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Abstract—A sensorless stand-alone control scheme of a DFIG-DC system is investigated in this paper. In this layout, the stator voltage is rectified by a diode bridge that is directly connected to a dc bus. The rotor side Voltage Source Inverter (VSI) is the only controlled converter required in this system and is directly powered by the same dc-bus created by the stator-side rectifier. Dc voltage and stator frequency are regulated by two independent PI regulators that give the references for inner current controllers implementing field oriented control. As it is capable of creating a stable and regulated dc-bus, this system can be conveniently adopted to supply dc loads or to form a dc grid. Due to the constraint imposed by the stator diode bridge, the DFIG has to operate under a constant stator voltage, and the conventional stator field oriented control implemented in stand-alone ac DFIG must be modified. The paper presents the control structure and the theoretical framework for the controller synthesis. Simulation and experimental validations on a small-scale rig are included.

Index Terms—Dc grid, Dc-link, Doubly-fed induction machine, Field oriented control, Rectifier.

NOMENCLATURE

is , iR stator, rotor (-model) current (p.u.)idc1 , idc2 diode bridge, inverter dc current (p.u.)k inductance ratio Ls/MLs , M stator, magnetizing inductance (p.u.)rs , rr stator, rotor resistance (p.u.)TC closed-loop rotor current time constant (s)TL , T' dc-bus time constants (s)TiV , Ti dc-voltage, frequency PI controller time constant (s)UL inner dc-load voltage (p.u.)udc , us dc-bus, stator voltage (p.u.)s ,m, sr stator flux, mechanical, slip angles (electr. rad)s stator flux linkage magnitude (p.u.)b rated (base) stator angular frequency (rad/s)s, sr, m stator frequency, slip speed, rotor speed (p.u.)

Superscripts space vector quantity

* set point valueSubscripts0 quiescent point in the small-signal analysis

Manuscript received March 14, 2016; revised May 23 and Sept. 9; accepted October 11, 2016. This work was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT), with reference UID/CEC/50021/2013.

G. D. Marques is with the INESC-ID, Instituto Superior Técnico (IST), Universidade de Lisboa, Av. Rovisco Pais, no 1, 1049-001 Lisbon, Portugal (e-mail: gil.marques@tecnico.ulisboa.pt). M. F. Iacchetti is with the School of Electrical and Electronic Engineering, at the University of Manchester, Manchester, U.K. (e-mail: matteo.iacchetti@manchester.ac.uk).

dc dc sided , q oriented frame axess , R stator, rotor in the equivalent circuit , stationary axes

I. INTRODUCTION

Wind power capacity is experiencing a massive growth in recent years, with a record in 2015 when new installations amounted to 51 GW [1]. Middle-term forecasts predict that wind energy might contribute up to 18% of the global electricity production by 2050 [2]. The increasing penetration of wind energy into the power system brings new challenges, which need to be addressed through appropriate power conversion and control layouts. DC-networks are seen as potentially highly-beneficial to achieve an efficient integration of renewables into power systems, particularly for off-shore plants [3]-[4]. Minimizing the number of conversion stages and paralleling constraints make dc micro-grids attractive for supplying energy to final users [5]-[7]. The available variety of generators and power electronics converters allows a wide range of interface solutions for variable-speed wind turbines [8]-[9]. In spite of their relatively low cost, induction generators need to be connected to a dc-link via a fully-rated and fully controllable voltage source inverter (VSI) which also provides the necessary magnetizing current [10], [11]. Permanent-magnet synchronous generators can replace the VSI with a diode bridge and fully-rated dc-dc converter [12], but at the price of a low dynamics in the power control. Wound field synchronous generators (WFSGs) may theoretically implement the cheapest power electronics, which might reduce to a simple diode bridge and to a low-power chopper handling the excitation current [12]. However, the variable-speed, constant-voltage operation required by the connection to a constant voltage dc-grid is critical for the WFSG and causes the generator to be oversized proportionally to the max/min speed ratio.

The doubly fed induction generator (DFIG) has been deeply studied for ac wind power generation [13] as an effective way to reduce the cost of power electronics, by preserving high-performance regulation via either field-oriented control or direct-power control. Stand-alone DFIGs with frequency and voltage regulation have also been considered [14]-[17], for supplying ac loads in remote areas or in ac microgrids.

The DFIG has been recently recognized as potentially able to be interfaced to a dc system, bringing a significant reduction of the power electronics cost as it does in ordinary ac-grid connected DFIGs. A layout with two VSIs rated to half the global power has been proposed in [18]: the VSIs work in regenerative mode and their dc-links are directly

Sensorless Frequency and Voltage Control in Stand-Alone DFIG-DC System

Gil D. Marques, Senior Member, IEEE and Matteo F. Iacchetti, Member IEEE

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paralleled to the dc grid. An alternative solution called DFIG-DC system has been investigated in [19]-[22], where a unique de-rated VSI and a fully-rated diode bridge are used to interface the DFIG to the dc grid. Being in a DFIG the stator frequency independent of speed, the DFIG is well-suited to operate at variable speed and constant stator voltage, as demanded when the stator diode bridge is connected to a constant voltage dc-link or grid. This is the major advantage for using a DFIG: the max/min speed ratio does not affect the machine sizing, and the DFIG also allows the optimization of the stator frequency as a function of power, to maximize efficiency [22]. Similar benefits can be achieved with dual-stator induction generators [23]. Relevant applications for the DFIG-DC system range from dc micro-grids to on-board dc generation and off-shore wind turbines, where the DFIG-DC system may directly feed a voltage boost and insulation stage [3].

In the DFIG-DC system, the instantaneous torque regulation achievable by the Field Oriented Control (FOC) through the rotor VSI is potentially able to compensate for the main torque ripple component produced by the diode commutation [24]. This however requires the implementation of resonant or multiple-frame PI current controllers [25]-[26]. Torque ripple can also be conveniently mitigated with multi-pulse rectifiers. The control developed in [19] drives the air-gap reference flux-linkage at constant speed and adjusts the magnitude to control power. Schemes in [20] and [21] are based on the fact that in DFIG-DC systems the product flux × frequency is almost constant, making the frequency controllable through the d-axis rotor current.

Existing studies on the DFIG-DC system only consider the operation under torque reference control, because the dc voltage is assumed to be controlled by another voltage source. Although such a scenario is relevant to a dc-grid connected system, voltage control is desirable to participate to the voltage regulation and properly share the generated power with other units [27]. Dc-voltage regulation is obviously necessary for stand-alone operation. Therefore, dc-voltage control must be implemented in the DFIG-DC system in order to achieve fully-controllable, variable-speed, constant-voltage generation.

Control techniques for ac stand-alone DFIGs, such as open- [14] or closed-loop [17] schemes with the stator angle (simply obtained as integral of the reference frequency) do not take into account the peculiarity of the DFIG-DC system, where d-axis rotor current, rather than the q- one, is the most relevant control variable for frequency regulation.

A first proposal of stand-alone control for the DFIG-DC system has been made in [28] using a proportional-integral (PI) voltage controller to directly set the reference torque value, via the q-axis rotor current. However, [28] only discusses a basic design approach narrowly focusing on the operation with a well-defined dc-load, and only reporting introductory simulation results.

Unlike [28], this paper presents extensive study and experimental investigations on the stand-alone DFIG-DC system. The paper derives a comprehensive small-signal

model of the system, which allows the controller design to be addressed for generic operating conditions. A sensorless implementation is adopted to achieve field orientation and regulate stator frequency and dc voltage with a reduced number of sensors. Experimental responses to reference frequency, dc voltage and load changes are reported, also showing the start-up capability.

The paper is organized as follows. Section II introduces the system layout and the necessary modeling background. Section III reports the control scheme for voltage and frequency control, derives the complete small-signal model of the system and discusses the control synthesis. Sections IV and V validate the theory with simulations and experimental results.

II. SYSTEM TOPOLOGY AND MODELING Fig. 1 shows the system investigated in this paper. A

generic dc active load is considered in this study: it might represent either a stand-alone load or even a weak dc-grid.

Fig. 1 DFIG-DC system feeding a stand-alone dc load.

This paper considers a control scheme with fast rotor-current controllers. Thus, for frequency and voltage control purpose only the stator equations are relevant for the machine. Using per unit (p.u.) quantities except for time and considering the stator field oriented frame d-q, the stator equations are

,

(1)

The base frequency b (in rad/s) appears in (1) as time t is still in seconds. The stator frequency s is the derivative of the stator flux angle s: then the right-hand side equation in (1) remains unchanged at steady state, where s is simply constant.

The DFIG -model is used throughout this paper. Hence rotor currents (subscript “r”) are transformed with the inductance ratio k=Ls/M to obtain the -model values (subscript “R”).

, , with . (2)

Flux-current relations under field-oriented conditions are

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then

, . (3)

The p. u. torque, in generator convention, is given by:

(4)

Since the diode bridge is connected to bulk capacitors in the dc-side, stator current and voltage are distorted. Nevertheless, as discussed in [12] and [29], an average model in terms of first harmonics is adequate for control purposes. This is because the amount of power delivered through the diode bridge is mostly related to first harmonic components. The diode-bridge average model is then established according to the simplified phasor-diagram in Fig. 2, where phasors represent first harmonics. Fig. 2 also shows reference frames and angles involved in the control algorithm.

Fig. 2 Simplified steady-state phasor diagram with first-harmonic components: es=ss is the stator electromotive force.

The phase shift between stator (terminal) voltage and current phasors has been proved to be less than 13° [21], and is then neglected. Additionally, the ratio between average dc voltage and first-harmonic stator voltage amplitude is rather constant and close to the theoretical limit 2/0.64.

The average-model technique for the diode bridge treats udc and idc1 as slowly-varying, ripple-free variables, and approximates stator-side space vector quantities with their first-harmonics. For this reason, capital letters for first harmonics will not be used anymore.

The dc-voltage and peak value of the stator voltage are related by

(5)

The negligible angle between stator voltage and current makes the stator power to be well approximated by . Thanks to (5), the power balance across the ideal diode rectifier gives

(6)

with isq = iRq, due to the negligible phase shift and to (3). Then,

(7)

In this paper the same base values for ac and dc variables are adopted. Thus, (5) and (7) hold also in p.u. variables.

III. CONTROL SCHEME

A. General principleThe main requirement in a stand-alone DFIG-DC system is

monitoring and controlling the dc voltage across the bulk capacitor. Being the stator feeding a diode bridge only, the stator frequency does not need to be strictly regulated at a precise value. The only constraint is that the stator flux does not exceed the machine rated value, to avoid saturation. This feature would allow the flux to be regulated to minimize losses [22], but this possibility is not considered in this paper, and a simple frequency regulation is implemented.

Sensorless vector control based on stator flux linkage is adopted to achieve a satisfactory decoupling between dc-voltage (torque) and stator frequency.

As shown in [20], the diode bridge imposes an almost constant stator voltage to the machine. Being the stator resistance negligible in usual DFIGs, the machine operates under a constant flux × frequency product at the stator side. As a consequence, the natural control variable for the frequency is the stator flux, namely the d-axis rotor current, in the field-oriented d-q reference frame. This is quite different from what happens in conventional stand-alone ac DFIGs, where frequency is controlled via the q-axis rotor current.

The constraint flux × frequency constant induces a further important difference with ac stand-alone systems, because it indirectly affects the stator flux position (integral of frequency). This makes possible to achieve the field orientation by setting the estimated slip angle in the reference frame transformations, rather than by driving the reference frame with a reference stator angle (integral of the reference frequency). This is of course possible as long as the diode bridge is conducting. By contrast, in a stand-alone ac DFIG the stator flux needs to be permanently driven by using a reference stator angle in the frame transformations.

The dc voltage across the capacitor is mainly affected by the active power flow through the stator and load. Thus, the dc-voltage is regulated through the q-axis rotor current: the voltage error is delivered to a proportional-integral (PI) regulator, which sets the q-axis reference current.

Fig. 3 reports the resulting control scheme: detailed explanations of the main subsystems are provided in the next sections. Fast current PI controllers are designed according to usual rules: as shown in [30], a reasonable bandwidth is 300 Hz.

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Fig. 3 FOC scheme for the dc voltage and stator frequency regulation.

B. Sensorless field oriented control and frequency regulationThe sensorless field-oriented control used in this paper has

been firstly proposed in [21] for a grid-connected DFIG-DC system, namely where the DC-link voltage was externally set and regulated. The slip angle estimation in [20] exploits the diode bridge property of imposing almost zero phase-shift between stator current and voltage first harmonics. This leads to the following definition of the generalized error

. (8)

The self-sensing scheme is shown in Fig. 4 and comprises a PI controller (parameters kp FOC and ki FOC) which forces the error (8) to zero and provides the slip angle after integration. No flux estimation is needed for this scheme.

Fig. 4 Self-sensing scheme to estimate the slip angle [21].

The frequency is estimated by a PLL (see Fig. 5) which tracks the stator voltage space-vector. A low-pass filter is used to reduce the ripple inherently affecting the stator frequency because of the distorted stator voltages [31]. The small signal model and design criteria for the PLL are thoroughly explained in [21].

Fig. 5 PLL scheme for the stator frequency detection [21].

C. Small-signal model for voltage and frequency control design

The small-signal flux-frequency relationship in the DFIG-DC has been derived in [20] for the case of constant dc voltage. The frequency perturbation is given by

(9)

The disturbance es includes the minor effect of the voltage drop across stator resistance, which makes the stator voltage slightly differ from the stator electromotive force (EMF). In the stand-alone DFIG-DC system considered in this paper, es must also incorporate a further contribution due to any change of the dc voltage in compliance with Fig. 1, (1) and (5):

(10)

The small signal model of the voltage loop is derived treating currents idc2 and iL as disturbances, with

. (11)

Then, the p. u. dc voltage varies according to

(12)

Using (7), the perturbation of (12) and the Laplace transform yields

(13)

For control synthesis purpose, (13) is rewritten as follows

, . (14)

The small signal model resulting from (9)-(14) is represented in the block diagram of Fig. 6, which comprises the frequency and voltage PI controllers and the PLL transfer function. Simplified first-order transfer functions representing current loops in field oriented conditions are also included: the time constant TC is the reciprocal of the current loop bandwidth. The reference voltage is processed by a low-pass filter with time constant Td =TiV to reduce

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voltage overshoots at the start-up. For the derivation of the PLL transfer function, the reader is referred to [21]. The transfer function is given by

(15)

, , . (16)

Fig. 6 Small signal model of the stand-alone DFIG-DC system

The coupling of the frequency loop with the dc-voltage loop is not a concern in this system, as there are no strict requirements in terms of frequency control. In addition, one of the two contributions to this coupling is inherently weak, because of the negligible value of rs. However, the gain s0/s0 in the frequency chain strongly depends on the quiescent operating point and affects the frequency controller design. This is particular relevant during the starting transient, when the dc voltage experiences a variation over a wide range. This issue was not considered in the implementation of the sensorless frequency control proposed in [21], because the operation connected to a stable dc grid was investigated, and all the tests only referred to constant frequency operation.

In this paper, a compensation gain is introduced in the frequency loop before the frequency controller, in order to address the issues of large dc-voltage and frequency variations. The compensation gain can be expressed in terms of the stator flux magnitude or stator frequency using (1) and neglecting rs:

(17)

Equation (17) can be used for practical implementation. From Fig. 6, the closed-loop transfer function for frequency is

(18)

D. Synthesis of the dc voltage controllerThe symmetry criterion for designing PI controllers can be

used in this case, due to the structure of the voltage loop in the block diagram of Fig. 6. The constant representing the diode bridge can be eliminated defining a new time constant T':

(19)

Once a proper damping V for the voltage loop is chosen, the parameters of the voltage PI controllers are

, , with (20)

IV. SIMULATION RESULTS

A. Model and control parameters.A Simulink model representing all the details according to

the descriptions above is built and used to study this system. DFIG data are those of the experimental rig (see Appendix).

According to Section III, the parameters of the frequency controller were set at: kp= 0.07 p.u., ki=70 p.u., kpll=0.75 p.u., Tf = 1.4ms, kpFOC =16 p.u. and kiFOC =0.15 p.u.. The dc-link voltage controller was synthesized for =3, using (19) and (20), giving TiV = 0.027 s, kpV =9.4 p.u., kiV =209 p.u.. A filter on the voltage reference is implemented using a time constant equal to TiV. The dc load is emulated using a controlled current source, and simulations are carried out at constant speed.

B. Response of the stator frequency controller.Fig. 7 shows the response of the system when the reference

of the frequency is changed from 1 p. u. to 1.5 p. u..

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Fig. 7 Response of the stator frequency controller.

As the stator frequency increases and the dc-link voltage is maintained constant, the stator flux, and consequently the d-axis rotor current, decreases. Since the dc load is maintained at the same level during this transient and the dc voltage is constant, the final load power does not change, and because the speed is constant, the average torque must be roughly constant too. Then, according to (4) the q-axis rotor current should increase to compensate for the flux reduction and achieve constant average torque: this can be seen in Fig. 7.

The transient on the frequency has some impact on the dc-voltage control loop because of the disturbance term idis in (13), due to the slight increase in the magnitude of the rotor current absorbed by the inverter.

C. Response of the DC voltage controllerFig. 8 shows the resulting waveforms of the response to a

step on the dc-link voltage reference at t=25 ms from 0.9 p.u. to 1 p.u followed by a step on the load current at t=250 ms from 0.2 to 0.5 p.u.. The transient frequency perturbation immediately after t=25 ms and t=250 ms is due to the coupling between voltage and frequency loops via the gain 2/(s0), as pointed out in Fig. 6. Notice that idc1 and irq have an almost identical trend, which validates (7). Slow components of rotor current reference commands are properly tracked. The ripple at 300 Hz is produced by the diode commutation and is not entirely compensated for by the current control. However, improving the tracking capability of current control can be interesting only when compensation strategies for the torque ripple are implemented using a suitably distorted reference command irq

*. In that scenario, PI controllers should be replaced by multi-frame PI or resonant controllers [25]-[26].

Fig. 8 Response of the dc-link controller.

V. EXPERIMENTAL RESULTS

A. Description of the laboratory setup.In order to validate the theory and the implementation of

the two control loops, tests have been conducted on the laboratory rig shown in Fig. 9: the parameters are reported in the Appendix. Because the machine was not sized for this purpose, it was decided to set the maximum stator flux level at 0.67 p.u., in order to allow an appropriate range for the rotor current component producing torque. Additionally, a step down transformer was used on the stator circuits to correct the stator/rotor turns ratio. This transformer increases the equivalent leakage impedance of the machine by 10% of its original value. The clamp dc voltage source ucl is adjusted to 230 V (1.15 p.u. in the dc-voltage base) and used as protection just in case of voltage overshoots. It was obtained using the dc network of the laboratory (40 kW dc machine driven by a cage-rotor induction machine). A similar way was used to implement the starting voltage source ust =100 V needed to provide initial excitation to the inverter. The dc load was implemented by a load resistor. To minimize the number of sensors, the dc voltage is estimated by the modulus of the stator ac voltage using (5).

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Fig. 9 Experimental test rig.

The voltage source inverter was controlled by a low cost fixed point dsPIC30F4011 produced by Microchip. To obtain results in real time, four 30 kHz PWM output channels were used feeding low-pass RC filters whose bandwidth was set at 270 Hz. The DFIG-DC system is connected to a separately excited dc motor whose armature voltage is adjusted using a simple three-phase variac and diode bridge. This results in small rotor speed variations depending on the load. No decoupling term -idis for the voltage loop has been implemented, to avoid the additional current sensor for the dc load current.

B. Response to the reference in the frequency chainFig. 10 shows the response to a step from 1 to 1.4 p.u. on

the reference of the frequency chain. The frequency increases as predicted. This can be seen

also in the sine of the estimated stator flux position sins. The rotor current components behave as expected and described in simulations. The dc-link voltage is only slightly affected by the frequency transient because of the change in the rotor current and then in disturbance idis (11) affecting (13) (see Fig. 6).

Fig. 10 Response to a step on the frequency reference set-point.

C. Response to the reference in the voltage chainFig. 11 shows the response of the system to a step on the

dc-link reference voltage from 0.8 p.u. to 1 p.u.. The

references were calculated in order to obtain a steady state dc voltage equal to 200 V (approximately 1 p.u. in the dc voltage base). Obviously, the dc-link voltage signal is characterized by ripple at 6s due to the diode bridge operation.

Fig. 11 Response to a step on the reference. Using stator voltage for dc link measurement.

The q-axis rotor current rises to produce more active power needed to increase the dc-link capacitor voltage. As already shown in simulations and according to (7), idc1 and irq

have the identical trend. The d-axis rotor current increases because the reference frequency is maintained constant and then the flux needs to increase in order to match with the new dc-voltage level (being ss (2/)udc). At the same time, the q-axis rotor current slightly increases in order to provide more generating torque and then the required active power at the stator side. However, part of the increase in the torque is also achieved through the increase in the stator flux. Fig. 11 includes the reference rotor current traces, confirming the reasonable tracking capability of current controllers already discussed in Sec. IV-C. Finally, the stator frequency exhibits a very small perturbation due to the coupling terms shown in Fig. 6.

D. Response to changes on the loadThe response shown in Fig. 12 was obtained increasing the

dc-load from 25% to 50% at a rotor speed close to the synchronous speed. However, unlike the test in Fig. 10, the reference values of the dc-voltage and stator frequency were set to 1 p.u. and were not changed during the test. As a result, the stator flux magnitude remains almost constant and the increase in the torque is entirely produced by the q-axis rotor current. This is clearly visible in Fig. 12, where the q-axis rotor current is almost doubled after the transient.

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Fig. 12 Response to a step on the load.

E. Starting transientIn Fig. 13 a starting transient is shown.

Fig. 13 Starting transient.

The voltage source for starting transients was set at ust

=100 V. However, the voltage in Fig. 13 starts from zero because it is calculated using the stator voltage: initially the stator voltage is zero (no excitation in the rotor) and the diode bridge is not conducting. The q-axis rotor current increases very fast to the maximum current and next decreases when the voltage is adjusted. The initial dc voltage variation over a large range causes an overshoot in the stator frequency, because of the cross-coupling term and the high initial gain 2/(s0) (the stator flux is proportional to iRd and starts from zero). Nevertheless, the frequency and dc voltage quickly stabilize to the prescribed set-point values.

F. Variable-speed results Fig. 14 shows the rotor speed, slip speed, cosine of the slip position, stator frequency and dc voltage during a low-acceleration transient obtained by increasing the speed of the dc motor within the usual range 0.66 pu - 1.33 pu. The dc load is set at 0.33 p.u.. The control system is able to maintain both reference stator frequency and dc voltage at the set-point values. The dc voltage exhibits no significant perturbations.

Fig. 14 Behavior during low-acceleration transient crossing synchronism.

G. Steady-state resultsIn Fig. 15 steady state results obtained at 1500 r/min are shown: the dc load is about 0.33 p.u.. Fig. 15 includes p. u. stator phase voltages us and current is

(-component in the stator frame), electromagnetic torque te, airgap power pg, slip angle error , diode-bridge dc current idc1 (see Fig. 1) and dc voltage udc. The slip angle error is defined as the difference between the actual slip angle (computed off-line using a stator flux estimator and the encoder signal) and the estimated slip position

given by

the block scheme in Fig. 4 and used to control the DFIG. As stated, the phase displacement imposed by the diode bridge on the stator is small. The torque has a 6 th-order harmonic due to the distorted flux and current. The torque ripple amplitude is about 0.15 p.u. and aligned to values reported in literature for grid-connected DC-DFIG systems [19]-[20] and can be reduced using several technologies such as multi-pulse rectifier arrangements or resonant controllers for the rotor current loops [24]. Air-gap power has a ripple of about 0.12 peak to peak, again due to the distortion of stator current and EMF. The error in the estimated slip position is less than 5 deg. As discussed in [21], the error in the estimated slip position depends mainly on the ratio k (2). The dc current idc1 coming from the diode bridge is distorted due to the diode commutation, but the dc voltage is quite smooth, thanks to the dc capacitor.

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Fig. 15 Steady-state waveforms.

The harmonic content for stator current, dc voltage and diode-bridge dc current is given in Table I. No significant harmonics are detected in the dc-voltage.

TABLE IHARMONICS IN THE THE STEADY-STATE STATOR CURRENT, DC VOLTAGE

AND BRIDGE CURRENT (NORMALIZED TO THE FUNDAMENTAL COMPONENTS)

Harm. 5 6 7 11 12 13 17 18 19 THD

is 0.141 - 0.017 0.017 - 0.014 0.001 - <10-3 16.3%

udc - <10-3 - - <10-3 - - <10-3 - 1.3%

idc1 - 0.091 - - 0.041 - - 0.004 - 10.4%

VI. CONCLUSION

A sensorless field-oriented control of the DFIG-DC system operating in stand-alone mode has been developed in this paper. Dc voltage and stator frequency regulations have been implemented by acting on the q- and d-axis rotor current in the stator field-oriented reference frame. A small-signal model for the system under field-oriented control has been derived, addressing the design of the controllers. A sensorless implementation avoiding encoder and dc-voltage sensing has been adopted in simulations and experimental tests to validate the proposed control. The system has been proved to be capable of delivering appropriate voltage and frequency regulation against load variation in the dc-link and can be used in stand-alone and grid-connected units when inherent dc-voltage regulation capability is required.

APPENDIX

Parameters of the wound-rotor machineStator 380 V, 50 Hz, 8.1 A, rotor 110 V, 19 A, 3.2 kW,

four poles, 1400 rpm, Ls = 1.5 p.u., M = 1.13 p.u., rs = 0.06 p.u., rr = 0.05 p.u..

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[16] A. Kumar Jain, V.T. Ranganathan, “Wound Rotor Induction Generator with Sensorless Control and Integrate Active Filter for Feeding Nonlinear Loads in a Stand-Alone Grid,” IEEE Trans. on Ind. Electron., vol. 55, No.1pp. 218 – 228, Jan. 2008.

[17] D. Forchetti, G. Garcia, M. I. Valla, “Adaptive Observer for Sensorless Control of Stand-Alone Doubly Fed Induction Generator,” IEEE Trans. on Ind. Electronics, Vol. 56, N° 10, pp. 4174 – 4180, Oct. 2009.

[18] Heng N., Yi Xilu, “Coordinated control strategy for doubly-fed induction generator with DC connection topology,” IET Renew. Power Gener., vol. 9, no. 7, pp. 747-756, 2015.

[19] M. F. Iacchetti, G. D. Marques, R. Perini, “A Scheme for the Power Control in a DFIG Connected to a DC-Bus via a Diode Rectifier,” IEEE Trans. Power Electron., vol. 30, no. 3, pp. 1286-1296, March 2015.

[20] G. D. Marques, M. F. Iacchetti, “Stator Frequency Regulation in a Field Oriented Controlled DFIG Connected to a DC Link,” IEEE Trans. Ind. Electron., vol. 61, no. 11, pp. 5930-5939, Nov. 2014.

[21] G. D. Marques, M. F. Iacchetti, "A Self-Sensing Stator-Current-Based Control System of a DFIG Connected to a DC-Link," IEEE Trans. Ind. Electron., vol.62, no.10, pp.6140-6150, Oct. 2015.

[22] G. D. Marques, M. F. Iacchetti, “Field Weakening Control for Efficiency Optimization in a DFIG Connected to a dc-link,” IEEE Trans. Ind.

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Electron., vol. 63, no. 6, pp. 3409-3419, Jun 2016. [23] Feifei Bu, Yuwen Hu, Wenxin Huang, Shenglun Zhuang, Kai Shi,

“Wide-speed-range-operation dual stator-winding induction generating system for wind power applications,” IEEE Trans. Power. Electron., vol. 30, no. 2, pp. 561-573 Feb. 2015.

[24] M. F. Iacchetti, G. D. Marques and R. Perini "Torque Ripple Reduction in a DFIG-DC System by Resonant Current Controllers," IEEE Trans. Pow. Electron., vol. 30, no. 8, pp. 4244-4254. 2015.

[25] Van-Tung Phan, Hong-Hee Lee, ”Control strategy for harmonic elimination in stand-alone DFIG applications with nonlinear loads,” IEEE Trans. Pow. Electron, vol. 26, no. 9, Sept. 2011, pp. 2662-2675.

[26] C. Liu, F. Blaabjerg,W. Chen, and D. Xu, “Stator current harmonic control with resonant controller for doubly fed induction generator,” IEEE Trans. Power Electron., vol. 27, no. 7, pp. 3207–3220, July 2012.

[27] S.Anand, B. G. Fernandes, M. Guerrero, "Distributed Control to Ensure Proportional Load Sharing and Improve Voltage Regulation in Low-Voltage DC Microgrids," IEEE Trans. on Pow. Electron., vol.28, no.4, pp.1900-1913, Apr. 2013.

[28] G. D. Marques, M. F. Iacchetti "Voltage control in a DFIG-DC system connected to a stand-alone dc load," Compatibility and Power Electronics (CPE), 2015 9th International Conference on, pp.323-328, Caparica (PT), 24-26 June 2015.

[29] J. T. Alt, S. D. Sudhoff, B. E. Ladd, “Analysis and average-value modeling of an inductorless synchronous machine load commutated converter system,” IEEE Trans. Energy Convers., vol. 14, no. 1, pp. 37-43, Mar. 1999.

[30] A. Petersson, “Analysis, modeling and control of doubly-fed induction generators for wind turbines,” Ph.D. dissertation, Chalmers Univ. Technol. Gothenburg, Sweden, 2005, page 49.

[31] Saeed Golestan, Mohammad Monfared, Francisco D. Freijedo, “Design-Oriented Study of Advanced Synchronous Reference Frame Phase-Locked Loops” IEEE Trans. Power Electron., vol. 28. no. 3, pp. 765-778, Feb. 2013.

G. D. Marques (M’95-SM’12) was born in Benedita, Portugal, on March 24, 1958. He received the Dipl. Ing. and Ph.D. degrees in electrical engineering from the Technical University of Lisbon, Lisbon, Portugal in 1981 and 1988, respectively.

Since 1981, he has been with the Instituto Superior Técnico, University of Lisbon, where he involves in teaching power systems in the Department of Electrical and Computer Engineering. He has been an Associate Professor since 2000. He is also a Researcher at INESC-ID. His current research interests include electrical machines, static power conversion, variable-speed drive and generator systems, harmonic compensation systems and distribution systems.

Matteo F. Iacchetti (M’10) received the Ph.D. in electrical engineering from the Politecnico di Milano, Milano, in 2008. From 2009 to 2014, he has been a PostdoctoralResearcher with the Dipartimento di Energia, Politecnico di Milano. He is currently a Lecturer with the School of Electrical and Electronic Engineering, at the University of Manchester, Manchester, U.K. His main research interests include design, modelling, and control of electrical machines and electrical drives for power conversion.

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