Title: Active Shunt Filter for Harmonic Mitigation in Wind Turbines Generators

Authors:Fernando Soares dos Reis, Member, IEEEReinaldo Tonkoski Jr., Student Member, IEEEJorge Villar Ale, Dr. Eng.Fabiano Daher Adegas, Mestrando**Syed Islam, Senior Member, IEEE**Kevin Tan, Student Member, IEEE

Address: Pontifícia Universidade Católica do Rio Grande do SulFaculdade de EngenhariaLEPUC – Laboratório de Eletrônica de Potência da PUCRSAv. Ipiranga, 6681CEP: 90619-900, Porto Alegre, RS - Brasil.

** Curtin University of TechnologyDepartment of Electrical and Computer Engineering

Tel: +55 (51) 3320 3686 / 3320 3500 Branch: 4156, 4571, 3686 Sub: 216, 224 and 225

Fax:+55 (51) 3320 3625

E-mail:f.dosreis@ieee.org

Contact author:Fernando Soares dos Reis

Topic area: TPC2- Power Electronics and Electrical Drives

Abstract – One of the preferred technologies in variable speed wind turbines (VSWT) is formed by a wind rotor, permanent magnet synchronous generator (PMSG), three-phase bridge rectifier (BR) with a bulky capacitor, and power electronics converter for grid interface. High-intensity, low-frequency harmonic currents flows into the PMSG as electric load has a non-linear characteristic.This paper presents an analysis and simulation of an active shunt filter (ASF) for harmonic mitigation in wind turbines generators. Currents are represented in d-q synchronous reference frame (SRF) and PWM carrier strategy is used to control the active filter. A new scheme to synchronize d-q currents using mechanical rotor angular speed is adopted.A dynamic wind turbine model and the active filter are implemented on software PSIM©. Representative waveforms and spectral analysis is presented. Simulations show that the proposed active filtering configuration can mitigate harmonic content into the PMSG.

Active Shunt Filter for Harmonic Mitigation in Wind Turbines Generators

F. S. Dos Reis, Member, IEEE, R. Tonkoski Jr., Student Member, IEEE, J. V. Alé, Dr. Eng., F. D. Adegas, **S. Islam, Senior Member, IEEE, **K. Tan, Student Member, IEEE

Pontifícia Universidade Católica do Rio Grande do Sul, Porto Alegre, Brazil.**Curtin University of Technology, Perth, Australia.

Abstract—One of the preferred technologies in variable speed wind turbines (VSWT) is formed by a wind rotor, permanent magnet synchronous generator (PMSG), three-phase bridge rectifier (BR) with a bulky capacitor, and power electronics converter for grid interface. High-intensity, low-frequency harmonic currents flows into the PMSG as electric load has a non-linear characteristic.

This paper presents an analysis and simulation of an active shunt filter (ASF) for harmonic mitigation in wind turbines generators. Currents are represented in d-q synchronous reference frame (SRF) and PWM carrier strategy is used to control the active filter. A new scheme to synchronize d-q currents using mechanical rotor angular speed is adopted.

A dynamic wind turbine model and the active filter are implemented on software PSIM©. Representative waveforms and spectral analysis is presented. Simulations show that the proposed active filtering configuration can mitigate harmonic content into the PMSG.

Index Terms—Active shunt filter, wind turbines, permanent magnet synchronous generator, wind energy conversion systems.

I. INTRODUCTION

ind power is the most rapidly-growing means of electricity generation at the turn of the 21st century

Global installed capacity has raised 20% in 2004 [1]. Developments in wind turbine technology follow this grown. Fixed speed wind turbines (FSWT) with passive power control are now giving place to variable speed wind turbines (VSWT) with active power control. VSWT has some advantages when compared to FSWT, e.g. lower mechanical stress, increased energy capture, active reactive power / voltage control [2].

W

Operation principle of VSWT is to decouple system electrical frequency from mechanical frequency. Power electronics has a main role on this task. Two VSWT topologies are emerging as preferred technologies.

Doubly-Fed Induction Generator (DFIG) wind turbines utilize a wound rotor induction generator, where the rotor winding is fed through back-to-back variable frequency, voltage source converters [3].

Developments in gearless, variable-speed generators with power electronics grid interface leads to a generation of quiet, reliable, economical wind turbines. The most usual technology of this direct-driven wind turbine is composed by a multi-pole permanent magnet synchronous generator (PMSG), three-phase bridge rectifier with a bulky capacitor, and current-controlled voltage source inverter (CC-VSI) or line-commutated SRC with active harmonic compensation for grid interface [4]. Three-phase bridge rectifier with bulky capacitor presents a non-linear characteristic and consequently harmonic current content flows into the PMSG. Asynchronous components in the air-gap field induces eddy currents in the solid rotor iron, increasing PMSG losses and temperature [5]

An alternative to mitigate harmonic content into PMSG is to use power electronics converter that actively cancel

harmonic currents, providing a sinusoidal waveform. One of the ways to compensate harmonic content is to use an active shunt filter. (ASF) ASF is being used with success to reduce harmonic content in industry and distribution lines [6]. The use of ASF in wind turbines must be investigated.

This paper presents an analysis and simulation of an active shunt filter (ASF) for harmonic mitigation in wind turbines generators. Currents are represented in d-q synchronous reference frame (SRF), and PWM carried strategy is used to control the active filter. A new scheme to synchronize d-q currents using rotor mechanical angular speed is adopted.

A dynamic wind turbine model and the active filter are implemented on software PSIM©. Representative waveforms and spectral analysis is presented. Simulations show that the proposed active filtering configuration can mitigate harmonic content into the PMSG.

II.WIND ENERGY CONVERSION SYSTEM MODEL The basic diagram of the wind energy conversion system

to be analyzed on this paper is illustrated in Fig. 1. The system is composed by a wind rotor which transforms the kinetic energy from the wind with uwind speed in mechanical torque in the shaft. The shaft drives directly the PMSG, which generates power with variable-frequency and alternate current. A rectifier bridge with a bulky capacitor Clink is responsible for AC-DC conversion to form the DC link. Grid interfacing DC-AC power converter is represented by a equivalent resistance Rload.

The ASF is connected on main bus between generator and bridge rectifier. It consists of a six-switch, three-phase voltage source inverter (VSI), a CDC capacitor on the DC side of the inverter, and a LF to suppress high-frequency currents originated by the switching of the VSI. A bank of capacitors C is used for filter high-frequency voltage occasioned by the inverter.

Fig. 1. Basic diagram of the wind energy conversion system.

A. Wind RotorThe fundamental dynamics of VSWT can be expressed by

this simple mathematical model

(1)

where J is the moment of inertia (rotor inertia plus generator inertia), ωm is the mechanical angular speed, Ta is the aerodynamic torque; Tf is the friction torque (rotor fiction plus generator friction); and Te is the electrical load torque from wind turbine.

Aerodynamic torque Ta is determined by

(2)

where CT is the rotor torque coefficient; is the air density; A is the rotor swept area; D is the rotor diameter; and uwind is the wind speed. Torque coefficient is a non-linear function of the tip-speed ratio and blades pitch angle β. This relation can be found by computational simulations or experimentally. Tip-speed ratio is expressed by

(3)

For a fixed-pitch blade rotor, CT is a function of only. The CT( curve to be used on this work is will be illustrated on Fig. 2 in the full paper version.

Friction torque is determined by

(4)

where B is the friction coefficient.

B. PMSGDynamic modeling of PMSG can be described in d-q

reference system [7].

(5)

(6)

where R is the stator winding resistance; Ld and Lq are stator inductances in direct and quadrature axis, respectively; id e iq

are the currents in direct and quadrature axis, respectively; ωe

is the electrical angular speed of the generator; λm is the amplitude of the flux linkages established by the permanent magnet viewed by the stator windings, and ρ is the operator d/dt.

The expression for the electromagnetic torque can be described as

(7)

where P is the number of poles. The relation between electrical angular speed ωe and mechanical angular speed ωm

is expressed by

(8)

C. Bridge Rectifier and DC LoadThe WECS uses the well-known three-phase six-pulse

bridge rectifier. The DC link is formed by the capacitance Clink Load characteristics applied to the wind turbine can be easily represented by changing the value of the resistor Rload, seen on Fig. 1.

High-intensity, low-frequency harmonic currents flows into the PMSG as BR has a non-linear characteristic. A study case is presented showing the PMSG output currents at WECS full load condition (20 kW resistive load, Clink=5000uF, RL=6.5 Ω, VL=360 V) using a conventional BR, at steady-state operation. The wind speed in this case is 12 m/s. A detail of the PMSG WECS simulated output current and line-to-line voltage (divided by 4), for the rated power deliver situation at 12 m/s wind speed, is shown in Fig. 3.

Fig. 3. PMSG output currents and line to line voltage div. by 4.

The harmonic content and the total harmonic distortion (THD) of the output PMSG current and voltage were obtained using Fourier analysis. The results are summarized in Fig. 4 and Fig. 5.

Fig. 4. Harmonic content of the PMSG output current.

Fig. 5. Harmonic content of the PMSG output voltage.

The fundamental component was omitted in these figures in order to remark the harmonic content. From these figures it is possible to observe that the 5th, 7th, 11th, 13th, 17th and 19th

harmonics are significant. The obtained total harmonic distortion was THD = 10.68 % and 29.15 % for current and voltage respectively, which are quite high. At full load, the harmonic content of the output current is minimized by the influence of the machine stator equivalent inductance and resistance which are Ls = 3 mH and Rs = 0.432 respectively. Unfortunately this effect is not so noticeable when the available wind decreases and, therefore, the maximum power output decreases and the THD increases.

III. 3-PHASE ACTIVE SHUNT FILTER

The basic compensation principle of the ASF is to control filter current in a closed loop manner to actively shape the source current is into the sinusoid. [8]

Applying Kirchoff’s law on the coupling point of the ASF to the main bus as seen on Fig. 1, current iF can be determined as

(9)

where iPMSG is the current supplied by the PMSG, iC is the current drained by the filter capacitor C and iNL is the non linear current drained by the load.

A. ASF Control CircuitControl circuit of ASF has three main objectives: to

calculate harmonic currents that must be compensated; to regulate voltage on the capacitor CDC; and to control current iF in order to inject as close as possible the calculated reference currents.

1) Reference Currents: The blocks diagram on Fig. 6 illustrates the harmonic currents calculation and voltage vDC

control of the capacitor.

Fig. 6. Block diagram of the ASF harmonic currents calculation and vDC

voltage control

Calculation of compensating currents is done by transforming three-phase load currents in the direct-quadrature synchronous reference frame (d-q SRF). For this, phase currents iNLa, iNLb and iNLc are measured and transformed in α-β coordinates,

(10)

α-β currents is transformed in d-q SRF coordinates by using a matrix of unitary amplitude sinus and cosines,

(11)

where θSRF is the synchronous reference frame angle.The θSRF, when ASF is applied to industry or distribution

lines, is usually determined by phase voltage detection and using a phase-locked-loop (PLL) system. To obtain θSRF in this work it was used the mechanical angular speed ωm. The idea is to use the relation between ωm and ωe expressed on Eq. (8) and integrate ωe, obtaining the SRF angle θSRF. In frequency domain,

(12)

where s is the Laplace operator.id contains fundamental and harmonics information of

active current, and iq contains fundamental and harmonics

information of reactive currents. A first order low-pass filter with unit gain is used to obtain the DC part of id, idDC, and iq, iqDC,

(13)

where k is the pole of the filter. idDC and iqDC contains information of the current’s fundamental frequency.

The dc bus nominal voltage vDC must be greater than or equal to line-to-line voltage peak to actively control iF. In order to maintain the vDC voltage on the capacitor, an amount of active current must be delivered to the ASF. The vDC is regulated by a closed-loop Proporcional-Integral (PI) control. The PI control signal Δid is summed with idDC, adjusting the amount of active fundamental current handled by the ASF.

The DC currents idDC+ Δid and iqDC returns to α-β coordinates using the inverse transformation of Eq. 14

(14)

The fundamental current components on 3-phase a-b-c coordinates, iaf, ibf, icf are obtained by the inverse transformation of Eq. 15,

(15)

The reference currents to the ASF per phase, i*Fa, i*

Fb and i*

Fc are determined by the subtraction of non-linear currents iNLa, iNLb, iNLc and fundamental currents iaf, ibf, icf.

(16)

Just harmonics and vDC control current information is contained on the reference currents.

2) Current Control by PWM Carrier Strategy: The filter current is controlled by a PWM carrier strategy. Reference currents i*

Fa, i*Fb and i*

Fb and measured currents iFa, iFb and iFc

are used in a PI loop control. Control signal is limited and then compared to a triangular PWM carrier signal in order to command VSI switches. Fig. 7 illustrates PWM control for ASF current.

Fig. 7. PWM carrier control for ASF current

2) Circuit Design: A practical choice of LF guarantees that the active filter can generate a current with a slope equal to the maximum slope of the load current [9]. The upper bound on filter inductance, for the switching scheme used in this work, is

(17)

where Vn is the line-to-neutral voltage and diLn is the load current of phase n, respectively.

The capacitor size CDC can be estimated based on load current iL and maximum accepted voltage ripple ΔvDCmax,

(18)

From ASF output voltage to PMSG output voltage, the inductance LF and capacitance C forms an LC filter which cutoff frequency is

(19)

The value of LF, CDC and C can be adjusted based on simulation results.

IV. POWER LOSSES CALCULATION 1) PMSG Losses: Basically the total power losses

generated into the machine can be divided into two big groups: copper losses and core losses. The copper power losses PCU are produced in the stator winding as function of the RMS current, according to Eq. 20,

(20)

where IAi is the RMS value of the ith harmonic component of the current IA and RA is stator equivalent resistance. [10, 11]. However, operating at higher current level resulted to have temperature rise. The change of Ra due to temperature rise was not included in the calculations. The high frequency flux changing generated by the harmonics causes hysteresis Ph

and eddy current power losses Pe in the core, represented by [11].

(21)

where: ke and kh are constants, Bmax is peak flux density, f is the rated frequency, weight represents the core and copper weight.

The influence of the voltage harmonic content in magnetic losses may be evaluated using Eq. 17 and 18 proposed by Kaboli et al in [10].

(22)

(23)

Ph1, Pe1 and V1 are the hysteresis and eddy current power losses and the PMSG line to line output voltage respectively at the nominal condition resistive load without harmonics, i is the harmonic order and Vi are the amplitude of the harmonic components of the PMSG line to line output voltage.

2) ASF Converter Losses: Losses generated by the ASF consists of passive and active component losses. Those losses will be fully explained in the full paper version.

V. SIMULATION RESULTS For simulation of the proposed configuration, PSIM®

software was used. On full paper version Table I will be a summary of the parameter values.

The waveforms of steady-state simulation at WECS full load condition (20 kW resistive load, C link=5000uF, RL=6.5 Ω, VL=360 V) with wind speed of 12 m/s is shown on Fig. 8.

Fig. 8. Main waveforms of WECS with ASF at full load condition.

Harmonic content in percent of fundamental component using ASF, for PMSG output current and voltage, is illustrated on Figs. 9 and 10 respectively.

The ASF filter reduces considerably the total harmonic distortion of current, from 10.68% to 2.60%.Voltage THD got better as well, from 29.15% to 20.77%. The lower harmonic content of voltage diminishes the core losses. Due to ASF voltage vDC control, a larger amount of fundamental current is required from the PMSG, implying in larger copper losses. The WECS system and its subsystems power losses and efficiencies are summarized in Tab. II.

0,0

0,2

0,4

0,6

0,8

1,0

1,2

%

2 7 12 17 22 27 32 37 42 47 52 57

OrderFig. 9. Harmonic content of the PMSG output phase current using ASF.

THD=2.60 %

0123456789

1011121314

%

2 7 12 17 22 27 32 37 42 47 52 57

OrderFig. 10. Harmonic content of the PMSG output line-to-line voltage using

ASF.

TABLE II – WECS COMPONENT LOSSES AND EFFICIENCIES

PMSG LOSSES

Topology

Copper Losses

(W)

Core Losses

(W)

Friction & Windage

(W)Total (W) η (%)

BR 2318.93 180.82 120 2619.75 88.42ASF 2790.24 150.73 120 3060.97 86.73

ASF LOSSES

IGBT Losses (W)

LF Losses (W)

C Losses (W)

CDC Losses (W) Total (W)

199.44 284.66 0.2166 116.00 600.33

ELECTRICAL SYSTEM LOSSES

Topology PMSG Total (W)

ASF Total (W)

Rectifier Total (W)

Efficiency (%)

BR 2619.75 0 95.16 88.05ASF 3199.92 603.03 211.82 84.74

WECS EFFICIENCY

Topology Aero dynamical (%)

Electrical (%) Overall (%)

BR 43.26 88.05 38.09ASF 43.88 84.74 37.18

VI. CONCLUSION

The use of active shunt filter in wind energy generation systems for harmonic mitigation was analyzed and computationally simulated. The ASF is able to mitigate harmonic content of current that flows on the permanent magnet synchronous generator. A capacitor bank filter was used to suppress high-switching frequency voltage component generated by the ASF on generator terminals. The d-q SRF synchronization using the angular rotor speed had worked, and its physical implementation using sensors must be investigated.

The ASF could diminish voltage core losses. Although, PMSG efficiency is lower because copper losses are higher when using ASF. Overall wind energy conversion system efficiency is lower as well, so the use of ASF could be justified if only the PMSG generator could have a larger life cycle.

VII. REFERENCES

[1] GWEC, “Global Wind Power Continues Expansion”,Global Wind Energy Council Release, march 4th, 2005.

[2] Spera, David A., ed. (1994). Wind Turbine Technology. New York, NY: The American Society of Mechanical Engineers.[3] J.B. Ekanayake, L. Holdsworth, N. Jenkins, “Comparison of 5th order and 3rd order machine models for doubly fed induction generator (DFIG) wind turbines” Electric Power Systems Research, vol. 67, pp. 207-215, April 2003: Elsevier.[4] Z. Chen, E. Spooner, “Wind Turbine Power Converters – A comparative study”, IEE Conference on Power Electronics and Variable Speed Drives, 21-23 September 1998, publ. no456.[5] J.L.F.van der Veen, L.J.J.Offringa, A. J .A. Van den put, “Minimising rotor losses in high-speed high-power permanent magnet synchronous generators with rectifier load” IEE Proc-Electr. Power Appl., Vol. 144, No. 5, September 1997.[6] Hirofumi Akagi, “New Trends in Active Filters for Power Conditioning” IEEE Transactions on Industry Applications, vol 32, no 6, November 1996.[7] Borowi, B. S., Salameh, Z. M., “Dynamic response of a stand alone wind energy conversion system with battery energy storage to a wind gust” IEEE Transactions on Energy Conversion, vol. 12, no 1, March 1997.[8] Akagi, H., Nabae, A. Atoh, S., “Control Strategy of Active Power Filters Using Multiple Voltage-Source PWM Converters” IEEE Transactions on Industry Applications, vol. IA-22, No. 3, May 1986 .[9] Al-Zamil, A. M., Torrey, D. A., “A Passive Series, Active Shunt Filter for High PowerApplications” IEEE Transactions on Power Electronics, vol. 16, no. 1, january 2001.[10] Kaboli, Sh.; Zolghadri, M.R.; Homaifar, A., “Effects of sampling time on the performance of direct torque controlled induction motor drive”, IEEE International Symposium on Industrial Electronics, 2003. ISIE '03, Volume: 2 , June 9-11, 2003, pp.:1049 – 1052.[11] Yao Tze Tat, "Analysis of Losses in a 20kW Permanent Magnet Wind Energy Conversion System", in the Department of Electrical and Computer Engineering. Western Australia: Curtin University of Technology, October 2003. pp. 101.

THD=20.77 %