IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 5, SEPTEMBER 2004
`
`1323
`
`Flexible Control of Small Wind Turbines With
`Grid Failure Detection Operating in
`Stand-Alone and Grid-Connected Mode
`
`Remus Teodorescu, Senior Member, IEEE, and Frede Blaabjerg, Fellow, IEEE
`
`Abstract—This paper presents the development and test
`of a flexible control strategy for an 11-kW wind turbine with
`a back-to-back power converter capable of working in both
`stand-alone and grid-connection mode. The stand-alone control
`is featured with a complex output voltage controller capable of
`handling nonlinear load and excess or deficit of generated power.
`Grid-connection mode with current control is also enabled for
`the case of isolated local grid involving other dispersed power
`generators such as other wind turbines or diesel generators.
`A novel automatic mode switch method based on a phase-locked
`loop controller is developed in order to detect the grid failure or re-
`covery and switch the operation mode accordingly. A flexible dig-
`ital signal processor (DSP) system that allows user-friendly code
`development and online tuning is used to implement and test the
`different control strategies.
`The back-to-back power conversion configuration is chosen
`where the generator converter uses a built-in standard flux vector
`control to control the speed of the turbine shaft while the grid-side
`converter uses a standard pulse-width modulation active rectifier
`control strategy implemented in a DSP controller. The design of
`the longitudinal conversion loss filter and of the involved PI-con-
`trollers are described in detail. Test results show the proposed
`methods works properly.
`Index Terms—Digital signal processor (DSP) control, grid
`failure, grid monitoring, phase-locked loop (PLL), renewable
`energy, wind turbine.
`
`I. INTRODUCTION
`
`T HE USE OF squirrel-cage induction generators (SCIG)
`
`for direct grid-connection wind energy conversion systems
`(WEC) is well established. With the last advances in power
`electronics, the use of variable-speed SCIG with a double stage
`ac–dc–ac power conversion has become quite attractive [1], in
`both low power and very high power levels [1]. Increased energy
`production at low wind, elimination of the excitation capacitor
`bank, and especially the possibility for stand-alone operation
`mode can thus be achieved at the expense of a back-to-back con-
`verter with a flexible control [2].
`Small efficient wind turbines (WT) in the range of 11 kW as
`depicted in Fig. 1 can be used to supply private houses or farms
`in remote locations in developing countries where low-cost ac-
`cess to the electrical power grid is impractical. The trend is that
`
`Manuscript received June 1, 2004; revised July 21, 2004. This work was sup-
`ported by the Danish Research Agency, Danish Technical Research Council
`through the Project “Reliable Grid Condition Detection” 2058–03–0003. Rec-
`ommended by Associate Editor F. Z. Peng.
`The authors are with the Institute of Energy Technology, Power Electronics
`Systems Section, Aalborg University, Aalborg 9220, Denmark (e-mail:
`ret@iet.aau.dk; fbl@iet.aau.dk).
`Digital Object Identifier 10.1109/TPEL.2004.833452
`
`they should be able to work in stand-alone mode but also con-
`nected to isolated local loads/grid in parallel with other gen-
`erators such as other wind turbines, photovoltaic generators,
`or diesel generators in the so called hybrid generator systems
`(HGS). Thus some new challenges on the control side of these
`WT occurred like reasonable voltage regulation in stand-alone
`mode with nonlinear load, grid-connection mode enabled, and
`automatic detection of grid failure. But in order to achieve these
`goals, relative complex control strategies need to be developed.
`Also grid failure detection and an automatic mode switching are
`required.
`A seamless transfer method from grid-connected to stand-
`alone and vice versa for critical loads is described in [3] where
`an extra static switch is required. The algorithm matches the
`magnitude and phase of the inverter voltage and the grid voltage
`at the time of disconnecting or reconnecting to the grid to min-
`imize any sudden voltage change across the load.
`A phase-locked loop (PLL) technique is commonly used in
`grid-connected converters mainly for grid-synchronization [5],
`[6]. In this paper, a novel PLL-based method for grid failure
`detection and automatic mode switching is proposed where the
`phase difference between the grid and the inverter is used to
`determine grid failure and restoring.
`The flexible control strategy featuring stand-alone mode
`and grid-connected control as well as the automatic mode
`switching strategy has been developed, implemented and tested
`for a 11-kW WT. The control strategy has been implemented
`on a development platform based on a dSPACE digital signal
`processor (DSP) controller [4] that allows flexible code devel-
`opment in Simulink and online tuning and monitoring. Thus a
`relative short development time is achieved.
`Both operation modes as well as the involved current and
`voltage controllers design are described in detail. Also, the de-
`sign of the longitudinal conversion loss (LCL) filter together
`with experimental results obtained with a drive-train emulating
`the 11-kW wind turbine are presented.
`
`II. CONCEPTS FOR STAND-ALONE WIND TURBINES
`The most common configurations of power converters for
`stand-alone SCIG WT are depicted in Fig. 2.
`The diode rectifier topology in Fig. 2(a) can only be used in
`one quadrant, it is simple and it is not possible to control it.
`This configuration is especially suitable for fixed-speed wind
`turbines and requires a capacitor bank between the generator
`and the diode rectifier in order to magnetize the induction gen-
`erator.
`The back-to-back voltage source converter is a bidirectional
`power converter consisting of two conventional voltage source
`
`0885-8993/04$20.00 © 2004 IEEE
`
`Vestas Ex 1010-p. 1
`Vestas v GE
`
`SGRE EX1045.0001
`SGRE v. GE, IPR2022-01279
`
`

`

`1324
`
`IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 5, SEPTEMBER 2004
`
`can be obtained by properly connecting the output terminals of
`the converter to the input terminals. Some advantages of the ma-
`trix converters are less thermal stress of the semiconductors for
`a low output frequency compared with the back-to-back solu-
`tion and the absence of the dc-link capacitor that may increase
`the efficiency and the lifetime. As drawbacks can be mentioned:
`the intrinsic limitation of the output voltage, the unavailability
`of a true bi-directional switch and there is no decoupling be-
`tween the input and the output of the converter as for the case
`of back-to-back converter and this may lead to some instability
`issues.
`A comparative study regarding different power converter
`technologies that can be used in wind turbine applications [9]
`concluded that the back-to-back converter is the least trou-
`blesome configuration mainly because it can use commercial
`converters at the generator side.
`
`III. SYSTEM DESCRIPTION
`
`The power configuration of the developed system is depicted
`in Fig. 3. It consists in a three-phase squirrel-cage induction gen-
`erator, a generator converter to control the speed of the shaft, a
`dc-link with breaking chopper, a full-bridge grid converter with
`LCL filter, in-rush resistors, and the three-phase 400-V/50-Hz
`grid.
`A flexible test and development platform has been built using
`a variable-speed drive to emulate the wind turbine mechanical
`characteristics.
`The control diagram of this platform is shown in Fig. 4 where
`the control of the wind turbine emulator is also shown.
`for
`Three
`commercial
`frequency
`inverters
`rated
`18.5 kVA/400 V are used. The first one of the type Dan-
`foss VLT5022 is feeding a 15-kW induction motor in order
`to emulate the wind turbine shaft and uses a standard scalar
`open-loop torque control.
`The second converter of type Danfoss VLT5022 Flux is used
`as generator converter and uses the built-in standard vector flux
`control to regulate the speed of the generator and provide the
`magnetizing flux for the induction generator.
`The last one is using only the power stage of a Danfoss VLT
`5022 inverter and is controlled by the dSPACE controller. It is
`used as grid converter and is connected to the grid through an
`LCL filter and employs a
`-axis control strategy for control-
`dq
`ling the active and reactive power independently. In-rush resis-
`tors are used to limit the dc-link capacitors charging current at
`startup (see Fig. 3).
`Both grid-connected and stand-alone mode for the grid con-
`verter have been implemented using the dSPACE controller. A
`mode switch can switch between the two operation modes auto-
`matically depending on the presence of the grid, as it is shown
`in VII.
`
`A. Wind Turbine Emulator
`The wind speed is calculated as an average value of the
`fixed-point wind speed over the whole rotor, and it takes the
`tower shadow and the rotational
`turbulences into account.
`The wind turbine mechanical shaft is emulated using a stan-
`dard six-pole 15-kW/400-V squirrel-cage induction motor
`controlled by a commercial frequency inverter operated in
`open-loop torque control mode. The aerodynamic model of the
`wind turbine rotor is based the
`curve as shown in Fig. 5.
`Cq->.
`
`Vestas Ex 1010-p. 2
`Vestas v GE
`
`Fig. 1. Small 11-kW GAIA (Denmark) wind turbine for households and
`remote location.
`
`Fig. 2. Stand-alone wind turbine configurations with squirrel-cage induction
`generators:
`(a) diode bridge rectifier and voltage source inverter,
`(b)
`back-to-back voltage source converter, and (c) matrix converter.
`
`inverters as shown in Fig. 2(b). To achieve full control of the
`output, the dc-link voltage must be boosted to a level higher than
`the amplitude of the isolated grid voltage. The power flow of
`the grid side converter is controlled in order to keep the dc-link
`voltage constant, while the control of the generator side is set
`to suit the magnetization demand and the reference speed or
`torque. A technical advantage of this topology is the capacitor
`decoupling between the grid converter and the generator con-
`verter. Besides affording some protection, this decoupling offers
`separate control of the two converters, allowing compensation
`of asymmetry both on the generator side and on the grid side,
`independently. Though, the dc-link capacitor is bulky and ex-
`hibits relative reduced lifetime.
`The matrix converter solution as shown in Fig. 2(c) should
`be an all silicon solution with no passive components in the
`power circuit [7], [8]. The basic idea of this converter is that
`the desired input current, output voltage and output frequency
`
`SGRE EX1045.0002
`
`

`

`TEODORESCU AND BLAABJERG: FLEXIBLE CONTROL OF WIND TURBINES WITH GRID FAILURE DETECTION
`
`1325
`
`SCIG
`
`Generator converter
`
`DC-link
`
`DC-Chopper
`
`Grid converter
`
`LCLFilter
`
`In-rush resistors Grid
`
`Ca
`
`Ca
`
`+
`VDc Raamp
`
`u
`
`V-
`
`J
`
`L1
`
`K1
`
`w
`
`R;nrush
`
`RD
`
`cFm
`
`B
`o-Q
`
`C
`o-Q
`
`Fig. 3. Power configuration of the 11-kW variable-speed wind generator.
`
`dSPACE Digital Controller/Control Panel
`
`v.,,
`
`Maximum Power Tracking
`Qopt :;;f(v"')
`
`r· = T
`1-----m-~_.o_-_o..c."''-+-~
`
`+, Wind Turbine Emulator
`
`Tmca,n=nop1 = f(Qopt)
`
`Generator Control
`
`Grid Converter Control
`
`v· d
`
`IM15kW/
`400V
`
`0.08 - - - - - - - - - - - - - - - - - - - - - - -~
`________ : ______ ----: ________ _: c~rn~~-(~_aptl_j __ ------- :---- __ ---:- ______ _
`
`0.07
`
`00 0.06
`
`-~ 0.05
`·u
`~ 0 u
`Q)
`::J
`E"
`0
`I-
`
`0.04
`
`0.03
`
`0.02
`
`0.01
`
`,
`
`I
`
`I
`
`I
`
`I
`
`I
`
`--------r- -------r---------,----------.---------,--------- ---------r-
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`
`--------~--------t---------!---------1--------- ---------~--------t
`
`Grid
`converter
`
`2
`
`4
`
`10
`8
`6
`Tip speed ratio A
`
`12
`
`14
`
`16
`
`LCL Filter
`
`Fig. 5. C  performance curve for the wind turbine. C is the torque
`Q
`Q
`coefficient.
`
`The wind turbine emulator uses a scalar open-loop torque
`controlled induction motor where the torque reference is chosen
`to be
`
`T* = Tmax,!1=!1opt
`
`(3)
`
`grid/
`isolated grid
`
`Fig. 4. Block diagram of the flexible development platform for the wind
`turbine with 11-kW generator.
`
`in order to extract the maximum power from the wind turbine at
`a given wind speed.
`
`The tip speed ratio
`
`is calculated as
`
`(1)
`
`is the
`
`R
`
`is the blade radius, and
`
`n
`is the shaft speed,
`where
`wind speed.
`The
`curve is very useful in modeling the torque pro-
`duction of the wind turbine at different wind speeds. Choosing
`the optimal
`for the maximum torque coefficient
`, max-
`imum power can be extracted by setting the reference speed and
`torque for the turbine emulator [1]
`n
`- Aopt. Vex,
`R
`opt -
`
`l p1r R 5CQ,max
`2
`
`>,~pt
`
`(2)
`
`where
`
`for the maximum torque coefficient
`is the optimal
`as depicted in Fig. 5, and
`is the the air density.
`p
`
`B. Generator Control
`The generator control is working in closed-loop speed control
`mode where the speed reference converter is chosen to be equal
`with the optimal speed in order to extract the maximum power
`from the wind turbine at a certain wind speed
`
`(4)
`
`C. Grid Converter Control
`The wind turbine grid converter can operate in both grid-con-
`nected control mode and stand-alone control mode.
`Grid-Connected Control Mode: In grid-connected control
`mode, basically all the available power that can be extracted
`from the wind turbine is transferred to the grid. Additionally,
`reactive power compensation is possible if required. The
`control structure for grid-connected control mode [10] is shown
`in Fig. 6. Standard PI-controllers are used to regulate the grid
`-synchronous frame in the inner control
`currents in the
`dq
`
`Vestas Ex 1010-p. 3
`Vestas v GE
`
`SGRE EX1045.0003
`
`

`

`1326
`
`IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 5, SEPTEMBER 2004
`
`loops and the dc-voltage in the outer loop. A decoupling of
`the cross-coupling is implemented in order to compensate the
`couplings due to the output filter [10], [11]. The reference
`current in the -axis of the current loop is typically set to zero in
`q
`order to achieve zero phase angle between voltage and current
`and so unity power factor can be achieved.
`The output of the current controllers sets the voltage reference
`for a standard space vector modulation (SVM) that controls the
`switches of the grid converter via a fiber optic link. Synchronism
`with grid is achieved by using a phase-locked loop (PLL) as
`described in [5] and [6]. The principle of the PLL is depicted in
`Fig. 7. The input signals are
`
`sin(l,)
`
`cos(l,) = J( 2
`V::2 )
`vx + y
`
`(5)
`
`where
`are the grid voltage
`and
`is the grid phase angle,
`-reference frame. The philosophy
`components in stationary
`xy
`of the PLL is that the sinus of the difference between grid phase
`0
`and the inverter phase angle
`can be reduced to zero
`angle
`using a PI-controller, and thus locking the grid inverter phase to
`the grid, knowing that for small arguments
`
`. (
`sm "(-
`
`0) ~ "1 - 0 = 6..0.
`-
`,
`
`(6)
`
`The output of the PI controller is the inverter output frequency
`that is integrated to obtain the inverter phase . In order to im-
`0
`prove the dynamic response at startup, the nominal frequency of
`is feed-forwarded to the output of the PI-controller.
`the grid
`can be used for
`In Section VII, it will be described how the
`6..0
`detecting the presence or disappearance of the grid in order to
`automatically switch between grid-connected and stand-alone
`control mode.
`Stand-Alone Control Mode: In stand-alone control mode, no
`grid exists so the output voltages need to be controlled in terms
`of amplitude and frequency and thus, the reactive and, respec-
`tively, active power flow is controlled [1]. In the case of unbal-
`ance between the generated and the load-required power, adjust-
`ment of the speed of the generator can regulate the produced
`power in a limited range. The potential excess of power will
`by starting the
`be quickly dissipated in the damp resistor
`Rv
`chopper control (see Fig. 4).
`The control structure for stand-alone control mode is depicted
`in Fig. 8 and it consists of output voltage controller, dc-link
`voltage controller, damping chopper control, and current lim-
`iter.
`The output voltage controller is aiming to control the output
`voltage with a minimal influence from the shape of the nonlinear
`load currents or load transients. A standard PI controller oper-
`ating in the synchronously rotating coordinate system where
`is kept to zero is used. The dc-voltage PI controller maintains
`the dc voltage to the reference.
`The dc-link voltage controller is acting only when the dc-link
`is below the reference and it lowers the voltage reference of the
`
`Voc'C..j... _____ _
`
`Fig. 6. Control structure for grid-connected control mode of operation.
`
`Fig. 7. PLL structure used to synchronize the inverter voltage with the grid.
`
`de-link voltage controller
`
`Fig. 8. Control structure for stand-alone mode of operation.
`
`main voltage controller in order to avoid inverter saturation. For
`fast response there is a direct forward connection to the voltage
`controller output.
`When the dc-link is higher than the reference, the damping
`chopper control is activated and discharges the energy in excess
`stored in the dc-link and thus reduces the dc-link voltage. The
`control is linear and increases the duty-cycle as a function of
`the overvoltage size. In the case of an over-production, the level
`of produced power can be reduced also by changing the shaft
`speed in the allowed speed range.
`When the load current exceeds the rated current, the current
`limiter will decrease the output voltage reference in the allowed
`range, and for fast response there is a direct forward connection
`to the voltage controller output. This situation can occur if at a
`certain load, the generated power decreases due to lower wind
`or during overloading.
`
`Vestas Ex 1010-p. 4
`Vestas v GE
`
`SGRE EX1045.0004
`
`

`

`TEODORESCU AND BLAABJERG: FLEXIBLE CONTROL OF WIND TURBINES WITH GRID FAILURE DETECTION
`
`1327
`
`loc,11 ( _ _ . , 1'11,d_, ~ .... _[dill!' -
`f\
`
`• . • tU c. .. -. •• •• • ••
`
`""'
`
`I
`ml <"
`x x
`i 0
`. ,o . ·»·~-~-----~--
`
`•
`
`•
`
`00
`
`~,._ [dt -
`l,li~ I.I
`
`•
`
`00
`
`D. Control Panel
`The whole control strategy of the wind turbine emulator and
`wind turbine control is implemented in Simulink [12] using a
`DS1103 dSPACE controller. A virtual control panel developed
`in ControlDesk [12] that controls the whole system is shown in
`Fig. 9. As it can be observed, the control layout is divided into
`two parts generator control and grid converter control. In the
`generator control panel, the reference for the generator speed
`and the mechanical power can be set. The speed and torque are
`shown in both graphs and digital displays.
`In the grid-converter control panel the control mode will
`be automatically switched between stand-alone and grid-con-
`nected according to the presence of the grid (see Section VII).
`In grid connection control mode, the references for the active
`and reactive power to be transferred to the grid are given. The
`dc-voltage reference can also be changed in the allowable
`range.
`In stand-alone control mode, the output voltage reference is
`set in terms of RMS value. The dc voltage reference can also be
`changed in the allowable range. Grid currents and voltages are
`displayed in scope-like graphs. Digital displays show the power
`balance, including the dissipated power in the dc chopper, as
`well as the output voltages and currents.
`A test control panel for online tuning of the controllers has
`also been done. It proved to be a very convenient method to
`fine-tune the PI-controllers in the whole system.
`In the following more details on the design of the LCL-filter,
`controllers in the two control modes and the Automatic Mode
`Switching will be explained.
`
`IV. LCL FILTER DESIGN
`The LCL filter gives a better attenuation of the switching
`ripple compared to a classic L filter as it is a third-order filter
`and therefore it can be designed using smaller components.
`The transfer function in the -plane of a single-phase LCL-
`s
`filter (see Fig. 3) with passive damping is shown in (7) at the
`h
`bottom of the page, where
`is the inverter voltage,
`is the
`inverter current,
`is the inverter-side inductance,
`is the
`Le
`grid-side inductance,
`is the filter capacitance, and
`are
`Rv
`the damping series resistors.
`The following design considerations are taken into account
`[10]:
`1) the capacitor value is limited by the tolerable decrease of
`the power factor at rated power (less than 5%). The total
`value of the inductance should be lower than 10% to limit
`the dc-link voltage;
`2) the voltage drop across the filter during operation in order
`to limit the dc-link voltage;
`3) the resonance frequency should be included in a range
`between ten times the line frequency and one half of
`the switching frequency in order not to create resonance
`problems in the lower and higher parts of the harmonic
`
`..,._,.=-=--=-=w.::.•,,Cljoe._=-__ _,1_...,«r,-,=-:•:::-_ __,)11e- -,ontni1Dt.o1c~-
`
`4 & N'>I
`
`s1t""
`
`Fig. 9. ControlDesk panel for testing the wind turbine control strategy both
`stand alone and grid-connected control modes.
`
`spectrum. The passive resistors should be chosen as a
`compromise between the necessary damping and the
`losses in the system.
`The following values for the LCL-filter have been calculated:
`Rv = 4.1 n
`mH,
`mH,
`F, and
`.
`Le= l.5
`Gp = 6µ
`
`V. GRID CONNECTION CONTROL MODE—CURRENT
`CONTROLLER DESIGN
`In order to design the PI current controllers in the syn-
`chronous
`-frame, the transfer function of the filter, con-
`dq
`sidered as the system plant, is discretized using a zero-order
`hold method at a sampling frequency of 8 kHz and it thereby
`becomes
`G( z) = 0.073 52z 2 + 0.077 93z + 0.022 64 _
`z 3 + 0.093 24z 2 - 0.7928z - 0.3004
`An additional delay of one switching period is inserted in the
`model due to the PWM control of the inverter. Then the transfer
`function of the PI-controller is
`
`(8)
`
`(9)
`
`The block diagram of the current control loop is first sim-
`ulated in Simulink using the model from Fig. 10 where one
`sample delay due to the effect of PWM inverter is included.
`A standard criterion to achieve an acceptable step response is
`used for tuning the PI controller [11].
`Fig. 11(a) shows pole-zero plot of open loop system without
`the controller. There are two complex conjugated poles and one
`real pole. Because of complex conjugated poles, compensation
`techniques cannot be used. Instead a pole-zero placement tech-
`nique is used. An integrator time constant
`ms is selected
`as a compromise between good dynamics and still a good noise
`
`H(s) = h(s) =
`Vi(s)
`
`L1Cps 2 + RvCps + l
`L1LeCFs 3 + (RvL1CF + RvLeCF )s 2 + (L1 + Le)s
`
`(7)
`
`Vestas Ex 1010-p. 5
`Vestas v GE
`
`SGRE EX1045.0005
`
`

`

`1328
`
`IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 5, SEPTEMBER 2004
`
`o .073:52z2+o .07793z+0 .02264
`
`z3+0.09324z2•0 .7928z•0 .3004
`
`Discrete transferf. of plant
`
`0.8
`
`0 .6
`
`0.4
`
`{~ ./
`
`:
`/f.41&4._j
`
`Fig. 10. Simulink model of current control loop in z-domain for the wind
`turbine.
`
`R:>otl00.1s
`
`t~1eot
`. / ,;.:.:_\·:··• \i4:,
`\,;,;;·
`·· .. ,; .. ·.·;.;~;.L:~::~;~(
`
`-0.4
`
`-0 .6
`
`-0.8
`
`-~1
`
`-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
`Real Axis
`a)
`
`1
`
`R001Locu1
`
`b)
`
`-08
`
`-0 8 -0.6 -0.4 -0.2 0 0 2 0.4 0.6 0 8
`Real Axis
`
`1
`
`a)
`
`Real Axis
`
`b)
`
`Fig. 11. Pole-zero placement of (a) open-loop system and (b) closed loop
`system for the current controllers in grid-connected control mode.
`
`is selected using root locus method so
`rejection. The gain
`that the dominant poles have a damping of 0.7. In Fig. 11(b),
`the pole-zero placement for optimized closed loop of the control
`is shown. The dominant poles have now a damping of 0.7 at a
`frequency of 580 Hz. The gain of the controller is found to be
`.
`KP
`4.8
`
`VI. STAND-ALONE CONTROL MODE—VOLTAGE
`CONTROLLER DESIGN
`The output voltage controller is aiming to control the output
`voltage with minimal influence of the shape of the nonlinear
`load currents or load transients. The transfer function of the grid
`with a load impedance
`in terms of grid voltage
`and in-
`Ve
`verter voltage
`is representing the plant and can be expressed
`in the -domain as (10) shown at the bottom of the page, where
`s
`is the grid impedance at nominal power.
`Zc
`Synthesis of the voltage regulator is again made in the
`-plane, using a Simulink equivalent model, where the grid
`z
`transfer function has been converted into the
`-plane using
`z
`zero-order-hold method [12]. The switching frequency is
`chosen to be 8 kHz. The pole-zero placement of the plant
`shown in Fig. 12(a) show, that there is a real pole that can be
`compensated by setting the integral time of PI-controller to
`ms. Using the root locus method [12] depicted
`0.306
`T;
`in Fig. 12(b), a gain of
`can be chosen to achieve
`KP
`0.32
`1
`a damping of the loop of
`. From the compensated
`D
`Bode-plot shown in Fig. 12(c), the bandwidth of the voltage
`controller can be determined as the minimum frequency for
`3-dB attenuation or 45 phase [12] as
`Hz.
`131
`
`0
`
`Bode Diagram
`.......... / .. ~~·~~:~ : : : : : ....
`1 F~ (Hz): 2A6
`········••i••·· ~ ( dB t; -3.02 ....
`. 1 : : ~-i r
`;
`~
`.; .. : .. :.: .. :.::• ........... :.
`
`-5
`
`al
`C!!.
`
`-15 ·.f
`IC
`I -20 ···\
`
`.2s~-~~~~~--~~~~~-~~
`
`OfT=,-:=,::;::;:m---r--r-TTTTI~-~
`
`I -90
`ffl -180 !-.. , ..... , .... , ... , __ , __ ,_,_,., ......... , ................ , ., .. , .,,, .......... _, __ • ·I
`
`~ -270 , ................... , .. , .. , .................. , ................ , ............... , ..... , ... , .. ,
`
`10'
`Frequency (Hz)
`c)
`
`10'
`
`Fig. 12. Design of the voltage controller in stand-alone control mode:
`(a) pole-zero map for the plant, (b) root-locus map for closed-loop system, and
`(c) Bode-plot of the closed loop system.
`
`The controller is now tested at very light load conditions (1%
`of nominal load) and a low damping at the resonance frequency
`of the LCL-filter was noticed as shown in Fig. 13(a). The re-
`sponse of the system depicted in Fig. 13(b) shows high oscilla-
`tions due to a high gain.
`Redesigning the controller for light load using the same tech-
`nique (root locus) leads to a lower gain of
`. The
`KP
`0.1
`Bode-plot shown in Fig. 14(a) shows much better attenuation
`at the switching and sampling frequency of 8 kHz and the step
`response depicted in Fig. 14(b) was considered acceptable in
`terms of compromise between the speed and damping of the
`higher order harmonics at low load conditions.
`From the compensated Bode-plot shown in Fig. 14(a), the
`bandwidth of the voltage controller can be obtained as
`Hz. The final parameters for the main output voltage con-
`76.5
`troller are
`,
`ms.
`0.1 I';
`0.3
`
`VII. AUTOMATIC MODE SWITCHING
`
`Switching between stand-alone and grid-connection opera-
`tion modes is done using the difference between the measured
`and the angle
`generated by the phase-
`grid voltage angle
`0
`locked loop (PLL) [5] as control variable (see Fig. 7). When
`(see Fig. 15) is exceeding a certain
`this phase error
`level grid failure is considered and the operation mode is con-
`sequently switched.
`
`(10)
`
`Vestas Ex 1010-p. 6
`Vestas v GE
`
`SGRE EX1045.0006
`
`

`

`TEODORESCU AND BLAABJERG: FLEXIBLE CONTROL OF WIND TURBINES WITH GRID FAILURE DETECTION
`
`1329
`
`Bode Diagram
`
`Step Response
`
`ci -90
`Q)
`'O
`~ -180
`OJ .c
`CL -270
`
`<I)
`
`a)
`
`2
`
`3
`Time (sec)
`
`4
`
`5
`
`6
`X 10-3
`
`b)
`
`Fig. 13. Voltage controller characteristics at 1% load in stand-alone control mode with K = 0:32: (a) Bode plot and (b) step response.
`p
`
`co
`:3.
`Q)
`'O
`
`2 ·c
`::a
`
`C)
`OJ
`
`0
`
`-5
`
`-10
`
`-15
`
`-20
`
`-25
`0
`
`Q)
`
`<I)
`
`ci
`:3.
`., -180
`OJ .c
`CL -270
`
`-90
`
`-360
`
`Bode Diagram
`
`Step Response
`
`:
`System: fz
`:
`..
`.
`:
`,
`...... ; ..... , •.. , .... : .,.,., .......... : ..... Frequency(Hz): 1.64e+003 .... ; .. .
`Magnitude (dB): -9.33
`:
`'
`:
`:
`: : : :
`:
`
`... ,........... +·
`··--( ;·· )j-j-j············(·
`---r·--r-· r · · · -.
`----r---i-- ·-r-r r i··----------:
`······'·····~ ___ : .. --~- ~- ~- ;············;·······; ····:···~--~--~- ~--:-: ........... : .. .
`. ' ' '
`. ' . .
`.
`
`:
`
`........... , ... , ... -f-. System: fz
`! '
`: Frequency (Hz): 76.5
`.. ) ... \ .. ) .• Phase (deg): -45.2
`. '
`... '
`. '
`.. '.
`' ' . '
`'
`'
`' .. '
`' ' .. ---------------------------- --
`' ' . '
`'
`'
`'
`'
`'
`'
`l l ~
`~
`j
`.
`····'··· .. ·· '·'·'· ................. .
`102
`Frequency (Hz)
`
`a)
`
`.,..~-- .. -------,---
`' '
`'
`' '
`'
`' '
`'
`' '
`'
`f~---
`······~---
`
`...............
`' '
`'
`'
`
`0.8
`
`···· •········· ·· ········--·--·(cid:173)
`
`., 0.6
`'O
`::,
`
`~ a.
`E
`<( 0.4
`
`0.2
`
`--------·······
`
`'
`'
`'
`'
`'
`'
`·· ·- ····-··················-···········--········
`.
`.
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`
`. ·······1·········l·········1·········\········· ........ .
`
`0.002 0.004 0.006 0.008 0.01
`
`0.012
`
`T ime (sec)
`
`b)
`
`Fig. 14. Voltage controller characteristics at 1% load in stand-alone control mode with K = 0:1: (a) Bode-plot and (b) step response.
`p
`
`q
`
`y
`
`X
`
`Fig. 15. Phase angle detection with PLL in xy-coordinate system.
`
`In grid-connection mode the system is using the PLL-gener-
`ated phase angle that is less noise sensitive than the phase angle
`-components using arctan
`directly calculated from the voltage
`dq
`function [11].
`Fig. 7 depicts the PLL loop principle. A settling time of 20 ms
`was considered in order to get a satisfied high bandwidth of
`
`is
`the PLL controller. When the grid fails, the phase error
`starting to increase and when it exceeds a certain threshold the
`system switches to stand-alone mode. In stand-alone mode the
`is integrated to
`PLL is disabled and the reference frequency
`0
`(see. Fig. 8).
`generate the angle
`The grid-connection to stand-alone transition is demon-
`strated experimentally in Fig. 16 at nominal load of 11 kW. The
`was set to 0.3 radians. Thus
`threshold for the phase error
`110
`an efficient way to detect the grid failure is achieved, and as it
`can be observed, in this case the system continues to operate
`in stand-alone mode.
`In stand-alone operation the system uses its own generated
`voltage phase angle, which is normally different from grid
`phase voltage angle. When the grid is recovered, due to the
`fact that the two voltage systems are not synchronized, a high
`voltage across the LCL filter would cause high currents to flow
`through the inverter. The high currents will trip the inverter
`and the presence of the grid is investigated by measurements.
`If the grid is recovered, the coasted inverter waits for the PLL
`to perform synchronization. The system is then considered
`
`Vestas Ex 1010-p. 7
`Vestas v GE
`
`SGRE EX1045.0007
`
`

`

`1330
`
`IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 5, SEPTEMBER 2004
`
`o.8 _____________ \ __________ _j _____________ l ___________ J _________ := =
`~ ,..
`
`:
`:
`:
`i:
`! ! synchronizing signal
`·
`T ~
`i
`!
`ii
`i
`
`i
`
`o.6
`
`1.2,:-::-:::r-:7==:::::;(cid:173)
`-etheta
`------·-------·-------- ----- PLLe
`:
`:
`: :
`: :
`'
`'
`'
`'
`'
`'
`0.Bf-------+-------1------ ·--------;---,---;--------;-------;--------;-------:-------
`~
`0
`
`\ \ synchr~nizing sign~
`
`,
`
`i iTT i i :
`
`6
`·
`
`~
`
`~ :::'-________________ , ________________ , ____ , __ ,.rr r+ '
`
`0.02
`
`0.03
`
`0.04
`
`0
`
`0.01
`t[s]
`(a)
`
`-0.2'----_L__L,_---'-----'----------'------'------'-----'-----'-----
`-0_02 -0.01
`0
`0.01 0.02 0.03 0.04 0.05 0_06 0.07 0.08
`t[s]
`(a)
`
`-0.01
`
`0
`
`0.01
`t[s]
`(b)
`4 0 0 . - - - - - -~ - -~ -~ - -~ -~ -~
`:
`:
`;
`:-ua
`
`0.02
`
`0.03
`
`0.04
`
`-20
`
`-30 L___L__L,_---'---'---'-----'----~'----~-L,_-'
`-0.02 -0.01
`0
`0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
`t[s]
`(b)
`
`200
`
`~ 100
`0
`
`~ 0
`::::i
`oi
`::::l-100
`
`-400 L , _ _
`-0.02
`
`_L_ _ _ L,__---'------'--------'--__J
`0_02
`0.03
`0.04
`-0.01
`0.01
`0
`t[s]
`(c)
`
`-400 L___L__L,_---'-----'----------'---'-------'------'----------'-
`-0.02 -0.01
`0
`0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
`t[s]
`(c)
`
`Fig. 16. Measured grid-connection to stand-alone transition: (a) phase error
`  (etheta) and synchronization signal (PLLe), (b) phase currents, and (c) phase
`voltages;.
`
`falls below the
`synchronized again when the phase error
`threshold and now the inverter is started in grid-connection
`mode, as it can be seen in Fig. 17 where the threshold was
`set again to 0.3 radians.
`A state-machine has been built and implemented in order to
`handle the transition between the three states: idle (I), stand-
`alone (SA), and grid-connected (GC) as depicted in Fig. 18,
`and
`represent the presence and, respectively,
`where
`Va
`/Ve
`nonpresence of the grid voltage condition, PLLe represents the
`..:10 > 0.3 radians
`, TRIP and /TRIP stands for trip
`condition
`signal enabled, and, respectively, not-enabled and START and
`
`Fig. 17. Measured stand-alone to grid-connection transition: (a) phase error
`  (etheta) and synchronization signal (PLLe),