ADVANCED SIGNAL PROCESSING METHODS FOR EVALUATION OF HARMONIC DISTORTION CAUSED BY DFIG WIND GENERATOR

Transcription

1 ADVANCED SIGNAL PROCESSING METHODS FOR EVALUATION OF HARMONIC DISTORTION CAUSED BY DFIG WIND GENERATOR Przemyslaw Janik, Zbigniew Leonowicz, Jacek Rezmer Wroclaw University of Technology Wroclaw, Poland Abstract Intensified growth of wind ower generation emhasizes the need for detailed evaluation of disturbances caused by wind generators. The aer resents a hysical model of doubly fed induction generator (DFIG) connected to low voltage distribution grid. Harmonic distortions caused by wind generator under various oerational conditions regarding wind seed, active and reactive ower have been investigated. Fourier transform, ESPRIT and Prony analysis have been alied simultaneously to evaluate distortion levels. Keywords: wind turbine, doubly feed induction generator, ower quality, Prony method, ESPRIT INTRODUCTION Wind generation is one of the most mature and cost effective resources among different renewably energy technologies []. Further intensification of wind farms roliferation into electric systems is suorted by ecologists and governments. The target of Euroean Community is to increase the share of renewable energy resources to % by []. A forward-looking energy suly olicy imlies the use of wind turbines with good grid comatibility and measures for grid reinforcement as well [3]. The quality of energy suly and comatibility issues underlay standardization. Power quality criteria defined in various standards [4], [5] are not only imortant from the technical oint of view. Also the deregulated energy market forces high quality of electricity suly and reliability [6], [7]. Utilities have develoed interconnection requirements to which new wind generators must abide [9]. Stricter requirements demanding accurate reactive ower control and voltage regulation caability has led to the integration of ower electronic converter in many of wind generator designs [8]. This allows better control of the generator in terms of reactive ower control and also limited control of real ower characteristics. There are various design concets which allow fulfillment of those requirements [3]. Examles are conversion systems with synchronous generator (with exciter and ermanent magnet) and converter-inverter units. Additionally, there are short circuit rotor asynchronous machines also with converter-inverter units or asynchronous machines with static comensators []. Steffen Schostan Detlef Schulz Helmut-Schmidt-University Hamburg, Germany steffen.schostan@hsu-hh.de detlef.schulz@hsu-hh.de One of the oular and efficient designs is the doubly fed induction generator DFIG [3]. The DFIG allows the regulation of reactive ower and the adjustment of angular velocity to maximize the outut ower by given wind seeds. The generator can also stay connected to the grid during voltage sags. However, one of the drawbacks is current with harmonic content introduced into the system []. The urose of the aer is the evaluation of harmonic distortion in various oeration conditions of the DFIG. Prony method and ESPRIT algorithm were alied to get information on harmonics arameters. It was assumed that those advanced methods could give more detailed information, then using traditional FFT. The laboratory model of DFIG allowed quite free regulation of active and reactive ower and angular velocity of the shaft. The interest was focused on the harmonics generated by DFIG. Due to restrictions imosed by utilities on wind ark oerators it is difficult to run such research activity on real object within widesread range of arameters changes in accetably short time. Firstly, the hysical, grid connected model consisting of induction generator, direct converter, DC machine and control unit is introduced. Secondly, the Prony method and ESPRIT algorithms are resented. Then, the measurement rocedure and assessment of grid arameters follow. Current measurements and harmonics estimation results are finally resented and discussed. MODEL OF DOUBLY FED INDUCTION GENERATOR Simlified model of DFIG is shown in Fig.. The rotor of induction machine is connected to the grid with a back-to-back voltage source converter which controls the excitation system. This most significant feature enables sub synchronous and suer synchronous oeration seeds in generator mode and adjustable reactive ower generation. Model comonents are shortly characterized below.. Grid The generator was connected to a three hase low voltage distribution grid. In order to assess the system 6th PSCC, Glasgow, Scotland, July 4-8, 8 Page

2 influence on current harmonic roagation measurement of system imedances has been carried out. currents, rotor side currents and grid side converter currents..5 Figure : Doubly fed induction generator The current harmonic roagation limits defined in [] also bear reference to grid imedances. A grid imedance analyzer allowed grid imedance vs. frequency estimation u to khz. Fig. shows grid imedances of three hases seen from cc. Visible are unsymmetrical conditions at cc, esecially for higher frequencies. imedance Z [Ω] Z Z Z frequency [Hz] Figure : Grid imedance vs. frequency at a time instant. Wind Turbine The wind turbine was modeled with a searately excited 3 kw DC machine. Torque and angular velocity could be in a controlled manner in accordance to seed-torque characteristic of a real three blade rotor adated for steady state oeration of the 5 kw DFIG model. At a given wind seed there is an otimal angular velocity at which the maximum mechanical ower is available [3]. Usually the maximum mechanical ower should be fed in the induction generator and transferred into the grid. That imlies an exact seed-ower or resectively seedtorque oerational characteristic of the DFIG. The characteristic shown in Fig.3 was obtained through data scaling of a real 5 MW rotor and necessary adotion of number of oles and gear box translation to the laboratory model..3 Rectifier and Inverter In the rotor circuit [3] two IGBT ulse width modulated converters are installed. A stator flux oriented vector control strategy has been alied to control the active and reactive ower outut of the DFIG. Practical realization of the control scheme required measurement of stator side voltages and M mech [Nm] n = 67 min P =.996 kw mech n syn = 5 min n = 4 min P =.8 kw mech n [min ] Figure 3: The seed-torque characteristic of a three blade rotor simulated with DC machine. The schematic electrical control blocks of the wind turbine are shown in Fig. 4. The DFIG control consists of two cascaded controlloos, connected with the rotor side and grid side converters resectively. The rotor side converter controller cascade tries to maintain the active and reactive ower at a redefined level. The first block, the ower-controller, comares the and values of active and reactive ower. Its outut, the values of i d and i q are comared in the second block with the i d and i q values. The second control block oututs the desired voltages of the rotor side rectifier. P S Q S Q Grid U IC Q Grid P S,QS Q S Q Grid U IC P S U IC i qr i dr i dgrid i qgrid i r i dr i qr i Grid i dgrid i qgrid Figure 4: The structure block diagram of DFIG control Rotorside Converter Gridside Converter The grid side converter controller cascade regulates the intermediate circuit voltage and the grid side reactive ower in the rotor circuit. The reactive ower controller comares the and reactive ower values and oututs the i d value. The intermediate circuit voltage controller comares the and value of intermediate circuit voltage and oututs the i q value. The final block comares and i d and i q values and oututs desired voltages of the gird side rectifier. 6th PSCC, Glasgow, Scotland, July 4-8, 8 Page

3 .4 Filter and Transformer A assive filter scheme (LCL inductance caacitance inductance) was installed behind the grid side converter to minimize harmonic distortion introduced in the grid. The filter comonents arameters were tled with accordance to grid and transformer inductances and converter characteristic. The Y/Y 3/ V not grounded transformer was used to match the converter voltage level with the low voltage grid. 3 PRONY ALGORITHM The Prony method is a technique for modeling samled data as a linear combination of exonential functions [4]. Although it is not a sectral estimation technique, the Prony method has a close relationshi to the least squares linear rediction algorithms used for AR and ARMA arameter estimation. Prony method seeks to fit a deterministic exonential model to the data in contrast to AR and ARMA methods that seek to fit a random model to the second-order data statistics. Assuming N comlex data samles the investigated function can be aroximated by exonential functions can be aroximated by exonential functions: ( k j k )( n ) T j k y[ n] = A e α + ω + ψ () k = k where n =,,..., N, T - samling eriod, α k - daming factor, ω k - angular velocity, A k - amlitude, ψ k - initial hase. The discrete-time function may be concisely exressed in the form y[ n] = h z () k = n where j k hk = Ak e ψ ( k j k ) T, zk = e α + ω The estimation roblem is based on the minimization of the squared error over the N data values N δ = ε n (3) ε n= where [ ] n [ n] x[ n] y[ n] x[ n] h z = = (4) k= This turns out to be a difficult nonlinear roblem. It can be solved using the Prony method that utilizes linear equation solutions. If as many data samles are used as there are exonential arameters, then an exact exonential fit to the data can be made. Consider the -exonent discrete-time function: x[ n] = h z (5) k= n The equations of (5) may be exressed in matrix from as: z z z h x[ ] h z z z x[ ] = (6) h z x[ ] z z The matrix equation reresents a of linear equations that can be solved for the unknown vector of amlitudes. Prony roosed to define the olynomial that has the exonents as its roots: F z z z z z z z z z (7) ( ) = ( k ) = ( )( ) ( ) k = () The olynomial may be reresented as the sum: ( ) [ ] F z m = a m z = [ ] [ ] [ ] [ ] = a z + a z + + a z + a (8) Shifting the index on (5) from n to n-m and multilying by the arameter a[m] yield: n m [ ] [ ] [ ] a m x n m = a m h z (9) k = Equation (9) can be modified into: [ ] a m x[ n m] = (9) n m = hk zk a[ m] zk k= The right-hand summation in () may be recognized as a olynomial defined by (8), evaluated at each of its roots yielding the zero result: [ ] a m x[ n m] = () The equation can be solved for the olynomial coefficients. In the second ste the roots of the olynomial defined by (8) can be calculated. The daming factors and sinusoidal frequencies may be determined from the roots z k. For ractical situations, the number of data oints N usually exceeds the minimum number needed to fit a model of exonentials, i.e. N >. In the overdetermined data case, the linear equation () should be modified to: [ ] [ ] = [ ] a m x n m e n () The estimation roblem is based on the minimization of the total squared error: r n= + [ ] E = e n () 6th PSCC, Glasgow, Scotland, July 4-8, 8 Page 3

4 4 ESPRIT METHOD ESPRIT method belongs to the subsace arametric sectrum estimation methods. It allows determining the arameters of harmonic comonents with high accuracy. It is based on eigenvector decomosition of the autocorrelation matrix of the signal where define two subsaces (signal and noise subsaces) are defined. The rotational invariance between both subsaces allows extracting of the arameters of sectral comonents resent within the investigated waveform [6]. The assumed signal model is the following: M ( j kn) y[ n] = Ak e ω + w[ n] (3) k = where w[ n ] reresents additive noise. The eigenvectors U of the autocorrelation matrix of the signal define two subsaces (signal and noise subsaces) by using two selector matrices Γ and Γ. S = ΓU S = ΓU (4) The rotational invariance between both subsaces leads to the equation: S = ΦS (5) where: jω e jω e Φ = jω M e (6) The matrix Φ contains all information about M comonents frequencies. Additionally, the TLS (total least-squares) aroach (alied for solving of (6) for Φ ) assumes that both estimated matrices S can contain errors and finds the matrix Φ as minimization of the Frobenius norm of the error matrix. 5 MEASUREMENT AND ANALYSIS During the sub and suer synchronous mode measurements were done at three oints of the DFIG system indicated in Fig.. Currents were catured at cc and additionally at rotor and grid side converter leads. The measurements were carried out during steady state oeration. The ower quality recorder used enabled the cature of currants and voltages with samling frequency of khz. Additionally, ower factor, active and reactive owers were observed to ensure desired generation conditions of the DFIG. 5. Sub Synchronous Mode The measurements in sub synchronous mode corresond with the oint fixed at 4 rm on the seed-moment characteristic of the wind turbine (Fig. 3). The 8 W of the mechanical art could be not measured at the cc side due to losses. Accordingly to () in sub synchronous mode the stator active ower is comensated in art by the active ower in rotor circuit. The control system (Fig. 4) values are summarized in Table. Active Power Stator -6 W Reactive Power Stator - var Intermediate Circuit Voltage V Reactive Power Rotor var Table : Set values of the control system at 4 rm and ower factor near to one. The mean active ower value introduced into the grid at cc was significantly smaller, about 7 W. The total losses included losses caused by rotection devices, converter, transformer and LCL filter. Alone, the active ower introduced in the rotor circuit of the induction machine was about 87 W. Tyically, the ower factor at cc during the oeration of a wind generator should be equal to one. Due to unsymmetrical conditions highest accessible ower factor was about.94. Fig. 5 deicts the three hase current sulied into the grid, samled with khz. Current [A] 3 i (t) i (t) i 3 (t) time [s] Figure 5: Three hase current mesured at cc Sectral comonents were obtained using a windowed signal with the length adated to ten eriods of fundamental 5 Hz comonent. Fig. 6 shows the current measured at cc in hase one and aroximated with a Prony model. Following figures deicts the FFT sectrum (Fig. 7) and sectral comonents comuted with Prony algorithm (Fig 8). With a view to the harmonic comonents the magnitude axis was zoomed, so the 5 Hz fundamental art of ca..5 A is not visible. The tyical harmonics comonents, e.g. of order 3, 5, 7, were comuted wit similar magnitudes by both methods. Prony however gave more information regarding interharmonic comonents. Detailed information on most significant comonents around Hz is given in Tab.. Additionally, the comonents about Hz are zoomed and deicted in Fig. 9 and Fig.. Besides characteristic harmonics the interharmonics are visible. 6th PSCC, Glasgow, Scotland, July 4-8, 8 Page 4

5 Amlitude [A] 3 i (t) mes i (t) ar Table : The harmonic comonents in current obtained by Prony method Time [s] Figure 6: The measured and aroximated current in hase one Figure 7: The FFT transform of the current signal Figure 8: Sectral estimation of current with Prony model. The analysis using the ESPRIT method (Fig. ) delivered aroriate values of harmonics. However this method indicated interharmonic comonents about Hz, signal arameters values (Table 3) differ slightly form those obtained by Prony and Fourier analysis. Amlitude [A] Figure 9: Current comonents obtained with Prony for frequencies about Hz Figure : Current comonents obtained with FFT for frequencies about Hz Figure : Analysis done by ESPRIT algorithm. 6th PSCC, Glasgow, Scotland, July 4-8, 8 Page 5

6 Amlitude [A] ,7.48 Table 3: Interharmonic comonents in current obtained by ESPRIT 5. Suer Synchronous Mode The oerating oint in suer synchronous mode was also redefined by the seed-moment characteristic (Fig. 3). The ower of the wind turbine itself was.9 kw at 67 rm. Contrary to sub synchronous mode the active ower is fed into the gird on stator and rotor side (). The control system (Fig. 4) values are summarized in Table 4. Active Power Stator -8 W Reactive Power Stator -35 var Intermediate Circuit Voltage V Reactive Power Rotor var Table 4: Set values of the control system at 67 rm and ower factor near to one. The ower factor was also ket ossibly near one and was equal to.96. No higher value was achievable in unsymmetrical conditions. Fig. shows the measured and aroximated current in hase one. The discreancy between measured and aroximated signal is smaller, than in sub synchronous mode. Amlitude [A] 5 5 i (t) mes i (t) ar Time [s] Figure : The measured and aroximated current in hase one Fig. 3 shows the FFT transform and Fig. 4 Prony analysis of the current with interharmonic comonent visible. These comonents are different from those obtained in sub synchronous mode and significantly smaller in amlitude, therefore more difficult to identify. Some arameters of the current signal are given in Table Figure 3: The FFT transform of the current signal Figure 4: Sectral estimation of current with Prony model Amlitude [A] , Table 5: Harmonic comonents in current obtained by Prony Fig. 5 shows the sectral arameters, obtained with ESPRIT method, which are also given in Table 6. Those arameters corresond with signal arameters obtained with Prony method (Table 5). Characteristic is the high content of interharmonics. The ESPRIT method seemed to have lower frequency resolution then Prony, some frequencies were skied or merged. 6th PSCC, Glasgow, Scotland, July 4-8, 8 Page 6

7 Figure 5: Current analysis with ESPRIT Amlitude [A] Table 6: Harmonic comonents in current obtained by ESPRIT 6 CONCLUSION Currents fed into the grid by the investigated DFIG system have a considerable harmonic content. Uncharacteristic harmonics and interharmonics were observed. Unfortunately, interharmonics are often not taken into account during ower quality comatibility tests of wind generator systems. Interharmonics may cause unexected resonances, damage caacitors, insulation and various control and rotection devices. Monitoring and accurate estimation of ower quality arameters is a crucial issue in guaranteeing reliable and save oeration of a ower system with wind generation. That s also an imortant rerequisite for an adequate roosal of harmonic mitigation systems. Alied sectral estimation methods, showed high content of interharmonics in the currents. Nevertheless, the Prony Method delivered most satisfactory results. Esecially in comarison to traditional Fourier analysis, the Prony Method shoved better resolution and was alicable for decaying signals. Higher harmonic content in sub synchronous than by suer synchronous mode is caused by extensive use of the converter. Suer synchronous mode is ossible without converter. The comuted amlitudes and frequencies of sectral comonents varied, deending on the generation mode of the investigated DFIG system. Assumingly, nonsymmetrical conditions regarding grid imedances and voltages intensified the harmonic distortion caused by wind generator. In consequence, ractical evaluation of harmonic content in wind generation system should be done over a long eriod of time covering various arameters of the generation unit and the grid. REFERENCES []T. Hammons, Status of integrating renewable electricity roduction in Euroe into the grids, Proceedings of UPEC Conference, Cork (Ireland), 5,.75 []/77/EC Directive on the romotion of electricity roduced from renewable energy sources in the internal electricity market [3]S. Heier, Grid Integration of Wind Energy Conversion Systems, Chichester, Wiley, 6 [4]IEC 64- Wind turbine generators systems Part : Measurement and assessment of ower quality characteristics of grid connected wind turbines [5]EN 56 Voltage characteristics of electricity sulied by ublic distribution [6]Chaman R. Reliability and Quality You get What you exect in The Evolution of Electric Power Transmission under Deregulation, IEEE Press, Piscataway,, [7]J. Arrillaga, N. R. Watson, Power System Quality Assessment, Chichester, Wiley, [8]C. Abby et al. Transient Modeling and Comarison of Wind Generator Toologies, Proceedings of IPST Conference, Montreal, (Canada), 5, aer no. IPST5-3 [9]Netzanschluss- und Netznutzungsregelnder Vattenfall Euroe,:htt:// netzz/index.js []A. Arulamalam, M. Barnes, N. Jenkins and J.B. Ekanayake Power quality and stability imrovement of a windfarm using STATCOM suorted with hybrid battery energy storage IEE Proc.-Gener. Transm. Distrib., Vol. 53, No. 6, November 6,.7-7 []G. J. Wakileh Power System harmonics. Fundamentals, Analysis and Filter Design, Berlin, Sringer, []IEC 6-3-4: Electromagnetic comatibility-part 3-4 Limits of emission of harmonic currents in low voltage ower suly systems for equiment with rated current greather than 6A, 998 [3]Y.Lei, A. Mullane, G. Lighbody, R. Yacamini, Modeling of the Wind Turbine with a Doubly Fed Induction Generator for Grid Integration Studies, IEEE Trans. On Energy Convertion, vo., No., march 6, [4]T. Lobos, J. Rezmer, H-J. Koglin, Analysis of Power System Transients using Wavelets and Prony Method. Proceedings IEEE Power Tech Conference, Porto, Portugal, Setember, aer ID EMT-3 6th PSCC, Glasgow, Scotland, July 4-8, 8 Page 7