Harmonic Current Predictors for Wind Turbines

Transcription

1 Energies 2013, 6, ; doi: /en Article OPEN ACCESS energies ISSN Harmonic Current Predictors for Wind Turbines Jen-Hao Teng 1, *, Rong-Ceng Leou 2, Cuo-Yean Cang 2 and Sun-Yu Can Departmental of Electrical Engineering, National Sun Yat-Sen University, Kaosiung, Taiwan; Department of Electrical Engineering, Ceng-Siu University, Kaosiung, Taiwan; s: leou@csu.edu.tw (R.-C.L.); cycang@mail.csu.edu.tw (C.-Y.C.); ingres@csu.edu.tw (S.-Y.C.) * Autor to wom correspondence sould be addressed; jteng@ee.nsysu.edu.tw; Tel.: (ext. 4118); Fax: Received: 21 October 2012; in revised form: 21 December 2012 / Accepted: 22 February 2013 / Publised: 4 Marc 2013 Abstract: Te armonic impact caused by wind turbines sould be carefully investigated before wind turbines are interconnected. However, te armonic currents of wind turbines are not easily predicted due to te variations of wind speed. If te armonic current outputs can be predicted accurately, te armonic impact of wind turbines and wind farms for power grids can be analyzed efficiently. Terefore, tis paper analyzes te armonic current caracteristics of wind turbines and investigates te feasibility of developing armonic current predictors. Field measurement, data sorting, and analysis are conducted for wind turbines. Two armonic current predictors are proposed based on te measured armonic data. One is te Auto-Regressive and Moving Average (ARMA)-based armonic current predictor, wic can be used for real-time prediction. Te oter is te stocastic armonic current predictor considering te probability density distributions of armonic currents. It uses te measured armonic data to establis te probability density distributions of armonic currents at different wind speeds, and ten uses tem to implement a long-term armonic current prediction. Test results use te measured data to validate te forecast ability of tese two armonic current predictors. Te ARMA-based predictor obtains poor performance on some armonic orders due to te stocastic caracteristics of armonic current caused by te variations of wind speed. Relatively, te prediction results of stocastic armonic current predictor sow tat te armonic currents of a wind turbine in long-term operation can be effectively analyzed by te establised probability density distributions. Terefore, te proposed stocastic armonic current predictor is elpful in

2 Energies 2013, predicting and analyzing te possible armonic problems during te operation of wind turbines and wind farms. Keywords: wind turbine; armonic current predictor; ARMA; probability density distribution 1. Introduction In te past few years, wind power generation as become te fastest growing renewable energy power generation tecnology in te World. Due to te mature tecniques and commercialized bulk production, wind turbine cost as been reduced. In addition, severe commercial competition as resulted in rapidly decreasing costs in te past. At present, more tan 40 countries in te World ave wind turbines installed, mostly located in Europe, Nort America, and East Asia. Countries wit large wind power generation are Denmark, Spain, Germany, U.S., etc. As more and more wind power generation systems ave been connected to power systems, countries ave begun to study regulations regarding interconnecting wind turbines and wind farms to power systems, and to analyze te resulting steady-state and dynamic impacts. Steady-state impact analysis includes voltage fluctuation, sort-circuit current rus, power quality impact, and protection coordination. Dynamic impact analysis at least includes stability and voltage flicker [1 13]. Te armonic impact caused by wind turbines sould be carefully investigated before te interconnection of wind turbines; especially, wen wind power generation accounts for a certain percentage of te system power output. However, te armonic currents of wind turbines are not easily predicted due to te variations of wind speed. If te armonic current outputs can be predicted accurately, te armonic impact of wind turbines and wind farms for power grids can be analyzed efficiently, terefore, tis paper analyzes te armonic current caracteristics of wind turbines and investigates te feasibility of developing armonic current predictors. In general, te armonic current outputs of a power converter wit constant power output can be formulated matematically. However, wen te power converter is used in wind turbines, its armonic current outputs are difficult to formulate due te inertia of te blades and generator, especially wen te wind speed canges instantaneously. Te control algoritms and parameters used in te power converter of a commercialized wind turbine cannot be easily obtained also. Tose factors make te armonic current outputs stocastic and difficult to analyze. Terefore, ow to use te measured armonic data to develop armonic current predictor to analyze te armonic impact of te wind turbines and wind farms on power systems is an important issue [3,6 13]. Harmonic current prediction is difficult to some extent; tus, many previous studies ave used neural networks for armonic current prediction [14 16]. If te armonic current caracteristics can be known in advance, te armonic current predictor for wind turbines can be realized effectively. Altoug some literature [11 13] as analyzed te armonic current caracteristic of wind turbines, tis paper furter analyzes tese armonic current caracteristics at different wind speeds, and uses te measured data and armonic current caracteristic to propose armonic current predictors. Field measurements, data sorting, and analysis are conducted for wind turbines in tis paper. Two armonic current predictors are proposed based on te measured armonic data. One is te armonic current predictor implemented by te Auto-Regressive and Moving Average (ARMA) model, wic

3 Energies 2013, considers te cange in wind speed and uses te measured armonic data to calculate ARMA parameters. Te ARMA model can ten be used to predict te real-time armonic current for te next time point. Altoug te prediction results of te ARMA-based armonic current predictor can predict all orders of armonic currents of wind turbine, te results aren t quite acceptable, especially for some armonic orders. Te presently measured wind turbine uses te power converter-based doubly fed inductor generator and is equipped wit a armonic filter, so te control results of tis equipment will become very stocastic as te wind speed canges and consequently, te ARMA-based predictor as poor performance on some armonic orders. Tis paper proposes anoter stocastic armonic current predictor tat considers te probability density distribution of armonic currents. Te measured armonic data is ten used to establis te probability density distribution for different orders of armonic currents at different wind speeds. Te proposed stocastic armonic current predictor can ten be implemented for long-term armonic current prediction. Te prediction results of te proposed stocastic armonic current predictor sow tat te armonic currents of a wind turbine in long-term operation can be effectively analyzed. Terefore, it will be elpful in predicting and analyzing te possible armonic problems during te long-term operation of wind turbines and wind farms. 2. Field Measurements of Wind Turbine Tis paper conducts long-term power quality measurements for a commercialized wind turbine of a doubly fed inductor generator type. Te measured power quality parameters include tree-pase voltages, currents, powers, armonics, etc. Te nameplate of te 1.5 MW rated power converter used for te wind turbine is illustrated in Figure 1. Te arcitecture and measurement point of te wind turbine are sown in Figure 2. Te average power output of te wind turbine (kw) and average wind speed (m/s) per our measured in a week are illustrated in Figure 3. Tere are occasionally iger wind speeds, but no corresponding outputs, as te wind turbine was sut down for some reasons at te time. Te wind turbine power output, te wind turbine rotation speed, and te wind speed are obtained from te power generation database of te wind turbine monitoring system, tus, te relationsip between wind speed and power output can be establised. Figure 4 sows te voltage armonic and current armonic spectra at a wind speed of 9.2 m/s. Oter voltage armonic and current armonic spectra wit respect to different wind speeds are also measured and recorded. Te total number of measurements was 23,289. Te field measurements can ten be used to test and validate te proposed predictors. Figure 1. Nameplate of power converter used in te wind turbine.

4 kw m/s Energies 2013, Figure 2. Arcitecture and measurement point of te wind turbine. Figure 3. Average power output and wind speed per our Generation(kW) Wind Velocity(m/s) Hour Figure 4. Voltage and current armonic spectra at wind speed 9.2 m/s. Voltage armonic spectra; Current armonic spectra Harmonic Voltage (%) Va Vb Vc Harmonic Order

5 Energies 2013, Figure 4. Cont Harmonic Current (%) Ia Ib Ic Harmonic Order 3. Harmonic Current Predictor for Wind Turbines Tis paper uses te measured armonic data to design two armonic current predictors. One is te real-time armonic current predictor implemented by te ARMA model, wic considers te cange in wind speed. Te oter is te stocastic armonic current predictor, wic considers te output probability distribution of all orders of armonic. Te two armonic current predictors proposed in tis paper are described below ARMA-Based Harmonic Current Predictor Te ARMA model contains Auto Regressive (AR) and Moving Average (MA). Te p-order AR, AR(p), can be expressed as: zt zt 1 p zt p at 1 (1) were z t is te time series of te measured value; µ is te mean value; φ 1, φ 2, φ p are te parameters to be estimated, and a t is te residual. Te q-order Moving Average (MA), MA(q), can be written as: z a a t t a 1 t 1 q t q (2) were θ 1, θ 2,θ p are parameters to be estimated. In certain cases, te simple AR model or MA model may require additional parameters to effectively establis te time series, te required parameters can be reduced by combining tese two models. Te ARMA(p,q) model is expressed as te following Equation (3): zt 1 zt 1 p zt 1 1at 1 qat q (3) Te parameters for te ARMA model can be easily obtained by a computer program [17]; terefore, te parameters calculation procedure is not sown ere. According to te basic formulas of ARMA as expressed in Equations (1 3), wen te parameters in te ARMA model ave been calculated for different armonic orders using te measured data, te ARMA model can be used for real-time armonic

6 Energies 2013, current prediction. Using te t order armonic current as an example, te ARMA (2,3)-based armonic current predictor can be expressed as: pred mea mea I, t, t 1, t 1 I, t 1, t 1, t 2 I, t 2, t 1 q, t 1 a, t 1 q, t 2 a, t 2 q, t 3 a, t 3 (4) t, 1 t 1 t 1 mea Ii, i 1 (5) a,x = I mea,x I pred,x x = t 1, t 2, t 3 (6) were I pred,t is te predicted current for te t order armonic current at time period t. I mea,t 1, I mea,t 2 and I mea,t 3 are te measurements for te t order armonic current at time periods t 1, t 2 and t 3, respectively. φ,t 1, φ,t 1 and θ,t 1, θ,t 2, θ,t 3 are parameters for AR(2) and MA(3) for te t order armonic current, respectively. µ,t 1 calculated by Equation (5) is te mean value of te t order armonic current. a,t 1, a,t 2, a,t 3 calculated by Equation (6) are te residuals for te t order armonic current at time periods t 1, t 2 and t Stocastic Harmonic Current Predictor Based on Density Distributions of Harmonic Currents Te aforesaid ARMA model can be used to predict all armonic outputs for te next time point. Most wind turbines at present use a power converter and are equipped wit armonic filters. Since te wind speed as large uncertainty and te control algoritms and parameters used in te power converter of commercialized wind turbine cannot be easily obtained, te armonic current outputs of a wind turbine become igly stocastic and are difficult to predict especially wen te wind speed cange instantaneously. For example, Figure 2 sows te system arcitecture of te wind turbine measured in tis paper. Te wind turbine uses a power converter based doubly fed inductor generator and a armonic filter is mounted at te output end. Te control results of te wind turbine will become very stocastic as te wind speed canges. Terefore, te armonic output must not be simply related to te armonic output at previous time points. Even if tere is a sligt difference in te wind speed, armonic output of wind turbine will be quite different. Figure 5 sows te 5/7/11t order armonic currents of wind turbines wen te wind speed (v ws ) is m/s. Te x-axis in Figure 5 is te measurement no. and te y-axis is its corresponding armonic current. It is observed tat a sligt difference in te wind speed would cause considerable canges in te armonic current. Altoug Figure 5 sows te armonic currents of a wind turbine are very stocastic, if armonic currents are segmented and te probability density distributions are calculated, ten different viewpoints can be observed, as sown in Figure 6. It is seen tat te probability density distribution is very close to normal distribution; terefore, Equations (7) and (8) are used to calculate te mean and standard: ws ws ws ws 1 f I ;, e 2 ws 2 2 ws I ws ws 2 2 (7)

7 Energies 2013, were f ws (I ws ; µ ws armonic current establised by µ ws, (σ ws ) 2 )is te probability density function of normal distribution for te t order and σ ws is of Equation (7) wen te wind speed is witin range v ws. I ws te random variable for te t order armonic current wen te wind speed is witin range v ws. Figure 5. Output caracteristics of te 5/7/11t order armonic currents. 5t order armonic current; 7t order armonic current; (c) 11t order armonic current. 8 = 5, v ws = m/s Measurement No. = 7, v ws = m/s Measurement No. = 11, v ws = m/s Measurement No. (c)

8 Energies 2013, Figure 6. density distributions of te 5/7/11t order armonic currents. 5t order armonic current; 7t order armonic current; (c) 11t order armonic current = 5, v ws = m/s Normal Distribution = 7, v ws = m/s Normal Distribution = 11, v ws = m/s Normal Distribution (c) Te cumulative distribution function of normal distribution can be establised by Equation (9) and be expressed as: ws ws 2 I ws 2 2 ws 1 I 2 F I ;, e di ws 2 ws ws ws ws ws (8)

9 Cumulative Energies 2013, were F ws (I ws ; µ ws, (σ ws ) 2 ) is te cumulative distribution function of normal distribution of te t order armonic current wen te wind is witin range v ws. Te cumulative distribution function, as Equation (10) establised by actual measurement, can be used for armonic current prediction. For example, wen te wind speed range is m/s, te measured cumulative distributions and cumulative distributions of normal distribution for te 5/7/11t order armonic currents of wind turbine are illustrated in Figure 7. Once te cumulative distribution functions, as sown in Figure 7, are establised, it can be used to transfer te value of cumulative probability to te armonic current. A random variable wit numerical value between 0 and 1 can be generated by a computer program randomly and used to simulate te value of cumulative probability. Te armonic current can ten be obtained by inversing te value of cumulative probability from te cumulative distribution function. Te concept is as sown in Figure 7a. In Figure 7a, x ws is te generated random variable and I ws,for is te predicted t order armonic current obtained by inversing x ws from te cumulative distribution function. Figure 7. Cumulative probabilities of te 5/7/11t order armonic currents. 5t order armonic current; 7t order armonic current; (c) 11t order armonic current. = 5, v ws = m/s = 7, v ws = m/s Normal Distribution

10 Cumulative Energies 2013, Figure 7. Cont. = 11, v ws = 6.0~6.5 m/s Normal Distribution (c) 4. Test Results and Discussions Te proposed two armonic current predictors are tested and teir applicability is validated. Due to limited space, only te prediction results for te armonic orders wit larger armonic currents suc as te 5t, 7t and 11t armonic orders are tested in tis paper. However, te metods proposed in tis paper can also be used to predict oter armonic orders i.e., te 3rd order armonic currents. Te number of measured data points used in te following tests is 23, Prediction Results of ARMA-based Harmonic Current Predictor Tis paper uses multiple ARMA models to build te prediction model for all orders of armonic current. Te 18,289 data of te measured 23,289 data are used to calculate various parameters in te ARMA model, and 5000 data are reserved to validate te prediction accuracy of ARMA model. Te forecasted error of te model is calculated by Equation (11): ER I I mea for, i, i, i mea I, i 100% (9) were ER,i is te percentage error of te t armonic current of data number i. I mea,i and I for,i are te measured value and predicted value, respectively. Table 1 uses 18,289 data points to build te ARMA models, and φ 1 and θ 1 are parameters of armonic order 5, 7, 11, 13, 17, and 19. Due to limited space, te parameters for oter ARMA models are not stated ere. Te armonic prediction results of ARMA (1,1) and ARMA (2,3), implemented by te reserved 5000 data points are as sown in Tables 2 and 3. According to Tables 2 and 3, te ARMA (1,1) or ARMA (2,3) ave only better prediction results for parts of armonic orders; owever, te wole forecasting errors are relatively large. As mentioned above, te measured wind turbine uses te power converter based doubly fed inductor generator and is equipped wit a armonic filter, te control results of tese devices are igly stocastic as wind speed canges. Terefore, te ARMA model cannot accurately predict te armonic output of wind turbine. Tat is to say, te armonic currents of a wind

11 Energies 2013, turbine cannot be predicted by a simple time series model. In addition, te armonic currents at several time points must be used for te ARMA-based armonic current predictor. Namely, te wind turbine must be equipped wit a power quality analyzer to provide armonic measurements to predict te armonics at te next time point. Since most wind turbines ave not been equipped wit a power quality analyzer, te practicability of te ARMA model is furter reduced. Table 1. Parameters of ARMA (1,1) model. Harmonic order Parameters φ 1 θ Table 2. Prediction results of ARMA (1,1). Harmonic Order Error Max. Min. Average Standard deviation Table 3. Prediction results of ARMA (2,3). Harmonic Order Error Max. Min. Average Standard deviation Prediction Results of Stocastic Harmonic Current Predictor In general, a smaller analyzed wind speed range requires more measurements for modeling. If more measurements are used, ten a more accurate prediction can be anticipated. Since te modeling and validation of te stocastic armonic current predictor bot require more measurements; terefore, about a alf of te measurements are used for model formation and te oters are used for validation. In tis paper, 55% of te measured data points in eac wind speed range are used for model formation, and 45% are used for model validation. Besides, tere are only 23,289 measured data, so te wind speed

12 probability Energies 2013, ranges are terefore divided into 4 6 m/s, 6 8 m/s, 8 10 m/s, and above 10 m/s ranges. For simplicity, only te prediction results for te 4 6 m/s and 6 8 m/s wind speed ranges are discussed below. Figure 8 sows te probability density distribution of 5t armonic current using 55% data for model formation, and te corresponding normal distribution for te different wind speed ranges. It is proved again by Figure 8 tat te distributions of armonic currents of wind turbine are very close to normal distribution. Te mean and standard deviation corresponding to te normal distributions of all armonic current orders in te wind speed ranges 4 6 m/s and 6 8 m/s are as sown in Table 4. Figures 9 11 sow te forecasted probability density distributions of te 5/7/11t armonic currents generated by te armonic predictor and te 45% of measured data for validation. Figures 9 11 illustrate tat te prediction results are very consistent wit te measurement results for validation. Altoug te prediction results of stocastic armonic current predictor are quite accurate, as compared wit te prediction results of ARMA model in Tables 2 and 3, tere remain some differences in prediction, as sown in Figures Te reason is te armonic measurement data volume for establising and validating probability distribution of all armonics are sligtly insufficient, tus, long-term measurement sall be conducted in te future and accuracy will be validated. Tis paper focused on te predictions of integer armonics suc as te 5t, 7t, 11t and 13t armonic currents, since te inter-armonic currents are not considered in most of te interconnection requirements. Te inter-armonic currents of wind turbine migt cause some specified power quality problems for power grids; terefore, te extension of te proposed predictor for te low frequency inter-armonic currents will be studied in te future. Figure 8. density distributions of te 5t armonic currents. Wind speed range 4 6 m/s; Wind speed range 6 8 m/s = 5, v ws = m/s Normal Distribution = 5, v ws = m/s Current(A) Normal Distribution Table 4. Normal distribution parameters for te different order armonic currents. Harmonic order Wind speed (4 6 m/s) Wind speed (6 8 m/s) Mean Standard Deviation Mean Standard deviation

13 Energies 2013, Figure 9. Measured and forecasted probability distributions of te 5t armonic currents. Wind speed range 4 6 m/s; Wind speed range 6 8 m/s. = 5, v ws = m/s Forecasted Harmonic Current Current(A) = 5, v ws = m/s Forecasted Harmonic Current Measured Harmonic Current Figure 10. Measured and forecasted probability distributions of te 7t armonic currents. Wind speed range 4 6m/s; Wind speed range 6 8m/s = 7, v ws = m/s Forecasted Harmonic Current Measured Harmonic Current = 7, v ws = m/s Current(A) Forecasted Harmonic Current Figure 11. Measured and forecasted probability distributions of te 11t armonic currents. Wind speed range 4 6 m/s; Wind speed range 6 8 m/s. = 11, v ws = m/s Forecasted Harmonic Current = 11, v ws = m/s Measured Harmonic Current Forecasted Harmonic Current Current(A)

14 Energies 2013, Conclusions Tis paper conducted field measurements, data sorting, and analysis for te wind turbine, and uses te measured armonic data to propose two armonic current predictors. One was te real-time armonic current predictor implemented by te ARMA model. Te oter was te stocastic armonic current predictor considering te probability density distribution of armonic currents. Test results of te ARMA-based armonic current predictor sowed tat te prediction performances on some armonic orders are poor. Relatively, te prediction results of stocastic armonic current predictor sowed tat te armonic currents of a wind turbine in long-term operation can be effectively analyzed by te establised probability density distributions. Terefore, te proposed stocastic armonic current predictor sould ave great potential to be used to analyze te armonic impact caused by te grid-connected wind turbines and wind farms. Altoug test results demonstrated te performance of te proposed stocastic armonic current predictor, oter factors suc as te effects of te grid supply conditions, magnetic loading of macine, te state of te DFIG drive itself, te armonic filter installed in wind turbine etc. on te proposed armonic current predictors sould be furter studied. Tose topics will be investigated in te future researc. Acknowledgement Tis work was supported in part by National Science Council under Contracts NSC E and NSC P Te autors would also like to tank te staff of Nuclear Power Plant 3, Taiwan Power Co., Ltd. for teir assistance. References 1. Wind Turbine Generator Systems-Part 21: Measurement and Assessment of Power Quality Caracteristic of Grid Connected Wind Turbines, IEC ; IEC Standard, Feijoo, A.E.; Cidras, J. Modeling of wind farms in te load flow analysis. IEEE Trans. Power Syst. 2000, 15, Cen, Z.; Spooner, E. Grid power quality wit variable speed wind turbines. IEEE Trans. Energy Convers. 2001, 16, Larsson, A. Flicker emission of wind turbines caused by switcing operations. IEEE Trans. Energy Convers. 2002, 17, Moammed, H.; Nwankpa, C.O.; Stocastic analysis and simulation of grid-connected wind energy conversion system. IEEE Trans. Energy Convers. 2000, 15, Tenca, P.; Rockill, A.A.; Lipo, T.A.; Wind turbine current-source converter providing reactive power control and reduced armonics. IEEE Trans. Ind. Appl. 2007, 43, Tentzerakis, S.T.; Papatanassiou, S.A. An Investigation of te armonic emissions of wind turbines. IEEE Trans. Energy Convers.2007, 22, Melicio, R.; Mendes, V.M.F.; Catalao, J.P.S. Harmonic assessment of variable-speed wind turbines considering a converter control malfunction. IET Renew. Power Gener. 2010, 4, Herrera, J.I.; Reddoc, T.W.; Lawler, J.S.; Harmonics generated by two variable speed wind generating systems. IEEE Trans. Energy Convers. 1988, 3,

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