Control Strategy for Harmonic Elimination in Stand ... - IEEE Xplore

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 26, NO. 9, SEPTEMBER 2011

Control Strategy for Harmonic Elimination in Stand-Alone DFIG Applications With Nonlinear Loads Van-Tung Phan, Member, IEEE, and Hong-Hee Lee, Member, IEEE

Abstract—This paper proposes a new control strategy of effective fifth and seventh harmonic elimination in the stator output voltage at the point of common coupling for a stand-alone doubly fed induction generator (DFIG) feeding a three-phase diode rectifier. This load regularly causes such harmonic distortions, which harmfully affect the performance of other loads connected to the DFIG. In order to allow the DFIG to deliver a pure sinusoidal stator output voltage, these harmonics must be rejected. The proposed elimination method is investigated based on the rotor current controller employing a proportional integral and a resonant controller, which is implemented in the fundamental reference frame. In this frame, both positive seventh and negative fifth voltage harmonic can be eliminated by using only single resonant compensator tuned at six multiples of synchronous frequency in the rotor current controller. The control scheme is developed in the rotor-side converter for the control and operation of the DFIG. Simulations and experimental results with 2.2-kW DFIG feeding a nonlinear load are shown to verify prominent features of the proposed control method. Index Terms—Doubly fed induction generator (DFIG), nonlinear loads, resonant controller, stand-alone system, wind turbine system.

NOMENCLATURE vs , vr vP vN S Vdc is , ir , im s λs , λr Ls , Lr , Lm R s , Rr ωs , ωr , ωsl θs , θr , θsl σ d/dt, Δ

Induced stator voltage and rotor voltage. Stator output voltage at the point of common coupling. The nonlinear voltage drop on the internal stator impedance. DC-link voltage. Stator current, rotor current, and stator magnetizing current. Stator and rotor fluxes. Stator, rotor, and mutual inductances. Stator and rotor resistences. Synchronous, rotational rotor, and slip speeds. Synchronous, rotational rotor, and slip angles. Total leakage factor. Differential operator and error value.

Manuscript received August 9, 2010; revised September 7, 2010 and December 17, 2010; accepted February 28, 2011. Date of current version September 16, 2011. Recommended for publication by Associate Editor Z. Chen. V.-T. Phan is with the School of Electrical and Electronics Engineering, Nanyang Technological University, 639–798 Singapore (e-mail: vtphan@ ntu.edu.sg). H.-H. Lee is with the School of Electrical Engineering, University of Ulsan, Ulsan 680-749, Korea (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPEL.2011.2123921

Superscripts 1, 5, 7 Fundamental synchronous, fifth, and seventh reference frames. ∗ Reference values. Subscripts d, q Synchronous rotating d–q axes. s, r Stator, rotor. a, b, c Stationary three-phase axes. 1, 5, 7 Fundamental, fifth, and seventh sequence components.

I. INTRODUCTION HE doubly fed induction generator (DFIG) has been widely used in variable-speed wind energy conversion systems over the past decade. One of the most prominent advantages of the DFIG is that the power converter to operate the control scheme only handles a fraction of the machine nominal power. The DFIG can be used in either the grid [1]–[11] or the stand-alone mode [5], [12]–[19]. The majority of research interests related to DFIG systems in the literature have concentrated on the grid-connected wind power applications. In this case, the control scheme and operation of the DFIG are mainly focused on modeling of DFIG [20], active and reactive power control [2], [7], [11], ride-through capability [3], [6], and compensation of unbalanced network [2], [7], [11], [13]. However, in order to assess the full potential of the DFIG, control strategies of the stand-alone operation mode should be investigated because the control performance under such condition is so sensitive to control schemes, unbalanced or nonlinear loads, and harmonic distortions. Among them, unbalanced and nonlinear loads have a strong influence on the performance of stand-alone configurations. Taking into account unbalanced loads in stand-alone mode of the DFIG, authors in [13]–[15] proposed appropriate algorithms to compensate for unbalanced output voltages. The control of a DFIG based on the load-side converter (LSC) for unbalanced operation was introduced for stand-alone applications in [13], but no modifications were applied to the rotor-side converter (RSC). In [14] and [15], an improved control strategy using a PI–resonant controller (PI–R) in the RSC was proposed in the positive rotating reference frame to eliminate the stator voltage imbalance. The nonlinear load under consideration is the three-phase six-pulse diode rectifier that has been widely used in power converters and ac machine drives with dc-link voltage. The typical characteristic of this load type is causing the nonlinear

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PHAN AND LEE: CONTROL STRATEGY FOR HARMONIC ELIMINATION IN STAND-ALONE DFIG APPLICATIONS WITH NONLINEAR LOADS

current with high THD factor. Due to the effect of this nonlinear current, the stator output voltage of the DFIG at the point of common coupling (PCC) becomes a nonsinusoidal waveform with odd harmonics 6n ± 1 (n = 1, 2,. . .) multiples of the fundamental frequency ωs , which directly deteriorates the performance of other loads connected to the generator. Therefore, it is necessary to improve the quality of stator output voltages of the DFIG by rejecting low order voltage harmonic components, i.e., fifth and seventh harmonics that are the most severe ones. In [16], the effect of harmonics of the auxiliary diode rectifier load on the control system in a stand-alone DFIG was investigated, but no compensation of harmonics and design of an LC filter were shown. A control scheme with an LC output filter was designed to remove harmonics due to the influence of nonlinear load for the DFIG in aircraft applications [17]. However, the installation of an LC filter at the stator side had many drawbacks such as resonance and parameters tuning problem in which the latter disadvantage was depending on the impedance of the generator. In [18], a proposed direct method to control output voltage for a DFIG in stand-alone operation was introduced. However, in tests with the nonlinear load, no specific algorithm to compensate harmonic components was mentioned in this paper. Meanwhile, a novel and simple sensorless control scheme for a stand-alone DFIG generation system was introduced in [19] where the active power filter theory was adopted in the LSC to reduce harmonic components. Therefore, the control algorithm had to be implemented in both the RSC and the LSC. The controller structures of studies mentioned earlier have been developed based on commonly used proportional-integral (PI) controllers that are simple and effective in use. However, it has disadvantages of steady-state errors in amplitude and phase when regulating the ac quantities due to the negative sequence or harmonic components. To overcome this drawback, the resonant controller is considered as a promising solution, and the proportional plus resonant regulators have been proposed in the literature for the current control at the fundamental frequency for pulse-width modulation (PWM) inverters [21]–[23] and selective harmonic frequencies for active power filter applications [24], [25]. With high gain at the resonant frequency, these controllers are capable of completely eliminating the steadystate control error at the selected frequency. Each specific compensator is tuned at the selective harmonic frequency in its reference frame to eliminate the respective harmonic. However, most of voltage or current controllers in [21]–[25] have been realized in the stationary reference frame, requiring a large number of resonant compensators. In addition, there have been no researches that exploit the resonant compensator to eliminate harmonics in DFIG applications. Based on the aforementioned research motivations, this paper develops a new control scheme implemented in the fundamental reference frame to eliminate selective fifth and seventh voltage harmonics at the PCC for a stand-alone DFIG with nonlinear loads. In this frame, both these harmonics become the same order sixth harmonics. These harmonic components are then eliminated based on the rotor current controller employing a proportional integral and a resonant controller (PI–R). The novelty of the proposed development is that a single

Fig. 1.

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Typical stand-alone DFIG configuration with a nonlinear load.

resonant compensator of the rotor current controller is capable of eliminating one pair of both seventh positive and fifth negative harmonics in the stator voltage at the PCC. Therefore, the number of resonant compensators is reduced to a half compared with the case implemented in the stationary frame, which considerably simplifies complexity for the control scheme. The paper is organized as follows. Section II describes the harmonic problem caused by the nonlinear load in the DFIG. Voltage control loops realized in respective harmonics frames to eliminate fifth and seventh voltage harmonics and a rotor current reference generation strategy are also shown in this section. Section III discusses the proposed PI–R rotor current controller in details whereas simulations and experimental results with 2.2-kW DFIG are presented in Section IV. Finally, Section V draws the conclusion.

II. PROPOSED HARMONIC COMPENSATION METHOD A. Harmonic Problem in Stand-Alone DFIG Fig. 1 shows the general configuration of a stand-alone DFIG with a nonlinear load, which is three-phase diode bridge rectifier supplying a dc load. As mentioned earlier, under such nonlinear load type, there have been voltage harmonic components that are multiples 6n ± 1 (n = 1, 2, . . .) of the fundamental frequency ωs of the stator voltage. These harmonics seriously deteriorate the quality of stator voltage of the DFIG and directly affect the performance of other loads connected to the DFIG. The main reason to produce these harmonics is the effect of the nonlinear current iN drawn by the nonlinear load. Therefore, the elimination of these harmonics is an essential task to improve the voltage quality at the PCC. Fig. 2 shows the connection interface between the DFIG and different load types connected to the PCC. Rs and Ls are the stator resistance and the stator inductance of the DFIG and are considered as the internal impedance of the DFIG. As seen, the presence of nonlinear loads directly causes distortions for the stator voltage vp at the PCC, which harmfully affect other loads connected to this point of the DFIG. This can be explained that the nonlinear load current iN leads to a nonlinear voltage drop vN S on the internal stator impedance including the fundamental and harmonic components, and the voltage at the PCC is

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this frame, dynamic equations of the DFIG can be expressed as dλ1sdq + jωs λ1sdq dt

(5)

dλ1r dq + j(ωs − ωr )λ1r dq dt

(6)

1 = Rs i1sdq + vsdq

vr1dq = Rr i1r dq +

Fig. 2.

Connection interface between the DFIG and different load types.

λ1sdq = Ls i1sdq + Lm i1r dq

(7)

λ1r dq = Lr i1r dq + Lm i1sdq .

(8)

From (5)–(8), the rotor voltage in the fundamental reference frame can be determined as

determined as vP = vs − vN S = vs − Rs is − Ls

dis . dt

(1)

Taking into account both the fundamental and harmonic components, (1) yields ⎞ ⎛ dis1 dish ⎠ vP = vs − Rs is1 −Ls ish +Ls − ⎝R s dt dt h= 1

h= 1

(2)

di1r dq Lm dλ1sdq + dt Ls dt Lm 1 1 + jωsl λsdq + σLr i1r dq Ls

vr1dq = Rr i1r dq + σLr

1 = ωs − ωr . where σ = 1 − (L2m /Lr Ls ), ωsl In stand-alone DFIG applications, the magnetizing current im s is supplied directly from the RSC by a d-axis rotor current. The equations used to express the dynamic response and the steady state of the magnetizing current are given as

where the fundamental voltage at the PCC is vP 1 = vs − Rs is1

dis1 − Ls dt

τs (3)

and the voltage distortion due to harmonic components is determined as ⎞ ⎛ dish ⎠. vP h = − ⎝ R s (4) ish + Ls dt h= 1

h= 1

Accordingly, despite sinusoidal stator output voltage vs , the voltage at the PCC is a distorted waveform due to the nonsinusoidal voltage component vN S . To produce a sinusoidal voltage vP , a compensation method with an LC passive filter placed on the stator side was developed in [17] and [18]. Generally, a stand-alone DFIG system can be controlled by inverter systems in order to produce a desired output voltage to eliminate harmonics mentioned earlier. This paper deals with harmonic elimination method for the DFIG, which is based on the PI–R controller in the RSC. The purpose of this proposed controller is to generate a proper voltage waveform vs in order to compensate the nonlinear voltage drop vN S . As a result, a pure sinusoidal voltage waveform can be produced at the PCC without a passive filter.

(9)

dim s (1 + σs ) 1 + im s = i1r d1 + vsd1 dt Rs

im s = i1r d1 + (1 + σs ) i1sd1

(10)

where τs = Ls /Rs and σs = Ls /Lm − 1 are the electrical time constant of stator circuit and stator leakage factor, respectively. As evidenced by (10), the induced stator voltage, which is controlled by the stator magnetizing current, can be directly regulated from the direct rotor current i1r d1 in the fundamental reference frame. The output of the PI controller for voltage magnitude regulation is the d-axis fundamental sequence component of the reference rotor current. The reference q-axis rotor current can be regulated according to the q-axis stator current as (11) in order to force the fundamental reference frame along the vector of stator flux Ls 1 ∗ i . (11) i1r q = − Lm sq

B. DFIG Model in the Fundamental Rotating Frame

Once the control condition in (11) is satisfied, the stator flux vector is aligned to the d-axis reference frame. Then, the frequency control loop of the DFIG can be obtained. In stand-alone DFIG, the stator flux angle θs∗ of the reference frame can be obtained from a free-running integral of the stator frequency demand ωs∗ (60 Hz), given as θs∗ = ωs∗ dt. (12)

The control and operation of the DFIG under the nonlinear load is developed based on the induction machine dynamic model in the fundamental synchronous reference frame where the stator flux-oriented vector control strategy is performed. In

This angle is combined with the rotational rotor angle to determine the slip frequency of rotor current to be used for the demodulation of the reference voltage between the fundamental and rotor reference frames. It means that the frequency of


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Fig. 4. PI controllers used to eliminate the stator voltage harmonic components at the PCC.

Fig. 3. Vector diagram representing the relationship between different reference frames.

the rotor current is controlled according to the rotor speed, and hence a constant frequency of the stator output voltage can be obtained. In order to investigate the DFIG under the nonlinear load, a vector diagram for both the positive and negative reference frame is used and shown in Fig. 3. This figure shows the relationship between a stator stationary frame αs βs , a rotor frame αr βr rotating with an angular speed ωr , the fundamental synchronous reference frame dq 1 , a positive seventh harmonic frame dq 7 rotating with an angular speed 7ωs , and a negative fifth harmonic frame dq 5 rotating with an angular speed −5ωs . The vector F stands for voltage, current, torque, and flux of the generator. According to this figure, the relationship of the vector F between different frames is illustrated as follows: 5 = Fα s β s ej 5ω s t Fdq 7 Fdq = Fα s β s e−j 7ω s t .

(13)

In addition, the vector F can be expressed in the fundamental reference frame with their respective the fundamental, fifth, and seventh sequence components, given as 1 1 1 1 = Fdq Fdq 1 + Fdq 5 + Fdq 7 1 5 −j 6ω s t 7 j 6ω s t = Fdq + Fdq . (14) 1 + Fdq 5 e 7e

As seen in (14), a control variable in the fundamental rotating frame under a nonlinear load condition consists of both dc and ac components. If a control variable is the rotor current, it is possible to use the PI–R controller to regulate the rotor current to reject harmonics in the stator output voltage. This relation was addressed in (10). C. Proposed Method for Voltage Harmonic Rejection and Reference Rotor Current Generation Strategy As analyzed in Section II-A, the control scheme is responsible for producing a proper induced voltage vs to compensate the nonlinear voltage drop vN S . In order to do this task, the positive seventh and the negative fifth harmonic sequence components, i.e., vP7 dq 7 and vP5 dq 5 , in the stator voltage at the PCC

must be detected and compensated. First, four bandpass filters are used to extract the fifth and seventh harmonic components from the measured stator voltage vP . These filters have the task to remove all different frequency voltage components but the selective fifth and seventh ones. Second, these harmonic voltages are transformed to their harmonic reference frames rotating at the rotating frequency 7ωs and −5ωs to obtain their dc quantities vP7 dq 7 and vP5 dq 5 , respectively. Finally, to eliminate these selective harmonics in vP totally, four PI voltage controllers are adopted in which the reference values are set zero, as seen in Fig. 4. The outputs of these controllers are the reference harmonic sequence components of rotor currents, i.e., ∗ ∗ i5r dq 5 and i7r dq 7 . Once these reference rotor currents are regulated adequately by the proposed current controller, a corresponding proper induced stator voltage vs will be generated to satisfy the desired control target. The proposed PI–R current controller is used to precisely track the reference rotor currents, which are determined based ∗ ∗ ∗ on six dc rotor current components, i.e., i1r dq 1 , i5r dq 5 , and i7r dq 7 , and implemented in the RSC. In order to apply the PI–R current controller in the fundamental rotating reference frame, these six reference rotor current values are transformed into coordinates the fundamental frame using six multiples of the synchronous angle 6θs . As a result, the reference rotor currents for current controller are the sum of three voltage controller outputs, determined as ∗

∗

∗

∗

i1r dq = i1r dq 1 + i1r dq 5 + i1r dq 7 ∗

∗

∗

= i1r dq 1 + i5r dq 5 e−j 6ω s t + i7r dq 7 ej 6ω s t

(15)

where i1r dq 1 is the output of a PI controller for voltage amplitude regulation and is the dc value, as shown in Fig. 5. The two remaining components are the ac values with the same six multiples of the synchronous frequency of the generated voltage. D. Proposed RSC Control Scheme As mentioned before, the proposed harmonic elimination method for the DFIG stator output voltage is developed solely in the RSC. The main idea of the proposed harmonic elimination method is to generate a pure sinusoidal voltage waveform at the PCC of a stand-alone DFIG system. This task can be performed by controlling the proper rotor current in the RSC as shown in (15). Once high quality stator voltage at the PCC is obtained with reduced harmonic contents, the performance of other loads connected to the same PCC will not be affected. Since the proposed control strategy is not dependent on and is not affected by the control and operation of the LSC, developments on this converter are out of the scope of this paper. In this case, the LSC is used conventionally for dc-link voltage regulation only,

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Fig. 5.

Block diagram of rotor current control scheme using PI–R controller in the RSC for the DFIG under the nonlinear load.

Fig. 6.

Block diagram of conventional vector control scheme for the LSC of the stand-alone DFIG.

which is described in the next section. The proposed block diagram of the RSC in the stand-alone DFIG with the stator voltage harmonic compensation method is presented in Fig. 5. The control system consists of a stator voltage control loop and a series of fundamental and selective harmonic rotor current controllers in the fundamental reference frame rotating at the synchronous frequency of the stator voltage. The stator voltage control loop is implemented by using a PI controller in order to regulate the voltage magnitude in a stable manner. This control loop mainly aims to reject the voltage variations due to the effect of electric loads or speed changes. The fundamental magnitude of the

stator voltage is controlled directly with a given specific command value vP∗ by adding an external voltage control loop. The specific magnitude of the measured stator voltage is obtained from the fundamental sequence components of the measured voltage signals, given as

(16) vP 1 = (vP1 d1 )2 + (vP1 q 1 )2 . To determine stator voltage components vP1 dq 1 , a low-pass filter is used to remove all high frequency harmonics in the measured stator voltage vP .


The reference rotor currents determined in (15) are compared with the respective measured rotor currents, and their errors are inputs of the PI–R controllers. The outputs of the PI–R controllers are the reference rotor voltages to control the RSC. These reference rotor voltages are nonsinusoidal waveforms and are compared with a triangular waveform to generate PWM signals. Simultaneously, the stator voltage vs also becomes a proper waveform that compensates the nonlinear voltage drop vN S and hence enables the DFIG to deliver a pure sinusoidal voltage at the PCC. It can be seen in the Fig. 5 that no decomposition for the positive and negative sequence harmonics of the measured rotor currents is required in the closed-loop current control. This significantly reduces the control time delay and improves the performance of control system. The detailed description of rotor current controller is presented in the following sections. E. LSC Control Scheme The LSC control scheme in this paper is responsible for the dc-link voltage regulation. In [19], a proposed control method developed in the LSC to compensate harmonic of the stator current was already presented comprehensively. In this paper, a new development for voltage harmonic rejection has been developed based on the RSC. Therefore, this section just briefly describes the control scheme of the LSC without special control efforts employed for harmonics compensation. For more detailed description of control and operation of the LSC, it can be referred to [13], [19]. The vector control scheme adopts the rotating reference frame aligned along the stator voltage vector. Fig. 6 shows the block diagram of the conventional LSC for a stand-alone DFIG system. The active and reactive power between the PCC and the LSC can be independently controlled by controlling the line current iL . The d-axis current iL d is used to control the dc-link voltage irrespective of the power flow direction through the rotor side whereas the q-axis iL q is used to control the reactive power. The reference voltage for the LSC can be expressed by Ki vL∗ d = − Kp + (i∗L d − iL d ) + ωs LiL q + vP d (17) s Ki ∗ ∗ iL q − iL q − ωs LiL d vL q = − K p + (18) s where Kp and Ki are the proportional and integral gain of PI current controllers. L is the line inductance. III. IMPROVED ROTOR CURRENT CONROL USING PI–R CONTROLLER A. PI–R Controller in the Fundamental Reference Frame Once obtaining the reference rotor currents in the fundamental reference frame in (15), they are controlled to achieve the control target, i.e., eliminating fifth and seventh harmonics in the stator voltage. It should be noted that decomposing the positive and the negative sequence components of the control variables with a filter causes more time delays due to

Fig. 7.

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Proposed PI–R rotor current controller.

computational complexity and hence degrades the performance of control system. The decomposition process of measured rotor currents can be practically implemented by digital bandpass or low-pass filters. Under the nonlinear load condition, the control system for a DFIG must be precisely controlled in either the transient process or the steady state. Therefore, the fact that decomposes control signals in inner current control loops significantly degrades the system stability and overall efficiency. To improve the accuracy of the control system, the PI–R controller applied to the RSC of the DFIG is employed in this paper. A closed-loop current control scheme in the RSC is described in Fig. 7. In the fundamental reference frame, the fundamental components become dc quantities, whereas the positive seventh and negative fifth sequence harmonics become ac quantities, which have the same six multiples of the synchronous frequency. By adopting the PI–R controller in this frame, it is possible to regulate both of components in which the dc value is controlled by the PI controller and the ac value is controlled by the resonant compensator. One of the most important features of the resonant compensator is that it is capable of sufficiently tracking the ac reference current and, therefore, can eliminate steady-state control variable errors at the chosen (resonant) frequencies. The open-loop transfer function of the proposed PI–R current controller is expressed in both the ideal (19a) and nonideal (19b) cases Go (s) = Kp +

Kr s Ki + 2 s s + (±6ωs )2

(19a)

Go (s) = Kp +

Kr ω c s Ki + 2 s s + 2ωc s + (±6ωs )2

(19b)

where Kp is the proportional gain that has the same function in the PI controller, Kr denotes the resonant gain that provides the infinite gain for ac component tracking, ωc is the cutoff frequency, and ωs = 2.π.60 (rd/s) is the synchronous frequency of the stator output voltage. The ideal resonant transfer function with infinite gain sometimes causes instability due to limited accuracy in the digital implementation. Therefore, the nonideal transfer function (19b) can be used instead of (19a) in practical cases. According to [22], the gain of the nonideal PI–R controller becomes finite, but it is still relatively high to guarantee zero steady- state errors. This characteristic will be described by the Bode plot in Section III-C. According to Fig. 7, the closed-loop transfer function of the control scheme based on the nonideal open-loop transfer

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function and the load model is determined as shown (20), at the bottom of this page.

transfer function of the control scheme can be expressed in relation to the rotor current input and output as follows:

B. Choosing Current Controller Gains

Gc (s) =

Designing the controller gains for the PI–R is not straightforward task when the order of compensators is high. As mentioned earlier, the current controller design is implemented based on the Naslin polynomial technique and is used to determine the controller gains, which was introduced in [26]. The characteristic polynomial of the closed-loop transfer function in (20) is P (s) = (σLr s + Rr ) s s2 + 2ωc s + ω02 + Kp s s2 + 2ωc s + ω02 (21) + Ki s2 + 2ωc s + ω02 + Kr s2 where ω0 = 6ωs is the resonant frequency of the PI–R controller. The parameters of the controller are computed based on the fourth-order Naslin polynomial s2 s3 s4 s + + 3 3 + 6 4 (22) N (s) = a0 1 + ωn αωn2 α ωn α ωn where α = 4ξ 2 is the characteristic ratio where ξ is the damping factor, a0 is the coefficient, and ωn is the Naslin frequency. From these quantities, matching the coefficients for (21) and (22) gives controller gains to be used in the proposed current controller α6 ωn3 − α3 ω02 ωn + 2ωc ω02 α6 ωn4 = 2 ω0 2ωc σLr α6 ωn4 ω02 σLr 2 5 2 ω α ωn − ω02 − α6 ωn4 ωc ω02 0 −2ωc ω02 α3 ωn − 2ωc .

Kr =

(23)

According to [18], the characteristic ratio of the Naslin polynomial is generally chosen to be α = 2 with respect to the damping factor ξ = 0.7. Thus, the appropriate gains of the proposed current controller can be calculated as (23) where the cutoff frequency ωc value of 7 rad/s is chosen in practical implementation according to [22]. C. Analysis of the PI–R Controller Performance In order to determine if the proposed controller effectively guarantees zero steady-state error, an analytical investigation regarding its frequency response in a closed-loop system is employed. For the sake of simplification, the ideal open-loop transfer function (19a) is adopted in this case. The closed-loop

M (s) (σLr s + Rr ) s (s2 + ω02 ) + M (s)

(24)

where 1 (σLr s + Rr ) M (s) = Kp s s2 + ω02 + Ki s2 + ω02 + Kr s2 . L(s) =

Substituting s = ±j6ωs into (24), we can see that the frequency response of the closed-loop transfer function at the positive resonant frequency 6ωs and the negative resonant frequency −6ωs are equal to 1, and similarly the phase errors at such frequencies are also equal to 0 as computed in (25). This means that good performance of the control system can be obtained with unity gains and zero-phase errors at different resonant frequencies. Gc (s)|s=±j 6ω s =

M (±j6ωs ) =1 (±j6ωs σLr + Rr ) × (±j6ωs ) × 0 + M (±j6ωs ) (25a)

Kp = σLr α3 ωn − Rr − 2ωc σLr Ki =

=

i1r dq (s) Go (s)L(s) = ∗ 1 ir dq (s) 1 + Go (s)L(s)

Gc (s)|s=±j 6ω s = 0.

(25b)

It is concluded that the proposed controller can precisely regulate the rotor current with zero steady-state error at a specific resonant frequency ±6ωs regardless of the effect of the generator parameters Rr and σLr . To evaluate the possibility of rejecting the effect of load disturbances, the transfer function from Er1dq to the controlled rotor current i1r dq is determined as (26). The value Er1dq represents unknown quantities equivalent to the disturbances caused by the rotor back-electromagnetic force (EMF). i1r dq (s) L(s) = 1 Er dq (s) 1 − L(s)Go (s) s s2 + ω02 . = (σLr s + Rr ) s (s2 + ω02 ) − M (s)

Qc (s) =

(26)

Likewise, substituting s = ±j6ωs into (26), yielding Qc (±j6ωs ) = 0. At all resonant frequencies, the value of transfer function Qc (s) is always zero regardless of the generator parameters. This indicates that the proposed control scheme is capable of rejecting

Kp s s2 + 2ωc s + ω02 + Ki s2 + 2ωc s + ω02 + Kr s2 Gc (s) = . (σLr s + Rr ) s (s2 + 2ωc s + ω02 ) + Kp s (s2 + 2ωc s + ω02 ) + Ki (s2 + 2ωc s + ω02 ) + Kr s2

(20)


Fig. 8.

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Bode plot of the open-loop transfer functions of PI and PI–R. Fig. 9.

completely the influence of disturbances from rotor side. Consequently, the effectiveness and stability of the proposed PI–R controller in the fundamental reference frame are proved comprehensively. To further analyze the performance of PI–R controller graphically, the Bode plots of the open-loop and closed-loop transfer functions in (19b) and (20) are shown. The controller gains used for the Bode plots are calculated according to (23). For the purpose of comparing, Fig. 8 describes the magnitude and phase characteristics of the open loop transfer functions for both the PI controller and the PI–R with respect to different values of the resonant gain Kr . Among them, the value Kr = 12 000, which is calculated from (23), is used in the control system. The large gain obtained at the resonant frequency of the PI–R controller ensures that the steady-state errors in the rotor currents can be completely eliminated. It can be seen that the selection of different resonant gain values affects the gain and phase margins, and the dynamic response of the control system with the resonant compensator is totally robust. As illustrated in Fig. 8, a low Kr gives a very narrow bandwidth, whereas a high Kr leads to larger bandwidth. Fig. 9 shows the Bode diagram of the closed-loop transfer functions of the PI–R current controller compared with the conventional PI controller. As shown in Fig. 9, the proposed current controller with the resonant controller provides more accurate control with the characteristics of unity gain (0 dB) and zero-phase error at the resonant frequency. This result strongly confirms the theoretical analysis in (25). In contrast, the control bandwidth of the PI controller is not sufficient to regulate at the same resonant frequencies. Consequently, the PI–R controller is the best solution to effectively regulate the rotor current of the DFIG that contains the harmonic rejection components. D. Calculation of Reference Rotor Voltage for the RSC ∗

According to Fig. 7, the rotor control voltages vr1dq for the RSC are calculated by ∗

vr1dq = σLr vr1dq + Er1dq

(27)

Bode plot of the closed-loop transfer functions of PI and PI–R.

where the voltages vr1dq are the outputs of the PI–R controller and are determined as

∗

vr1dq = Go (s)(i1r dq − i1r dq ) Kr ω c s Ki ∗ + 2 = Kp + (i1r dq − i1r dq ). s s + 2ωc s + (±6ωs )2 (28) In order to improve the decoupling effect between the dq components of the rotor currents, the disturbances of rotor backEMF Er1dq are added in (28), and hence the rotor control voltages of (27) become (29) and (30), respectively. ∗

1 vr1d = σLr vr1d + Rr i1r d − ωsl σLr i1r q Lm 1 ∗ 1 λsd . vr1q = σLr vr1q + Rr i1r q + ωsl σLr i1r d + Ls

(29) (30)

Because the modulation index of the doubly fed induction machine must be performed in the rotor reference frame, these rotor control voltages have to be transformed from the fundamental reference frame to the rotor reference frame. This transformation 1 in the fundamental is performed using the positive angle slip θsl reference frame. IV. SIMULATION RESULTS In order to verify the performance and effectiveness of the proposed control method, both simulations and experiments are carried out with a DFIG under nonlinear load conditions. The simulation is performed using PSIM software. The machine parameters are shown in Appendix. The rotor speed of the DFIG is adjusted by a dc motor that has a role of the prime mover. The controller gains defined in (23) are used in both simulations and experimental implementation. The stator-phase voltage magnitude is controlled at 300 V. First, to investigate the harmonic problem on the DFIG system, a test without harmonic compensation method is

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Fig. 10.

Distorted voltages at the PCC without harmonic compensation method and the nonlinear load currents.

Fig. 11. voltage.

Voltage waveforms at the PCC after compensation and their harmonic spectrum. (a) Stator voltages after compensation. (b) Harmonics spectrum of the

performed. Fig. 10 shows the performance of the stator output voltages and load currents under the nonlinear load condition without the compensation method. Due to the effect of the nonlinear load current, the stator voltages at the PCC are distorted with presence of fifth and seventh harmonics as analyzed before. With the proposed compensation method using the PI–R controller, the DFIG effectively produces a pure sinusoidal stator output voltage as seen in Fig. 11(a). It can be observed from the

harmonic spectrum of induced stator voltage vP in Fig. 11(b) that fifth and seventh harmonic components are totally removed. Fig. 12(a) shows the steady-state tracking performance of the rotor current with the proposed PI–R controller. According to (15), the reference rotor current in the fundamental frame is composed of both dc and ac components. The frequency of this ac component is 360 Hz. As seen, the measured rotor current i1r d is well regulated to follow the reference value in order to


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Fig. 12. Rotor current regulating performance with the PI–R controller. (a) Reference and measured direct rotor current, the compensated stator voltage vP a , and nonlinear load current v N a . (b) Frequency spectrum of dq rotor current in the fundamental frame.

compensate the stator voltage harmonics. The zero steady-state error of the rotor current can be obtained with the proposed PI–R current controller. As mentioned earlier, the resonant frequency of PI–R controller is tuned at the six multiples of synchronous frequency, which can be seen in Fig. 12(b). The sinusoidal voltage at the PCC after compensation and the nonlinear load current are also shown in this figure. Fig. 13 shows the measured rotor-phase current with the proposed control algorithm. Because the rotor current i1r dq includes the harmonic injection components, the measured rotor-phase currents become distorted waveforms. These currents will induce a proper stator output voltage vs in the DFIG in order to compensate the effect of nonlinear voltage drop vN S . As a result, a sinusoidal voltage waveform can be produced at the PCC as seen in Fig. 11.

Fig. 13. Steady state performance of three-phase rotor currents and voltage at the PCC.

V. EXPERIMENTAL VERIFICATIONS To confirm the simulated results, the experimental implementation was carried out with the DFIG using the same control strategies. Fig. 14 shows the detailed structure of proposed

DFIG system and Fig. 15 shows the configuration of the experimental setup in laboratory. The system is composed of a 2.2-kW DFIG, rotated by a dc motor that is emulated as a prime mover

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Fig. 14.


Block diagram of proposed DFIG system.

Fig. 16. Stator voltage at the PCC and load current without harmonic compensation method.

Fig. 15.

Configuration of the experimental setup. Fig. 17. Stator voltage at the PCC and load current with the proposed harmonic compensation method.

with the speed control. The stator output voltage is connected to the three-phase diode rectifier to supply a resistance load with rated power of 1.5 kW and is controlled at 125 V which is smaller than the control value in simulations due to limited load rating used. The rotor speed is maintained at the constant value for tests. The RSC and LSC are fed by an insulated gate bipolar transistor (IGBT)-based PWM inverter in which the switching frequency is 10 kHz. The system is controlled by two individual controller boards of DSP TMS320F28335 of Texas Instruments. As seen in Fig. 14, the proposed control scheme is composed of the RSC and the LSC. Here, the LSC is connected to the stator terminals via a transformer to match two voltage levels between the PCC and dc-link voltage. The LSC is responsible for supplying a desired dc-link voltage to feed the RSC while the RSC is capable of rejecting harmonic components of the stator voltage at the PCC. In addition, a Y-connected filtering capacitor C (50 μF each phase) is equipped with the stator terminals for the following functions: 1) reducing stator output voltage ripples; 2) providing a part of excitation current for the DFIG; 3) filtering high frequency components produced by the rotor PWM inverter due to the commutation noise. Three inductors L (2 mH each phase) are connected between the LSC and the PCC. Fig. 16 shows the same results with simulations to evaluate the effect of the nonlinear load on the quality of the stator

voltage at the PCC. Without the compensation method, these voltage waveforms become nonsinusoidal due to the presence of harmonics. It can be observed that very good agreement with respect to voltage waveform can be achieved with the simulated and experimental results. Fig. 17 shows the sinusoidal stator voltage at the PCC after rejecting fifth and seventh harmonic components totally. Therefore, the nonlinear load connected to the DFIG with the proposed PI–R controller has no effect on the performance of other loads at the PCC. The quality of the supply voltage is significantly improved. In Figs. 16 and 17, the fast Fourier transform analysis of the PCC voltage with and without compensation method is also shown to verify good performance of the PI–R controller. The performance of the PI–R controller when regulating the rotor current to achieve the control target is shown in Fig. 18. This figure displays the d-axis rotor current tracking performance, the nonlinear load current, and the output voltage. The performance of the q-axis rotor current in the fundamental frame is also the same but is not shown here due to space limitation. The frequency of d-axis rotor current is six multiples of the synchronous stator voltage frequency as analyzed previously. Considering error between the reference and measured rotor direct current Δi1r d , it is seen that the adequate and accurate control for the current controller can be achieved with the PI–R


Fig. 18. Steady state performance of the proposed PI–R controller with the ∗ harmonic compensation strategy: reference i1r d and measured d-axis rotor current (25 A), stator voltage at the PCC after compensation v P a , and the nonlinear load current iN a .

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Fig. 20. Three-phase rotor current response with the proposed control algorithm and the voltage v P a .

Fig. 21. Dynamic performance of the rotor current with the rotor speed variations.

Fig. 19. Steady state performance of the conventional PI controller with the ∗ harmonic compensation strategy: reference i1r d and measured d-axis rotor current (25 A), stator voltage at the PCC after compensation v P a , and the nonlinear load current iN a .

compensator. Once the rotor current is well regulated, the output voltage at the PCC becomes sinusoidal without harmonics as indicated. The same test is performed with the conventional PI controller without the resonant regulator to regulate the same reference rotor current in Fig. 19. Based on the nonzero steadystate error of the rotor current, it is concluded that the conventional PI controller is not able to result precise and adequate control, and high performance due to its insufficient bandwidth at the selected frequency. As a result, the corresponding voltage at the PCC is not fully compensated, as seen in Fig. 19. Therefore, the proposed PI–R controller offers the better performance for the DFIG system under such load conditions. Fig. 20 shows the steady-state performance of three-phase rotor currents with the use of the proposed control algorithm. These measured rotor currents have ripples due to the harmonic rejection components, which are detected from the stator volt-

age harmonic controllers and are injected into the reference rotor current values. The sinusoidal voltage after compensation, which is measured at the PCC, is also shown in this figure. In addition, the proposed method is also applicable to variablespeed DFIG wind turbines. Fig. 21 shows dynamic response of the three-phase rotor current when the rotor speed of the DFIG changes from 1100 r/min (subsynchronous speed) to 1300 r/min (supersynchronous speed). This result shows that the proposed control scheme is totally robust to the rotor speed variations even through the synchronous speed point. In all cases, the experimental results match with the simulated results using the same control strategy. Consequently, the feasibility of the proposed control scheme in harmonic rejection for the DFIG systems is clearly verified. Fig. 22 shows the experimental waveforms of relationship between the stator current, the load current, and the line current of the LSC. As seen, with a conventional vector control scheme for the LSC without harmonic compensation for the nonlinear load current, the phase line current iL a is the sinusoidal waveform. Meanwhile, the stator current isa becomes distorted due to the nonlinear load current iN a caused by the nonlinear load. The nonsinusoidal stator current can be compensated by injecting a proper line current in the LSC as presented in [13] and [19].

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Stator inductance: Ls = 0.052953 H Mutual inductance: Lm = 0.04847 H Nonlinear diode rectifier: Resistance load: 1.5 kW, 5 A REFERENCES

Fig. 22. Experimental waveforms of the stator current is a , load current iN a , and line current iL a of the LSC.

However, this paper has not concentrated on this control target as mentioned before. VI. CONCLUSION The effect of nonlinear loads on the quality of the stator output voltage at the PCC in the stand-alone DFIG is investigated clearly in this paper. To improve the PCC voltage quality, a new fundamental reference frame control scheme for fifth and seventh voltage harmonics elimination is proposed. The proposed harmonics elimination method is developed based on the PI–R rotor current controller implemented in the fundamental frame. The PI–R controller in this frame has the possibility of eliminating both seventh positive and fifth negative harmonic components of the stator voltage at the PCC without decomposing the measured rotor current. Both simulations and experimental results are shown to confirm the feasibility and effectiveness of the proposed control algorithm. In addition, experimental tests are also performed with the conventional PI regulator to compare with the proposed PI–R controller. The obtained results demonstrate that the proposed control scheme has more satisfactory performance in harmonic elimination. The control principle of proposed method can be applied to eliminate 11th, 13th, 17th, 19th. . . voltage harmonic components on the fundamental reference frame using the proposed PI–R controller tuned at 12 and 18 multiples of synchronous frequency. APPENDIX DFIG parameters: Rated power: 2.2 kW Number of poles: 6 Stator voltage: 440 V/6.5A–60 Hz Rotor voltage: 40 V/34 A Rotor resistance: Rr = 0.56 Ω Stator resistance: Rs = 2.14 Ω Rotor inductance: Lr = 0.052953 H

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Van-Tung Phan (S’07–M’11) received the M.S. and Ph.D. degrees in electrical engineering from University of Ulsan, Ulsan, Korea, in 2007 and 2010, respectively. He is currently a Research Fellow at the School of Electrical and Electronics Engineering, Nanyang Technological University, Singapore. He has been involved in industrial projects of Rolls-Royces related to cooling systems of electric machine used in marine applications. His current research interests include magnetocaloric effect, electric machine cooling system, and power electronics in the area of renewable energy resources.

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Hong-Hee Lee (S’88–M’91) received the B.S., M.S., and Ph.D. degrees in electrical engineering from Seoul National University, Seoul, Korea, in 1980, 1982, and 1990, respectively. From 1994 to 1995, he was a Visiting Professor with Texas A&M University. Since 1985, he has been with the Department of Electrical Engineering, University of Ulsan, Ulsan, Korea, where he is currently a Professor of School of Electrical Engineering. He is also the Director of the Network-based Automation Research Center (NARC), which is sponsored by the Ministry of Knowledge Economy (MKE). His research interests are power electronics, network-based motor control, and control networks. Dr. Lee is the member of Korean Institute of Power Electronics (KIPE), the Korean Institute of Electrical Engineers (KIEE), and the Institute of Control, Robotics and Systems (ICROS).