, for instance, the logarithmic transitional station between NWR and SWR, whereas and the power-law method (Gipe 1995), which both Oletta (not numbered in Fig. 1) results were unreliable require an estimation of the surface roughness. Archer so that it was not taken into account both in that clus- and Jacobson (2003) developed a more sophisticated tering procedure and in the present paper. methodology to evaluate the wind speeds at 80 m AGL In the framework of the present paper, the concept of from sounding and surface data. anemological regions will be used to calculate the op- In the present paper, we have adopted a methodol- timal distribution of wind power among ER, NWR, and ogy that makes use of wind speed measurements at SWR (section 4a). Subsequently we have applied the 10 m AGL and numerical simulations of three- minimization procedure also to single stations, as a gen- dimensional wind fields. These simulations were per- eralization to the case of clusters with just one element formed with three different numerical models. The each (section 4b). Therefore, we have calculated the wind fields over the northwestern region, where Ile minimization in both cases so as to verify whether our Rousse and Calvi are placed, and over the southwest- classification into three anemological regions is suffi- ern region, which comprises Ajaccio, Pila-Canale, and cient to define an optimal spatial distribution of wind Sartene (ARIA Technologies 2002), were simulated by power plants consistently or if a further subdivision in means of the model “MINERVE” (Finardi et al. 2001). 10 regions is recommended. The wind fields over the southern area of Figari (Ratto et al. 2000) were simulated by the wind-field interpola- 3. Conversion of wind measurements into wind tion by nondivergent schemes (WINDS; Ratto et al. energy output 1990; Burlando et al. 2007). Both MINERVE and WINDS are mass-consistent models (Ratto et al. 1994). Wind speed measurements are usually available at The wind fields over eastern Corsica, which Solenzara, the international standard reference height of 10 m Alistro, and Bastia belong to (OptiFlow 2002a), and AGL, while the power curve of a wind turbine refers to over the northern part of the island, where Cap Corse

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC 3104 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 47

FIG. 2. (left) Distribution of the calculated wind speed at 50 m AGL at Calvi for 2004 and energy output at given wind speeds for (right) the power curve of the Enercon E40/600 turbine. is found (OptiFlow 2002b), were simulated by means of If we had had at our disposal the individual simulated a more sophisticated code (Ferziger and Peric´ 2002) wind fields, we could have defined the scale factor in [i.e., a Reynolds averaged numerical simulation more refined ways, for example by taking into account (RANS)]. Unfortunately, we only had available the the dependence on wind direction, speed, and, possibly, mean wind fields resulting from the simulations men- atmospheric stability. This would have explicitly taken tioned above, apart from those concerning the southern into account the local effects of topography. In the au- area, on which we directly performed the simulations thors’ opinion, however, this drawback is not that rel- (Burlando et al. 2002). evant in the present context, since we are interested in Therefore, the transformation of wind speed mea- presenting the methodology rather than obtaining the surements at 10 m AGL into wind speeds at higher most accurate evaluation of the wind potential. On the levels above ground level was performed through the contrary, more sophisticated procedures would be rec- subsequent steps: ommended whenever possible. In comparison with Archer and Jacobson’s paper h • the 10-yearly mean wind speeds, j , at the hub height (2007), the time series used in the present work have a of the turbine, h, are obtained from the cited wind larger sampling time, that is, 3 h instead of 1 h. The flow simulations (see column 10 in Table 1); reasons to use this time step have been explained in 10 • the 10 long-term time averages at 10 m AGL, j , are section 2. This means that we are filtering out the wind calculated from measurements; speed fluctuations with a shorter period. However, on h • a scale factor j is defined as the ratio between j and the one hand these datasets are expected to reproduce 10 the mean wind speed at 10 m AGL, j , namely j properly the most important atmospheric phenomena, h 10 j / j ; from local thermal circulations to mesoscale and syn- • the 10 time series of the wind speed at the level of optic motions, which occur with larger periodicities h interest, ij, that is, the time series of wind speed at (Van der Hoven 1957); on the other hand, from a sta- 50 m AGL, are obtained by multiplying the wind tistical point of view, the frequency distributions of 3- 10 measurements at 10 m, ij , by the factor j as and 1-h sampled datasets should present similar shapes, 50 10 ij j ij , being (i 1,..., I 8317) the time at least when time series are sufficiently long. index.

For example, the nondirectional frequency distribu- b. Comparison between measured and calculated tion of the wind speed at 50 m AGL calculated at Calvi wind speeds and obtained through this procedure is shown in the left We have tested our procedure with wind data ob- panel of Fig. 2. The last column of Table 1, moreover, tained from the Punta Aja wind farm, near Calvi. More reports the average wind speed values at 50 m AGL precisely, we have calculated the wind speeds at 50 m corresponding to the considered 10 stations. AGL in Calvi and compared them with measurements

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC DECEMBER 2008 CASSOLAETAL. 3105

calculated values for intensities greater than 5 m s1, whereas for weaker values the calculated wind speeds usually are more intense than the measured ones. The reason of this mismatch is better explained in Fig. 4, which shows the differences between measured (Punta Aja) and calculated (Calvi) wind speeds as a function of time. The black line, which represents the polynomial regression of order five of these differences, shows that, apart from random fluctuations, the daily mean wind speeds at Calvi are greater on average from March to mid-October, while the opposite happens during the rest of the year. This behavior, that is, the higher wind speeds at Calvi than at Punta Aja in spring and sum- mer, might be caused by the land and sea breezes that dominate the atmospheric circulation during those pe- riods of the year when thermal flows prevail (see also Burlando et al. 2008), and are particularly strong just along the coasts. This is also clear analyzing the total

FIG. 3. Comparison between the daily mean wind speeds mea- wind blown at Calvi and Punta Aja, shown in Fig. 5, sured on the mast at Punta Aja and the corresponding values defined as the cumulative distance (km) traveled by the obtained at Calvi. wind during a given time. Indeed, the two curves are nearly coincident until early May, when they begin di- verging since the wind speeds at Calvi are higher than from an anemometer placed within the wind farm at at Punta Aja. From late October, due to the reduced approximately the same height above ground. influence of sea breezes and the prevalence of synoptic- The Punta Aja wind farm became operative in the driven circulations, the wind speed is on average higher end of 2003, so that a direct comparison with the wind at Punta Aja than at Calvi so that the gap between the data described in section 2, relative to the period 1996– two curves decreases. 99, was not possible. Therefore, the validation of the The percentage error, defined as the ratio of the ab- methodology described in the previous subsection solute difference between the two winds blown at Punta has been applied to two new datasets, both ranging Aja and Calvi over the wind blown at Punta Aja, is from 1 January to 31 December 2004: about 7% at the end of the year. This value is obviously conditioned by the particular year taken into account, • the database of wind speed measurements collected that is, 2004, but we do not expect, in principle, very at 10 m AGL at the Calvi station, 10 (being for this i6 different values if another year were considered. dataset i 1,...,2920),withasamplingrateevery 3h(t 3 h); c. Calculation of wind energy output • the database of daily wind speed measurements Once wind speed time series at the hub height be- (minimum, mean, and maximum) at 48 m AGL taken come available, these can be converted into time series on the mast of an anemometric station placed at of wind power produced by whatever turbine if the Punta Aja, within the area of the wind farm, at a corresponding power curve is known. Wind turbine distance of about 10 km from Calvi. manufacturers usually issue the power curve of their Since the second database has a daily frequency wind turbines so that the conversion from wind speed while the first one is 3-hourly, some kind of elaboration to wind power is almost straightforward. It is worth is required to make them comparable. Indeed, after noting that, in fact, measured power curves by field having converted the eight wind speed data measured measurements consist of a swarm of points spread every day at 10 m AGL at Calvi into wind speeds at around the curve issued by the manufacturer. The 50 50 m, i6 , as described in the previous subsection, we reason for that is twofold: on the one hand, the an- have calculated the corresponding daily mean wind emometer that measures the wind speed is placed on a speeds at this height to obtain a database homogeneous mast reasonably close to the wind turbine, but not on with data available for the mast at Punta Aja. the turbine itself; on the other hand, the wind speed The result of such a comparison is shown in Fig. 3, always fluctuates, and one cannot measure exactly the which shows a better agreement between measured and column of wind that passes through the rotor of the

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC 3106 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 47

FIG. 4. Time series of the difference between the daily mean wind speed measured on the mast of a turbine at Punta Aja and the corresponding daily mean wind speed obtained at Calvi.

turbine. This is why power curves are based on mea- odology to evaluate the optimal spatial distribution of surements in areas with low turbulence intensity, wind power over Corsica, rather than an accurate whereas for a wind turbine placed on complex terrain, evaluation of the wind potential of the island. local effects may mean higher turbulence intensity and The conversion from wind speed data to wind power wind gusts. It may therefore be difficult to reproduce and wind energy has been tested with the wind speed the power curve exactly in any given location. In the data at 50 m AGL calculated at Calvi (see section 3b). 50 context of the present study, however, it is not so rel- The transformation of wind speeds, i6 , into wind pow- 50 evant to use the exact power curve of the chosen wind ers, P i6 , is performed with the power curve of the wind turbine, since, as we have already stated, the purpose of turbine Enercon E40/600 of nominal power 600 kW and the research concerned the establishment of the meth- hub height 50 m. This is the same kind of turbine with

FIG. 5. The total wind blown evaluated at the mast at Punta Aja and at Calvi.

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC DECEMBER 2008 CASSOLAETAL. 3107

wind speed database. The corresponding wind energy output distribution is shown in the left panel of Fig. 2.

d. Comparison between measured and calculated wind energy outputs We have evaluated the consistency of the transfor- mation of wind speeds at 50 m AGL at Calvi into the 50 corresponding wind energy output E i6 of one wind tur- bine E40/600 through the comparison between calcu- lated and actually produced daily cumulated wind en- ergy. The comparison between the calculated (Calvi) and actually produced (Punta Aja) daily cumulated ener- gies is shown in Fig. 6. Analogous to the behavior al- ready presented in Fig. 3 and discussed in the previous section 3b, there exists a pretty good agreement on average for high energies, while for low values, likely FIG. 6. Comparison between the daily energy production from associated with land and sea breeze regimes, the calcu- a turbine belonging to the Punta Aja wind farm and the corre- lated energy is overestimated with respect to the mea- sponding production calculated from wind speed measurements sured one. In general, however, the dispersion of data at Calvi. around the bisector is larger than the dispersion of wind speeds in Fig. 3. This is also evident from Fig. 7, which which the Punta Aja wind farm is equipped (http:// shows the comparison between the time series of the www.suivi-eolien.com/). The power curve of this tur- daily energy produced by a turbine at Punta Aja and 50 bine is shown in the right panel of Fig. 2. Then, P ij data the corresponding daily energy output calculated from 50 have been converted into energy output, E ij , multiply- wind speed measurements at the Calvi station, “trans- ing the wind power time series by the discrete time ported” to the height of 50 m AGL. Once again, the interval t 3 h, according to the sampling time of the calculated values are higher from mid-March to mid-

FIG. 7. Comparison between the time series of the daily energy production from a turbine at the Punta Aja wind farm and the corresponding production calculated from wind speed measurements at Calvi.

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC 3108 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 47

FIG. 8. Cumulated energy corresponding to a turbine at the Punta Aja wind farm and calculated from the wind speed measurements at Calvi.

October, especially in case of low wind speed, coher- erage, at Punta Aja than at Calvi during the winter ently with the hypothesis of stronger breezes at Calvi season (see Fig. 4). than at Punta Aja. On the contrary, the peaks associ- Following these considerations, the production of ated with synoptic-driven conditions are reproduced wind energy, higher at Punta Aja in the first half of the quite well. year, higher at Calvi in the second one, turns out to be Finally, the cumulated energy outputs for the calcu- the combined and antithetical effect of higher wind lated daily energy output at Calvi and the actually pro- speeds during the summer at Calvi and higher wind duced values at Punta Aja during year 2004 are plotted speeds during the winter at Punta Aja. As a result, the in Fig. 8. In this case, the produced cumulated energy is percentage error between calculated and produced higher than the calculated one until late June, when the cumulated energy at the end of the year is only 1%. The two curves cross each other because of the growing exact value of the error is not essential, however, in contribution of the sea breeze at Calvi. This pattern is the context of this research because the explicit consid- somewhat different from that in Fig. 5, however, since eration of uncertainties is not required to solve the the wind power output exhibits a cubic dependence on present optimization problem and, in particular, to the wind speed and it is conditioned by the cut-in and evaluate the most convenient repartition of wind cut-out values (3 and 26 m s1, respectively) of the cho- power. On the contrary, if the present procedure were sen wind turbine. This is particularly important during applied to obtain the most accurate evaluation of the summer when below cut-in winds blow in Punta Aja wind potential of a territory, a detailed study of the and do not produce any wind energy output, whereas at effects of the topography to distinguish different tur- the same time above cut-in land or sea breezes contrib- bine positions would be recommended. Indeed, in the ute to the cumulated wind energy at Calvi. The cut-out present paper, all sites surrounding an anemometric value also has influence in the present analysis since, station are characterized by the same anemology, but even if the considered daily mean wind speeds are al- this drawback could be overtaken if more sophisticated ways lower than this threshold (see Fig. 3), maximum numerical tools were adopted to estimate directly the intensities up to 35 m s1 have been recorded, clearly spatial correlation between stations and specific sites. affecting power production. From early November the Moreover, in the case of a wind farm, if the same power influence of thermally driven winds decreases and the curve were used for all turbines, wake effects should be gap between calculated and produced energy starts re- explicitly considered. However, provided that the dis- ducing because wind speeds are slightly higher, on av- tance between the turbines is more than 8–10 times

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC DECEMBER 2008 CASSOLAETAL. 3109 the diameter of the rotor along the prevailing wind di- northwestern region including stations 4, 5, and 6, and rection and more than 6 times the diameter along the the southwestern region including stations 8, 9, and 10. direction perpendicular to the prevailing one, wake ef- In this analysis, station 7 (Ajaccio) has not been con- fects should be less than 10% of the total (Lissaman et sidered, since the clustering technique revealed that it is 50 al. 1982). Therefore, the energy output NjE ij can be a transitional station between NWR and SWR. used as a rough estimation of the energy produced by The minimization procedure requires a single time

Nj turbines distributed around the corresponding jth series of wind energy for each anemological region. anemometric station. Therefore, the wind energy time series, E ij, obtained for the single anemometric stations (see section 3c) have to be arranged according to a weighted averaging 4. Minimization methodology and results to obtain the corresponding time series for each region.

For instance, the time series of wind energy of ER E i,ER The procedure we propose here aims at calculating can be calculated as jwjE ij, where j 1, 2, 3 and the optimal allocation of fractions of wind power over a jwj 1. The value of weights wj corresponds to the territory through the minimization of either the wind repartition of wind turbines among the areas surround- energy variability or the ratio between energy variabil- ing stations 1, 2, and 3. In the present study, in the ity and energy input into the power system. In such a absence of other information, we have assumed a uni- way, undesired power fluctuations in the power system, form distribution of the wind turbines within every re- due to the intermittent nature of the wind energy gen- gion, namely wj 1/3. eration, can be reduced. Suppose we now place N turbines into ER, N into To check if the minimization procedure is turbine NWR, and N into SWR, where N is the total number independent, as expected, and to evaluate how much of turbines all over the territory of Corsica and the the performances change by increasing the turbine coefficients , , and , which add up to unity ( nominal power, two different kinds of wind turbine 1), represent the distribution of N among the have been considered in the analysis: the Enercon E40/ anemological regions. The time series of the overall 600, which is the same model already considered in energy output can be written as section 3, and the Enercon E48/800 of nominal power ␣ ␤ ␥ ␣ ␤ ␥ 800 kW. For both turbines the hub height is 50 m AGL. Ei , , N Ei,ER Ei,NWR Ei,SWR , 1 The methodology can be applied to the 10 areas around single anemometric stations as well as to the where E i,ER, E i,NWR, and E i,SWR are the wind energy three clusters of stations. The possibility of grouping time series of the three anemological regions, calcu- stations based on an objective classification criterion is lated from the time series of the corresponding anemo- particularly important to reduce the overall computa- metric stations. tional time when a large number of stations is available, It is now straightforward to calculate the correspond- especially if very close to each other. ing total energy output: In the present work, we have applied the minimiza- E ⌺ E , 2 tion procedure in both cases: i i its variability, defined as follows: • to the three distinct anemological regions of Corsica, identified by clusters of anemometric stations (sec- ⌬E ⌺ E E 2 , 3 tion 4a); i i i1 • and to the single 10 anemometric stations, as a gen- and their ratio, E/E, as a function of the three eralization to the case of clusters with just one ele- parameters (, , ). The calculation is performed as- ment (section 4b). suming different triplets in the space of the parameters ∈ Յ Յ Յ Յ Յ Յ Finally, it is worth noting that all the following analyses S { , , R:0 1; 0 1; 0 1}. have been performed with the 3-yr-long datasets de- The equilateral triangle shown in Fig. 9 represents scribed in section 2. the space of the , , and parameters, which range from 1 in the corresponding vertex to 0 on the opposite side along the medians: the condition 1is a. The case of three regions then satisfied, as the sum of the distances from any As discussed in section 2, we have identified three point inside an equilateral triangle to the sides is con- different wind climate regions along the coasts of Cor- stant. The shaded contours represent the values of the sica: the eastern region including stations 1, 2, and 3, the three calculated variables E, E, and E/E, nor-

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC 3110 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 47

FIG. 9. (left) Wind energy output E / E max, (center) wind energy variability E / E max, and (right) ratio between energy variability and energy output ( E / E )/( E / E )max as a function of ( 1,.., 10). malized with respect to the corresponding maximum quite similar, 32%, but the energy loss turns out to be value. only 21%.1 These values are almost the same for both The distribution that maximizes wind energy output E40/600 and E48/800. (Emax) is trivial, as it shows a maximum for the triplet ( 0, 1, 0), which corresponds to b. The case of 10 regions locate all the turbines into the windiest region, that is, A straightforward extension of the procedure shown the NWR (see the left panel in Fig. 9). The minimum in the previous subsection is the calculation of the shown in the center panel corresponds to the distribu- Emin distribution and the E/Emin distri- tion ( 0.46, 0.26, 0.28) that minimizes the bution for the ten areas around the single anemometric wind energy variability (Emin). It can be seen stations, each considered an independent anemological that in this case the highest percentage of turbines is region. found in the least windy region, that is, the ER. Finally, Suppose we place N turbines in the Solenzara re- the minimum shown in the right panel in Fig. 9 corre- 1 gion, N turbines in the Alistro region, and so forth, sponds to the distribution ( 0.27, 0.48, 0.25) 2 until N turbines are in the Figari region, with that minimizes the ratio between energy variability and 10 N being the overall number of wind turbines to install energy output (E/Emin). We have verified that and the fraction of N assigned to region j, so that all these triplets are turbine independent, as they do not j 1 ••• 1. change if the two considered different power curves are 2 10 The time series of the overall energy output can be used. written as follows: The mean annual energy production per turbine ␣ ␣ ␣ иии ␣ (N 1) corresponding to these three distributions is Ei 1,..., 10 N 1Ei1 10Ei10 , 4 1568, 1075, and 1235 MWh, respectively, if Enercon where E (j 1,...,10)arethewindenergytimese- E40/600 wind turbines are considered. Applying the ij ries of each anemometric station. The total energy out- same methodology, but considering 800-kW nominal put, E, and its variability, E, as a function of the power turbines (Enercon E48/800), the mean annual parameters ( ,..., ) follow analogously to Eqs. (2) energy production for the three distributions rises to 1 10 and (3), respectively. 2270, 1570, and 1795 MWh, respectively. Note that by The results are summarized in Table 2, where the adopting the higher nominal power turbine, the values values of the parameters for the three considered dis- of annual energy production increase by a factor about tributions as well as the corresponding values of E, 1.45. E, and E/E are reported. The results for the The E/Emin distribution permits a larger en- case of three anemological regions, discussed in section ergy production together with relatively low power 4a, are also reported to highlight the consistency be- fluctuations, whereas the Emin distribution tween the higher- and the lower-resolution analysis. reaches this goal at the expense of the energy output. Indeed, for the Emin distribution, the variability reduction with respect to its maximum value (corre- 1 Variability reduction and energy production loss are defined sponding to have all the turbines in NWR) is about analogous to the “percentage error” of E (column 6 of Table 2) 37% and the energy production loss is 31%; for the or E (column 5 of Table 2) between the distribution that maxi- E/Emin distribution the variability reduction is mizes wind energy output and another distribution.

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC DECEMBER 2008 CASSOLAETAL. 3111

TABLE 2. Values of the parameters ( , , and ) and ( 1,..., 10) for the three considered distributions (columns 2–4), and of the corresponding wind energy output, E, wind energy variability, E,and ratio between energy variability and energy output, E/E (columns 5–7), calculated assuming the E40/600 (E48/800) wind turbine.

E (MW h E (MW h Distribution 1 2 3 4 5 6 7 8 9 10 per turbine) per turbine) E / E E max 0.00 1.00 0.00 1568 (2270) 1022 (1349) 0.65 (0.59) 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 1830 (2600) 1770 (2277) 0.96 (0.88) E min 0.46 0.26 0.28 1075 (1570) 631 (850) 0.58 (0.54) 0.22 0.14 0.09 0.11 0.06 0.06 0.08 0.09 0.09 0.06 1010 (1480) 613 (841) 0.60 (0.57) E/E min 0.27 0.48 0.25 1235 (1795) 680 (911) 0.55 (0.51) 0.04 0.16 0.07 0.21 0.11 0.14 0.06 0.00 0.00 0.21 1410 (2030) 727 (981) 0.51 (0.48)

It is worth noting that the energy output is maxi- equal to the value of the corresponding parameter mized if one places all the turbines in the fourth region 0.46 found for such a region (see Table 2 and section (i.e., Cap Corse), characterized by the highest average 4a). wind speed (see column 10 of Table 1). For this distri- Considering the E40/600 (E48/800) wind turbine, the bution, if Enercon E40/600 turbines are considered, the mean annual energy production per turbine corre- annual energy production per turbine would be 1830 sponding to the Emin distribution is 1010 (1480) MW h, whereas this value would increase up to 2600 MW h, which is not very different from the value found MW h if E48/800 turbines are assumed. in the case of three regions. On the contrary, for the For the other two distributions, Fig. 10 shows the E/Emin distribution, these values become sig- values of j for all 10 stations. Furthermore, it is evident nificantly higher than for the three-region case [i.e., that the Emin distribution is relatively more uni- 1410 (2030) MW h against 1235 (1795) MW h]. This is form than the E/Emin distribution. Consistently not surprising, because we are now taking into account with the results obtained for three anemological regions all stations without any kind of averaging. In such a introduced in section 2, the highest percentage of tur- way, local features filtered out by the clustering proce- bines is found in the least windy regions ( 1, 2, 8, and dure can be retained, permitting a more efficient rep- 9) for the E min distribution, and in the most artition of wind power throughout the territory. The windy regions ( 4, and 10) for the E / E min variability reduction with respect to its maximum value distribution. Moreover, the sum of the parameters j is pretty high (about 64% for the E min distribu- corresponding to the areas of the three anemological tion and 58% for the E/Emin distribution) and regions gives a value close to the one obtained by the not very different for the two distributions. As far as the minimization procedure when applied to three regions energy production loss is concerned, a value of 45% only. For instance, as far as the Emin distribution (43%) is found for the E min distribution, and the eastern region (consisting of stations 1, 2, and whereas for the E/Emin distribution it is only 3) are concerned, 1 2 3 0.45; that is nearly 23% (22%). Thus, the E / E min distribution

FIG. 10. Value of the parameter j for the 10 regions (corresponding to data from a single anemometric station): (top) Emin and (bottom) E/E min.

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC 3112 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 47

FIG. 11. Frequency of given power intervals corresponding to the (top to bottom) five different spatial distributions. combines a significant damping of power fluctuations responding to the case of P 0 kW. The first class with large energy production values. corresponds to all the wind speeds below the cut-in or above the cut-out thresholds, while the last class c. Considerations about wind power production 700 P Յ 800 kW comprehends the wind speed inter- and variability val between the saturation of the power curve at the In this subsection the spatial distributions for the case nominal power of the wind turbine and the cut-out of 10 regions, mentioned in section 4b, are analyzed threshold. Two distributions correspond to place all the from the point of view of wind integration in the power turbines in one region: the Emin distribution, in system and the ability of interconnected wind farms to the least windy region of Pila Canale; and the E provide base load power. All results here presented and max distribution, in the windiest region of Cap Corse. discussed are per turbine. The other three distributions are “scattered” ones: the Figure 11 shows the frequency of given intervals of “uniform” distribution, where the total number of tur- wind power input into the power system for five differ- bines is equally subdivided among the 10 regions, the ent spatial distributions. More precisely, these frequen- Emin, and the E/Emin distributions, cies represent the time during which a given wind whose repartitions of the total number of turbines power per turbine is inserted into the grid with respect among regions are reported in Table 2. to the total time. In abscissa, the considered power in- It is worth noting that only the two distributions cor- tervals, which refer to the Enercon E48/800 wind tur- responding to the total number of turbines placed into bine, are divided into classes of 100 kW from 0 P Յ a single region show non-null frequencies in the first 100 kW to 700 P Յ 800 kW, plus the first class cor- class P 0 kW. They also show relatively high frequen-

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC DECEMBER 2008 CASSOLAETAL. 3113

FIG. 12. Frequency of given intervals of 3-hourly power variability corresponding to the (top to bottom) five different spatial distributions.

Յ cies in the last interval, corresponding to 700 P variability over 3 h, that is, Pi (Ei Ei1)/ t (where 800 kW. On the contrary, the repartition of wind tur- t 3 h) as a function of the same wind power classes bines around the perimeter of the island reduces to zero as those reported in Fig. 11. The frequencies of class the probabilities that the wind speed is null or above P 0 kW are greater than zero only for the Emin the cut-out everywhere. Analogously, also the probabil- and Emax distributions, which correspond to ity of high, but below the cut-out, wind speeds contem- placing all turbines in the same region. Although in a porarily all around the island is low, so that the fre- single region the probability that the wind speed does quency of class 700 P Յ 800 kW is almost zero for not change over a period longer than 3 h is rare, these distributions different from the Emin and E frequencies describe the situations when wind speed max ones. As far as the intermediate intervals are con- variation over 3 h remains below the cut-in or above cerned, however, the frequencies are in general much the cut-out so that the power output persists being higher when the wind turbines are not concentrated zero. The same situation does not occur for the scat- within a single region. Finally, note that the Emin tered distributions because their power output is always distribution shows higher frequencies for the interval 0 P 0 kW, as shown in Fig. 11, and the probability that P Յ 300 kW when compared with the E/Emin the wind speed does not change over 3 h contemporar- distribution, which shows higher frequencies for P ily all around the island is practically zero. As far as all 300 kW instead, accounting for the higher values of the other classes are concerned, the frequencies of annual energy production (see section 4b). power variability for 0 P Յ 200 kW are almost Figure 12 shows the frequencies of the wind power doubled for the scattered distributions relative to the

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC 3114 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 47

FIG. 13. Power duration curve for the five different spatial distributions given in the legend.

Emin and Emax distributions, comparable for larger amount of energy than scattered ones as re- 200 P Յ 300 kW, and much lower for P 300 kW. ported in Table 2. In particular, about 70% of the cases belong to the class The yearly averaged wind power of the considered corresponding to 0 P Յ 100 kW for scattered dis- distributions ranges from 118 kW for the Emin tributions, so that a more regular and slowly varying distribution to 297 kW for the Emax distribution, power output is expected when interconnected wind corresponding to capacity factors, defined as the frac- farms are considered. tion of the rated power actually produced in a year, of Finally, Fig. 13 shows generation duration curves as 0.15 and 0.37, respectively. The uniform and E defined by Holttinen and Hirvonen (2005). This kind of min distributions have values between 185 and 169 kW, graph represents a reversed cumulative probability respectively, whereas the yearly power of the E/ distribution, in which each point of the abscissa repre- Emin distribution is 232 kW and its capacity factor sents the probability (in terms of number of hours in a is 0.29. year) of wind power production greater than or equal The firm capacity of the distributions, which is the to the corresponding wind power value on the curve. fraction of installed wind capacity (here 800 kW) that is The area below the generation duration curve repre- online at the same probability as that of a coal-fired sents the total energy (kW h) produced in a year by the power plant, is then considered so as to evaluate the corresponding spatial distribution. As already seen in base load wind power. We shall assume the threshold of Fig. 11, the power generation is 0 kW for about 20% 87.5% as the probability that coal plants are free from (39%) of the hours of the year for the Emax (E scheduled maintenance (see Archer and Jacobson min) distribution, while it is never equal to 0 kW in 2007). At this threshold, the distributions that corre- the other cases. For about 10% (40%) of the hours the spond to place all the turbines in one region do not Emin (Emax) distribution produces more en- guarantee any power generation. Instead, the guaran- ergy than scattered distributions. For the Emin teed power generation for uniform and Emin distribution, this higher production over 10% of the distributions is 33 and 32 kW, respectively, and 38 kW time is largely made up for by the higher production of for the E/Emin distribution. These values cor- scattered distributions over the remaining 90% of the respond to firm capacities of 0.04, 0.04, and 0.05, or hours. On the contrary, the larger production for 40% analogously, to 18%, 19%, and 16% of the yearly of time by the Emax distribution is not completely power produced, respectively. The latter values, in compensated, because such distribution still produces a principle, represent the percentages of yearly averaged

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC DECEMBER 2008 CASSOLAETAL. 3115 wind power that can be used as reliable base load elec- production per turbine has been found (2030 versus tric power. 1795 MW h). Moreover, this distribution, which splits the total number of turbines among 10 regions, was found to have 16% of yearly averaged wind power to be 5. Conclusions used as a reliable base load into the power system. It is In the present paper, we have proposed a procedure worth noting that this value is in between the corre- to calculate the optimal allocation of wind power plants sponding values obtained by Archer and Jacobson over a territory to minimize the variability of energy (2007) for the cases of 7 (14%) and 11 (23%) intercon- input into a power supply system. The optimization can nected wind farms. be performed under the constraint of obtaining the ab- Finally, the procedure can be easily applied assuming solute minimum temporal variability or the minimum the contemporary use of different wind turbines, using ratio of the temporal variability over the overall wind different wind power curves and/or hub heights when energy input. wind measurements are converted into wind energy The adopted methodology makes use of wind mea- outputs. This further improvement has been already surements at ground level, and the conversion from implemented and tested in software that we have pre- wind data at 10 m AGL to wind aloft at the hub height pared on behalf of ADEME. is based on the use of three-dimensional numerical simulations. Acknowledgments. This research has been funded by We have shown that some kind of statistical tech- Agence De l’Environment et de la Maîtrise de nique can be applied to group different anemometric l’Energie (ADEME) and Collectivité Territorial de stations that belong to the same anemological region, Corse. In particular, we warmly thank Dr. Philippe Is- instead of analyzing each station independently. This is tria from ADEME (Délégation Corse), with whom we particularly relevant when a large number of stations is had valuable and constructive exchanges of ideas and available whose spatial representativeness partially results throughout this research activity. We thank overlaps, and a reduction of the total number of de- Prof. Roberto Festa for his numerous and helpful com- grees of freedom of the problem could be recom- ments and suggestions. We are grateful to Mrs. Marina mended to reduce the computational time required for Pizzo for her assistance in the drafting of this paper. the calculation of the aforementioned optimal distribu- tions. REFERENCES We tested the procedure over Corsica, the fourth largest island in the Mediterranean, located in the Archer, C. L., and M. Z. Jacobson, 2003: Spatial and temporal distribution of U.S. winds and wind power at 80 m derived northwestern part of the basin. In the beginning we from measurements. J. Geophys. Res., 108, 4289, doi:10.1029/ subdivided the territory of Corsica into three anemo- 2002JD002076. logical regions by means of a cluster analysis of the wind ——, and ——, 2007: Supplying baseload power and reducing data, so that the spatial distributions of wind tur- transmission requirements by interconnecting wind farms. bines have been calculated considering three parameters J. Appl. Meteor. Climatol., 46, 1701–1717. only. The distribution that minimizes the ratio between ARIA Technologies, 2002: Evaluation of the wind potential of different regions of Corsica (in French). Tech. Rep., 69 pp. energy variability and energy output, E/Emin, Burlando, M., F. Castino, and C. F. Ratto, 2002: Validation of a permits a pretty high annual energy production (1795 method for wind power estimation: The case of Bonifacio. MWh for an 800-kW turbine) together with rather low Proc. World Wind Energy Conf. and Exhibition, Berlin, Ger- power fluctuations (911 MW h). On the contrary, the many, World Wind Energy Association. distribution that minimizes the variability, Emin, ——, E. Georgieva, and C. F. Ratto, 2007: Parameterisation of the reduces the power fluctuations (850 MW h) but at the planetary boundary layer for diagnostic wind models. Bound.-Layer Meteor., 125, 389–397, doi:10.1007/s10546-007- expense of the energy output (1570 MW h). 9220-7. Then, it was a straightforward extension to apply the ——, M. Antonelli, and C. F. Ratto, 2008: Mesoscale wind climate calculation of such distributions to ten independent analysis: Identification of anemological regions and wind re- anemological regions, each corresponding to a single gimes. Int. J. Climatol., 28, 629–641. anemometric station. The results have shown that the Buzzi, A., and S. Tibaldi, 1978: Cyclogenesis in the lee of the Alps: increase of the spatial resolution of the analysis has A case study. Quart. J. Roy. Meteor. Soc., 104, 271–287. provided a refined repartition of the overall power, al- Chinchilla, M., S. Arnalte, J. C. Burgos, and J. L. Rodríguez, 2005: Power limits of grid-connected modern wind energy systems. though in agreement with the lower-resolution one. As Renewable Energy, 31, 1455–1470. far as the E/Emin distribution is concerned, in Egger, J., 1988: Alpine lee cyclogenesis—Verification of theories. particular, a significantly higher mean annual energy J. Atmos. Sci., 45, 2187–2203.

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC 3116 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 47

Ferziger, J. H., and M. Peric´, 2002: Computational Methods in Mosetti, G., C. Poloni, and B. Diviacco, 1994: Optimization of Fluid Dynamics. 3rd ed. Springer-Verlag, 437 pp. wind turbine positioning in large wind farms by means of a Finardi, S., G. Tinarelli, A. Nanni, G. Brusasca, and G. Carboni, genetic algorithm. J. Wind Eng. Ind. Aerodyn., 51, 105–116. 2001: Evaluation of a 3-D flow and pollutant dispersion mod- OptiFlow, 2002a: Realisation of wind potential maps through nu- elling system to estimate climatological ground level concen- merical simulations over the study area “Plaine Orientale” trations in complex coastal sites. Int. J. Environ. Pollut., 16, (in French). Tech. Rep., 41 pp. 472–482. ——, 2002b: Realisation of wind potential maps through numeri- Giebel, G., J. Badger, I. Perez, P. Louka, G. Kallos, A. M. Palo- cal simulations over the study area “Cap Corse” (in French). mares, C. Lac, and G. Descombes, 2006: Short-term forecast- Tech. Rep., 40 pp. ing using advanced physical modelling—The results of the Pantaleo, A., A. Pellerano, and M. Trovato, 2003: Technical issues Anemos Project. Proc. EWEC 06, Athens, Greece, European for wind energy integration in power systems: Projections in Wind Energy Association, 29 pp. Italy. Wind Eng., 27, 473–493. Gipe, P., 1995: Wind Energy—Comes of Age. John Wiley and Persaud, S., B. Fox, and D. Flynn, 2003: Effects of large scale wind Sons, 560 pp. power on total system variability and operation: Case study Global Wind Energy Council, 2006: Global Wind 2006 Report, 56 of Northern Ireland. Wind Eng., 27, 3–20. pp. [Available online at http://www.gwec.net/fileadmin/ Ratto, C. F., R. Festa, O. Nicora, R. Mosiello, A. Ricci, D. P. documents/Publications/gwec-2006_final_01.pdf.] Lalas, and O. A. Frumento, 1990: Wind field numerical simu- Holttinen, H., and R. Hirvonen, 2005: Power system requirements lation: A new user-friendly code. Proc. European Community for wind power. Wind Power in Power Systems, T. Acker- Wind Energy Conf., Madrid, Spain, 130–134. mann, Ed., John Wiley and Sons, 143–167. ——, ——, C. Romeo, O. A. Frumento, and M. Galluzzi, 1994: Kahn, E., 1979: The reliability of distributed wind generators. Mass-consistent models for wind fields over complex terrain: Electr. Power Syst. Res., 2, 1–14. The state of the art. Environ. Softw., 9, 247–268. Kariniotakis, G., and Coauthors, 2006: Next generation short- ——, M. Burlando, F. Castini, and L. Rusca, 2000: Evaluation and term forecasting of wind power—Overview of the ANEMOS cartography of the wind potential of the Bonifacio munici- project. Proc. EWEC 06, Athens, Greece, European Wind pality in southern Corsica (in French). Department of Physics Energy Association, 10 pp. of the University of Genoa Tech. Rep., 73 pp. Kaufmann, P., and C. D. Whiteman, 1999: Cluster-analysis classi- fication of wintertime wind patterns in the Grand Canyon Sánchez, I., 2006: Short-term prediction of wind energy produc- tion. Int. J. Forecasting, 43–56. region. J. Appl. Meteor., 38, 1131–1147. 22, Lissaman, P. B. S., G. W. Gyatt, and A. D. Zalay, 1982: Numerical Simonsen, T. K., and B. G. Stevens, 2004: Regional wind energy modeling sensitivity analysis of the performance of wind tur- analysis for the Central United States. Proc. Global Wind bine arrays. Pacific Northwest Laboratory Rep. PNL-4183, Power 2004, Chicago, IL, American Wind Energy Associa- Richland, WA, 97 pp. tion, 16 pp. Madsen, H., P. Pinson, G. Kariniotakis, H. Aa. Nielsen, and T. S. Steinbuch, M., W. W. de Boer, O. H. Bosgra, S. A. W. M. Peters, Nielsen, 2005: Standardizing the performance evaluation of and J. Ploeg, 1988: Optimal control of wind power plants. short term wind power prediction models. Wind Eng., 29, J. Wind Eng. Ind. Aerodyn., 27 (1–3), 237–246. 475–489. Trigo, I. F., T. D. Davies, and G. R. Bigg, 1999: Objective clima- Milligan, M. R., and T. Factor, 2000: Optimizing the geographic tology of cyclones in the Mediterranean region. J. Climate, distribution of wind plants in Iowa for maximum economic 12, 1685–1696. benefit and reliability. Wind Eng., 24, 271–290. Van der Hoven, I., 1957: Power spectrum of horizontal wind ——, and K. Porter, 2005: Determining the capacity value of wind: speed in the frequency range from 0.0007 to 900 cycles per A survey of methods and implementation. National Renew- hour. J. Meteor., 14, 160–164. able Energy Laboratory Rep. NREL/CP-500-38062, Golden, Weibull, W., 1951: A statistical distribution function of wide ap- CO, 30 pp. plicability. J. Appl. Mech., 18, 293–297.

Unauthenticated | Downloaded 09/26/21 12:40 PM UTC