Wind Turbines Part 10 doc

Wind Turbines 350 Fig. 10. The simplified model connected with wind turbine GWT L PP P + = (4) GWT L QQ Q + = (5) The voltage V PCC at the grid connected point can be shown as (6). PCC voltage is composed of the first term by the existing internal voltage source V G and the second one by current source IWT of the wind turbine from the principle of superposition shown in Fig. 11. () LL PCC G G WT LL G Z VVZI ZZ ⎛⎞ =+ ⎜⎟ + ⎝⎠ (6) Fig. 11(a) shows the case that wind turbine is not working (I WT =0), and PCC voltage is determined as (7) by impedance distribution between power side and load one. The PCC voltage without wind power generation(I WT =0) can be considered as nominal voltage V PCC0 in (7). The nominal voltage is determined by source voltage V G and the impedance distribution. From (6) and (7) the PCC voltage variation, △V PCC due to the wind power is proportional to I WT and the equivalent effective impedance Z effect as (8). These results can also be explained using the principle of superposition in Fig. 11. Z effect corresponds to parallel impedance of Z G and Z LL as shown in (9). There is one thing to watch out here that line impedance Z WT connected to current source I WT in series does not affect PCC voltage variation; instead, it affects port voltage V WT of the wind turbine according to the change of current I WT as shown in (10). 0 LL PCC G LL G Z VV ZZ ⎛⎞ = ⎜⎟ + ⎝⎠ (7) p CC e ff ect WT VZI Δ =⋅ (8) LL G effect LL G ZZ Z ZZ ⋅ = + (9) A Simple Prediction Model for PCC Voltage Variation Due to Active Power Fluctuation for a Grid Connected Wind Turbine 351 WT p CC WT WT VV ZI = +⋅ (10) Here, V G : output voltage of internal generator I WT : output current of wind turbine Z Load : equivalent load impedance Z G : equivalent circuit impedance between internal generator and PCC Z L : equivalent line impedance between PCC and load Z WT : line impedance between PCC and wind turbine a) The case that wind turbine is not working (I WT =0) b) The analysis of voltage variation port by I WT in case of operating wind turbine Fig. 11 The analysis of equivalent circuit of the connected model with wind turbine In order to verify the analysis, the analysis is done by converting impedance in Fig. 8 into the actual impedance parameter such as in Table 3. Classification Explanation Reference Ideal Generator Sapsido power plant (3 phase) 380[V] Z T1 750[kVA] transformer impedance (380[V] scale value) 0.013∠71.57 Z T2 120[kVA] transformer impedance (380[V] scale value) 0.076∠71.57 Z T3 15[kVA] transformer impedance (380[V] scale value) 0.611∠71.57 Z G Line impedance of high voltage side (380[V] scale value) 0.0002∠7.13 Z L1 Load impedance of whole island except for 2 houses in the village on the seashore 1.35∠25.73 Z L2 Load impedance of 2 houses in the village on the seashore 4.45∠23 Z WT Line impedance of wind turbine side 0.085∠5.05 Table 3. The actual impedance parameter The simplified impedance shown in Fig. 10 is indicated in Table 4 below. Wind Turbines 352 Classification Explanation Value Ideal Generator Sapsido power plant (3 phase) 380[V] Z G Scale line impedance 0.625∠72.37 Z LL Scale load impedance 4.19∠22.24 Z WT Line impedance of wind turbine side 0.085∠5.05 Table 4. Scale impedance parameter 0.57 66.4 LL G effect LL G ZZ Z ZZ ⋅ ∴ ==∠° + (11) 0.57 66.4 p CC WT VI ∴ Δ=∠°× (12) The final equation on voltage variation occurring at the actual PCC with data in Table 4 is shown in (11) and (12). 2.4 The actual measurement Data is measured by installing a power measuring instrument at the PCC step within the actual system in Sapsido to enhance reliability in this study. Fig. 12 shows the location where measurement is carried out. Valid/invalid power graph of the wind turbine according to time based on this measured data is shown in Fig. 13. Fig. 12. Measuring location of power in Sapsido Fig. 14 shows voltage variation amount for the output. The measured dots show the tendency of increase proportional to the power output and are represented as a solid line. Dots inside the circle, near zero output power, show the voltage variation in normal operating conditions at the PCC even without wind power generation. An approximate 7[V] voltage variation is shown in case of producing about 5.5[kW]. Table 5 shows the comparative results of the voltage variation using two simulation models and one experimental measurement. At first, the voltage variation of 6.4V results from the PSCAD simulation model which has full modeling of the wind turbine and complex line impedance parameters. The second result of 6.5V comes from the proposed simplified prediction model of PCC voltage using (8). The last result of 6.9V PCC voltage deviation is a measured value as shown in Fig. 14 during the field test. A Simple Prediction Model for PCC Voltage Variation Due to Active Power Fluctuation for a Grid Connected Wind Turbine 353 From this comparison the result of the proposed prediction model highly matches the simulation and measurement results. Fig. 13. PCC valid·invalid power in case of wind speed change Fig. 14. Measured value of PCC voltage variation amount for the output of wind turbine Classification Amount of voltage variation in case of 5.5[kW] generation (V) PSCAD Model 6.4 Simplified prediction model 6.5 Results of actual measurement 6.9 Table 5. The comparative table of PCC voltage variation amount in case of active power fluctuation of wind turbine Wind Turbines 354 3. Conclusion This study analyzed voltage variation according to the active power fluctuation of a wind turbine connected with the existing generating facilities in parallel in a small-sized isolated system, e.g. an island. The prediction of the voltage variation amount at the connected point is possible under the consideration of the change of installation location of a wind turbine and load fluctuation in the future. The variations of voltage drop happen according to the fluctuation of generated wind amount, and voltage change (rising) in receptive value inevitably. The simulation model was developed by using PSCAD/EMTDC to analyze voltage variation of the simplified model in the small-sized isolated system; and suggested the method to analytically obtain voltage variation amount through the analysis of a lot more generalized equivalent circuit. It was confirmed that the suggested method, simulation and the results of actual measurement matched in the error range of about less than 7%. It is considered that the study on the additional control method of a wind turbine to make the penetration ratio of wind plant increase in comparison to load capacity is necessary along with the development of a much more precise simulation model by taking account of the uniqueness of the excessive condition of generators in the future. 4. References Bialasiewicz, J; Muljadi, E. & Drouilhet, S. & Nix, G. (1998) Modular Simulation of a Hybrid Power System with Diesel and Wind Turbine Generation, Windpower '98 Bakersfield, CA E-ON Netz Gmbh, (2006) Grid Code-High and Extra High Voltage IEEE 1547 (2003) IEEE Standard for Interconnecting Distributed Resources with Electric Power Systems Jeong, W.; Yoon, K. & Kim, S. & Lee, H. (2007) The analysis of voltage variation according to grid connection at wind plant in Yangyang, International Spring Academy Conference of Korea Wind Energy, papers, 35-40 Kim, J. & Song, H. (2005) The development of PSCAD/EMTDC simulation model of variable speed wind plant system by permanent magnet synchronous generator, Society of Power & Electronics, papers, 610-617 Korea Electric Power Corporation (2005) Technology standard connected with the distributed power supply system Rajendiran, K.; Keerthipala, W. & Nayar, C. PSCAD/EMTDC Based Simulation of a Wind- Diesel Conversion Scheme Sim, M.; Palle, B. & Chakraborty, S. & Uriarte, C. (2007) Electrical Model Development and Validation for Distributed Resources, Subcontract Report, NREL Slootweg, J. & Kling, W. (2003) Is the Answer Blowing in the Wind?, IEEE Power & Energy Magazine, No., 6, 26-33 Song, S.; Kim, I. & Han, B. (2003) Electric characteristics of wind turbine and interaction in case of grid connection, Power & Electronics Magazine, Ed., Vol., 8, No., 6, 21-27 www.windturbinewarehouse.com/pdgs/bergey/BergeyExcel-S 10kW Turbine Specs.03.pdf 15 Markovian Approaches to Model Wind Speed of a Site and Power Availability of a Wind Turbine Alfredo Testa, Roberto Langella and Teresa Manco Second University of Naples Italy 1. Introduction This chapter is devoted to markovian approaches to model first the wind speed in a given site starting from experimental results and, then, power availability of a wind turbine installed in assigned wind conditions. The chapter organization is as follows: section 2 is devoted to wind data and their treatment; section 3 presents two wind models with different accuracy; section 4 describes produced power models for wind turbines, first in hypotheses of ideal failure-free turbine and, then, accounting for a real behaviour; section 5 is devoted to model analytical solutions; section 6 reports the results of numerical examples developed for a very simple case-study; section 7 describes some possible model applications; section 8 concludes the chapter; section 9 is constituted of an appendix on the basic Markov model concepts. A significant part of the chapter content derives from references (Manco & Testa, 2007 and to other references of the chapters’ authors reported in Section 10). 2. Wind data and their treatment The power generated from a wind turbine depends on the site specific wind speed, which randomly fluctuates with time. Therefore, wind power studies require accurate models to forecast wind speed variations for wind farm locations of interest (Billinton et al., 2006). Historical data for a wind farm site in Sardinia for a measurement campaign of one year are considered. The data are collected every twenty minutes. In Fig. 1 the wind speed profile versus the sample number is represented. Being the duration of a single measurement exactly of twenty minutes, the sample number coincides with the number of twenty minutes interval elapsed from the beginning to the end of the observation year. The wind speed range of interest can be divided into classes equally spaced. The wind classes, W ( ⋅ ) , with the respective speed ranges, the number of samples observed for each class, N ( ⋅ ) , and the consequent estimated probability of each class frequency, f ( ⋅ ) , are reported in Table 1. N T is the total number of samples considered, so an estimation of f ( ⋅ ) has been obtained as: Wind Turbines 356 () () ˆ T N f N ⋅ ⋅ = . (1) 0 0.5 1 1.5 2 2.5 x 10 4 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 sample number wind speed (m/s ) 4500 4550 4600 4650 4700 4750 4800 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 sample number wind speed (m/s) W 17 [16, ∞] W 16 [15,16[ W 15 [14,15[ W 14 [13,14[ W 13 [12,13[ W 12 [11,12[ W 11 [10,11[ W 10 [9,10[ W 9 [8,9[ W 8 [7,8[ W 7 [6,7[ W 6 [5,6[ W 5 [4,5[ W 4 [3,4[ W 3 [2,3[ W 2 [1, 2[ W 1 [0,1[ wind classes [ m/s ] Fig. 1. Wind speed values versus the number of samples and wind classification. Wind Class Speed range (m/s) Samples in the class, N (·) Class frequency, f (·) W 1 [0,1[ N 1 f 1 W 2 [1,2[ N 2 f 2 W 3 [2,3[ N 3 f 3 W 4 [3,4[ N 4 f 4 W N [W max , ∞[ N N f N Table 1. Wind classification according to wind profile. Markovian Approaches to Model Wind Speed of a Site and Power Availability of a Wind Turbine 357 In Fig. 2 the pdf of the wind speed is depicted, and compared with a Weibull distribution characterized by the same mean value. Weibull distribution parameters assume the following values: α=0.3407, β=1.4052 (Allan & Billinton, 1992). It is possible to observe that the Weibull distribution correctly estimates the high speed wind pdf values while the lower values are overestimated for some classes and underestimated for some other. 0 2 4 6 8 10 12 14 16 18 0 0.05 0.1 0.15 0.2 0.25 wind speed (m/s) pdf Fig. 2. Wind speed pdf versus wind speed classes; the histogram represents the distribution observed while the black line represents Weibull distribution. 3. Wind models The wind speed range of interest is divided into N classes that are not equally spaced, because of the nonlinear characteristic of the turbines, as shown in next Section 4. In the first class all the values of wind speed under the cut in (w min ) and over the cut off (w max ) of the wind turbine are considered. The wind classes, W ( ⋅ ) , with the respective speed ranges, the number of samples observed for each class, N (·), and the consequent estimated probability of each class, p (·), are reported in Table 2. N T is the total number of samples considered, so an estimation of p (·) has been obtained as: () () T N p N ⋅ ⋅ = . (2) Wind Turbines 358 Wind class Speed range (m/s) Samples in the class, N (·) Class probability, p (·) W 1 [0, w min [∪ [w max + ∞[ N 1 p 1 W 2 [w min , w 2 [ N 2 p 2 W 3 [w 2 , w 3 [ N 3 p 3 W 4 [w 3 , w 4 [ N 4 p 4 … … … … W N-1 [w N-1 , w N [ N N-1 p N-1 Table 2. Wind classification according to wind profile. Two models of different accuracy are presented in the following subsections. 3.1 Models accounting for transitions among all states In Table 3 the number of transitions n ij , from the i-th wind class to the j-th wind class, are reported observed passing from each sample to the subsequent sample. The rows represent the i–th state, the columns the j–th state. The i-i transitions stay for a permanence in the i-th state. i\j 1 2 3 4 N 1 n 11 n 12 n 13 n 14 n 1N 2 n 21 n 22 n 23 n 24 n 2N 3 n 31 n 32 n 33 n 34 n 3N 4 n 41 n 42 n 43 n 44 n 4N N n N1 n N2 n N3 N N4 n NN Table 3. Number of transitions observed in the wind sample. In Fig. 3 the Markovian model of the wind is shown. Each state corresponds to a class, with a proper wind speed. The model is constituted by n states. Each state is represented with explicit reference to the level of wind speed. ϕ 41 ϕ 14 ϕ 21 ϕ 12 1 W 1 2 W 2 4 W 4 3 W 3 ϕ 32 ϕ 23 ϕ 43 ϕ 34 ϕ 31 ϕ 13 ϕ 42 ϕ 24 Fig. 3. Proposed Markovian model of the wind, N=4. The time spent in each of the four states is exponentially distributed, so the process can be viewed as a homogeneous Markov process. ϕij represents the transition rate between the state i and the state j. The transition rates among different states (different wind classes) and the permanence in the i-th state can be calculated from the measurement campaign considered by these formulas: [...]... Power models The wind turbine is characterized by its operational curve An example of wind turbine power versus wind speed is reported in Fig 5 wind turbine power (W) 15 x 10 5 10 5 0 0 5 10 15 wind speed (m/s) 20 25 Fig 5 Power of the wind turbine on the wind The typical operational data of a turbine are reported in Table 6 Cut-in wind speed (m/s) wmin Nominal wind speed (m/s) wn Table 6 Wind Turbine... samples during the observation period) Wind class Speed range (m/s) Samples in the class, N(·) Class probability, p(·) W1 W2 W3 W4 W5 [0, 4[∪ [25,+ ∞[ [4,7[ [7 ,10[ [10, 15[ [15,25[ 41 106 416 159 0 0.0568 0,1468 0,5762 0,2202 0 Table 9 Wind classification according to wind profile 15 wind speed (m/s) 10 5 0 0 100 200 300 400 500 sample number = time [h] 600 700 Fig 10 Wind speed values versus the number... under medium to high wind conditions and it is available in a wide range of tower heights from 40-86 m Its power curve is reported in Fig 11 Fig 11 Power of the wind turbine on the wind speed at different sound levels The operational data of the wind turbine, in particular referred to in this paper, are reported in Table 15 Cut-in wind speed (m/s) 4 Nominal wind speed (m/s) 16 Stop wind speed (m/s) 25... converter connected to the rotor windings Both modern pitch-controlled variable speed wind turbines technologies are emerging as the preferred technologies and have become the dominating type of yearly installed wind turbines in recent years 2 Wind energy development Worldwide, the development of wind energy is experiencing dramatic growth During the last decade, the installed wind energy capacity has grown... floating wind turbine applications Fig 1 Size evolution of wind turbines over time 4 Wind energy conversion A wind turbine is a rotary engine that captures power from a fluid flow (the wind) using aerodynamically designed blades and convert it into useful mechanical power The available power depends on the wind speed but it is important to be able to control and limit the power at higher wind speeds... between the turbines are linked to a transformer substation, which, at most cases, is placed offshore near the wind farm due to the long distance to shore (more than 5 km from the shore) Basically, a wind energy conversion system consists of a turbine tower which carries the nacelle, and the wind turbine rotor, consisting of rotor blades and hub Most modern wind turbines are horizontal-axis wind turbines. .. placed upwind of the tower and the nacelle, as illustrated in Fig 3 On the outside, the nacelle is usually equipped with anemometers and a wind vane to measure the wind speed and direction, as well as with aviation lights The nacelle contains the key components of the wind turbine, i.e the gearbox, mechanical brake, electrical generator, control systems, yaw 378 Wind Turbines drive, etc The wind turbines. .. with a partial-scale power converter connected to the rotor windings Based on these concepts, the most commonly applied wind turbine designs can be classified into four wind turbine concepts, as described below Modelling and Control Design of Pitch-Controlled Variable Speed Wind Turbines 379 5.1 Type A – Fixed speed wind turbine This topology corresponds to the constant or fixed speed controlled wind. .. installations climbed to 600 kW Today, the manufactured turbines for onshore applications are specified to deliver 23 MW output power In this sense, the world’s first wind park with novel "multi-mega power class” 7 MW wind turbines was manufactured by the German wind turbine producer Enercon (11 E-126 units) and put into partial operation in Estinnes, Belgium, in 2 010 (to be completed by July 2012) The key objective... being the largest onshore wind turbine presently under development a 10 MW unit At least four companies are working on the development of this "giant power class” 10 MW turbine for sea-based applications, namely American Superconductors (U.S.), Wind Power (U.K.), Clipper Windpower (U.K.) and Sway (Norway) Even more, it is likely that in the near future, power rating of wind turbines will increase further, . The wind turbine is characterized by its operational curve. An example of wind turbine power versus wind speed is reported in Fig. 5. 0 5 10 15 20 25 0 5 10 15 x 10 5 wind speed (m/s) wind. W 5 [15,25[ 0 0 Table 9. Wind classification according to wind profile. 0 100 200 300 400 500 600 700 0 5 10 15 sample number = time [h] wind speed (m/s) Fig. 10. Wind speed values versus. 4800 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 sample number wind speed (m/s) W 17 [16, ∞] W 16 [15,16[ W 15 [14,15[ W 14 [13,14[ W 13 [12,13[ W 12 [11,12[ W 11 [10, 11[ W 10 [9 ,10[ W 9 [8,9[