7-1
Chapter 7
Conclusions and Future Work
7.1 Conclusions
In this thesis the operation of and winding short-circuit fault detection in a Doubly-Fed Induction Generator (DFIG) based Wind Turbine Generator System (WTGS) have been investigated. A review of the available wind turbine condition monitoring systems in industry indicates that the focus is mainly on the gearbox and bearing faults. However, according to surveys, generator faults are the fifth most frequent cause of WTGS failure accounting for 9 % of downtime. Thus, it is important to dedicate some effort on faults such as winding short-circuits, which can develop into a failure quickly due to the presence of high current in the shorted turns. To achieve this, it is necessary to understand the modelling detail required, the operation of the DFIG and the design of the control system. To validate the algorithms, a test bench is a valuable tool since it provides the possibility to observe phenomena that do not appear in simulations due to the trade-off between modelling detail and simulation speed.
The faultless operation of the DFIG has been discussed in Chapter-3. The modelling requirements for the system have been investigated based on literature review, which suggests that it is necessary to consider both the stator and rotor flux dynamics to accurately determine the machine currents. A lumped-mass model of the drive train can be used while wind speed can be considered constant during the time frame of interest for machine electrical faults, which is around one second. Such a model of the WTGS has therefore been studied where the controllers have been designed for both the start-up and grid- connected power production mode of operation. Two simulators have been developed, one for each mode of operation. The first simulator of the WTGS that models the generator, the converters and the grid in the dq domain provides the possibility for fast simulations, at any operating point for the grid-connected mode of operation, and has been used to compare the Proportional Integral (PI) controller against the Linear Quadratic Gaussian (LQG) controller for both the power and torque control strategy. It has been concluded that the torque control strategy is better as compared to the power control strategy as it offers less degradation in performance at operating points different from the one for which the controller was tuned. The LQG control technique is superior to PI control technique since it considers the Multiple Input Multiple Output (MIMO) nature of the system while the design based on PI control breaks the system down into a Single Input Single Output (SISO) subsystem for each of the d and q axis. The second simulator uses the three-phase component models of Matlab/SimPowerSystems and is used to simulate the start-up sequence of the DFIG based WTGS. The procedure for correcting the phase error between the generated stator voltage and the grid voltage has been simplified by using a sample-and-hold technique thereby eliminating the need to design a separate controller for this function. The modelled system corresponds to the laboratory test bench and both the controllers and the developed phase difference correction technique have been validated through experiments.
7-2 The faulted operation of the DFIG has been studied in Chapter-4 where the third simulator developed for this purpose is used for winding turn-turn fault simulation in the DFIG based WTGS. The procedure for modelling the machine using the winding-function approach has been detailed. The developed machine model is validated as a shorted-rotor singly-fed induction machine by observing the harmonics in the stator currents, torque and the speed. It has been shown that the model is able to reproduce the harmonics used extensively in literature as indicators for squirrel-cage induction machine stator winding short-circuit faults. The modelled machine is then used in a DFIG based WTGS with the control system implemented. It has been concluded that it is necessary to consider the effect of fault location as well as the control system. The current frequency harmonic magnitudes have been shown to differ widely with the location of the fault within the phase winding whereas the control system attenuates these harmonic magnitudes altogether while introducing some new harmonics. This is important when the presence of specific slip related harmonics is used as a fault indicator and for the selection of a threshold value for the harmonic magnitudes for alarm generation. The negative-sequence current component, as a fault residual, has been shown to be less dependent on fault location and the number of faulted turns (fault severity) in the presence of a control system. The effect of noise, filter delays and stator voltage unbalance that also effect the detection system performance has been taken into account.
The dimensioning of the major components for the test bench has been discussed in Chapter-5. A number of sources have been consulted for the required information. The necessary interface cards and protection circuits have been developed and included for signal conditioning and protection against over- voltage and over-current and over-temperature. The system has been used in other applications and works satisfactorily.
The experimental results are provided in Chapter-6 where the tests to determine the necessary parameters for simulation have been carried out. The operation of the Grid-Side Converter (GSC) and the Rotor-Side Converter (RSC) has been analyzed in the context of the DFIG based WTGS start-up.
7.2 Future Work
• The WTGS model can be extended with a detailed model of the drive train and of the wind for simulations over a longer period of time to test the control algorithms for power quality performance. The effect of parameter variation should be included as well.
• It is important for a fault detection system based on the negative- sequence current component to differentiate between the internal faults of the generator and the current unbalance due to the non-symmetric grid faults and sensor faults. The short duration grid faults are temporary as opposed to winding short-circuits and do not require disconnection from the grid but rather to ride through the fault. The effects of eccentricity can be included by modifying the air-gap function in the developed generator model thereby extending the range of faults can that be simulated.
7-3
• The test bench can be modified to include a crowbar to study the Low Voltage Ride Through (LVRT) capability of the DFIG based WTGS for grid faults. However, since the trend in WTGS is towards synchronous generators with full-rated converters, to be able to comply with the evolving grid codes, more effort can be placed on converter operation.
The model of a wind turbine for emulation on the test bench needs to be implemented. An LCL filter can be designed which is becoming popular for grid-interfaced converters.
R-1
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S-1
Symbols and Abbreviations
Abbreviations
AC : Alternating Current
ADC : Analogue to Digital Converter(s) ANSI : American National Standards Institute
CMOS : Complementary Metal Oxide Semiconductor CUSUM : Cumulative Sum
DAC : Digital to Analogue Converter(s) DC : Direct Current
DFIG : Doubly-Fed Induction Generator DSP : Digital Signal Processing
EMC : Electro-Magnetic Compatibility EMI : Electro-Magnetic Interference EPVA : Extended Park’s Vector Approach ESL : Equivalent Series Inductance ESR : Equivalent Series Resistance
EVAM : Evaluated Vibration Analysis Method EWEA : European Wind Energy Association
FACTS : Flexible AC Transmission System(s) FFT : Fast Fourier Transform
GE : General Electric GSC : Grid-Side Converter GUI : Graphic User Interface
IGBT : Isolated Gate Bipolar Transistor I/O : Input(s)/Output(s)
LLR : Log-Likelihood Ratio LQG : Linear Quadratic Gaussian LVRT : Low Voltage Ride Through
MCSA : Motor Current Signature Analysis MIMO : Multiple Input Multiple Output MMF : Magneto-Motive Force
MPPT : Maximum Power Point Tracking
NEMA : National Electrical Manufacturers Association n.d. : no date
PCC : Point of Common Coupling PI : Proportional Integral PLL : Phase Locked Loop
S-2 PWM : Pulse-Width Modulation
RMS : Root Mean Square RPM : Revolutions per Minute RSC : Rotor-Side Converter
SCIG : Squirrel-Cage Induction Generator SISO : Single Input Single Output
SPM : Shock Pulse Method STATCOM : Static Compensator SVM : Space Vector Modulation
THD : Total Harmonic Distortion TSR : Tip Speed Ratio
TTL : Transistor-Transistor Logic
UART : Universal Asynchronous Receiver and Transmitter UK : United Kingdom
VUF : Voltage Unbalance Factor
WRIG : Wound-Rotor Induction Generator WTGS : Wind Turbine Generator System(s)
Symbols
a : Distance of the pole along the real axis from the origin Aag : Cross-sectional area of the air-gap
Ablade : Area covered by the rotor blades
Ac : Transfer matrices of the PI controller state-space model Am : Transfer matrices of the machine state-space model Asys : Transfer matrices of the closed-loop state-space model
b : Distance of the pole along the imaginary axis from the origin B : Magnetic flux density
Bc : Transfer matrices of the PI controller state-space model Beq : Total viscous friction of the lumped-mass model
Bm : Transfer matrices of the machine state-space model Bsys : Transfer matrices of the closed-loop state-space model
C(s) : Transfer function of the controller in continuous time C(z) : Transfer function of the controller in discrete time C1, C2 : DC-link capacitors in series
Cc : Transfer matrices of the PI controller state-space model CDC : Capacitance of the DC-link
Cf1 , Cf2 : Capacitance values used in the measurement filter Cm : Transfer matrices of the machine state-space model
Col,vDC(s) : Open-loop transfer function for DC-link voltage control in continuous time
CP : Aerodynamic efficiency coefficient CP,max : Efficiency coefficient at optimal TSR
S-3 Csys : Transfer matrices of the closed-loop state-space model
CvDC(s) : Controller transfer function for DC-link voltage control in continuous time
Dc : Transfer matrices of the PI controller state-space model Dg : Generator rotor damping
Dm : Transfer matrices of the machine state-space model Dsys : Transfer matrices of the closed-loop state-space model Dt : Turbine rotor damping
DCa : Duty-cycle for phase a voltage DCb : Duty-cycle for phase b voltage DCc : Duty-cycle for phase c voltage
e : Error input to the PI controller in the PLL Ew : Energy contained in the wind
fcontrol : Frequencies introduced by the control system fcurrents : Frequencies in the current
fd : Drive electric supply frequency
fPLL : Frequency of the voltage input to the PLL
fref : Frequency of the reference voltage to the converter for the delay test
fsync : Grid electric supply frequency ft&s : Frequencies in torque and speed F : Magneto-motive force
F1 : MMF of coil 1
Fab : Magneto-motive force drop along segment ab Fcd : Magneto-motive force drop along segment cd
g : test function
gag : Length of the air-gap
Gcl,if(s) : Closed-loop transfer function for GSC current control in continuous time
Gcl,ir : Closed-loop transfer function for RSC current control in continuous time
GCDC(s) : Transfer function of the DC-link capacitor in continuous time Gf1 , Gf2 : Conductance of the resistances Rf1 , Rf2 used in the measurement
filter
GLf(s) : Transfer function of the inductance filter in continuous time
Gps(s) : Process transfer function for stator power control in continuous time
Gr(s) : Transfer function of the rotor circuit in continuous time
GTe(s) : Process transfer function for electromagnetic torque control in continuous time
GvDC(s) : Process transfer function for DC-link voltage control in continuous time
Gvs(s) : Process transfer function for stator voltage control in continuous time
S-4
h : Harmonic order
H : Magnetic field intensity
Hf(s) : Transfer function of the measurement filter in continuous time Hg : Generator rotor inertia in seconds
Ht : Turbine rotor inertia in seconds
+is : Positive-sequence stator current component -is : Negative-sequence stator current component
is
o : Zero-sequence stator current component i1 : Current flowing through coil 1
iar : Current of rotor phase a
iar x Hz : Rotor current harmonic with x Hz frequency ibr : Current of rotor phase b
icr : Current of rotor phase c idr : Current of rotor shorted turns ias : Current of stator phase a
ias x Hz : Stator current harmonic with x Hz frequency ibs : Current of stator phase b
ics : Current of stator phase c ids : Current of stator shorted turns iDC : Current on the DC side of a converter iDC,RSC : Current on the DC side of the RSC converter iDC,GSC : Current on the DC side of the GSC converter ifa : Current of filter phase a
ifb : Current of filter phase b ifc : Current of filter phase c
ifd : GSC output current component along the d axis ifq : GSC output current component along the q axis ih : h order harmonic current
inet : Current through the DC-link capacitor ird : Rotor current component along the d axis
ird,0 : Rotor current component along the d axis before the step change irq : Rotor current component along the q axis
irq,0 : Rotor current component along the q axis before the step change irr : Rotor current vector
isd : Stator current component along the d axis isq : Stator current component along the q axis iss : Stator current vector
I1 : RMS value of the fundamental frequency current Ih : RMS value of the harmonic frequency current
IGBTTop : Switching signals for the upper IGBT in one branch of a 2-level converter
IGBTBot : Switching signals for the lower IGBT in one branch of a 2-level converter
Jeq : Total inertia of the lumped-mass model Jg : Generator rotor inertia
k : Sample number
S-5 kn : Gain of the measurement filter transfer function
Ki : Integral gain of the PI controller
Ki,if : Integral gain of the PI controller for GSC current control Ki,ir : Integral gain of the PI controller for RSC current control Ki,ps : Integral gain of the PI controller for stator power control
Ki,Te : Integral gain of the PI controller for electromagnetic torque control
Ki,vDC : Integral gain of the PI controller for DC-link voltage control Ki,vs : Integral gain of the PI controller for stator voltage control Kp : Proportional gain of the PI controller
Kp,if : Proportional gain of the PI controller for GSC current control Kp,ir : Proportional gain of the PI controller for RSC current control Kp,ps : Proportional gain of the PI controller for stator power control Kp,Te : Proportional gain of the PI controller for electromagnetic torque
control
Kp,vDC : Proportional gain of the PI controller for DC-link voltage control Kp,vs : Proportional gain of the PI controller for stator voltage control
l : Length defined on the closed path abcda lw : Length of the air cylinder
L1 : Peak value of the fundamental component of inductance LB1 : Mutual inductance of winding B and coil 1
Lf : Inductance of the filter
Lh : Peak value of the hth order inductance harmonic Ljk : Mutual inductance between coil j and coil k Llr : Leakage inductance of rotor
Lls : Leakage inductance of stator Lm : Magnetizing inductance
Lmut c1As-c4Ar : Mutual inductance between coil 1 of stator phase a and coil 4 of rotor phase a
Lmut c1As-Ar : Mutual inductance between coil 1 of stator phase a and rotor phase a
Lmut As-Ar : Mutual inductance between stator and rotor phase a
Lmut AsAr-AsCr-CsAr-CsCr : Mutual inductance between stator and rotor phases for implementation as line model.
Lr : Inductance of a rotor phase Lrr : Rotor self-inductance matrix
Lrs : Rotor to stator mutual inductance matrix Ls : Inductance of a stator phase
Lsr : Stator to rotor mutual inductance matrix Lss : Stator self-inductance matrix
Lstk : Length of the stack
m : Number of coils in winding B mma : Amplitude modulation index mw : Mass of the wind
M : Winding function of coil with turns function n M1 : Winding function of coil 1
S-6 nc : Number of capacitors in series on the DC-link
nj : Number of turns in coil j nk : Number of turns in coil k nm : DFIG speed in rpm nt : Turns function of a coil nt2 : Turns function of coil 2-2’
ntB : Turns function of winding B
p : Number of poles of the machine pCu,loss : Total Copper losses of the generator
pf : Active power on the GSC side of the inductance filter pg : Active power on the grid side of the inductance filter pr : Active power at the rotor terminals
ps : Active power at the stator terminals
pol : Poles of the measurement filter transfer function P : Permeance of the flux path
Pe, pe, Pout : Total electrical power output of the DFIG
Pe,0 : Total electrical power output of the DFIG before the step change Prated : Rated power of the DFIG
Pt : Power extracted by the aerodynamic system Pt,opt : Turbine power at optimal TSR
Pw : Power of the wind
qe, Qe : Total reactive power exchange of the DFIG
qg : Reactive power on the grid side of the inductance filter qs, Qstator : Reactive power at the stator terminals
rag : Average radius of the air-gap
rt : Turns ratio between the stator and rotor windings Rblade : Length of the rotor blade
Rch : Resistors used to charge the DC-link capacitor RDC : Equivalent series resistance of the DC-link capacitor Rf : Resistance of the inductance filter
Rf1 , Rf2 : Resistance values used in the measurement filter
RL : Phase resistance of the lighting load connected at the transformer secondary side
Rr : Resistance of a rotor phase Rrr : Rotor resistance matrix Rs : Resistance of a stator phase Rss : Stator resistance matrix
Rvsr1 : Voltage sharing resistance across the DC-link capacitor C1
s : Slip or the Laplace operator in continuous time as evident si : Log-likelihood ratio
S : Surface (enclosing the cylindrical volume) Sconv : Apparent power of the converter
Sk : Cumulative sum
Skg : Three-phase short-circuit fault level at the secondary side of the transformer
S-7
t : Time
tf : Fall time tr : Rise time
trise,if : Rise time for the GSC current with close-loop current control trise,ir : Rise time for the RSC current with close-loop current control tPHL : Propagation time for high to low logic
tPLH : Propagation time for low to high logic Tcd : Delay of the converter
Tdt : Dead time for IGBT switching Tem : Electromagnetic torque
Tem,0 : Electromagnetic torque of the DFIG before the step change Tem x Hz : Electromagnetic torque harmonic with x Hz frequency T*em : Electromagnetic torque reference at the low speed shaft Tfd : Delay of the measurement filter
Tm : Mechanical driving torque at the turbine shaft
Tmax : Maximum tolerance value of the DC-link capacitor in p.u.
Tmin : Minimum tolerance value of the DC-link capacitor in p.u.
Tm,est : Torque estimate at the turbine shaft
Tm,opt : Mechanical driving torque at the turbine shaft at optimal TSR Ts : Sampling time period
Tsd : Total system delay for the generation, measurement and conversion of the converter voltage
Tsw : Switching time period of the converter
u : Input vector to the state-space model
∆u : Small perturbation in the inputs to the state-space model u0 : Steady-state value of the inputs to the state-space model uc : Input vector of the PI controller state-space model um : Input vector of the machine state-space model usys : Input vector of the closed-loop state-space model
∆vDC : Peak DC-link voltage ripple
|vpktri| : Absolute peak value of the triangular wave
vα : Voltage component along the α axis of the αβ stationary reference frame
vβ : Voltage component along the β axis of the αβ stationary reference frame
va : Voltage of phase a
v*a : Control system output voltage for phase a vac : Voltage between phase a and phase c
vac,stator : Voltage between phase a and phase c of the stator var : Voltage of rotor phase a
vas : Voltage of stator phase a vb : Voltage of phase b
vbc : Voltage between phase b and phase c
vbc,stator : Voltage between phase b and phase c of the stator vbr : Voltage of rotor phase b
vbs : Voltage of stator phase b
S-8 vc : Voltage of phase c
vcap : Voltage on the minimum value capacitance in the DC-link vcr : Voltage of rotor phase c
vcs : Voltage of stator phase c
vd,grid : Grid voltage component along the d axis vdr : Voltage of rotor shorted turns
vds : Voltage of stator shorted turns
vDC : DC-link voltage of the back-to-back converter vDC,0 : DC-link voltage before the step change
vfd : GSC output voltage component along the d axis
v’fd : Voltage component along the d axis, GSC PI controller output vfdcomp : Voltage component along the d axis, GSC feed-forward
compensation
vfq : GSC output voltage component along the q axis
v’fq : Voltage component along the q axis, GSC PI controller output vfqcomp : Voltage component along the q axis, GSC feed-forward
compensation
vh : h order harmonic voltage
vq,grid : Grid voltage component along the q axis vr : Rotor voltage
vrd : Rotor voltage component along the d axis
v’rd : Voltage component along the d axis, RSC PI controller output vrdcomp : Voltage component along the d axis, RSC feed-forward
compensation
vrd,0 : Rotor voltage component along the d axis before the step change vreference,a : Reference voltage to the converter for phase a
vrel : Relative wind speed vrr : Rotor voltage vector
vrq : Rotor voltage component along the q axis
v’rq : Voltage component along the q axis, RSC PI controller output vrqcomp : Voltage component along the q axis, RSC feed-forward
compensation
vrq,0 : Rotor voltage component along the q axis before the step change vs : Stator voltage
vsd : Stator voltage component along the d axis vsq : Stator voltage component along the q axis vss : Stator voltage vector
vtip : Linear speed of the blade tip vtri : Voltage of the triangular wave vw : Velocity of the wind
V : Volume of the cylinder
Vo : No-load phase-phase voltage at the secondary side of the transformer
Vrms : RMS line (phase-phase) voltage
∆x : Small perturbation in the states of the state-space model x : State vector of the state-space model
x0 : Steady-state value of the state variables of the state-space model xc : State vector of the PI controller state-space model
S-9 xm : State vector of the machine state-space model
xrd : State of the PI controller in the d axis xrq : State of the PI controller in the q axis
xsys : State vector of the closed-loop state-space model XCDC : Reactance of the DC-link capacitor
Xf : Reactance of the inductance filter
XL : Phase reactance of the inductance load connected at the transformer secondary side
Xlr : Rotor leakage reactance Xls : Stator leakage reactance Xm : Magnetizing reactance
∆y : Change in the outputs of the state-space model y : Output vector of the state-space model
y0 : Steady-state value of the outputs of the state-space model yc : Output vector of the PI controller state-space model yi : Value of the residual at sample i
ym : Output vector of the machine state-space model ysys : Output vector of the closed-loop state-space model
z : Laplace operator in discrete time
zro : Zeros of the measurement filter transfer function
ZL : Phase impedance of the load connected at the transformer secondary side
ZT : Phase impedance of the transformer
αj : Pitch of coil j αk : Pitch of coil k
αjk : Overlap angle of coil j and coil k β : Pitch angle of the blades
γ : Position in radians of the voltage space vector w.r.t. the α axis
θ : Rotor position angle defined w.r.t a stator coil θ0 : Mean value of the residual before the fault θ1 : Mean value of the residual after the fault θc : Mean value of the residual
θcorr : Phase difference between stator voltage and grid voltage
θd : Angle between the d axis of the dq reference frame and a axis of the stator
θdA : Slip angle after compensation θ’dA : Slip angle before compensation
θPLL : Position in radians of the voltage space vector input, PLL output θr : Electrical angle of the rotor
θr,initial : Initial rotor position in electrical radians when the RSC control is enacted
λ21 : Flux-linkage of coil 2-2’ due to current in coil 1-1’
S-10 λB1 : Flux-linkage of winding B due to current in coil 1-1’
λrd : Rotor flux-linkage component along the d axis
λrd,0 : Steady-state value of the rotor flux-linkage component λrd
λrq : Rotor flux-linkage component along the q axis
λrq,0 : Steady-state value of the rotor flux-linkage component λrq
λsd : Stator flux-linkage component along the d axis λsq : Stator flux-linkage component along the q axis λTSR : Tip speed ratio
λTSR,opt : Optimal TSR w.r.t. the specific blade design μ0 : Permeability of free space
ρ : Density of air
σ : Leakage coefficient σr : Variance of the residual
τcl,if : Time constant of the closed-loop transfer function for GSC current control
τcl,ir : Time constant of the closed-loop transfer function for RSC current control
φ : Angle of the segment cd φ1 : Angle of coil-side 2 φ’1 : Angle of coil-side 2’
Φ : Flux
фm : Phase margin for DC-link voltage control
ωcl,if : Closed-loop bandwidth for GSC current control ωcl,ir : Closed-loop bandwidth for RSC current control ωcl,ps : Closed-loop bandwidth for stator power control
ωcl,Te : Closed-loop bandwidth for electromagnetic torque control ωcl,vDC : Closed-loop bandwidth for DC-link voltage control
ωcl,vs : Closed-loop bandwidth for stator voltage control ωd : Electrical radian frequency on the stator side
ωdA : Electrical radian frequency on the rotor side (slip frequency) ωdA,0 : Steady-state value of the slip frequency
ωm : Mechanical angular velocity of rotor
ωopt : Optimal angular velocity of the turbine w.r.t. optimal TSR ω*opt : Angular velocity reference for MPPT
ωr : Electrical angular velocity of rotor ωsync : Grid electrical radian frequency ωt : Angular velocity of the turbine
