Abstract
The doubly-fed induction generator (DFIG) is considered to provide a low-reactance path in the negative-sequence system and naturally comply with requirements on the negative-sequence reactive current in emerging grid codes. This paper shows otherwise and how the control strategy of converters plays a key role in the formation of the active and reactive current components. After investigating the existing control strategies from the perspective of grid code compliance and showing how they fail in addressing emerging requirements on the negative-sequence reactive current, we propose a new coordinated control strategy that complies with reactive current requirements in grid codes in the positive- and negative-sequence systems. The proposed method fully takes advantage of the current and voltage capacities of both the rotor-side converter (RSC) and grid-side converter (GSC), which enables the grid code compliance of the DFIG under unbalanced three-phase voltages due to asymmetrical faults. The mathematical investigations and proposed strategy are validated with detailed simulation models using the Electric Power Research Institute (EPRI) benchmark system. The derived mathematical expressions provide analytical clarifications on the response of the DFIG in the negative-sequence system from the grid perspective.
θa, θb, θc Phase angles of three-phase quantities
θU+ Initial phase of positive-sequence voltage
Angle of negative-sequence voltage vector in negative phase lock loop (PLL) reference frame
Leakage factor
, Stator and rotor flux linkage vectors
Synchronous angular velocity
, Angular velocity and angle of rotor
, Angular velocity and angle of PLL
, Current vectors of stator and rotor
, Current vectors of grid-side converter (GSC) and wind turbine generator (WTG)
The maximum current of rotor-side converter (RSC)
The maximum current of GSC
I1A, I1R Positive-sequence active and reactive currents
I2A, I2R Negative-sequence active and reactive currents
, Coefficients for I1R and I2R injections
, Proportional and integral parameters of RSC current control
, Proportional and integral parameters of GSC current control
, Proportional and integral parameters of PLL control
, , Stator, rotor, and magnetizing inductances
Inductance of choke filter of GSC
Turn ratio between rotor and stator windings
, Active and reactive power
, Stator and rotor resistances
Slip
, Voltage vectors of stator and rotor
, Voltage and power references of per-unit values
* Reference value
Conjugate complex
abc, αβ Three- and two-phase reference frames
dq+, Positive and negative synchronous reference frames rotating at and
, Positive and negative PLL reference frames
Negative-sequence stator voltage reference
+, Positive- and negative-sequence components
, d- and q-axis projections of vector
g, WTG GSC and WTG
, Before and after limiter
, Stator and rotor
WIND turbine generators (WTGs) play a key role in the decarbonization of power grids and there is a worldwide increase in the share of these renewable energy sources in the generation fleet of power grids. Wind parks (WPs) consisting of WTGs should comply with a series of grid interconnection requirements introduced by grid codes [
Early grid codes [
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Fig. 1 Additional (Δ) I1R and I2R requirements in German grid code versus variation in voltage in positive- and negative-sequence systems.
There is a number of studies on the control of doubly-fed induction generator (DFIG)-based WTGs (also referred to as Type-III WTGs) to meet fault ride through (FRT) requirements including grid connection and I1R injection requirements [
In [
Given that the stator winding of the DFIG is directly coupled to the grid, a DFIG-based WTG is simply regarded as a squirrel-cage induction machine (IM) or replaced with a fixed impedance (mainly reactive) as in [
The impact of control strategies on the fault current of the DFIG has been shown to be important and plays a role in circuit breaker ratings and protection settings [
The existing I2R control strategies proposed for the FSC-based WTGs cannot be transferred to the DFIG-based WTGs owing to their differences in topology. The complexity and challenges are as follows.
1) Extra degree of freedom: the FSC is interfaced to the grid through its grid-side converter (GSC), which in consequence supplies all the fault current from WTG. The fault current of DFIG-based WTG consists of the GSC current as well as the stator current that is governed by its rotor-side converter (RSC). To generate I1R and I2R components in compliance with grid codes, eight different current references need to be coordinated, namely the active and reactive currents of the RSC and GSC in the positive- and negative-sequence systems.
2) Reduced (non-full) size converters: the GSC of the FSC is designed to convert the rated voltage and current, whereas the RSC and GSC of the DFIG are both rated to convert the slip power (typically 30% of the rated power) [
3) Special control configurations: apart from the classical balanced positive-sequence control (BPSC), a well-known control strategy for DFIG-based WTGs under unbalanced voltages is to generate negative-sequence currents through the RSC to eliminate the double grid frequency oscillations in electromagnetic torque (Tem) [
This paper has two main contributions. We first derive detailed mathematical expressions of WTG currents in the positive- and negative-sequence systems under existing control strategies. The objective is to fill the gap of knowledge regarding the DFIG’s detailed behaviors in the negative-sequence system from the grid perspective. Then, we propose a new coordinated control scheme for DFIG converters, called flexible control of the reactive current in the positive- and negative-sequence systems and denoted by PNSC-I12R, to comply with I1R and I2R requirements in emerging grid codes under practical unbalanced voltages following asymmetrical faults on the grid.
The remainder of this paper is organized as follows. Section II briefly introduces the space vector notation and then deduces mathematical equations governing the behavior of IM of DFIG in the positive- and negative-sequence systems. In Section III, the existing control strategies for DFIG-based WTGs are introduced. In Sections IV and V, the positive- and negative-sequence currents of the DFIG are analyzed under the existing strategies. The new coordinated control scheme PNSC-I12R is proposed in Section VI. In Section VII, the performances of DFIG-based WTGs under the existing and proposed control strategies are compared by simulations. Finally, conclusions are drawn in Section VIII.
This section briefly presents the space vector notation used in this paper and then develops basic equations of the IM in the positive- and negative-sequence systems. Further details on space vector theory and dynamic modeling of DFIG are available in [
In the steady state, the frequency of the three-phase voltages, currents, and flux linkages are the same as the grid frequency. A generic set of three-phase variables is considered, which is expressed as:
(1) |
where x stands for the instantaneous value; and stands for the magnitude.
Due to the three-phase transformer connection in WPs, there is no zero-sequence component in the voltages, currents, or flux linkages of the DFIG. By applying the Clark transformation, the variables can be transformed into the two-phase stationary reference () as:
(2) |
By rewriting (2) in the space vector form and then applying symmetrical components [
(3) |
(4) |
(5) |
(6) |
In this paper, vectors are represented in italic and bold type. The superscript indicates the reference frame that the vector is measured.
The above expressions indicate that three-phase voltages, currents, and flux linkages of a DFIG can be regarded as the superposition of projections of a positive-sequence vector rotating at and a negative-sequence vector rotating at . The locus of the resultant vector is an ellipse [
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Fig. 2 Asymmetrical three-phase variables and their space vector expressions.
By changing the reference frame from to and , the vector measurements become:
(7) |
(8) |
The equations indicate that, in the frame, positive-sequence components correspond to a stationary vector, and the negative-sequence components correspond to a vector rotating with .
In the frame, using the motor convention, the dynamic model of the DFIG can be expressed in the space vector form as:
(9) |
By substituting (3) into (9), the dynamics can be decomposed into positive- and negative-sequence quantities as:
(10) |
(11) |
By substituting (4) into (10), the model in the positive-sequence system is obtained as:
(12) |
(13) |
Since positive-sequence components correspond to a stationary vector in the dq+ frame, it is possible to remove the derivation terms in (12). By further ignoring the voltage drop on resistances, the positive-sequence quantities become:
(14) |
By substituting (5) into (11), the model in the negative-sequence system is obtained as:
(15) |
If the derivation terms are removed and the voltage drop on resistances are neglected, the negative-sequence quantities become:
(16) |
The control strategies of the RSC and GSC are designed to independently regulate the active power and reactive power [
To achieve SVO, the BPSC employs a synchronous reference frame phase lock loop (SRF-PLL) to keep the d-axis of the control reference frame (denoted as PLL+) oriented along the positive-sequence voltage vector. A basic block diagram of the SRF-PLL is shown in
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Fig. 3 Basic block diagram of SRF-PLL.
When SVO is achieved, the angles of the PLL+ with respect to the and frames are:
(17) |
Moreover, according to (5) and (17), the measurements of the positive- and negative-sequence vectors in the PLL+ are:
(18) |
(19) |
According to (19), the negative-sequence voltage vector introduces a 120 Hz oscillation to . A low-pass filter (LPF) is adopted to filter this disturbance.
Under SVO, the positive-sequence voltage vector is:
(20) |
The positive-sequence active and reactive power at the stator and GSC sides are:
(21) |
(22) |
where and are the positive-sequence active currents at the GSC and stator sides, respectively; and and are the positive-sequence reactive currents at the GSC and stator sides, respectively.
If FRT is activated, the required I1R in grid codes is typically given by:
(23) |
The I1R is first contributed from the stator side (controlled by the RSC). By substituting (23) into (14), the required positive-sequence rotor current reference (before the limiter) is:
(24) |
If the current reference in (24) is greater than the RSC current capacity, the GSC will generate the remaining I1R as:
(25) |
Different from the normal operation, the priority is switched to reactive current during FRT as shown in
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Fig. 4 Limiter and priority settings of BPSC during FRT. (a) RSC. (b) GSC.
To realize the four positive-sequence current references in
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Fig. 5 Coupled inner-loop control in BPSC. (a) RSC. (b) GSC.
The impact of negative-sequence currents on the coupled inner-loop control should be highlighted here. As given in (19), negative-sequence currents introduce 120 Hz disturbances in measurements (marked by red dotted block in
The PNSC-Tem is designed to independently control the positive- and negative-sequence quantities. This paper also studies the PNSC-Tem under SVO as a general case.
To decompose the sequence quantities from measurements, a decoupled double synchronous reference frame phase lock loop (DDSRF-PLL) [

Fig. 6 Basic block diagram of DDSRF-PLL.
The positive-sequence current references of the PNSC-Tem strategy are the same as those of the BPSC. In addition, the negative-sequence rotor current references of the PNSC-Tem are carefully designed to eliminate the double grid frequency oscillations in Tem [
(26) |
Based on (26), the magnitude relationship between positive- and negative-sequence rotor currents is expressed as:
(27) |
To avoid overcurrent, the current limitation and priority level are set as
(28) |

Fig. 7 Limiter and priority settings of PNSC-Tem and existing coordinated control during FRT. (a) RSC. (b) GSC.
In addition to the PNSC-Tem, the negative-sequence current references of GSC have been used in the existing coordinated control strategy to provide I2R. In [
(29) |
To realize these eight current references in

Fig. 8 Decoupled inner-loop control of RSC in PNSC-Tem. (a) Positive sequence. (b) Negative sequence.

Fig. 9 Decoupled inner-loop control of GSC in PNSC-Tem. (a) Positive sequence. (b) Negative sequence.
Based on the expressions of the DFIG in Section II and the space vector expressions of the BPSC in Section III, this section mathematically analyzes the positive- and negative-sequence current contributions of a DFIG-based WTG controlled with the BPSC strategy.
The reference tracking performance of the coupled inner-loop control of the BPSC is good [
(30) |
Based on (14), the positive-sequence current contribution of the WTG is expressed as:
(31) |
Based on Section III-A and
(32) |
By substituting (19) into (32), it follows that:
(33) |
Since the angular velocity of the disturbance signal is , the equivalent gain of the integrator is negligible . So, the integral term in (33) is neglected. According to (19), the negative-sequence rotor voltage vector in the frame is expressed as:
(34) |
By substituting (34) into (16), the negative-sequence equivalent circuit of the DFIG under the BPSC is obtained as in
(35) |

Fig. 10 Negative-sequence equivalent circuit of DFIG under BPSC.
where is defined as the negative-sequence equivalent impedance of the DFIG under the BPSC and given by:
(36) |
where , .
Note that consists of not only a reactance (imaginary part) but also a resistance. As a result, the negative-sequence stator current includes both the I2A and I2R.
Similarly, the negative-sequence current of the GSC is:
(37) |
So, the negative-sequence current contribution of the DFIG-based WTG under the BPSC strategy is:
(38) |
The current capacity of RSC and GSC is determined by the switching device, typically the insulated gate bipolar transistor (IGBT). It withstands up to 200% of its rated current but only for a very short period (typically no more than 10 ms). It can continuously withstand 120% of its rated current [
In the BPSC strategy, almost all the current capacity of RSC is assigned to positive-sequence currents. As a result, when there are negative-sequence components circulating in the rotor winding, the rotor current will easily exceed 1.2 p.u..
According to
(39) |
Consider the practical parameters of a 1.5 MW DFIG-based WTG given in
(40) |
This indicates that, under the BPSC, the coupled inner-loop control introduces a low-impedance path through rotor winding (see
Based on the DFIG equations in Section II and the space vector formulations in Section III, this section theoretically analyzes the positive- and negative-sequence current contributions of a DFIG-based WTG controlled with the PNSC-Tem and the existing coordinated control.
The positive-sequence current contribution of a DFIG-based WTG under the PNSC-Tem has the same form in (31).
The PNSC-Tem and the existing coordinated control have independent RSC inner-loop controllers to regulate the negative-sequence rotor currents, as shown in
(41) |
Based on (16), the negative-sequence current of DFIG is:
(42) |
where the negative-sequence current of GSC should be accounted when the existing coordinated control is employed.
By substituting (26) into (42), we have:
(43) |
Note that, the d-axis component of does not correspond to I2A since is not aligned with the negative sequence voltage vector. Similarly, its q-axis component does not correspond to I2R. The negative-sequence voltage reference frame needs to be introduced to align these components with I2A and I2R.
In steady state, the transformation from to frames is:
(44) |
where is from the DDSRF-PLL in
By substituting (44) into (26), the negative-sequence rotor current in is expressed as:
(45) |
By substituting (45) into (43), the I2R contributed by WTG is expressed as:
(46) |
During FRT, will be negative to provide the required I1R from the stator side (see (24)). As a result, the second term of (46) is also negative, which will increase the negative-sequence voltage level and voltage unbalance because the required I2R is positive as shown in
Since the existing coordinated control and PNSC-Tem have the same RSC negative-sequence control, the I2R contributed by stator is also negative. Although the GSC negative-sequence control is designed to provide positive I2R, according to (46), the I2R contributed by the WTG cannot reach the required value.
According to the steady-state relationship in Section II, the rotor voltage demand of the RSC control can be expressed as:
(47) |
(48) |
(49) |
Since the PNSC-Tem and the existing coordinated control have the same RSC control, they have the same rotor voltage demand. By substituting (45) into (49) and considering that is dominated during FRT, (49) can be simplified as:
(50) |
Since is negative during FRT, the control target of eliminating the oscillation of Tem increases the rotor voltage demand. As a result, under the PNSC-Tem and the existing coordinated control, the RSC is more likely to be over-modulated under voltage imbalance. Considering the two-level VSC and the space vector modulation, the RSC voltage capacity seen from the stator winding in per unit should satisfy:
(51) |
When the rotor voltage demanded by the decoupled inner-loop controller is greater than the maximum value in (51), the RSC cannot achieve the rotor voltage references and the rotor current is out of control. As a result, the overcurrent protection will be triggered again.
The analysis in Sections IV and V shows that the existing control solutions (BPSC, PNSC-Tem, and the existing coordinated control) cannot comply with I2R requirements under severe voltage unbalance following asymmetrical faults at the grid side. To overcome this challenge, this section proposes a new coordinated control strategy (PNSC-I12R) for the DFIG converters.
First, the new proposed strategy needs to comply with the I1R requirements, and the positive-sequence current references in Section III-A are adopted.
According to [
(52) |
By substituting (52) into (16), the rotor current reference before the limiter is expressed as:
(53) |
When the RSC current capacity is not sufficient, the limiter will function. The negative-sequence stator current taking the reference current after the limiter is given by:
(54) |
The rest of I2R will be contributed by GSC, and the I2R current reference before the limiter is:
(55) |
I2A is set to be 0 to spare the current capacity of converters.
To avoid overcurrent and meet I1R and I2R requirements, the priority levels are set as shown in

Fig. 11 Limiter and priority settings in proposed control strategy PNSC-I12R. (a) RSC. (b) GSC.
A schematic of the PNSC-I12R is shown in

Fig. 12 Schematic of the proposed coordinated control strategy PNSC-I12R.
Since is set to zero, the negative-sequence rotor voltage in (49) becomes:
(56) |
Under the PNSC-I12R scheme, is negative to provide the required I2R (as shown in (53)). As a result, the rotor voltage demand of the PNSC-I12R is smaller than that of the PNSC-Tem and the existing coordinated control. It enables the DFIG-based WTG to provide the required I1R and I2R within the current and voltage capacities of converters under severe voltage unbalances following asymmetrical short circuits.
The 120 kV 60 Hz EPRI benchmark system in
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Fig. 13 Single-line diagram of 120 kV 60 Hz EPRI benchmark system.
The simulation results of the DFIG under the BPSC strategy are shown in the left column of

Fig. 14 Simulation results of DFIG-based WTG under three different control strategies. (a) Three-phase voltage at faulted bus. (b) Three-phase stator voltage. (c) Magnitudes of positive- and negative-sequence stator voltage vectors. (d) Positive-sequence active and reactive currents. (e) Negative-sequence active and reactive currents. (f) Tem. (g) Three-phase rotor current and limit. (h) Rotor voltage demand and limit.
The difference between the PNSC-Tem and the existing coordinated control is on the negative-sequence control of the GSC. The existing coordinated control [

Fig. 15 Resultant I2R and its components under the existing coordinated control.
The simulation results of the DFIG under the PNSC-I12R are shown in the right column of
Moreover, as shown in
In terms of I1R, all the three control strategies have similar performances that comply with the requirement in (23), as shown in
In terms of I2R, the BPSC and the existing coordinated control cannot meet the requirement in (52) as shown in
In some recent grid codes, WTGs are not only required to provide I1R but also I2R. This paper first investigates the I2R characteristics of DFIG-based WTGs under existing control strategies, namely the BPSC, PNSC-Tem, and an existing coordinated control. Both the mathematical analysis and simulations show that these control strategies fail to comply with the requirements on I2R under severe voltage unbalance due to asymmetrical faults. Then, this paper proposes a new coordinated control strategy denoted by PNSC-I12R to solve this shortcoming of the existing control schemes.
The performances of the above control strategies are summarized as follows.
1) Under the conventional BPSC strategy, almost all the current capacity of RSC is allocated to the positive-sequence currents. Moreover, the coupled inner-loop control of RSC introduces a low-impedance path through the rotor winding with a resistive component. Consequently, the DFIG contributes not only I2R but also I2A to the grid, and the negative-sequence rotor current is also significant. The I2A and I2R components can be simply predicted with the proposed negative-sequence equivalent impedance in (38). Under practical voltage unbalance due to asymmetrical faults, the rotor current would easily exceed the current capacity of the RSC (1.2 p.u.) and trigger overcurrent and crowbar protections.
2) Under the PNSC-Tem and the existing coordinated control, after fulfilling the I1R requirement, the rest of the RSC current capacity is allocated to the negative-sequence current to eliminate the double grid frequency oscillations in Tem. However, from the grid perspective, the elimination of the double grid frequency oscillations is achieved at the expense of producing an I2R that is the opposite of what is required. As a result, under practical voltage unbalance following asymmetrical short circuits, even though the existing coordinated control provides a positive I2R through the GSC, the resultant I2R is still insufficient. It cannot help suppress overvoltages on healthy phases. On the contrary, it aggravates the overvoltage problem under unbalanced fault conditions. Moreover, under these control strategies, the rotor voltage demand of the RSC control can easily exceed the maximal value. It will result in RSC over-modulation and make the rotor current out of control.
3) The proposed coordinated control strategy, i.e., PNSC-I12R, primarily allocates the current capacity to the I1R and I2R components. The DDSRF-PLL provides the reference frames ( and ) for the evaluation of the active and reactive components in the positive- and negative-sequence systems. Then, eight different current references are calculated according to the proposed expressions. On one hand, the control target is proven to effectively reduce the rotor voltage demand of the RSC control. On the other hand, this strategy reduces the negative-sequence and healthy phase voltages at the grid side effectively by making full use of the current and voltage capacities of the converters. These advantages make the proposed control strategy become a better solution for practical voltage unbalances due to asymmetrical faults. In addition, the amplitude of the oscillations in Tem is also less compared with the BPSC.
Considering the proposed control strategy and the analytical investigations in this paper, future work and applications include: ① developing sequence-domain circuit models of DFIG-based WTGs and WPs by considering various types of control strategies and grid codes for practical short circuit studies; ② investigating the impact of different control strategies on protection elements such as negative sequence-based elements including the differential protection element based on the alpha plane and fault identification element.
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