Data-Driven Noise-Resilient Method for Wind Farm Reactive Power Optimization

Abstract

Accurate reactive power optimization in wind farms (WFs) is critical for optimizing operations and ensuring grid stability, yet it faces challenges from noisy, nonlinear, and dynamic Supervisory Control and Data Acquisition (SCADA) data. This study proposes an innovative framework, WBS-BiGRU, integrating three novel components to address these issues. Firstly, the Wavelet-DBSCAN (WDBSCAN) method combines wavelet transform’s time–frequency analysis with density-based spatial clustering of applications with noise (DBSCAN)’s density-based clustering to effectively remove noise and outliers from complex WF datasets, leveraging multi-scale features for enhanced adaptability to non-stationary signals. Subsequently, a Boomerang Evolutionary Optimization (BAEO) with the Seasonal Decomposition Improved Process (SDIP) synergistically decomposes time series into trend, seasonal, and residual components, generating diverse candidate solutions to optimize data inputs. Finally, a Bidirectional Gated Recurrent Unit (BiGRU) network enhanced with an attention mechanism captures long-term dependencies in temporal data and dynamically focuses on key features, improving reactive power forecasting precision. The WBS-BiGRU framework significantly enhances forecasting accuracy and robustness, offering a reliable solution for WF operation optimization and equipment health management.

1. Introduction

Wind energy has rapidly emerged as a pivotal element in the global shift towards sustainable energy systems [1,2]. With the increasing scale and complexity of wind power systems, reactive power fluctuations have become significant challenges to the secure operation of the grid, reducing the efficiency of wind power integration and system stability [3,4]. Maintaining grid stability requires suppressing reactive power fluctuations.

Extensive studies [5,6,7,8,9] propose model-based methods to manage reactive power in wind farms (WFs). A sensitivity analysis-based approach is developed [5] for optimal reactive power allocation in doubly fed induction generator (DFIG)-based wind farms, improving voltage profiles. In [6], a dynamic reactive power optimization model incorporating wind farms and energy storage is proposed, minimizing losses during fluctuating conditions. In [7,8], Particle Swarm Optimization (PSO) and genetic algorithms are employed for multi-objective reactive power dispatch in distribution networks with wind integration. In [9], a robust linear optimization is used to leverage wind farms’ reactive power range for uncertain system conditions. These methods, though effective, rely on accurate models, causing computational complexity and linearization errors. Model-free methods [10,11,12,13,14] include data-driven clustering for wind power prediction [10], scenario-based optimization for reactive power management [11], and sensitivity analysis for loss reduction [12]. A wavelet packet decomposition for smoothing wind power fluctuations is employed in [13], while Ref. [14] uses empirical mode decomposition for hybrid reactive power control. These methods struggle with nonlinear system complexity.

Advancements in artificial intelligence have driven research in intelligent WF control methods using historical data, demonstrating efficacy in data prediction and fitting [15,16,17,18,19,20]. In [15], a hybrid Convolutional Neural Network and Long Short-Term Memory (CNN-LSTM) model is proposed to regulate reactive power by learning patterns from SCADA time series data. A deep neural network (DNN) is employed in [16] for direct power control to reduce dispatch time. However, these self-supervised methods struggle with long-term temporal dependencies.

Thus, Refs. [17,18] introduce Recurrent Neural Network (RNN)-based methods with LSTM networks to optimize reactive power and mitigate anomalous data effects, reducing computational complexity. Reference [19] uses the gated recurrent unit (GRU) for capturing dependencies in wind power signals, while [20] integrates attention mechanisms for enhanced forecasting. Self-supervised methods for WF control depend on accurate training data labels, limiting adaptability. Unsupervised learning, particularly deep reinforcement learning (DRL), addresses these issues [21,22,23,24,25]. A DRL-based volt/var control with entropy regularization is proposed in [21] for optimizing WFa voltage. In [22], a multi-agent DRL scheme develops an autonomous voltage control algorithm using a Multi-Agent Deep Deterministic Policy Gradient (MADDPG), learning from SCADA data. Refs. [23,24,25] integrate the Monte Carlo method with RL. A quantum Monte Carlo optimization is introduced in [23] for DFIG parameters. In [24], offline learning with MCTS is combined for wind power restoration, and Ref. [25] uses a double-network DRL to coordinate power. However, the expensive training cost limits the adaptability. To address these limitations, this study proposes the WBS-BiGRU framework for reactive power optimization in WFs. First, the Wavelet-DBSCAN (WDBSCAN) method combines wavelet transform’s time–frequency decomposition with DBSCAN’s density-based clustering to remove noise and outliers, preserving multi-scale signal features. Second, the Boomerang Evolutionary Optimization with the Seasonal Decomposition Improved Process (BAEO-SDIP) leverages a stochastic differential equation framework and adaptive evolutionary optimization to decompose cleaned data into trend, seasonal, and residual components, generating a 24-dimensional feature matrix for predictive modeling. Finally, an attention-enhanced Bidirectional Gated Recurrent Unit (BiGRU) captures long-term temporal dependencies and dynamically weights key features, improving reactive power control precision. The contributions of this paper can be summarized as follows:

• Wavelet-DBSCAN (WDBSCAN) for data cleaning is proposed, which innovatively integrates the time–frequency analysis capability of wavelet transform with the density-based clustering property of DBSCAN. This approach effectively eliminates noise and outliers from complex wind power SCADA datasets. WDBSCAN leverages multi-scale features extracted via wavelet decomposition to enhance adaptability to non-stationary signals.
• An approach combining Boomerang Evolutionary Optimization (BAEO) with the Seasonal Decomposition Improved Process (SDIP) is developed to achieve synergistic enhancement of trend decomposition and model parameter tuning. SDIP decomposes time series data into trend, seasonal, and residual components to generate a diverse set of candidate solutions.
• A Bidirectional Gated Recurrent Unit (BiGRU) network is proposed with an attention mechanism to improve the accuracy of reactive power forecasting in WFs. The BiGRU architecture captures long-term dependencies in temporal wind power data by modeling both forward and backward time sequences. The attention mechanism further improves prediction performance by dynamically focusing on key features. This combination enables the model to extract more informative representations from complex SCADA data, leading to enhanced forecasting precision.

The rest of the paper is organized as follows. Section 2 gives an overview of the proposed WBS-BiGRU. Section 3 describes the WDBSCAN model. Section 4 describes the Bi-GRU-based model; simulation results are presented and discussed in Section 5, followed by conclusions.

2. Materials and Methods

In this section, a WBS-BiGRU is proposed to achieve the reactive power optimization dispatch in WFs. The flowchart of the proposed WBS-BiGRU is shown in Figure 1. Firstly, the WF data $\left[w_g,F_t,T_s,P_w,Q_w,w_s,T_g\right]$, are optimized by the WDBSCAN algorithm to enhance the data quality, combining wavelet transform and DBSCAN to remove noise and outliers, enhancing data quality. Second, BAEO-SDIP optimizes reactive power outputs of WT groups. SDIP decomposes data into trend, seasonal, and residual components, while BAEO tunes control parameters. Finally, a BiGRU-Attention model predicts reactive power, capturing temporal dependencies and focusing on key features for accurate dispatch. WBS-BiGRU ensures efficient reactive power optimization and grid stability.

2.1. Modeling of WT and Noise Analysis

The state space of the WT can be expressed as

$$\left\{\begin{array}{l}\dot{x}\left(t\right)=f_s\left(x\left(t\right),u\left(t\right),z\left(t\right)\right)+\omega \left(t\right)\\ y\left(t\right)=g_s\left(x\left(t\right),u\left(t\right),z\left(t\right)\right)+v\left(t\right)\end{array}\right.$$

(1)

with

$$A_x=\left[\begin{array}{ccccccc}{a}_1& 0& 0& 0& 0& a_2& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& c_1& 0& 0& 0& 0\\ 0& d_1& 0& d_2& 0& 0& 0\\ 0& 0& 0& 0& 0& e_1& 0\\ f_1& 0& 0& 0& 0& 0& 0\\ 0& g_1& 0& 0& 0& 0& g_2\end{array}\right],\hspace{1em}{A}_u=\left[\begin{array}{c}0\\ 0\\ 0\\ 0\\ e_2\\ 0\\ 0\end{array}\right],\hspace{1em}{A}_z=\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& b_3\\ 0& c_3& 0\\ 0& 0& 0\\ e_3& 0& 0\\ 0& 0& f_3\\ 0& 0& 0\end{array}\right]$$

(2)

$$f_{nl}\left(x\left(t\right),u\left(t\right),z\left(t\right)\right)={\left[{a_3{I}_t\left(t\right)w_g\left(t\right)}^2,{b_1{w}_s\left(t\right)}^3+b_2{\theta }_p\left(t\right)P_w\left(t\right),c_2{\theta }_p\left(t\right)P_w\left(t\right),d_3{F}_t{\left(t\right)}^2,0,f_2{I}_t\left(t\right)w_s\left(t\right),0\right]}^T$$

(3)

$$C_x=\left[\mathrm{0,0},c_1,\mathrm{0,0},\mathrm{0,0}\right],C_u=\left[c_2{P}_w\left(t\right)\right],C_z=\left[0,c_3,0\right]$$

(4)

The above state space equation can be linearized in the operating point $\left(x_0,u_0\right)$, where it corresponds to the steady-state values of the WT. The linearization by Taylor expansion can be expressed as

$$\mathrm{St} \mathrm{It} \left\{\begin{array}{l}{f}_s\left(x,u,z\right)\approx f_s\left(x_0,u_0,z_0\right)+A∆x+B∆u+E\Delta z+R_2^{f_s}(x,u,z)\\ g_s\left(x,u,z\right)\approx g_s\left(x_0,u_0,z_0\right)+C∆x+D∆u+F\Delta z+R_2^{g_s}(x,u,z)\end{array}\right.$$

(5)

with

$$A=A_x+{\displaystyle \frac{\partial f_{nl}}{\partial x}}{|}_{\left(x_0,u_0,z_0\right)},B={\displaystyle \frac{\partial f_s}{\partial u}}{|}_{(x_0,u_0,z_0)},E={\displaystyle \frac{\partial g_s}{\partial z}}{|}_{(x_0,u_0,z_0)}$$

(6)

$$C=C_x,D=c_2{P}_w\left(t_0\right),F=C_z$$

(7)

$${\displaystyle \frac{\partial f_{\mathrm{n}\mathrm{l}}}{\partial x}}=\left[\begin{array}{ccccccc}2a_3{I}_t(t_0)w_g(t_0)& 0& 0& 0& 0& 0& 0\\ 0& b_2{\theta }_p(t_0)& 0& 0& 0& 3b_1{w}_s{(t_0)}^2& 0\\ 0& c_2{\theta }_p(t_0)& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 2d_3{F}_t(t_0)& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& f_2{I}_t(t_0)& 0\\ 0& 0& 0& 0& 0& 0& 0\end{array}\right]$$

(8)

$$R_2^{f_s}=\left[\begin{array}{c}{a}_3{I}_t(t_0)\Delta x_1^2+a_3{w}_g(t_0)\Delta x_1\Delta z_1\\ {\displaystyle \frac{1}{2}}{b}_2\Delta x_2\Delta u\\ {\displaystyle \frac{1}{2}}{c}_2\Delta x_3\Delta u\\ d_3\Delta x_5^2\\ 0\\ 3b_1{w}_s(t_0)\Delta x_6^2+{\displaystyle \frac{1}{2}}{f}_2\Delta x_6\Delta z_1\\ 0\end{array}\right],\hspace{1em}{R}_2^{g_s}={\displaystyle \frac{1}{2}}{c}_2\Delta x_2\Delta u$$

(9)

The linearization error is

$$\left\{\begin{array}{l}{e}_{\dot{x}}=f_s\left(x,u,z\right)-f_s\left(x_0,u_0,z_0\right)-A∆x-B∆u-E\Delta z-R_2^{f_s}\left(x,u,z\right)\\ e_y=g_s\left(x,u,z\right)-g_s\left(x_0,u_0,z_0\right)-C∆x-D∆u-F\Delta z-R_2^{g_s}\left(x,u,z\right)\end{array}\right.$$

(10)

As the system deviates further from the nominal operating point, these errors increase exponentially, leading to reduced prediction accuracy and degraded control performance. Therefore, improving data quality is essential to maintain the effectiveness of data-driven approaches.

2.2. WDBSCAN

To achieve reactive power optimization in WFs, the proposed methodology integrates WDBSCAN data cleaning. The WDBSCAN process cleans with the Biomedically Informed Adaptive Evolutionary Optimization with the BAEO-SDIP model and the multi-dimensional SCADA data, denoted as $x\left(t\right).$ The cleaned data $x^c$ (t) is then fed into the BAEO-SDIP model to optimize the reactive power $Q_{\mathrm{W}}\left(t\right)$. This section details the mathematical formulation of this integrated process.

As shown in Figure 2, F1 (Wavelet Coefficients after Denoising) and F2 (Clustered Feature Space), with noise/outliers marked in red and clusters in blue/green

$$W_{x_i}\left(j,k\right)={\sum }_t{x}_i\left(t\right){\psi }_{j,k}\left(t\right)$$

(11)

where ${\psi }_{j,k}\left(t\right)=2^{-j/2}\psi {(2}^{-j}t-k)$ is the wavelet basis function, $\psi \left(t\right)$ is the mother wavelet, $j$ is the scale, and $k$ is the time shift. The signal is reconstructed using denoised coefficients:

$$x_i^c(\mathrm{t})={\sum }_k{c}_{J,k}{\varphi }_{J,k}\left(t\right)+{\sum }_{j=1}^J{\sum }_k{d}_{j,k}{\psi }_{j,k}\left(t\right)$$

(12)

where ${\varphi }_{J,k}\left(t\right)$ is the scaling function, $c_{J,k}$ are approximation coefficients, $d_{j,k}$ are denoised detail coefficients, and $J=⌊{\log }_{2}N⌋$ is the maximum decomposition level for N time steps. Denoising is performed via soft thresholding as

$$d_{j,k}=\left\{\begin{array}{l}sign\left(d_{j,k}^{\left(m\right)}\right)·\left(\left|d_{j,k}^{\left(m\right)}\right|-{\lambda }_j\right), if \left|d_{j,k}\right|>{\lambda }_j\\ 0,else\end{array}\right.,{\lambda }_j={\sigma }_j\sqrt{2lnN}$$

(13)

where ${\sigma }_j$ is the robust standard deviation estimate. The denoised data is standardized to eliminate scale differences:

$$x^{std}={\left[x_1^{std},\cdots ,x_i^{std}\right]}^T,x_i^{std}\left(t\right)={\displaystyle \frac{x_i\left(t\right)-{\mu }_i}{{\sigma }_i}}$$

(14)

where ${\mu }_i={\displaystyle \frac{1}{N}}{\sum }_t{x}_i^c\left(t\right)$ and ${\sigma }_i=\sqrt{{{\displaystyle \frac{1}{N}}{\sum }_t(x_i^c\left(t\right)-{\mu }_i)}^2}$. DBSCAN then identifies clusters using the neighborhood definition as

$$N_{ϵ}\left(x^{std}\left(t_i\right)\right)=\left\{x^{std}\left(t_j\right)|{‖x^{std}\left(t_i\right)-x^{std}\left(t_j\right)‖}_2\le ϵ\right\}$$

(15)

where ${‖·‖}_2$ is the Euclidean distance, and ϵ is chosen based on k-nearest neighbor distances. The output data of WDBSCAN is

$$x^c={\left[x_1^c,\cdots ,x_i^c\right]}^T$$

(16)

2.3. BAEO-SDIP

The BAEO-SDIP model processes the cleaned data $x^c\left(t\right)$ to decompose each dimension into trend, seasonal, and residual components, generating features suitable for subsequent control. As shown in Figure 3, the process leverages a stochastic differential equation (SDE) framework optimized by a biomedically informed adaptive evolutionary algorithm (BAEO).

2.3.1. Stochastic Differential Model for Decomposition

For each dimension $x_i^c\left(t\right)$, the dynamics are modeled using an SDE,

$$d{x}_i^c\left(t\right)=\left[{\mu }_i^{trend}\left(t;{\theta }_i\right)+{\mu }_i^{seanonal}\left(t;{\theta }_i\right)\right]dt+{\sigma }_i\left(x^c\left(t\right);{\theta }_i\right)dW\left(t\right)$$

(17)

where ${\mu }_i^{trend}\left(t;{\theta }_i\right)$ represents the long-term trend, ${\mu }_i^{seanonal}\left(t;{\theta }_i\right)$ captures periodic components, ${\sigma }_i\left(x^c\left(t\right);{\theta }_i\right)=\sqrt{k_{v_i}{w_s^c\left(t\right)}^2}$ models residual stochasticity, and $W\left(t\right)$ is a Wiener process. The trend and seasonal terms are parameterized as

$$\left\{\begin{array}{l}{\mu }_i^{trend}\left(t;{\theta }_i\right)=a_i\left(t\right)+b_i\\ {\mu }_i^{seanonal}\left(t;{\theta }_i\right)={\sum }_m^M\left[c_{i,m}\mathrm{s}\mathrm{i}\mathrm{n}\left({\displaystyle \frac{2\pi mt}{T_{seasonal}}}\right)+d_{i,m}\mathrm{c}\mathrm{o}\mathrm{s}\left({\displaystyle \frac{2\pi mt}{T_{seasonal}}}\right)\right]\end{array}\right.$$

(18)

where $T_{seasonal}$ is the seasonal period, and $M$ is the number of harmonic components.

2.3.2. BAEO

BAEO optimizes the parameters ${\theta }_i$ for each dimension by minimizing the decomposition error,

$$J\left({\theta }_i\right)={\displaystyle \frac{1}{N}}{\sum }_{t\in T}{\left(x_i^c\left(t\right)-\left[{\mu }_i^{trend}\left(t;{\theta }_i\right)+{\mu }_i^{seanonal}\left(t;{\theta }_i\right)\right]\right)}^2$$

(19)

where T is the set of time steps in $x^c\left(t\right)$. A population $\mathsf{\Theta }=\left\{{\theta }_{i,1},\cdots ,{\theta }_{i,P}\right\}$ is initialized, with $P$ individuals. Evolution proceeds via selection, crossover, and adaptive mutation as

$$\left\{\begin{array}{l}{\theta }_{i,child}=\alpha {\theta }_{i,j}+\left(1-\alpha \right){\theta }_{i,k}\\ {\theta }_{i,j}^{\prime }={\theta }_{i,j}+\eta \left(t_{gen}\right)N\left(0,{\sigma }_{mut}^2\right)\end{array}\right.$$

(20)

where $\alpha ~U\left(\mathrm{0,1}\right)$, $\eta \left(t_{gen}\right)={\eta }_0{e}^{-\beta t_{gen}}$, and ${\sigma }_{mut}={\sigma }_0·{\displaystyle \frac{Var\left(\mathsf{\Theta }\right)}{{Var}_0}}$. The optimal parameters are

$${\theta }_i^{\mathrm{*}}=\mathrm{a}\mathrm{r}\mathrm{g} \underset{{\theta }_{i,j}\in \mathsf{\Theta }}{\min }J\left({\theta }_i\right)$$

(21)

The decomposed components are extracted as

$$\left\{\begin{array}{l}{x}_i^{trend}\left(t\right)={\mu }_i^{trend}\left(t;{\theta }_i^{\mathrm{*}}\right)\\ x_i^{seasonal}\left(t\right)={\mu }_i^{seasonal}\left(t;{\theta }_i^{\mathrm{*}}\right)\\ x_i^{residual}\left(t\right)=x_i^c\left(t\right)-x_i^{trend}\left(t\right)-x_i^{seasonal}\left(t\right)\end{array}\right.$$

(22)

The feature matrix is constructed as

$$M_F={\left[x_1^{trend}\left(t\right),x_1^{seasonal}\left(t\right),x_1^{residual}\left(t\right),\cdots ,x_1^{trend}\left(t\right),x_i^{seasonal}\left(t\right),x_i^{residual}\left(t\right)\right]}^T$$

(23)

augmented with control input $u\left(t\right)=\left[{\theta }_p\left(t\right)\right]$ and disturbance $z\left(t\right)=\left[I_t\left(t\right),{\varphi }_{\omega }\left(t\right),W_e\left(t\right)\right]$,

$$M_{F,aug}\left(\mathrm{t}\right)={\left[{M_F\left(t\right)}^T,{\theta }_p\left(t\right),I_t\left(t\right),{\varphi }_{\omega }\left(t\right),W_e\left(t\right)\right]}^T$$

(24)

2.4. BiGRU-Attention

The augmented feature matrix $M_{F,aug}\left(\mathrm{t}\right)$ is processed by an Attention Network to weigh the importance of each feature across time steps, enhancing the capture of temporal dependencies for BiGRU input.

For a sequence of feature vectors $\left\{M_{F,aug}\left(t-\tau +1\right),\cdots ,M_{F,aug}\left(t\right)\right\}$ over a time window of length τ, the attention mechanism computes a context vector. Each feature vector is first transformed through a fully connected layer,

$${\iota }_t=tanh\left(W_{\iota }{M}_{F,aug}\left(t\right)+b_{\iota }\right)$$

(25)

Attention weights are computed as

$$\left\{\begin{array}{l}{\alpha }_t^w={\displaystyle \frac{\exp \left(u_t^T{u}_w\right)}{{\sum }_{s=t-\tau +1}^{t}exp\left(u_s^T{u}_w\right)}}\\ u_t=W_u{\iota }_t+b_u\end{array}\right.$$

(26)

where $W_u$, $b_u$, $u_w$ is a learnable context vector, and ${\alpha }_t^w$ represents the attention weight for time $t$. The context vector is

$$c_t={\sum }_{s=t-\tau +1}^t{\alpha }_s^w{M}_{F,aug}\left(s\right)$$

(27)

The attention-weighted output is $\left[c_t,M_{F,aug}\left(t\right)\right]$, combining the context vector and current features to capture both historical and current information. The attention-weighted output is fed into a BiGRU to model temporal dependencies and predict reactive power $Q_w\left(t+∆t\right)$. The BiGRU processes the sequence $\widehat{x}=\left\{\left[c_{t-\tau +1},M_{F,aug}\left(t-\tau +1\right),\cdots ,c_t,M_{F,aug}\left(t\right)\right]\right\}$; the process of the bidirectional GRU can be expressed as,

$$\left\{\begin{array}{l}{z}_t=\sigma \left(W_z{\widehat{x}}_t+U_z{h}_{t-1}+b_z\right)\\ r_t=\sigma \left(W_r{\widehat{x}}_t+U_r{h}_{t-1}+b_r\right)\\ {\tilde{h}}_t=\tanh \left(W_h{x}_t+U_h\left(r_t⨀h_{t-1}\right)+b_h\right)\\ h_t^{\to }=\left(1-z_t\right)⨀h_{t-1}^{\to }+z_t{\tilde{h}}_t\end{array}\right.$$

(28)

The output $h_t=\left[h_t^{\to },h_t^{\leftarrow }\right]$, and the final prediction is obtained via a fully connected layer: ${\widehat{Q}}_w\left(t+\Delta t\right)=W_o{h}_t$. The BiGRU is trained to minimize the mean squared error, and the loss is

$$\mathcal{L}={\displaystyle \frac{1}{N_{train}}}{\sum }_{t\in T_{train}}{\left(Q_w^c\left(t+∆t\right)-{\widehat{Q}}_w\left(t+∆t\right)\right)}^2$$

(29)

The parameters are optimized via AdamW using backpropagation. The structure of BiGRU-Attention is demonstrated in Figure 4.

3. Results

3.1. Test System

To validate the effectiveness of the WDBSCAN method in data denoising, a 500s simulation test was conducted on a WF comprising 10 × 5 MW WTs. The results demonstrated that WDBSCAN significantly improved data quality by effectively reducing noise in the WF data. Furthermore, to evaluate the performance of the WBS-BIGRU in active power fluctuation suppression and voltage fluctuation suppression, corresponding simulation tests were performed. The results confirmed that the WBS-BIGRU provides excellent control performance, effectively stabilizing the WFs’ reactive power output. The simulation and method parameters are in

Table 1. Simulation and method parameters.

	Parameter	Value/Description	Unit/Notes
Grid Configuration	Wind Farm Scale	10 × 5 MW	Total of 50 MW, DFIG-type turbines
	Connection Voltage Level	0.69 kV/35 kV	Turbine–transformer–collector line
	Line Impedance	R = 0.092 Ω/km, X = 0.47 Ω/km	Based on simplified IEEE 33-bus
	Load Power Factor	0.85	Simulated grid load
Data Sampling and Simulation	Simulation Duration	500 s	Total steps: 500 (real-time constraint: computation cycle < 1 s)
	Sampling Rate	1 Hz	SCADA data acquisition frequency
	Time Window Length	24	For BiGRU input feature matrix
SCADA Noise Characteristics	Noise Type	Gaussian white noise	Simulates sensor/transmission errors
	Noise Standard Deviation	0.02	Applied to wind speed/power (SNR ≈ 20 dB)
	Outlier Proportion	5%	Randomly injected for WDBSCAN testing
MPC Parameters	Prediction Horizon	10	Steps
	Control Horizon	3	Steps
	Weight Matrices	Q = 1, R = 0.1	State/control weights [26]
	Constraint Bounds	Q ∈ [−0.5, 0.5] pu	Reactive power limits
PD Parameters	Proportional Gain	0.8	/
	Derivative Gain	0.2	Time constant: 0.1 s
PSO Parameters	Number of Particles	30	/
	Inertia Weight	0.9 → 0.4 (linear decay)	Over 50 iterations
	Acceleration Coefficients	2.0, 2.0	Global/local best
GA Parameters	Population Size	50	/
	Crossover Rate	0.8	Single-point crossover
	Mutation Rate	0.01	Over 100 iterations
General Optimization Parameters	Max Iterations	200	For BAEO/PSO/GA
	Convergence Threshold	1.00 × 10−4	Objective: MSE

.

3.2. Data Cleaning

To demonstrate the superiority of the proposed WDBSCAN in data cleaning in reactive power, $w_g$, and $T_g$, a 500 s simulation was performed to denoise the reactive power, $w_g$, and $T_g$ of the WFs. In this simulation, the proposed WDBSCAN is compared with the model predictive control method (MPC) [26]. The 3D visualization of reactive power, $w_g$, and $T_g$ is shown in

Table 2. Relevant data in WFs.

	Reactive power (Var)		Wg (rad/s)		Tg (N·m)
Methods	WDBSCAN	MPC	WDBSCAN	MPC	WDBSCAN	MPC
WT1	4.861 × 105	5.291 × 105	1.207 × 102	1.206 × 102	1.980 × 104	1.983 × 104
WT2	4.835 × 105	5.272 × 105	1.310 × 102	1.308 × 102	1.853 × 104	1.858 × 104
WT3	4.817 × 105	5.243 × 105	1.265 × 102	1.264 × 102	1.903 × 104	1.906 × 104
WT4	4.788 × 105	5.225 × 105	1.211 × 102	1.310 × 102	1.998 × 104	2.300 × 104
WT5	4.861 × 105	5.303 × 105	1.296 × 102	1.295 × 102	1.869 × 104	1.874 × 104
WT6	4.865 × 105	5.291 × 105	1.377 × 102	1.375 × 102	1.730 × 104	1.732 × 104
WT7	4.836 × 105	5.266 × 105	1.291 × 102	1.290 × 102	1.890 × 104	1.894 × 104
WT8	4.814 × 105	5.248 × 105	1.425 × 102	1.423 × 102	1.657 × 104	1.657 × 104
WT9	4.647 × 105	5.063 × 105	1.348 × 102	1.346 × 102	1.830 × 104	1.835 × 104
WT10	4.640 × 105	5.053 × 105	1.287 × 102	1.286 × 102	1.868 × 104	1.872 × 104
Sum	4.796 × 106	5.226 × 106	1.302 × 103	1.408 × 103	1.858 × 105	2.161 × 105
Percentage	−8.22%	/	−7.53%	/	−14.02%	/

.

Figure 5 presents a 3D visualization of the key performance indicators, reactive power, Wg, and Tg, for the proposed WDBSCAN method and the conventional MPC method. As demonstrated in Figure 5, the WDBSCAN points are clustered in a lower-value region for reactive power and torque compared to MPC, indicating smoother and more efficient operation. For instance, the WDBSCAN cluster centers around reactive power values of approximately 4.8 × 10⁵ Var, generator speeds of 1.3 × 10² rad/s, and generator torque of 1.8 × 10⁴ N·m, while MPC points are shifted to higher values (around 5.2 × 10⁵ Var, 1.4 × 10² rad/s, and 2.1 × 10⁵ N·m). This shift demonstrates WDBSCAN’s ability to minimize reactive power consumption and torque stress, reducing the overall system load by 8.22% in reactive power, 7.53% in rotor speed, and 14.02% in torque, as quantified in the table sums. The tighter clustering of WDBSCAN points, which is a smaller spread in all dimensions, reflects consistent performance across WTs, with reduced variability due to effective noise removal and outlier detection. In contrast, MPC points exhibit greater dispersion, particularly in generator torque, suggesting sensitivity to data noise and non-stationarities in SCADA inputs. The 3D separation between the two clusters underscores WDBSCAN’s superiority in handling nonlinear dynamics and noise, leading to lower energy losses and improved grid stability.

As seen in Table 1, WDBSCAN consistently outperforms MPC across all metrics, highlighting WDBSCAN’s ability to optimize torque distribution under fluctuating conditions. WDBSCAN’s superiority stems from its hybrid wavelet-DBSCAN approach, which effectively removes noise and outliers, providing cleaner input for optimization compared to MPC, which relies on raw data and suffers from linearization errors and computational overhead. By leveraging multi-scale wavelet decomposition, WDBSCAN adapts to non-stationary signals like wind speed variations, leading to more accurate parameter estimates and reduced system stress.

3.3. Control Performance

Figure 6 compares the convergence of BAEO-SDIP, Standard BAEO, PSO, and GA. BAEO-SDIP achieves the lowest terminal error (2.559943 × 10⁻¹), slightly outperforming Standard BAEO and PSO, and substantially surpassing GA. In the early stage (1–50 iterations), both BAEO variants converge rapidly, with BAEO-SDIP reducing the error by 85.63%. Although Standard BAEO shows a marginally faster transient, BAEO-SDIP overtakes from iteration 100 onward and continues to refine stably, with minimal oscillation. PSO requires larger mid-stage corrections, while GA exhibits persistently higher errors. The 3D search trajectories corroborate these findings: BAEO-SDIP follows a compact and monotonic path to the low-MSE region, indicating effective exploration–exploitation balance; Standard BAEO requires longer refinement; PSO shows broader excursions; and GA remains distant from the optimum.

Figure 7 illustrates reactive power regulation for WT 1 to WT 10 under proposed, BiGRU, and PD methods.

Figure 7 illustrates the spatial–temporal distributions of reactive power under WBS-BiGRU, plain BiGRU, and PD control. The proposed method maintains a narrow amplitude band which is around 0.41 to 0.47 MVar with smooth gradients along both turbine and time axes, effectively suppressing abrupt steps. BiGRU reduces some fluctuations but exhibits striping and mild chattering, while PD spans the widest range, which is around 0.36 to 0.50 MVar with frequent step changes, indicating weak ramp-rate regulation. In spatial terms, WBS-BiGRU preserves small cross-sectional gradients, reflecting coordinated VAR sharing, whereas BiGRU shows periodic non-uniformity and PD exhibits discontinuities across turbines. Temporally, WBS-BiGRU achieves monotone adjustments with minimal overshoot, while BiGRU oscillates during ramps and PD amplifies noise with frequent corrections.

As shown in Figure 8, WBS-BiGRU exhibits the lowest ripple and smallest overshoot across all WTs, rapidly tracking profile changes without undershoot. In contrast, PD produces repeated multi-peak corrections and BiGRU shows mild lag. The WBS-BiGRU further demonstrates highly consistent responses across turbines, indicating robustness against noise and parameter dispersion, while PD traces vary considerably in amplitude and settling pattern. Moreover, the control performance of DDPG is overall inferior to BiGRU, mainly due to the high difficulty of convergence and its strong dependence on noise during training.

This paper presents a comprehensive evaluation of the performance of the methods, which employs the evaluation index. The selection of the specific index is motivated by the necessity to provide a robust quantitative assessment of the noise suppression of the collected data, thereby enabling a comprehensive evaluation of the predictive capability of the investigated method. The index is standard deviation (SD), as follows:

$$\mathrm{SD}=\sqrt{{\displaystyle \frac{1}{n-1}}{\sum }_{i=1}^n{\left|s_i-{\widehat{s}}_i\right|}^2}$$

(30)

where $s_i$ denotes measured value, $\stackrel{-}{s}$ denotes average value of measured values, and ${\widehat{s}}_i$ denotes the output of the evaluated method.

To statistically validate the reductions in reactive power SD achieved by WBS-BiGRU, we conducted paired t-tests against each baseline method.

For the paired t-test, let $X=\left[x_1,\cdots ,x_n\right]$, and $Y=\left[y_1,\cdots ,y_n\right]$ denote the SD samples from WBS-BiGRU and a baseline, respectively. Define the difference $d_i=x_i-y_i$ for $i=1,\cdots ,n$ with mean $\overline{d}$ and standard deviation $s_d$,

$$\overline{d}={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{d}_i,s_d=\sqrt{{\displaystyle \frac{1}{n-1}}{\sum }_{i=1}^n{\left(d_i-\overline{d}\right)}^2}$$

(31)

The t-statistic is then computed as

$$t={\displaystyle \frac{\overline{d}}{s_d/\sqrt{n}}},d_f=n=1$$

(32)

and the two-tailed p-value is

$$p=2·P\left(T_{df}\ge \left|t\right|\right)$$

(33)

where $T_{df}$ denotes the student’s t-distribution with df degrees of freedom. For independent baselines with potentially unequal variances, the Welch t-test is applied as

$$t={\displaystyle \frac{\overline{x}-\overline{y}}{\sqrt{\frac{s_x^2}{n_x}+\frac{s_y^2}{n_y}}}},d_f={\displaystyle \frac{{\left(\frac{s_x^2}{n_x}+\frac{s_y^2}{n_y}\right)}^2}{\frac{{\left(s_x^2/n_x\right)}^2}{n_x-1}+\frac{{\left(s_y^2/n_y\right)}^2}{n_y-1}}}$$

(34)

The p-value is shown in

Table 3. p-value.

Comparison	p-Value
WBS-BiGRU and BiGRU	1.45 × 10−5
WBS-BiGRU and DDPG	3.04 × 10−7
WBS-BiGRU and PD	6.43 × 10−7

.

Figure 9 presents the SD of reactive power outputs across 10 wind turbines for WBS-BiGRU and baseline methods (BiGRU, DDPG, and PD). To statistically validate the observed fluctuation reductions, paired t-tests were conducted for each turbine. The results indicate that WBS-BiGRU achieves significant suppression of reactive power variability compared with all baselines: WBS-BiGRU with BIGRU (p = 1.45 × 10⁻⁵), WBS-BiGRU with DDPG (p = 3.04 × 10⁻⁷), and WBS-BiGRU with PD SCADA (p = 6.43 × 10⁻⁷). These extremely low p-values confirm that the reductions are statistically significant, validating WBS-BiGRU’s robust noise mitigation across all turbines. Notably, the average SD reductions reach 7–10% relative to BiGRU, demonstrating that the integration of WDBSCAN and BiGRU-Attention effectively smooths reactive power fluctuations while preserving key temporal features. The SD of reactive power outputs demonstrates the superiority of the proposed WBS-BiGRU. The Original SCADA signals exhibit the highest variability, often exceeding 0.025 MVar, indicating strong fluctuations and weak ramp-rate compliance. By comparison, BiGRU reduces the SD to approximately 0.0123 to 0.0137 MVar, corresponding to a 45.27–50.56% reduction relative to the baseline. Notably, WBS-BiGRU consistently achieves the lowest SD across all ten turbines, typically in the range of 0.0111 to 0.0129 MVar, yielding an additional 7.09–10.55% improvement over BiGRU and nearly 50.05–55.21% lower variability than the Original. For instance, the SD decreases from 0.0255 to 0.0135 MVar, and further to 0.0121 MVar, and similar gains are observed across all other cases. This consistent reduction highlights the effectiveness of the wavelet-based preprocessing in suppressing noise and enhancing temporal stability. Overall, WBS-BiGRU provides the smoothest reactive power delivery with the lowest ripple, thereby reducing stress on turbines and auxiliary equipment while improving compliance with grid-code ramp-rate constraints.

As shown in Figure 10, the absolute difference analysis further demonstrates the superior performance of WBS-BiGRU in reactive power control. The Original signals exhibit the largest deviations, with values typically above 6700, reflecting substantial fluctuations and poor tracking of setpoints. BiGRU significantly reduces these differences to the range of 1500–1600, achieving an approximate 75.26–78.37% reduction relative to the Original. WBS-BiGRU attains the lowest absolute difference values, generally between 479 and 1270, corresponding to an additional 30.67–60.05% improvement over BiGRU and 85.02% reduction compared with the baseline. For example, WT1 decreases from 6904.5 (PD) to 1513.3 (BiGRU) and further to 941.7 (WBS-BiGRU), while similar trends are observed across all other turbines. These results indicate that WBS-BiGRU provides more accurate reactive power tracking, minimizes deviations from reference values, and ensures enhanced temporal consistency across all units, thereby supporting smoother reactive power delivery and improved compliance with grid-code requirements.

4. Discussion

The results indicate that the proposed WBS-BiGRU framework substantially improves data quality and reactive power stability in wind farms. The noise and outlier reduction achieved by WDBSCAN confirms the hypothesis that hybrid preprocessing methods are better suited to non-stationary SCADA signals. Likewise, the integration of BAEO-SDIP validates the benefit of combining optimization with temporal decomposition for robust parameter tuning, supporting the view that adaptability is essential in fluctuating wind conditions. The attention-based BiGRU further highlights the importance of capturing long-term dependencies for enhanced control performance. These findings extend previous evidence that advanced data-driven approaches can enhance grid reliability and operational efficiency. Future work should address computational complexity and real-time applicability while testing the framework across diverse wind farm and grid environments.

5. Conclusions

This study proposes an integrated method WBS-BiGRU for enhancing data quality and reactive power control in wind farms. The WDBSCAN method combines wavelet transform with density-based clustering to effectively remove noise and outliers from complex SCADA datasets, reducing 14.03% outliers and improving adaptability to non-stationary signals. The BAEO-SDIP approach synergistically integrates evolutionary optimization with seasonal decomposition, enabling more effective parameter tuning and robust exploration of candidate solutions. The BiGRU network with an attention mechanism captures long-term temporal dependencies and emphasizes key features, thereby improving the accuracy of reactive power control. Collectively, the WBS-BiGRU leads to smoother reactive power delivery, reducing 47.35% fluctuation of reactive power. The results confirm that the proposed framework offers a robust and efficient solution for advancing wind farm operational performance and grid reliability.