Improved LADRC Damping of Sub-Synchronous Oscillation in DFIG-Based Wind Power Systems Under Multiple Operating Conditions

Abstract

An active damping control technique based on improved linear active disturbance rejection control (LADRC) is suggested to address the inadequate damping of doubly fed induction generator (DFIG) systems coupled to the grid using series compensation capacitors. Conventional LADRC still has certain limitations under complicated operating conditions, primarily because of its inadequate periodic disturbance estimate capabilities, which limit the system’s dynamic performance and disturbance-rejection capability. An enhanced LADRC scheme is created for the inner current loop of the rotor-side converter (RSC) in the DFIG system in order to lessen these restrictions. To enable a real-time estimate and adjustment of sub-synchronous disturbances, a decoupled linear extended state observer (LESO) is first proposed. In order to effectively attenuate both sub-synchronous oscillation and periodic disturbances, a composite control structure with enhanced suppression capability is constructed by incorporating an improved repetitive control scheme into the linear state error feedback law. The results show that the improved LADRC significantly enhances damping performance and disturbance rejection capability in the subsynchronous frequency range, suppressing active power oscillations within approximately 0.3 s based on a ±10% settling band. Compared with the conventional LADRC, the average THD of the grid current is reduced from 3.43% to 0.56%.

1. Introduction

The penetration of renewable energy in power systems has continued to rise as the world’s energy problem has gotten worse recently [1]. Due to its clean and sustainable qualities, wind energy has been used extensively among many renewable energy sources [2,3]. In 2025, wind power generation reached approximately 1130 TW/h in China, 132.6 TW/h in Germany, and 49.6 TW/h in France. In Denmark, wind power accounted for about 58.7% of electricity generation; based on a total electricity generation of 38.42 TW/h, this corresponds to approximately 22.5 TW/h. These figures further highlight the growing importance of wind power in modern power systems and the practical relevance of improving damping control and oscillation stability under high renewable penetration [4,5,6,7,8].

However, the widespread grid integration of renewable energy sources, such as wind power, has also created new oscillatory stability problems, which pose serious challenges to the stable and safe operation of power systems [9,10]. Wind turbines based on doubly fed induction generators (DFIG) are among the most popular wind power generation technologies. Although series compensation devices are widely used to enhance transmission capacity and improve voltage stability in weak grids, their interaction with DFIG converter control systems can induce subsynchronous oscillation (SSO) [11].

In contrast to the SSO observed in conventional thermal power units, the SSO frequency in wind power systems is not constant. Instead, it is jointly influenced by the output level of the wind farm, the network configuration of the transmission system, and the converter control scheme [9,12]. The oscillation frequency usually shows notable time-varying characteristics since wind power generation is intermittent and unpredictable [13,14]. In order to improve the stability of wind farm grid integration, suppressing SSO under various operating conditions is of significant engineering importance [15,16]. Numerous suppression techniques have been documented in the literature to handle this oscillation problem.

In [17,18], a supplementary sub-synchronous damping control (SSDC) scheme was incorporated into the original control system of the DFIG to suppress SSO. In [19,20], SSDC was further implemented in a static var compensator (SVC) to mitigate SSO in the system. However, the introduction of additional hardware generally results in a more complex system configuration and a corresponding increase in implementation cost. In general, the main limitation of the SSDC strategy lies in its relatively restricted applicability. The controller parameters often need to be adjusted when the DFIG’s working conditions change.

To overcome the limitations of existing suppression strategies, the proportional–integral (PI) control employed in the rotor-side converter (RSC) has been replaced in some studies by more advanced control schemes for mitigating SSO. In [21,22], sliding mode control (SMC) and active disturbance rejection control (ADRC) were introduced, respectively, in place of PI control, and effective SSO suppression was achieved. However, parameter tuning remains relatively complex. In [23], linear active disturbance rejection control (LADRC) was adopted to replace the PI control for SSO suppression. Although the favorable dynamic performance of ADRC was retained and the tuning process was simplified to some extent, the disturbance observation capability of LADRC remained insufficient. As a result, when it is applied to the suppression of SSO in DFIG-based wind turbines, the overall disturbance rejection performance of the system may be limited. In [24], a particle swarm optimization-based LADRC was proposed to enhance controller tuning and disturbance rejection. However, this approach requires a significant computational effort and does not provide a noticeable improvement in the total harmonic distortion, limiting its practical applicability in engineering. In [25], a current harmonic suppression strategy for permanent magnet synchronous motors combining LADRC with a three-parameter notch filter was proposed to reduce current distortion and improve steady-state performance. However, its effectiveness is limited under variable-speed operation or harmonic frequency drift because it relies on fixed-frequency harmonic compensation and cannot adapt to changes in the harmonic spectrum.

As a weak-model-dependent disturbance-rejection control method, LADRC does not rely on an accurate mathematical model of the DFIG system; instead, it estimates and compensates the lumped total disturbance online, including parameter variations, unmodeled dynamics, external disturbances, and SSO-related oscillatory components [26].

This article presents a comparison table of the advantages and disadvantages of some modern control methods, as shown in

Table 1. A comparison of the advantages and disadvantages of some modern control methods.

Reference	Methods	Advantages	Limitations
[27]	Model Predictive Control	Strong dynamic response; can handle multivariable control.	Requires an accurate prediction model; higher computational burden
[28]	H∞ robust damping control	Suitable for uncertain DFIG wind farm systems.	A precise model of the uncertain state space is required; The order of the controller is very high, which may result in noise interference.
[29]	Variable-gain super-twisting sliding-mode control	Chattering is reduced compared with first-order SMC; suitable for nonlinear systems.	Control law and gain design are more complicated; they may face noise sensitivity
[30]	Adaptive harmonic current compensation	Strong frequency adaptability; effective for wide-band SSO variation	This depends on the accuracy of the frequency detection; multi-frequency SSO may require multiple compensation branches; the suppression speed is relatively slow

.

Thus, this research suggests an improved LADRC based on the conventional LADRC. This article has accomplished the following tasks:

(1)

An improved LADRC framework is developed for the DFIG system, where a decoupled linear extended state observer estimates the total disturbance and simplifies parameter tuning, enhancing the overall control structure. A feedforward repetitive control (RC) branch is integrated to suppress periodic subsynchronous components, which is further implemented as a fast repetitive control (FRC) structure to reduce delay while maintaining frequency-selective suppression.

(2)

The PI controller in the q-axis current inner loop of the RSC is replaced with the improved LADRC to suppress SSO. The mathematical model of the grid-connected DFIG system is established, and the principle of SSO suppression by the LADRC is analyzed.

(3)

The proposed improved LADRC demonstrates effective suppression of SSO and a reduction in total harmonic distortion (THD) across varying wind speeds, series compensation levels, and different numbers of DFIGs.

2. The Occurrence and Suppression Mechanism of Doubly Fed Wind Turbines

2.1. Mechanism of SSO in DFIG

Figure 1 depicts the architecture of a wind power plant connected to the main grid through a transmission line.

The transmission line of series compensation is primarily characterized by the line resistance R_l, line inductance L_l, and series compensation capacitor C_sc, and its impedance is expressed as follows [31]:

$$Z_{\mathrm{line}}=R_{\mathrm{l}}+s{L}_{\mathrm{l}}-{\displaystyle \frac{1}{s{C}_{\mathrm{sc}}}}$$

(1)

In the formula, s represents the complex frequency variable in the Laplace domain.

According to [32], the impedance expression of the DFIG is given by:

$$Z_{\mathrm{DFIG}}=R_{\mathrm{s}}+s{L}_{\mathrm{s}}+s{L}_{\mathrm{m}}\parallel Z_{\mathrm{RSC}}$$

(2)

$$Z_{\mathrm{sys}}={\displaystyle \frac{Z_{\mathrm{DFIG}}}{n}}+Z_{\mathrm{line}}$$

(3)

A DFIG-based wind farm linked to the electrical grid via a series-compensated transmission line has the following equivalent impedance:

$$Z_{\mathrm{sys}}={\displaystyle \frac{R_{\mathrm{s}}+s{L}_{\mathrm{s}}+s{L}_{\mathrm{m}}\parallel Z_{\mathrm{RSC}}}{n}}+R_{\mathrm{l}}+s{L}_{\mathrm{l}}-{\displaystyle \frac{1}{s{C}_{\mathrm{sc}}}}$$

(4)

Figure 2 depicts the equivalent impedance model of a DFIG-based wind farm linked to the electricity grid [33,34].

A sub-synchronous angular frequency ω_er is produced when the transmission line is linked to the series compensating capacitor C_sc [35]. Accordingly, the slip of the DFIG is expressed as s_slip:

$$s_{\mathrm{slip}}={\displaystyle \frac{{\omega }_{\mathrm{er}}-{\omega }_{\mathrm{r}}}{{\omega }_{\mathrm{er}}}}$$

(5)

Here, ω_r denotes the rotor angular frequency. Consequently, the grid-connected system’s equivalent impedance model at the resonant angular frequency ω_er can be written as follows:

$$\left\{\begin{array}{c}{R}_{\mathrm{eq}}={\displaystyle \frac{R_{\mathrm{r}}+R_{\mathrm{RSC}}}{s_{\mathrm{slip}}}}+R_{\mathrm{s}}+R_{\mathrm{l}}\\ X_{\mathrm{eq}}={\displaystyle \frac{{\omega }_{\mathrm{er}}(L_{\mathrm{r}}+L_{\mathrm{m}})}{n}}+{\omega }_{\mathrm{er}}{L}_{\mathrm{l}}-{\displaystyle \frac{1}{{\omega }_{\mathrm{er}}{C}_{\mathrm{sc}}}}\end{array}\right.$$

(6)

Once the system is disturbed, sustained electrical oscillations will be generated provided that the conditions in (7) and (8) are satisfied:

$$R_{\mathrm{eq}}={\displaystyle \frac{R_{\mathrm{r}}+R_{\mathrm{RSC}}}{s}}+R_{\mathrm{s}}+R_{\mathrm{l}}<0$$

(7)

$${\omega }_{\mathrm{er}}({\displaystyle \frac{L_{\mathrm{r}}+L_{\mathrm{m}}}{n}}+L_{\mathrm{l}})\approx {\displaystyle \frac{1}{{\omega }_{\mathrm{er}}{C}_{\mathrm{sc}}}}$$

(8)

When the equivalent resistance R_eq < 0, the system loses effective damping and may become unstable once a disturbance is introduced. This can be attributed to the amplification of the sub-synchronous current in the rotor winding by the positive and negative feedback actions within the RSC, thereby continuously strengthening the interaction between the converter and the series compensation capacitor [36].

As a result, the RSC exhibits a more pronounced negative-resistance characteristic, causing R_eq to decrease further into the negative region [37]. Therefore, it is necessary to improve the control strategy of the RSC. Figure 3 illustrates the operating principle of the RSC.

Previous studies have shown that the SSO frequency and damping level are influenced by the wind speed, the series compensation degree, and the number of in-service wind turbines [38,39]. Therefore, in this study, the proposed improved LADRC strategy is evaluated under different wind speeds, series compensation degrees, and numbers of in-service wind turbines.

2.2. The Mechanism of SSO Suppression

The improved LADRC suppresses SSO by estimating the lumped disturbance in the RSC q-axis channel, which includes external disturbances, parameter variations, and coupling effects. The estimated disturbance is actively compensated in the control input, providing additional damping and reducing the effect of the subsynchronous component on both the q-axis and coupled d-axis currents. This prevents amplification of SSO by the converter control loop and stabilizes the system. The dq-axis output voltage of the RSC current loop can be expressed as follows [40]:

$$\left\{\begin{array}{c}{u}_{\mathrm{rd}}=(r_{\mathrm{r}}+\sigma L_{\mathrm{r}}{\displaystyle \frac{d}{dt}})i_{\mathrm{rd}}-s_{\mathrm{slip}}\sigma L_{\mathrm{r}}{i}_{\mathrm{rq}}\\ u_{\mathrm{rq}}=(r_{\mathrm{r}}+\sigma L_{\mathrm{r}}{\displaystyle \frac{d}{dt}})i_{\mathrm{rq}}+s_{\mathrm{lip}}\sigma L_{\mathrm{r}}{i}_{\mathrm{rd}}-s_{\mathrm{slip}}{\displaystyle \frac{L_{\mathrm{m}}}{L_{\mathrm{s}}}}{\psi }_{\mathrm{s}}\end{array}\right.$$

(9)

where u_rd and u_rq are the d-axis and q-axis rotor voltage components; i_rd and i_rq are the d-axis and q-axis rotor current components; r_r is the rotor resistance; L_r is the rotor inductance; L_m is the mutual inductance between the stator and rotor windings; L_s is the stator inductance; σ is the leakage coefficient; s_slip is the slip angular frequency; and ψ_s is the stator flux linkage.

When DFIGs are connected to a series-compensated transmission line, the interaction between the converter control system and the compensated network may produce subsynchronous components in the transmission line current and rotor current. Under this condition, the current in the RSC current control loop can be expressed as follows:

$$\left\{\begin{array}{c}{\displaystyle \frac{d{i}_{\mathrm{rd}}}{dt}}={\displaystyle \frac{u_{\mathrm{rd}}}{\sigma L_{\mathrm{r}}}}-{\displaystyle \frac{r_{\mathrm{r}}}{\sigma L_{\mathrm{r}}}}{i}_{\mathrm{rd}}+s_{\mathrm{lip}}{i}_{\mathrm{rq}}+D_{\mathrm{l}}(\Delta i_{{\mathrm{rd}}_{-}\mathrm{sub}},\Delta i_{{\mathrm{rq}}_{-}\mathrm{sub}})\\ {\displaystyle \frac{d{i}_{\mathrm{rq}}}{dt}}={\displaystyle \frac{u_{\mathrm{rq}}}{\sigma L_{\mathrm{r}}}}-{\displaystyle \frac{r_{\mathrm{r}}}{\sigma L_{\mathrm{r}}}}{i}_{\mathrm{rq}}-s_{\mathrm{lip}}{i}_{\mathrm{rd}}+s_{\mathrm{lip}}{\displaystyle \frac{L_{\mathrm{m}}}{L_{\mathrm{s}}}}{\psi }_{\mathrm{s}}+D_2(\Delta i_{{\mathrm{rd}}_{-}\mathrm{sub}},\Delta i_{{\mathrm{rq}}_{-}\mathrm{sub}})\end{array}\right.$$

(10)

where D₁ (Δi_{rd_sub}, Δi_{rq_sub}) and D₂ (Δi_{rd_sub}, Δ_{irq_sub}) represent the disturbances of the d-axis and q-axis caused by the subsynchronous current.

When the improved LADRC replaces the conventional PI controller, it is able to observe and compensate for the subsynchronous components in real time. The dq-axis current dynamics under the improved LADRC become:

$$\left\{\begin{array}{c}{\displaystyle \frac{d{i}_{rd}}{dt}}={\displaystyle \frac{u_{rd}}{\sigma L_r}}-{\displaystyle \frac{r_r}{\sigma L_r}}{i}_{rd}+s_{\mathrm{lip}}{i}_{rq}\\ {\displaystyle \frac{d{i}_{rq}}{dt}}={\displaystyle \frac{u_{rq}}{\sigma L_r}}-{\displaystyle \frac{r_r}{\sigma L_r}}{i}_{rq}-s_{\mathrm{slip}}{i}_{rd}+s_{\mathrm{lip}}{\displaystyle \frac{L_m}{L_s}}{\psi }_s\end{array}\right.$$

(11)

This shows that under SSO conditions, the dq-axis rotor current output of the DFIG remains consistent with the stable operation case. The comparison between (11) and (9) indicates that subsynchronous components in the DFIG system are effectively suppressed by the improved LADRC through action on the q-axis RSC channel, preventing their amplification and propagation. Rapid transient response is ensured by the proportional feedback branch, while periodic residual SSO components are attenuated by the repetitive-control branch.

3. Improved LADRC Strategy

This section first presents the decoupled LADRC strategy, which improves the system’s resistance to periodic disturbances and enhances the suppression capability against interference in the sub-synchronous frequency band by integrating fast reactive control with the linear state error feedback law (LSEF). In order to effectively suppress SSO and enhance the current loop’s dynamic response capabilities and resilience to periodic disturbances, the RSC uses the upgraded LADRC in place of the conventional PI control in the q-axis inner current loop.

3.1. Decoupled LADRC Strategy

The rotor winding is energized, and oscillating currents within the subsynchronous frequency band are produced when a current flows through the series compensation circuit. In the rotor-side dq-axis current loop, the current components within this frequency range can be observed.

In the traditional LADRC, if a transition link is introduced into the current loop, the response speed is affected. Since rapid tracking is required in the current loop, the transition process is not adopted here, as shown in Figure 4.

In this paper, the controlled object is defined as the decoupled single-axis rotor current channel of the RSC. After dq-axis decoupling and feedforward compensation, this current channel can be approximated by a first-order RL-type model for controller synthesis, rather than by assuming the entire DFIG–RSC system to be first-order. Then the controlled object is set as:

$${\displaystyle \frac{d}{dt}}y=\epsilon +b_{0}u-a_{1}y$$

(12)

In the equation, u stands for the control system’s input, y for the system’s output, a₁ and b₀ are nonzero constants, and ε indicates the system’s unknown disturbance.

Then the LESO is designed as:

$$\left\{\begin{array}{c}{\displaystyle \frac{\mathrm{d}}{\mathrm{d}t}}{\widehat{x}}_1={\widehat{x}}_2+b_{0}u+h_1(x_1-{\widehat{x}}_1)\\ {\displaystyle \frac{\mathrm{d}}{\mathrm{d}t}}{\widehat{x}}_2=h_2(x_1-{\widehat{x}}_1)\end{array}\right.$$

(13)

In the equation, x₁ and x₂ are the system state variables, while h₁ and h₂ are the nonzero gains of the LESO. The feedback law of the proposed design strategy is given as follows:

$$u={\displaystyle \frac{u_0-\epsilon }{b_0}}$$

(14)

In the equation, the expression of u₀ is:

$$u_0=k_{\mathrm{p}}(\nu -{\widehat{x}}_1)$$

(15)

In the equation, k_p denotes the proportional coefficient, and v denotes the reference input variable of the control system.

Consequently, the following represents the analytical relationship between the specified bandwidth and the observer’s internal gains:

$$L={\left[\begin{array}{cc}{h}_1& h_2\end{array}\right]}^T=\left[\begin{array}{cc}2{\omega }_{\mathrm{eso}}& {\omega }_{\mathrm{eso}}^2\end{array}\right]$$

(16)

Consequently, the system’s closed-loop transfer function is:

$$G(s)={\displaystyle \frac{k_{\mathrm{p}}}{k_{\mathrm{p}}+s}}+{\displaystyle \frac{s^2+(h_1+k_{\mathrm{p}})s}{(s+k_{\mathrm{p}})(s^2+h_{1}s+h_2)}}$$

(17)

The traditional LADRC strategy is subject to certain limitations in engineering applications. Its parameter tuning is cumbersome and sensitive to system variations, resulting in a substantial tuning workload and a strong dependence on experience. In order to minimize parameter sensitivity and simplify the tuning process, the LADRC structure and tuning technique must be modified in order to increase the system’s robustness and flexibility.

Figure 5 displays the redesigned block diagram following the decoupling of the linear extended state observer. Consequently, this autonomous subsystem’s transfer function can be written as follows:

$$G_L(s)={\displaystyle \frac{s}{s^2+h_{1}s+h_2}}$$

(18)

The equivalent s domain representation of the independent LADRC architecture is given as follows:

$$G_{cl}(s)={\displaystyle \frac{k_{\mathrm{p}}}{s+k_{\mathrm{p}}}}+{\displaystyle \frac{s}{s^2+h_{1}s+h_2}}$$

(19)

As can be seen from Equation (19), the tracking performance of this strategy is determined only by k_p, whereas the disturbance rejection performance is determined solely by h₁ and h₂.

Through structural decoupling, disturbance suppression and command tracking can be considered independently. This optimization scheme makes the controller design more systematic and further improves the functions of each part of the controller to a certain extent.

The parameters of the improved LADRC are selected according to the bandwidth-based tuning principle. Since LADRC is weakly dependent on an accurate mathematical model, its parameters are mainly determined by the desired response speed, disturbance estimation capability, noise sensitivity, and converter control constraints. The parameter k_p affects the closed-loop response speed. A larger k_p can accelerate SSO attenuation, but an excessively large value may lead to overshoot, current fluctuation, or converter saturation. The observer bandwidth ω_eso determines the disturbance estimation speed. A larger ω_eso improves the estimation of SSO-related disturbances but may also amplify measurement noise and high-frequency components.

Figure 6 shows the Bode diagram of the decoupled LADRC. As indicated by Figure 6, an increase in ω_eso enhances the amplitude gain of the decoupled LADRC in the sub-synchronous frequency band, thereby improving its disturbance rejection capability in this band. Therefore, in this paper, the improved LADRC parameters are set as k_p = 30, ω_eso = 25, and b₀ = 0.005.

3.2. Improved Repetitive Control

The internal model concept is the foundation of RC. By superimposing the control deviation signal from the previous cycle on the current control input, periodic input signals can be effectively tracked, periodic disturbances can be suppressed, and the control quality of the system can be significantly improved. The traditional RC is shown in Figure 7. Owing to the existence of the delay time T₀, the effect of RC cannot be exerted during the initial stage of the system response, resulting in relatively weak dynamic response capability at this stage.

$$G_{\mathrm{RC}}(z)={\displaystyle \frac{k_{\mathrm{rc}}{Q}_1{z}^{-N}}{1-Q_1(z)z^{-N}}}S(z)$$

(20)

In this formulation, N denotes the total number of discrete data points within one fundamental period, k_rc is the RC gain, S(Z) is the correction link, and Q₁(Z) is the filter link.

Therefore, to ensure system stability while achieving a rapid dynamic response, an FRC scheme is designed, as shown in Figure 8.

The RC is implemented in the discrete-time domain with a sampling frequency of f_s = 900 Hz, and the corresponding sampling period is T_s = 1/900 s. The delay time of the repetitive branch is given by T_d = NT_s, where $N$ denotes the number of delay samples. In the conventional RC structure, the frequency spacing of the repetitive branch is determined by T_d = 384 × T_s = 0.426 s. To suppress the subsynchronous frequency component effectively, a narrow suppression frequency spacing of approximately 2∼3 Hz is generally required [41].

Although this structure can suppress the subsynchronous component, the long delay may slow down the transient suppression process. To enhance the dynamic response, an FRC structure is adopted by reducing the delay length to N/6 samples. FRC, while retaining the periodic compensation capability of RC, reduces the phase lag. As a result, the proposed approach is able to effectively suppress SSO and further enhance the operational robustness of the DFIG-based wind farm.

Q₁(Z) is generally designed as a zero-phase low-pass filter, and its expression is given as follows:

$$Q_1(z)={\displaystyle \frac{a_0+{\displaystyle \sum _{i=1}^M}(a_i{z}^{-i}+a_i{z}^i)}{a_0+2{\displaystyle \sum _{i=1}^M}{a}_i}}$$

(21)

In the equation, M is the order of the zero-phase filter. As the order increases, more frequency components can be suppressed, but the corresponding phase variation becomes more pronounced.

Considering that the filter is only used to construct the internal model coefficient in the FRC and only needs to satisfy the low-pass characteristic requirements, the order is set to M = 2.

Then the transfer function of FRC is as follows:

$$G_{\mathrm{FRC}}(z)={\displaystyle \frac{k_{\mathrm{rc}}{Q}_1{z}^{-N/6}}{1-Q_1{z}^{-N/6}}}S(z)$$

(22)

Figure 9 shows a comparison of the Bode plots of FRC and RC. As can be seen from Figure 9, unlike traditional RC, which exhibits dense resonant characteristics at multiple frequencies, FRC reduces the period delay, so that the control gain is concentrated in the dominant frequency band of SSO. The suppression ability of the improved FRC has significantly improved.

The zero-phase filter Q₁(Z) is configured with a₀ = 0.6, a₁ = 0.25, a₂ = 0.006. After normalization, these coefficients ensure that Q₁(Z) = 1, so that the unity gain in the low frequency range is preserved and the repetitive compensation capability around the target frequency is maintained. In addition, the relatively large central coefficient a₀ = 0.6 helps preserve the low frequency components, the moderate coefficient a₁ = 0.25 provides the main low-pass filtering effect, and the small coefficient a₂ = 0.006 is mainly used for fine-tuning of the high frequency response.

This ensures effective suppression of the target oscillation component while reducing the gain amplification and phase lag problems in non-target frequency bands. Consequently, the control parameters are selected as N = 387, with the phase compensator designed as S(Z) = z⁴.

At the same time, the FRC is introduced into the LSEF to improve the suppression capability against periodic disturbances, and the resulting improved LADRC strategy is shown in Figure 10. When this composite control strategy is implemented in the q-axis of the RSC, the overall robustness of the system and its capability to reject periodic disturbances are further improved.

3.3. Stability Analysis

The dynamic equation of the present observation error is developed as follows in order to examine the stability of the LESO:

$$\dot{e}=A_{e}e$$

(23)

$$\left[\begin{array}{c}{e}_1\\ e_2\end{array}\right]=\left[\begin{array}{c}{i}_q-{\widehat{i}}_q\\ d_q-{\widehat{d}}_q\end{array}\right]A_e=\left[\begin{array}{cc}0& 1\\ -h_2& -h_1\end{array}\right]$$

(24)

$$\det (sI-A_s)=s^2+h_{1}s+h_2=0$$

(25)

Equation (16) defines the gain of the LESO. When the LESO bandwidth ω_eso is positive, stability of the LESO is ensured.

When feedforward traditional RC is introduced, it is assumed that aperiodic disturbances can be completely suppressed by the LESO. Under this condition, the q-axis current loop can be approximately represented as a pure integral link regulated only by the LSEF, and the resulting equivalent q-axis current loop structure is presented in Figure 11.

To reconcile tracking accuracy with closed-loop robust stability, an FRC loop is incorporated. The transfer function in the discrete domain and the internal filter Q₁(Z) are expressed in (20) and (21). The filter-parameter set is designed in accordance with the frequency-domain stability criterion of discrete-time control systems. After normalization, the steady-state condition of Q₁(Z) is satisfied. In accordance with the internal model principle, a sufficiently high open-loop gain is achieved in the low frequency region and around the target characteristic frequency, thereby ensuring accurate tracking of periodic reference signals and effective suppression of periodic disturbances.

Meanwhile, with respect to the high-frequency components outside the target frequency band, the zero-phase filter is designed to strictly satisfy the following condition:

$$|Q_1(e^{j\omega T_s})|<1$$

(26)

By virtue of this high-frequency attenuation characteristic, the pole originally located on the unit circle is driven into the interior of the unit circle, thereby ensuring the stability of the closed-loop system. To further suppress the oscillation tendency caused by the positive-feedback loop in the internal model, the gain k_rc = 0.95 < 1 is employed. Consequently, a sufficient amplitude stability margin is ensured for the closed-loop system, and the robustness of the system is improved. By this means, a sufficient amplitude stability margin is preserved for the closed-loop system, and enhanced system robustness is achieved.

For the repetitive structure, full system stability is ensured when the following two conditions are satisfied:

• All poles of G_FRC(Z) are inside the unit circle.
• Satisfies the following equation.

$$\left\{\begin{array}{c}\left|Q_1(Z)\left[1-k_{\mathrm{rc}}S(Z)G_{\mathrm{cl}}(Z)\right]\right|<1;\\ \forall Z={\mathrm{e}}^{i\omega T_{\mathrm{s}}},0<\omega <{\displaystyle \frac{\pi }{T_{\mathrm{s}}}}\end{array}\right.$$

(27)

Figure 12 shows the Bode plot of the overall open-loop transfer function of the controlled system. According to the frequency-domain stability interpretation, the corresponding closed-loop system is stable under the designed controller parameters.

Since the decoupled LADRC loop remains stable and the RC branch is bounded over the entire frequency range, the above conditions can be satisfied. Consequently, asymptotic stability can be maintained by the proposed improved LADRC system, while the suppression of SSO is significantly enhanced.

4. Simulation and Analysis

4.1. Simulation Model of DFIG Grid-Connected System

The effectiveness of the proposed improved LADRC algorithm in alleviating SSO is demonstrated through time-domain simulation. Based on the first benchmark model of IEEE, this paper constructs a wind farm with a series-compensated DFIG in MATLAB/Simulink 2024a, as shown in Figure 13. The wind farm consists of 66 wind turbines, each with a rated voltage of 0.69 kV and a capacity of 1.5 MW. The wind turbines are boosted by transformers, and the generated electricity is transmitted to the grid through a transformer with a rated voltage of 572 V/161 kV and a series-compensated transmission line. The transmission line is represented by the equivalent reactance X_l, resistance R_l, and series compensation reactance X_C. A three-phase-to-ground fault and a phase-to-phase fault are applied at the location marked in the figure at t = 3.5 s. The parameters of the simulation system are shown in

Table 2. The main parameters of the system model.

Symbol	Parameter Specification	Numerical Value
P	Rated power	100 MW
fr	Natural frequency	60 Hz
Rr	Rotor resistance	0.016 p.u.
Rs	Stator resistance	0.025 p.u.
Lr	Rotor inductance	0.16 p.u.
Ls	Stator inductance	0.17 p.u.
Lm	Mutual inductance	2.8 p.u.
Xt1	T1 reactance	0.020 p.u.
Xt2	T2 reactance	0.020 p.u.
XL	161 KV line reactance	0.5 p.u.
RL	161 KV line resistance	0.02 p.u.

.

4.2. Simulation Verification

4.2.1. Verification of SSO Suppression at Different Series Compensation Levels

Since wind speed, series compensation degree, and the number of in-service wind turbines are key factors affecting the SSO frequency and damping characteristics of DFIG-based wind farms, they are selected as representative fixed scenarios for validation. In addition, the proposed improved LADRC estimates and compensates the lumped total disturbance online, including parameter variations, unmodeled dynamics, external disturbances, and SSO-related components, rather than relying on an explicitly parameterized uncertainty model. Therefore, its robustness is evaluated under these representative SSO-sensitive conditions, which directly reflect the main factors influencing SSO behavior in DFIG-based series-compensated systems.

To evaluate the damping capability of the improved LADRC scheme under different series compensation ratios, simulations were conducted for the 40% and 55% cases. When the LADRC is employed in the RSC, SSO can be effectively suppressed.

Figure 14 and Figure 15 show the active power and DC-link voltage responses of the PI, LADRC, and improved LADRC under 40% and 55% series compensation levels. The results indicate that both LADRC and the improved LADRC can suppress SSO, whereas the PI controller exhibits weaker damping performance. Compared with the conventional LADRC, the improved LADRC achieves faster oscillation suppression and better steady-state performance.

As shown in Figure 14, the active power oscillation is suppressed within approximately 0.3 s by the improved LADRC and remains within a ±10% band around its steady-state value. In addition, Figure 15 shows that the improved LADRC effectively reduces the fluctuation of the DC-link voltage under different compensation levels.

However, due to the limited disturbance observation capability of the conventional LESO, noticeable residual fluctuations can still be observed in the active power and DC-link voltage when the conventional LADRC is applied. To further evaluate the current quality, Figure 16 presents the time-domain single-phase current waveform under the 40% series compensation condition. It can be observed that current distortion remains under the conventional LADRC, while the improved LADRC provides a smoother current response. Furthermore, FFT analysis is performed on the single-phase current over a 0.5 s interval starting from t = 4 s, and the corresponding harmonic spectrum is also shown in Figure 16.

The FFT spectrum, extracted from the representative steady-state waveform, is specifically shown in the 0–120 Hz range to emphasize the SSO-related components. As illustrated in Figure 17, after the series compensation capacitor is connected, under PI control, the sub-synchronous and super-synchronous frequency components in phase-A current are mainly concentrated at 28 Hz and 96 Hz, respectively, and the THD of the grid current reaches 36.37%. By contrast, under both LADRC and the improved LADRC, phase-A grid current contains only the 60 Hz fundamental component, while no high-amplitude disturbance components appear at other frequencies. This indicates that both control strategies are capable of suppressing the generation of sub-synchronous components and thereby mitigating SSO.

However, when LADRC is adopted in the RSC, the THD of the grid current remains at 3.17% because of the limited observation accuracy of the controller. In comparison, when the improved LADRC is employed, the THD is further reduced to 0.54%, indicating that the quality of the grid’s current is significantly enhanced. Based on the above analysis, the proposed suppression strategy provides stronger disturbance-rejection capability and better steady-state performance than conventional LADRC, while effectively suppressing SSO.

The stability of the enhanced LADRC system under various wind speeds and DFIG counts was assessed using time-domain modeling. The suppressing impact of the enhanced LADRC on SSO was further examined under two operational circumstances of wind speeds of 8 m/s and 5 m/s. When the series compensation capacitor was attached at t = 3 s, with the compensation level set at 40%, the system experienced SSO. At the start of the simulation, the system was in a stable functioning condition.

As shown in Figure 18, the effective mitigation of SSO is achieved by the improved LADRC over a range of wind speeds. As shown in Figure 19, the grid’s current responses of the DFIG-based wind farm were examined for different numbers of grid-connected DFIG units under a 40% series compensation level. As demonstrated by the results, SSO is effectively suppressed by the improved LADRC under varying series compensation levels, wind speeds, and numbers of grid-connected wind turbines.

4.2.2. Multi-Scenario Statistical Validation of THD Reduction

Figure 20 shows the single-phase current waveforms and the corresponding FFT analysis under different operating conditions, including different wind speeds, different numbers of grid-connected DFIG units, and different series compensation levels. The results indicate that the proposed method can effectively reduce harmonic components under all tested scenarios, demonstrating that the THD reduction is not limited to a single operating condition.

As shown in Figure 17, under the 40% series compensation condition, the THD is reduced from 3.17% to 0.54%. When the number of grid-connected wind turbines varies, the THD decreases from 3.28% to 0.57% and from 3.01% to 0.49%, respectively. Under different wind speed conditions, the THD is reduced from 3.42% to 0.57% and from 3.64% to 0.59%, respectively. Moreover, when the series compensation level is increased to 55%, the THD decreases from 4.04% to 0.61%. These results demonstrate that the improved LADRC is not only effective in a representative operating case but also maintains good harmonic suppression performance under different wind farm and grid operating conditions.

Considering all tested cases, the average THD obtained with the conventional LADRC is approximately 3.43%, whereas that obtained with the improved LADRC is reduced to approximately 0.56%. This corresponds to an average THD reduction of about 83.7%. Meanwhile, the time-domain current waveforms show that the improved LADRC suppresses current oscillations more effectively and provides a smoother steady-state response. Therefore, the multi-scenario test results further verify the robustness and general applicability of the proposed improved LADRC.

4.2.3. Verification of SSOs Under System Failure

Power system faults, especially transmission line short-circuit and open-circuit faults, are regarded as serious threats to system stability. In a DFIG-based wind farm connected to a series-compensated network, the fault clearance process may excite the SSO of the compensated network. Therefore, phase-to-phase and three-phase-to-ground fault cases are considered to evaluate the post-fault SSO damping capability of the proposed improved LADRC under severe grid disturbances.

As shown in Figure 13, the phase-to-phase fault and the three-phase-to-ground fault were applied on the high voltage side of the 572 V/161 kV step-up transformer at t = 3.5 s after steady-state operation was achieved; the fault was cleared after 0.1 s The level of series compensation and wind speed were set to 40% and 11 m/s, respectively, and the capacitor of series compensation was turned on at t = 3 s.

As illustrated in Figure 21, severe oscillations were observed under both PI control and the improved LADRC during the fault period. However, under the improved LADRC, the system was rapidly restored to a stable operating state after fault clearance. It was demonstrated by the simulation results that the improved LADRC offers significant advantages under fault conditions.

4.3. Comparison Between Improved LADRC and SSDC

Supplementary damping control, especially SSDC, is widely used to mitigate subsynchronous instability in grid-side and generator-side converter systems. SSDC is also commonly adopted as a benchmark in existing studies [42]. To provide a more comprehensive comparison, this paper compares the improved LADRC with both conventional SSDC and H∞ control. The typical SSDC structure is shown in Figure 22, which consists of a band-pass filter (BPF), a phase compensation unit, and a gain unit. The BPF extracts the subsynchronous component from the rotor speed signal, and the processed signal is used to generate the damping signal. Compared with SSDC, H∞ control is a representative robust control method for improving damping performance under model uncertainties and operating condition variations. It should be noted that the performance of the H∞ controller may depend on the selected model and design parameters, which could affect its effectiveness under varying operating conditions [43].

The three controllers are tested under different series compensation levels. At t = 3 s, the series compensation level is set to 40%, while the other network parameters remain unchanged. As shown in Figure 23a, all controllers can suppress SSO. However, the improved LADRC provides faster stabilization and lower power oscillation amplitude. The H∞ controller shows better robustness than SSDC, but its transient response is slower than that of the improved LADRC.

A further test is conducted under 55% series compensation. As shown in Figure 23b, the change in compensation level shifts the system resonant frequency, which weakens the damping effect of SSDC due to its dependence on the BPF and phase compensation parameters. The H∞ controller maintains better robustness than SSDC, while the improved LADRC still achieves faster dynamic recovery and stronger oscillation suppression. This is because the improved LADRC can estimate and compensate for the total disturbance online.

Therefore, the simulation results indicate that the improved LADRC provides better transient damping performance than conventional SSDC and H∞ control under the tested conditions. Although H∞ control has strong robustness, it usually requires an accurate uncertain model and a more complex synthesis process. In contrast, the improved LADRC has a simpler structure and better adaptability to resonant-frequency variations.

5. Conclusions

This paper proposes an improved LADRC strategy for DFIG-based wind power systems to mitigate SSO by integrating a decoupling-based observer with FRC. The proposed method effectively suppresses SSO within approximately 0.3 s.

Time-domain simulations under various conditions, including different wind speeds, series compensation levels, number of grid-connected units, and fault scenarios, demonstrate that the improved LADRC enhances system stability, accelerates oscillation damping, and improves disturbance rejection capability. In addition, the THD is significantly reduced, indicating improved power quality. Compared with conventional LADRC, the proposed method shows superior overall performance.

Compared with SSDC and H∞ strategies, no parameter retuning is required for the proposed improved LADRC when the SSO frequency shifts due to variations in the series compensation level. By contrast, both SSDC and H∞ rely on predefined design parameters, and their performance may be affected if the system conditions change. The improved LADRC enhances system damping across different SSO frequencies and effectively suppresses the occurrence of SSO.

But hardware-in-the-loop testing has not yet been performed, and economic aspects, including implementation cost and engineering cost-effectiveness, have not been considered. These limitations may restrict the direct applicability of the results in practical engineering scenarios. Therefore, future work will include hardware-based validation, comprehensive economic assessment, and further testing under more complex operating conditions.