Coordinated Control of Standalone Brushless Doubly-Fed Induction Generator for Load Disturbance Suppression in Microgrid

Abstract

The anti-load-disturbance capability is one of the most important capabilities in a microgrid. In comparison with the grid-connected brushless doubly-fed induction generator (BDFIG), the output voltage of the standalone BDFIG in a microgrid is more susceptible to load disturbances. In order to address this issue, this paper presents a coordinated control method based on both the machine side converter (MSC) and line side converter (LSC) to reduce the amplitude of power winding (PW) voltage fluctuation and shorten transient response time, so as to significantly reduce the influence of the load disturbance on the output voltage under the limited power converter capacity. The proposed control strategy is validated through experiments conducted on a 3 kW wound-rotor BDFIG.

1. Introduction

In recent years, brushless doubly-fed induction generators (BDFIGs) have received more and more attention and development [1,2,3]. The BDFIG is equipped with two stator winding sets featuring distinct pole pairs, along with a specially designed rotor. The first winding, designated as the power winding (PW), serves as the main stator winding. The second winding, referred to as the control winding (CW), is utilized for control purposes [4,5]. These two stator windings are not directly linked but are instead coupled indirectly through the rotor windings. Compared with the traditional doubly-fed induction generator (DFIG), the special structure of the BDFIG eliminates the brushes and slip rings, thus greatly improving the stability and reducing the maintenance cost, which also makes the brushless doubly-fed motor more promising [6,7].

At present, the BDFIG can be employed at both grid-connected and standalone power generation modes in microgrids [8,9]. The grid-connected power generation system regulates the active and reactive power of the BDFIG [10], while the standalone power generation system needs to maintain the amplitude and frequency of the PW voltage constant [11]. Compared to the grid-connected BDFIG, the output voltage of the standalone BDFIG in microgrid is more susceptible to load disturbances, which places higher requirements on the stability control of the output voltage [12,13].

Some control methods have been proposed for BDFIG. The amplitude and frequency control method has been studied in [14,15], in which the amplitude and frequency of PW voltage are controlled by the amplitude and frequency of CW current. This method is simple and easy to implement, but its response is slow and cannot control the phase of the PW voltage. A vector control method based on the orientation of the PW voltage is mentioned in [16], which combines the relationship between the d- and q-axis PW voltages and the d- and q-axis CW currents, thereby controlling the amplitude and phase of the PW voltage. An improved sensorless control strategy was proposed in [17], which enables smooth and stable regulation of both active and reactive power, even under severe grid voltage fluctuations and parameter mismatches. Ref. [18] examines the low-voltage ride-through (LVRT) control of the BDFIG’s MSC and reveals that the BDFIG exhibits enhanced LVRT capability compared to the traditional DFIG. With the aim of enhancing the AC voltage control performance of DFIG in wind power systems, the study in [19] investigates an artificial neural network (ANN)-based control strategy, demonstrating its superiority over conventional proportional-integral (PI) controllers in both response time and stability.

In the standalone BDFIG power generation system, the PW voltage amplitude is one of the main control targets, which is susceptible to load disturbances. Some control methods have been proposed to address this issue. A vector control method utilizing CW current orientation is presented in [20], which accelerates the response of the CW current control loop through decoupling and feedforward compensation. However, this control method just only improves the CW current control loop, and does not significantly enhance the PW voltage quality under heavy load disturbance due to the limited machine side converter (MSC) capacity. In Ref. [21], a feedforward compensation method by means of PW flux orientation is mentioned. This method uses the d- and q-axis PW currents to calculate the feedforward compensation current of the d- and q-axis CW currents, thereby improving the system response speed and strengthening anti-load disturbance ability. This method not only requires a large number of machine parameters, but also cannot provide good results when the MSC capacity is insufficient. For the suppression of load disturbance by line side converter (LSC), a method is introduced in grid-connected power generation system. In the grid-connected system, when the grid voltage drops, the LSC transmits reactive current to the grid to improve the grid voltage [22]. For the standalone power generation system, when the PW voltage drops due to the inductive load, the LSC can deliver reactive current to the load to suppress the PW voltage fluctuation. In Ref. [23], the LSC is employed to supply the reactive power to the PW for improving the PW voltage stability. This control method needs no machine parameters and has good response speed, but the effect is unsatisfactory when the power factor of the load is high or the capacity of the LSC is not enough.

All of the control methods mentioned above only use the single power converter (i.e., MSC or LSC) as a means to suppress load disturbances, and do not make full use of the capacity of the dual power converters in the control system. In order to address this issue, this paper develops a new coordinated control method for the standalone BDFIG, which can make full use of the redundant capacity of MSC and LSC to significantly reduce the PW voltage amplitude fluctuation and shorten transient response time.

2. System Topology and Mathematical Model

2.1. Topology of Standalone BDFIG System

The system topology of the BDFIG-based AC power generation system is illustrated in Figure 1. The implemented power converter comprises two back-to-back voltage source converters, i.e., MSC and LSC, with a common dc bus. This topological structure can be used for either grid-connected or standalone mode. A critical distinction between these modes is the connection at the point of common coupling (PCC): it is coupled to the grid in the former case, and to the local loads in the latter.

The grid-connected BDFIG system is suitable for variable-speed constant-frequency (VSCF) applications in hydropower and wind generation. In such configurations, the primary control goal is to manage the active and reactive power delivered to the PW, typically accomplished through the MSC. Meanwhile, the LSC serves to stabilize the dc bus voltage irrespective of the power flow direction through the MSC. Additionally, the LSC can support fault ride-through capability during grid disturbances.

Standalone BDFIG systems are employed in scenarios such as remote wind or hydrogeneration, shipboard shaft generation systems, and so on. Unlike grid-connected operation, the standalone system aims to maintain constant amplitude and frequency of the PW voltage under varying rotor speeds and load conditions. Here, the CW is regulated via the MSC to establish a stable PW voltage for supplying the loads. The LSC ensures dc bus voltage stability and further contributes to damping voltage fluctuations at the PCC by injecting or absorbing reactive current as needed.

2.2. Dynamic Mathematical Model of BDFIG

The BDFIG supports several operational modes, including the doubly-fed, cascaded, and induction modes [5]. Among them, the doubly-fed mode is considered the most advantageous, in which the rotor speed can be described by

$${\omega }_r={\displaystyle \frac{{\omega }_1+{\omega }_2}{p_1+p_2}}$$

(1)

where p₁ and p₂ are the pole pair numbers of PW and CW, respectively; ω_r, ω₁ and ω₂ are the rotor speed, PW angular frequency, and CW angular frequency, respectively.

When ω₂ is zero, the rotor speed is called the natural synchronous speed ω_N. The rotor speed above ω_N is the super-synchronous speed, while that below ω_N is the sub-synchronous speed. To maintain the constant PW frequency ω₁ under varying rotor speeds, the CW frequency ω₂ should be regulated by

$${\omega }_2={\omega }_r(p_1+p_2)-{\omega }_1.$$

(2)

In the dq reference frame rotating at the angular speed ω₁, the dynamic mathematical model of the BDFIG is established as follows:

$${\mathit{U}}_1=R_1{\mathit{I}}_1+s{\mathit{\psi }}_1+j{\omega }_1{\mathit{\psi }}_1$$

(3)

$${\mathit{\psi }}_1=L_1{\mathit{I}}_1+L_{1r}{\mathit{I}}_r$$

(4)

$${\mathit{U}}_2=R_2{\mathit{I}}_2+s{\mathit{\psi }}_2+j[{\omega }_1-(p_1+p_2){\omega }_r]{\mathit{\psi }}_2$$

(5)

$${\mathit{\psi }}_2=L_2{\mathit{I}}_2+L_{2r}{\mathit{I}}_r$$

(6)

$$0=R_r{\mathit{I}}_r+s{\mathit{\psi }}_r+j({\omega }_1-p_1{\omega }_r){\mathit{\psi }}_r$$

(7)

$${\mathit{\psi }}_r=L_r{\mathit{I}}_r+L_{2r}{\mathit{I}}_2+L_{1r}{\mathit{I}}_1$$

(8)

where U, I, and ψ represent voltage, current, and flux vectors, respectively; the subscripts 1, 2, and r indicate PW, CW, and rotor, respectively; R₁, R₂, and R_r represent resistances of PW, CW, and rotor, respectively; L₁, L₂, and L_r represent self-inductances of PW, CW, and rotor; L_1r and L_2r represent coupling inductances between the stator and rotor windings.

3. Performance Analysis of the Traditional Control Scheme Under Load Disturbance

In the traditional control scheme for the standalone BDFIG system, the MSC can be regarded as an individual voltage source to regulate the air-gap flux. And the LSC can output power to loads or absorb power from PW for maintaining the dc bus voltage constant. In steady state, the LSC together with the filter can be seen as connected to a constant voltage source. Under this condition, the combination of the LSC and the filter can be regarded as a current source, which can output current to loads at the super-synchronous rotor speed and also can absorb current from PW at the sub-synchronous rotor speed.

According to the derivation in Section 1, the PW and CW voltages in steady state can be expressed as

$${\mathit{U}}_1=[R_1+j{\omega }_1(L_1-{\displaystyle \frac{L_{1r}^2}{L_r}})]{\mathit{I}}_1-{\displaystyle \frac{j{\omega }_1{L}_{1r}{L}_{2r}}{L_r}}{\mathit{I}}_2$$

(9)

$${\mathit{U}}_2=[R_2+j{\omega }_2({\displaystyle \frac{L_{2r}^2}{L_r}}-L_2)]{\mathit{I}}_2-{\displaystyle \frac{j{\omega }_2{L}_{1r}{L}_{2r}}{L_r}}{\mathit{I}}_1$$

(10)

Since the positive direction of the PW current is based on the motor convention in the dynamic mathematical model of BDFIG shown in Equations (3)–(8), it is necessary to set ${\mathit{I}}_1^{\prime }=-{\mathit{I}}_1$ to analyze the performance of the BDFIG under the generation mode. Hence, the PW voltage described in Equation (9) can be rewritten as

$${\mathit{U}}_1={\mathit{E}}_1-R_1{\mathit{I}}_1^{\prime }-j{\omega }_1{L}_1^{\prime }{\mathit{I}}_1^{\prime }$$

(11)

where ${\mathit{E}}_1=-(j{\omega }_1{L}_{1r}{L}_{2r}/L_r){\mathit{I}}_2$ is defined as the electromotive force (EMF) in the PW, which is induced by the CW current, and $L_1^{\prime }=L_1-L_{1r}^2/L_r$.

Similarly, the CW voltage in Equation (10) can be rewritten as

$${\mathit{U}}_2=R_2{\mathit{I}}_2+j{\omega }_2{L}_2^{\prime }{\mathit{I}}_2+{\mathit{E}}_2$$

(12)

where ${\mathit{E}}_2=-(j{\omega }_2{L}_{1r}{L}_{2r}/L_r){\mathit{I}}_1^{\prime }$ is defined as the EMF in the PW, which is induced by the PW current, and $L_2^{\prime }=L_{2r}^2/L_r-L_2$.

Based on the above analysis and Equations (11) and (12), the simplified equivalent circuit of the standalone BDFIG system can be illustrated in Figure 2.

When the load is changed and the CW current is not adjusted in time, the E₁ induced by the CW current can be regarded as unchanged. Consequently, the variation in the PW voltage can be expressed as

$$\mathsf{\Delta }{\mathit{U}}_1=-R_1\mathsf{\Delta }{\mathit{I}}_1^{\prime }-j{\omega }_1{L}_1^{\prime }\mathsf{\Delta }{\mathit{I}}_1^{\prime }$$

(13)

where $\mathsf{\Delta }{\mathit{U}}_1$ and $\mathsf{\Delta }{\mathit{I}}_1^{\prime }$ represent the variation in the PW voltage and PW current vectors, respectively.

In general, the value of R₁ is much smaller than that of ${\omega }_1{L}_1^{\prime }$, and the expression of the PW voltage variation can be simplified as

$$\mathsf{\Delta }{\mathit{U}}_1\approx -j{\omega }_1{L}_1^{\prime }\mathsf{\Delta }{\mathit{I}}_1^{\prime }.$$

(14)

Given that the initial phase angle of the PW voltage is zero, the PW current ${\mathit{I}}_1^{\prime }$ can be expressed as

$${\mathit{I}}_1^{\prime }=I_{1p}^{\prime }+j{I}_{1q}^{\prime }$$

(15)

where $I_{1p}^{\prime }$ and $I_{1q}^{\prime }$ indicate the active and reactive currents of PW, respectively.

Substituting Equation (15) with (14), the PW voltage variation can be given by

$$\mathsf{\Delta }{\mathit{U}}_1\approx -{\omega }_1{L}_1^{\prime }\mathsf{\Delta }{I}_{1q}^{\prime }-j{\omega }_1{L}_1^{\prime }\mathsf{\Delta }{I}_{1p}^{\prime }.$$

(16)

In the traditional control scheme, the LSC operates in the unit power factor, which means that the PW must therefore supply the entirety of the load’s reactive current. Equation (16) indicates that a substantial variation in the PW reactive current due to load changes can result in considerable PW voltage fluctuations. This effect is particularly pronounced during the direct start-up of induction motors. In addition, variations in the PW active current also contribute to significant voltage fluctuations at sub-synchronous rotor speeds. This occurs because, within this speed range, the PW must supply both the total active load current and the active current for the LSC.

4. Design of Control Scheme

To address the significant PW voltage fluctuations induced by load disturbances, a control scheme utilizing dual-converter compensation is derived in this section.

4.1. Basic PW Voltage Control Loop

The d- and q-axis component expressions of Equations (7) and (8) can be written as

$$\left.\begin{array}{l}0=R_r{i}_{rd}+s{\psi }_{rd}+({\omega }_1-p_2{\omega }_r){\psi }_{rq}\\ 0=R_r{i}_{rd}+s{\psi }_{rq}-({\omega }_1-p_2{\omega }_r){\psi }_{rd}\end{array}\right\}$$

(17)

$$\left.\begin{array}{l}{\psi }_{rd}=L_r{i}_{rd}+L_{1r}{i}_{1d}+L_{2r}{i}_{2d}\\ {\psi }_{rq}=L_r{i}_{rq}+L_{1r}{i}_{1q}+L_{2r}{i}_{2q}\end{array}\right\}$$

(18)

where ψ_rd and ψ_rq represent rotor flux d- and q-axis components, i_rd and i_rq rotor current d- and q-axis components, i_1d and i_1q PW current d- and q-axis components, i_2d and i_2q CW current d- and q-axis components.

Substituting Equation (18) with (17), the d- and q-axis rotor currents can be expressed as

$$\left.\begin{array}{l}{i}_{rd}=-{\displaystyle \frac{M}{L_r}}\left(L_{1r}{i}_{1d}+L_{2r}{i}_{2d}\right)+\left(1-M\right){\displaystyle \frac{\left({\omega }_1-p_1{\omega }_r\right)\left(L_{1r}{i}_{1q}+L_{2r}{i}_{2q}\right)}{R_r+L_{r}s}}\\ i_{rq}=-{\displaystyle \frac{M}{L_r}}\left(L_{1r}{i}_{1q}+L_{2r}{i}_{2q}\right)-\left(1-M\right){\displaystyle \frac{\left({\omega }_1-p_1{\omega }_r\right)\left(L_{1r}{i}_{1d}+L_{2r}{i}_{2d}\right)}{R_r+L_{r}s}}\end{array}\right\}$$

(19)

where $M={\displaystyle \frac{L_r^2{s}^2+L_r{R}_{r}s+L_r^2{({\omega }_1-p_1{\omega }_r)}^2}{{(L_{r}s+R_r)}^2+L_r^2{({\omega }_1-p_1{\omega }_r)}^2}}$.

The zeros and poles of the expressions of the variable M are very close. Hence, the variable M can be approximated to 1. Consequently, the d- and q-axis rotor currents can be simplified as

$$\left.\begin{array}{l}{i}_{rd}\approx -{\displaystyle \frac{L_{1r}{i}_{1d}+L_{2r}{i}_{2d}}{L_r}}\\ i_{rq}\approx -{\displaystyle \frac{L_{1r}{i}_{1q}+L_{2r}{i}_{2q}}{L_r}}\end{array}\right\}.$$

(20)

The d- and q-axis component expressions of Equations (3) and (4) can be written as

$$\left.\begin{array}{l}{u}_{1d}=R_1{i}_{1d}+s{\psi }_{1d}-{\omega }_1{\psi }_{1q}\\ u_{1q}=R_1{i}_{1q}+s{\psi }_{1q}+{\omega }_1{\psi }_{1d}\end{array}\right\}$$

(21)

$$\left.\begin{array}{l}{\psi }_{1d}=L_1{i}_{1d}+L_{1r}{i}_{rd}\\ {\psi }_{1q}=L_1{i}_{1q}+L_{1r}{i}_{rq}\end{array}\right\}$$

(22)

where u_1d and u_1q represent PW voltage d- and q-axis components, ψ_1d and ψ_1q indicate PW flux d- and q-axis components.

At an equilibrium point under steady-state conditions, the PW flux can be regarded as the constant quantity. Hence, Equation (21) can be simplified as

$$\left.\begin{array}{l}{u}_{1d}=R_1{i}_{1d}-{\omega }_1{\psi }_{1q}\\ u_{1q}=R_1{i}_{1q}+{\omega }_1{\psi }_{1d}\end{array}\right\}.$$

(23)

Substituting Equations (20) and (22) with Equation (23), the d- and q-axis PW voltages can be rewritten as

$$\left.\begin{array}{l}{u}_{1d}=R_1{i}_{1d}+{\omega }_1\left({\displaystyle \frac{L_{1r}^2}{L_r}}-L_1\right)i_{1q}+{\omega }_1{\displaystyle \frac{L_{1r}{L}_{2r}}{L_r}}{i}_{2q}\\ u_{1q}=R_1{i}_{1q}-{\omega }_1\left({\displaystyle \frac{L_{1r}^2}{L_r}}-L_1\right)i_{1d}-{\omega }_1{\displaystyle \frac{L_{1r}{L}_{2r}}{L_r}}{i}_{2d}\end{array}\right\}.$$

(24)

In Equation (24), the first two terms of the expressions of u_1d and u_1q are related to the PW current. Since the PW current is affected by the load and the rotor speed, the first two terms of each expression in Equation (24) are disturbance terms. Hence, Equation (24) can be rewritten as

$$\left.\begin{array}{l}{u}_{1d}=D_d+K_d{i}_{2q}\\ u_{1q}=D_q-K_q{i}_{2d}\end{array}\right\}$$

(25)

where

$$K_d=K_q={\omega }_1{\displaystyle \frac{L_{1r}{L}_{2r}}{L_r}}$$

(26)

$$D_d=R_1{i}_{1d}+{\omega }_1\left({\displaystyle \frac{L_{1r}^2}{L_r}}-L_1\right)i_{1q}$$

(27)

$$D_q=R_1{i}_{1q}-{\omega }_1\left({\displaystyle \frac{L_{1r}^2}{L_r}}-L_1\right)i_{1d}.$$

(28)

K_d and K_q indicate the linear relationship between the PW voltage and CW current. D_d and D_q represent the disturbance terms caused by the load and the rotor speed.

From Equation (25), ignoring the disturbance terms D_d and D_q, it can be noted that the voltages u_1d and u_1q exhibit linear dependence on the currents i_2q and i_2d, respectively. This linear relationship allows u_1d and u_1q to be regulated via i_2q and i_2d, respectively, using two PI controllers. The output of the two PI controllers can serve as the reference values of the CW currents i_2q and i_2d. In addition, the terms D_d + K_di_2q and D_q − K_qi_2d can be regarded as the controlled plants. Based on the above analysis, the basic PW voltage control loop can be presented in Figure 3.

4.2. Load Disturbance Suppression Based on MSC

According to Kirchhoff’s current law, the currents of the PW, load, and LSC are related, and the relationship can be described as follows:

$$\left.\begin{array}{l}{i}_{1d}={{\displaystyle i}}_{ld}{{\displaystyle -i}}_{sd}\\ i_{1q}={{\displaystyle i}}_{lq}{{\displaystyle -i}}_{sq}\end{array}\right\}.$$

(29)

where i_sd and i_sq are the d- and q-axis components of LSC current, and i_ld and i_lq are the d- and q-axis components of load current.

The CW power passes through MSC and is eventually delivered to the load by LSC. In practical applications, the BDFIG mainly works near the natural synchronous speed, so that the CW power is much smaller than the PW power. Hence, the LSC current is very small compared to the PW current and can be ignored. Consequently, Equation (29) can be simplified as

$$\left.\begin{array}{l}{i}_{1d}\approx {{\displaystyle i}}_{ld}\\ i_{1q}\approx {{\displaystyle i}}_{lq}\end{array}\right\}.$$

(30)

Substituting Equation (30) with Equations (27) and (28), Equations (27) and (28) can be approximated as

$${{\displaystyle D}}_d\approx R_1{i}_{ld}+{{\displaystyle \omega }}_1({\displaystyle \frac{{{\displaystyle L}}_{1r}^2}{{{\displaystyle L}}_r}}-{{\displaystyle L}}_1)i_{lq}$$

(31)

$${{\displaystyle D}}_q\approx R_1{i}_{lq}+{{\displaystyle \omega }}_1({\displaystyle \frac{{{\displaystyle L}}_{1r}^2}{{{\displaystyle L}}_r}}-{{\displaystyle L}}_1)i_{ld}.$$

(32)

Due to the effect of the disturbance terms D_d and D_q, the dynamic performance of the PW voltage control loop would be severely degraded, especially under great load disturbance. Hence, the compensation terms have to be added to the PW voltage control loop to suppress the load disturbance.

Substituting Equations (31) and (32) to Equation (25), Equation (25) can be rewritten as

$$\left.\begin{array}{l}{i}_{2q}={\displaystyle \frac{u_{1d}}{K_d}}+{\alpha }_1{i}_{ld}+{\alpha }_2{i}_{lq}\\ i_{2d}=-{\displaystyle \frac{u_{1q}}{K_q}}+{\alpha }_2{i}_{ld}-{\alpha }_1{i}_{lq}\end{array}\right\}$$

(33)

where ${{\displaystyle \alpha }}_1=-\left(R_1{L}_r\right)/\left({\omega }_1{L}_{1r}{L}_{2r}\right)$, ${{\displaystyle \alpha }}_2=\left(L_1{L}_r-L_{1r}^2\right)/\left(L_{1r}{L}_{2r}\right)$.

It can be defined that

$$\left.\begin{array}{l}{i}_{2q}^{\prime }=i_{2q}-{\alpha }_1{i}_{ld}-{\alpha }_2{i}_{lq}\\ i_{2d}^{\prime }=i_{2d}-{\alpha }_2{i}_{ld}+{\alpha }_1{i}_{lq}\end{array}\right\}$$

(34)

Substituting Equation (34) with (33), Equation (33) can be simplified as

$$\left.\begin{array}{l}{i}_{2q}^{\prime }={\displaystyle \frac{u_{1d}}{K_d}}\\ i_{2d}^{\prime }=-{\displaystyle \frac{u_{1q}}{K_q}}\end{array}\right\}.$$

(35)

From Equations (33) and (35), the feedforward terms ${\alpha }_1{i}_{ld}+{\alpha }_2{i}_{lq}$ and ${\alpha }_1{i}_{lq}-{\alpha }_2{i}_{ld}$ can be incorporated to the control loop to compensate the disturbance terms D_d and D_q, respectively. Consequently, the voltages u_1d and u_1q can exhibit a directly linear relationship with the currents $i_{2q}^{\prime }$ and $i_{2d}^{\prime }$, respectively. Hence, two PI controllers can be utilized to control u_1d and u_1q by regulating $i_{2q}^{\prime }$ and $i_{2d}^{\prime }$. Based on the above analysis, the simplified PW voltage control loop with the MSC compensation can be illustrated in Figure 4.

4.3. Load Disturbance Suppression Based on LSC

The tractional LSC control scheme adopts the unit-power-factor operation mode, which means the LSC reactive current is zero. And, generally, the active current of LSC is only used to regulate the dc bus voltage. Hence, the capabilities of LSC have not been fully exploited.

With the PW voltage orientation, i_1d and i_1q can be regarded as the active and reactive currents of PW. If the LSC can utilize the stored dc bus energy to provide instantaneous power to the load during load increasing, the instantaneous power that the PW needs to provide would be reduced, which means that the PW active and reactive currents i_1d and i_1q can be significantly decreased, thereby suppressing the impact of load disturbance on the PW voltage.

Therefore, from the preceding analysis, the reference current for the LSC can be derived as follows:

$$\left.\begin{array}{l}{{\displaystyle i}}_{sd}^{*}={{\displaystyle i^{\prime }}}_{sd}+{{\displaystyle i}}_{ld}\\ {{\displaystyle i}}_{sq}^{*}={{\displaystyle i}}_{lq}\end{array}\right\}$$

(36)

where ${{\displaystyle i^{\prime }}}_{sd}$ denotes the output signal from the PI controller regulating the dc bus voltage.

According to Equation (36), the final d- and q-axis reference values $i_{sd}^{*}$ and $i_{sq}^{*}$ are obtained by adding the corresponding feedforward terms $i_{ld}$ and $i_{lq}$ to the LSC current control loop. Thus, based on the basic LSC control strategy, the improved dc bus voltage and current control loop of LSC for load disturbance suppression can be shown in Figure 5, where K_sq indicates the open-loop first-order transfer function from i_sq to LSC q-axis voltage u_sq, and K_dc represents that from the dc bus voltage U_dc to i_sq.

4.4. Coordinated Control for Load Disturbance Suppression

From the above analysis, it can be seen that using the LSC to compensate the load current will make the dc bus voltage drop more obvious. When the dc bus voltage drops below the PW line voltage amplitude, the rectifier will not work properly. For the MSC, the capacity is also a big problem, and the insufficient capacity will also affect the compensation effect. Therefore, considering the capacity of both the MSC and LSC, the coordinated control of them is required.

Some other works on dual-converter control of BDFIG have been carried out in [24,25]. However, Ref. [24] emphasizes the coordinated control of converters under unbalanced loads, and [25] focuses on the coordinated control method of the double-side converters for standalone BDFIG under nonlinear load. In addition, Ref. [25] employs the weight coefficient λ to allocate the contributions of the two converters to harmonic suppression. Similarly, this study also distributes the load current compensation according to the weight coefficient λ.

For the control of the MSC, the d- and q-axis components of the PW voltage are separately regulated by PI controllers. The outputs of the PI controllers are then added to compensation terms derived from the coefficient λ and the load current, yielding the d- and q-axis reference values for the CW current. Subsequently, PI control is applied separately to the d- and q-axis components of the CW current to generate the required output voltage for the converter. Regarding the control of the LSC, the dc bus voltage is regulated by a PI controller. The PI output is added to a compensation term obtained from the coefficient λ and the load current to produce the d-axis reference value for the LSC current. The q-axis reference value for the LSC current is derived directly from the compensation term based on the weight coefficient λ and the load current. Finally, a separate PI control is applied to the d- and q-axis components of the LSC current to generate the required output voltage for the converter. The overall control block diagram is shown in Figure 6.

5. Experimental Results

5.1. Experimental Platform

A 3 kVA prototype BDFIG is adopted to establish the experimental platform (Figure 7), with its parameters listed in

Table 1. Main parameters of the 3 kVA BDFIG.

Parameter	Value	Parameter	Value
PW pole pairs	1	R1	4.21 Ω
CW pole pairs	2	R2	3.10 Ω
PW rated PF	0.85 (lag)	Rr	8.691 Ω
Natural synchronous speed	1000 rpm	L1	1.510 H
Speed range	800–1200 rpm	L2	0.8928 H
PW rated voltage	380 V	Lr	2.314 H
PW rated current	4.5 A	L1r	1.466 H
CW rated voltage	350 V	L2r	0.5911 H
CW rated current	8 A	Rotor type	Wound rotor

. The generator is mechanically coupled to a 3 kW induction motor (IM), which is driven by a 7.5 kW inverter. The 32-bit digital signal processor TMS320F28335 (Texas Instruments Co. Ltd., Dallas, TX, USA) is used for the control of MSC and LSC. To attenuate high-frequency harmonic components of the LSC output voltage, a three-phase LC filter (1.5 mH inductance and 20 μF capacitance per phase) is connected between the LSC and PW. The three-phase diode rectifier is employed to precharge the dc bus voltage. The system already contains 537 W of resistive load, and the 550 W induction motor and 484 W resistive load will be connected to the system later. Under the same load, the four sets of experiments are carried out at the sub- and super-synchronous speeds with different compensation modes.

5.2. Without Compensation

As shown in Figure 8b, when the load is applied to the system at 4.66 s, the load current rises from 1.15 to 8 A. At this point, it can be seen from Figure 8a that the PW voltage amplitude has dropped by 90 V, and the settling time is 114 ms. The dc bus voltage falls by 55 V, and the stabilization time is 380 ms. It shows that the q-axis CW current rises to the highest value 11 A and the steady-state value is 4.5 A, while the d-axis CW current has no obvious change before and after loading from Figure 8e. In Figure 8f, when the load is connected, both the d- and q-axis LSC currents oscillate. In steady state, the d-axis LSC current decreases a little and the q-axis LSC current recovers.

5.3. Compensation Based on MSC

When the load is applied to the system at 3.87 s, the load current rises from 1.15 A to 8 A, as shown in Figure 9b. At this moment, from Figure 9a in which the PW voltage drops by 40 V, and the stabilization time is 74 ms. The dc voltage decreases by 37 V, and the settling time is 147 ms. In Figure 9e, it is showed that the q-axis current of the CW rises to a maximum of 11.5 A and stabilizes at 4.5 A with no significant change in the d-axis of CW current before or after loading. It is illustrated from Figure 9f, when the load is connected, the LSC d and q-axis currents oscillate, then LSC d-axis current decreases a little and q-axis current is kept as it is in stable time.

5.4. Compensation Based on LSC

As shown in Figure 10b, the load current increases from 1.15 A to 9 A with the load adding into system at 4.48 s. At this time, the PW voltage is reduced by 30 V with a stabilization time of 70 ms, as shown in Figure 10a. The dc voltage drops by 70 V with a stabilization time of 680 ms. It is illustrated from Figure 10e that the current rises to a maximum of 5 A and remains stable at 4.5 A. In addition, the d-axis CW current changes to −4 A from −2.5 A. In Figure 10f, when the load is increased, the LSC d- and q-axis currents start to compensate, which decrease slightly during the settling time.

5.5. Cooperative Compensation Based on MSC and LSC

The cooperative compensation based on MSC and LSC is carried out when the weight coefficient λ is set to 0.4. As can be seen from Figure 11b, when the load is added into the system at 6.43 s, the load current rises from 1.15 to 9 A. At this moment, the PW voltage drops by 34 V, and the settling time is 65 ms, as shown in Figure 11a. The dc voltage falls by 50 V with the stabilization time of 330 ms, as shown in Figure 11d. From Figure 11e, it can be seen that the CW q-axis current goes up to 8 A and eventually stabilizes at 3.2 A. In addition, when the load is connected, the d- and q-axis LSC currents drop slightly within the stable time due to compensation, as shown in Figure 11f.

6. Conclusions

This paper proposes a cooperative control method based on both MSC and LSC to enhance standalone BDFIG system performance under load disturbances. Experimental results on a 3 kW prototype demonstrate that the proposed method effectively suppresses the PW voltage fluctuation and accelerates the transient response. Comparative tests show that the MSC compensation strategy primarily improves the dc bus voltage stability, while the LSC compensation strategy mainly enhances the anti-disturbance performance of the PW voltage. Combining the advantages of both MSC and LSC compensation, the proposed cooperative compensation strategy achieves satisfactory PW voltage dip with the short settling time, while maintaining acceptable performance on the dc bus voltage. The innovation of this paper lies in its coordinated control method that leverages the redundant capacity of both MSC and LSC, which quantitatively demonstrates a 62% reduction in voltage dip and a 43% faster settling time compared to the uncompensated scheme under heavy load disturbance.

The integration of the system with energy storage or the adoption of multi-machine systems may further enhance the load disturbance rejection capability. Since energy storage devices can provide additional reactive power, the LSC could theoretically achieve stronger capability for load disturbance suppression. However, the coordinated control of the BDFIG and the energy storage requires further investigation. For multi-machine systems, although the overall disturbance regulation capacity may be improved, voltage coordination at the PCC may introduce new challenges, which also warrants further research.