Localization method of subsynchronous oscillation source based on high-resolution time-frequency distribution image and CNN

0 Introduction

Owing to the increasing penetration rate of renewable energy such as wind power,a power grid with a high proportion of new energy will become the typical form of the power system,and large-scale wind power pooling access has been developed extensively [1].Subsynchronous oscillation,which is a widespread phenomenon in grids connected to wind farms,poses a significant risk to the secure and stable operation of power systems [2-4].The accurate localization of the subsynchronous oscillation source is critical for its suppression in large-scale interconnected power grids.The evolving synchronous phasor measurement unit and broadband measurement technologies [5-7] enable the acquisition of timing response data during subsynchronous oscillation events and provide a solid foundation for subsynchronous oscillation-source localization.

Currently,the methods for localizing oscillation sources are classified into two main categories∶ mechanism-and data-based analysis methods.The transient energy flow method,which is a typical mechanism-based analysis method [8,9],identifies the location of an oscillation source by monitoring the energy propagation path within the power system.However,a conventional thermal power generator serves as a key element in deducing the transient energy flow.This method has been predominantly employed to localize low-frequency oscillations.Owing to the intricate oscillation mechanisms of grid-connected wind power systems,their adaptability remains to be verified.Other localization methodologies include the traveling wave [10],oscillation phase [11],and half-cycle instantaneous power-difference methods [12].Mechanismbased analysis methods can extract criteria for localizing disturbance sources via analytical modeling.However,their effectiveness is limited by assumptions introduced.Considering the fluctuating operating conditions of the power system and the volatility of new energy generation units,simplified conditions may be invalid and thus significantly affect the accuracy of the established criteria.

The wide-area measurement system (WAMS),which is extensively implemented in power systems,enables the data-driven approach for localizing oscillation sources in power systems.Currently,WAMS data are used extensively to analyze oscillation modes in both time and frequency domains via the characterization of the spatial–temporal distributions of oscillations,thereby facilitating the localization of oscillatory sources.The concept of an empirical modal energy flow was proposed in [13],which enabled the extraction of perturbation source features via empirical mode decomposition.In another study [14],the oscillation frequency of a system was determined using the wavelet dissipation energy spectrum,thus realizing the frequency-domain localization of forced oscillation source in the power system.The authors of [15] introduced the extraction of intrinsic mode function components with forced oscillation modes by leveraging adaptive projection intrinsically transformed multivariate empirical mode decomposition for forced oscillation-source localization.Nevertheless,these studies did not consider the stochastic fluctuations of new energy-generation units.The oscillatory modes,which are affected by random wind speeds,do not remain constant during subsynchronous oscillation events,thus resulting in in frequency drift [16,17].Current time-domain mode decomposition and spectral analysis methods overlook the change in nonstationary signals within a time period,thus failing to capture the time-varying characteristics of the oscillation modes.

Machine learning excels in comprehending nonlinear and intricate relationships within voluminous data and rapidly adapts to randomly varying environments.The availability of extensive measurement data offers solutions for oscillation localization.Currently,various machine learning techniques,such as the decision tree (DT) [18],k-nearest neighbor [19],sparse Bayesian learning [20],and integrated learning [21],have been utilized for oscillationsource localization.CNNs,which are mainstream deeplearning models,have been successfully applied to power systems [22,23].A key advantage of the CNN is its ability to leverage convolutional kernels to extract spatial features from data,which is unattainable by other machine-learning techniques.The output of the CNN depends significantly on the selected inputs.Power systems provide time-series data with varying responses.The utilization of multidimensional time-series data requires significant storage,and coupling between response data results in storage wastage and extended training durations.Meanwhile,using onedimensional time series data necessitates a one-dimensional convolutional neural network (1D-CNN).However,a 1D-CNN captures only one-dimensional oscillatory features and thus do not provide the benefits of the convolutional kernel inherent in CNNs.

To address these challenges,we propose a subsynchronous oscillation-source localization method that accounts for the unpredictable volatility of wind turbines.First,we leverage the measured signals from each generation unit port to execute an enhanced short-time Fourier transform (STFT).This process captures the time-varying characteristics of each mode component,thus resulting in a high-resolution time-frequency distribution (TFD) image.Second,we combine the TFD images from each generation unit port to create subsynchronous oscillation feature maps.These maps serve as inputs for the CNN,which is trained using historical data.By transforming 1D data into twodimensional (2D) image using a 2D-CNN,the contrast in the oscillatory measurement data can be augmented,thereby maximizing feature differentiation.Finally,the trained subsynchronous oscillation localization model is applied to realize the online identification of subsynchronous oscillation sources.The effectiveness,accuracy,and training efficiency of the proposed method are verified through examples of simulated forced and natural oscillations using the Power Systems Computer Aided Design (PSCAD/EMTDC)platform.The enhanced STFT can portray the time-varying characteristics of the oscillations at each unit port.Thus,the proposed subsynchronous oscillation-localization method can be adapted to the time-varying nature of the oscillations,which is crucial for the suppression of subsynchronous oscillations.

1 Time-frequency analysis and instantaneous frequency estimation

1.1 STFT

The proposed time-frequency analysis method was enhanced based on the STFT,which is currently the most widely employed method for time-frequency analysis.It offers advantages such as negligible cross-term interference,low processing complexity,and the ability to capture the time-varying characteristics of the measurement data.Therefore,in this study,we used the STFT to initially characterize the time-frequency distribution.The STFT for the measurement data s(t) from the power system is expressed as

where STFT(t,f) is the TFD distribution of the measurement data after an STFT, t the time variable,f the instantaneous frequency variable,τ the integration variable,and gσ(τ) a Gaussian window function of width σ.However,the frequency resolution of the STFT cannot be optimized owing to the limitation of the window size,which results in the presence of pseudo-frequency components with a certain width near the actual instantaneous frequency.In conclusion,to accurately assess the time-varying features of frequency components in the frequency drift phenomenon,precise extraction of instantaneous frequencies based on the STFT is required.

1.2 Estimation of instantaneous frequency

To enhance the frequency resolution of the TFD,we applied a synchronized squeezing transform (SST) to the TFD processed using the STFT.The SST compresses and rearranges the time-frequency spectrum after the STFT within the time-frequency domain,positioning it at the estimated instantaneous frequency.The SST is expressed as

where Tf(t,η) is the TFD after the SST-STFT,f0(t,f ) the instantaneous frequency estimation,and η the instantaneous frequency after the SST-STFT.Precise extraction of the instantaneous frequency is crucial in SST.

The equation for f0(t,f ) in the classical SST is provided in (3).Despite the simplicity of its computation,it cannot effectively separate complex signals with multiple mode components;as such,further resolution improvements are necessitated.

For a signal comprising a single component,the instantaneous frequency manifests as a ridge line of concentrated energy within the TFD.The instantaneous frequency can be determined using ridge detection.The ridge-detection method identifies the instantaneous frequency of the signal by highlighting the maximum value of the frequency slice at each STFT(t,f ) time point and is expressed as follows∶

where IFRD(t) is the instantaneous frequency-estimated ridge obtained via ridge detection;F is the frequency point set of frequency slice,where F∈[ f — Δf,f +Δf ];Δf is the fluctuation range of frequency;and N is the count of sampling points of the measurement data.This method is fully nonparametric and can be adapted to different situations.Thus,it is highly suitable for addressing nonstationary signals created by subsynchronous oscillations.The detailed steps for ridge detection are as follows∶

Step 1∶ Determine the time and frequency (tm,fm)corresponding to the maximum value of |STFT(t,f)|,where m is the number of sequences corresponding to the maximum value.

Step 2∶ Establish the leftward detection frequency fL and the rightward detection frequency fR,both of which are centered at fm.Detect the instantaneous frequency ridges on both sides using (5).

Step 3∶ Use (6) to set the TFD near the instantaneous frequency ridges to zero.

2 High-resolution TFD acquisition

2.1 Enhanced STFT

In a power system,subsynchronous oscillations present multiple oscillatory modal components concurrently.Ridge detection is limited to the extraction of single-component instantaneous frequencies,where only the strongest component is isolated when addressing multicomponent signals.Furthermore,the ridge detection and extraction process is entirely nonparametric and susceptible to noise interference.To separate multicomponent instantaneous frequencies,we integrate intrinsic chirp component decomposition (ICCD) and ridge-path regrouping (RPRG)[24,25].By employing the filtering properties of the ICCD and ridge detection,we can sequentially shield the signal components of the extracted instantaneous frequencies.This approach enables the separation of multicomponent signals.The specific steps of the ICCD are as follows∶

Step 1∶ Calculate the TFD STFT(t,f) of s(t).

Step 2∶ Conduct ridge detection on STFT(t,f) to derive IFRDk(t),where IFRDk denotes the k th component via ridge detection.

Step 3∶ Calculate matrix (Gk)cd,as shown in (7).

where ,c=1,2,…,N — 1,F0 is the frequency resolution of the Fourier series,and L is the order of the Fourier basis.

Step 4∶ Calculate the Fourier coefficients using the regularized least-squares algorithm estimation to obtain the envelope estimation.

where α is the Tikhonov regularization parameter,I the unit matrix,and H the conjugate transpose.Subsequently,calculate the k th reconstruction component as follows∶

Step 5∶ Subtract the reconstructed componentsfrom theoriginal and obtain s=.Increment k by 1 (k=k +1).If k≤num,return to Step 2;otherwise,advance to the next step.Ultimately,we obtain num reconstructed frequency components.

Similarly,RPRG is entirely nonparametric and can be adjusted to accommodate various scenarios.It is superior to classical ridge-extraction methods because it can manage signals with overlapping components and cooperate with ICCD.RPRG involves the following steps∶

Step 1∶ Identify the interval where the reconstructed frequency components intersect.

whereanddenote the start and end of the intersection intervals of the reconstructed frequency components,respectively;Df is the threshold for the reconstructed frequency intersection intervals;anddenotes the i th reconstruction frequency component.

Step 2∶ Number the reconstructed frequency intersection intervals from Step 1,with the i th interval represented as

Here,denotes the set of cross-ridge numbers,and denotes the combination of the starting and ending times of the crossing ridge.

Step 3∶ Calculate the rate of change,denoted as and,for the i th interval in and ,respectively,using (12).

Here,Δt denotes a short time interval.The connectivity matrix CM is defined to measure the matching degree among different ridges within theandintervals.CM is calculated as shown in (13).

where I is the number of crossing ridges in Λ(i).The correct pair of ridge cross-connections (m0,n0) can be obtained by identifying the minimum value in CM as follows∶

The equation above indicates thatin the interval and in the intervalshould be connected in this cross interval because of their similar change rates.Subsequently,perform a linear interpolation between points.Step 4∶ Perform the aforementioned steps iteratively to obtain the instantaneous frequencies of num components.

Combining ICCD and RPRG,allows the multicomponent instantaneous frequency to be accurately extracted from the measurement data of the power system.The subsequent SST yields high-resolution TFDs.The overall flowchart of the enhanced STFT is shown in Fig.1.

Fig.1 Overall flowchart of enhanced STFT

Fig.2 Result based on ridge detection

Fig.3 Extraction of instantaneous frequency of each component

Fig.4 Comparative analysis of different TFD methods

2.2 Simulation example

We validate the effectiveness of the proposed method for high-resolution TFDs via an enhanced STFT using an ideal signal for testing.Specifically,we established a test signal s(t) with three components,as shown in (15).To assess the method’s practical engineering efficacy,a 20 dB Gaussian white noise η(t) was superimposed on the tricomponent signal.The parameters were set as follows∶sampling frequency,1024 Hz;sampling time,1 s,σ value,0.3;and window length,128.

Figure 2 shows the extraction results of the instantaneous frequency components after ridge monitoring.Owing to the overlapping components,ridge detection alone cannot accurately extract each frequency,thus necessitating subsequent steps.Figure 3 illustrates the ability of the proposed method to extract the instantaneous frequency of each component from the measured data using the proposed method.Figure 4 presents a comparative analysis of this method with other TFD methods,i.e.,the STFT,SST,synchroextracting transform (SET),reassignment transform(RS),and local maximum synchrosqueezing transform(LMSST).It reveals the superiority of the proposed method in capturing the instantaneous frequency of each component.The higher frequency resolution and smoother curves at the time-frequency intersection demonstrated by our method offer an effective solution for frequency-overlap issues.

The concept of the Rényi entropy applied to the TFD,which was originally introduced by Williams Brown,can be expressed as shown in (16).

where α is the order of the Rényi entropy Rα and TFD(t,f ) is the TFD.The Rényi entropy is an effective indicator of the convergence degree of the time-frequency spectral energy;a lower Rényi entropy signifies a more converged timefrequency spectral energy and thus better time-frequency analysis results.As shown in Table 1,different timefrequency analysis methods yield different Rényi entropy results.The method proposed herein yielded the minimum Rényi entropy,thus indicating its superior ability in characterizing TFDs.

Table 1 Rényi entropy derived from various TFD methods

3 CNN

3.1 Generation of input images

The enhanced STFT is applied to the active power of the generation unit ports in the power system to obtain high-resolution TFD images.This process transitions the data from 1D time-series arrays to 2D time-frequency spectrograms,which accurately depict the time-frequency distribution attributes of the active power at the generation unit ports.

We assume a power system with M generation units,where each unit comprises an active power-sampling signal denoted as sp,and n represents the number of samples.The active power sampling signal sp generates a TFD matrix TFD p of size (n/2) × n.The expression for TFD p is shown by (17).The elements situated in the i th row and j th column of TFD p are denoted as di, j.

Considering the correlation between the spectral energies of the active power for each generation unit within a system,the matrix D can be utilized to describe the subsynchronous oscillation data across the entire system during a single oscillation as follows∶

where D is the TFD matrix encapsulating the subsynchronous oscillation information of the entire power system,and TFD pi is the TFD matrix of the oscillation measurement data from the i th generation unit.Ultimately,a 302 × 302 pixel image is created,which serves as the subsynchronous oscillation feature map.This image is used as input for the CNN.

3.2 CNN construction

A CNN,which is a type of deep and feedforward neural network,is equipped with convolutional computations that enable it to extract,recognize,and classify image features.In recent years,owing to their superior performance in feature extraction,CNNs have been applied extensively in diverse fields such as image recognition and natural language processing.

A CNN primarily comprises an input layer,a convolutional layer,a pooling layer,and a fully connected layer.In the convolutional layer,a convolution operation is performed using a predetermined kernel size and the input.The output of the convolutional layer is obtained by adding a bias to the result of the convolution operation and applying the activation function.A rectified linear unit(ReLU) function is used as the activation function.The feature-extraction process of the convolutional layer and the ReLU function are expressed as shown in (19).

where Wj,k denotes the output value of the j th feature map in the k th layer of the convolutional neural network,uij,k the convolution kernel between the j th feature map in the k th layer and the i th feature map in the k-1th layer,bj,k the threshold value corresponding to the j th feature map in the bias vector of the k th layer,and Nj the pooling of the input feature maps.

Maximum pooling is employed in the pooling layer,as shown in (20).

where ak denotes the k th pooling surface and aij is a subsection of the output matrix from the preceding convolutional layer.

The number of fully connected layers is aligned with the number of generation units.The output layer incorporates a softmax layer for classification,which guides the network output to more closely resemble the values associated with the sample labels.The output of the softmax layer is expressed as

where al, j denotes the activation value of the j th neuron in the l th layer,zl, j the preactivation output of the j th neuron in the l th layer,and n the total number of neurons in the l th layer.

To mitigate the risk of overfitting,the L2 regularization term is incorporated into the network training cost function J(W,b;x,y),as shown in (22).

where hW,b(x) denotes the output of input sample x after it has been processed through the network,y the actual label value of the sample,λ the control strength,W the weight associated with each layer,and b the bias term.

The CNN structure adopted in this study is based on the LeNet5 framework,which is a widely used model because of its simplicity.The specific framework of the CNN employed is illustrated in Fig.5.A CNN is leveraged to uncover the relationship between the output active power at the generation unit port and the source of subsynchronous oscillation.

Fig.5 CNN framework employed in current study

Fig.6 presents the overall flowchart of the subsynchronous oscillation source-localization method based on high-resolution TFD images and the CNN.The CNN is trained using historical data,which aids the establishment of a subsynchronous oscillation localization model that facilitates the online localization of the subsynchronous oscillation source.

Fig.6 Overall flowchart of subsynchronous oscillation-source localization method

4 Simulation example

4.1 Forced oscillation

4.1.1 Enhanced STFT validity verification

To validate the effectiveness of the proposed highresolution TFD method using the enhanced STFT for actual power systems,we constructed a four-machine,14-node system on the PSCAD/EMTDC platform.We replaced the synchronous unit with a permanent magnetic synchronous generator (PMSG),which served as a subsynchronous oscillator.The system topology is shown in Fig.7,and Table 2 lists the parameters of the PMSG.Considering the frequency drift,we introduced a time-varying sinusoidal disturbance source into the Pref of the grid-side converter(GSC).Its frequency varied between 10 and 25 Hz,and its amplitude ranged from 0.05 to 0.15 p.u.The source was adjusted every 2 s and changed randomly under a uniform distribution.Based on the active power at the port of the forced oscillation source as an example,the variation is as shown in Fig.8.From 2 to 4 s,a subsynchronous oscillation of 13.76 Hz occurred with a disturbance amplitude of 0.0754 p.u.Between 4 to 6 s,the oscillation frequency was 14.61 Hz,with a disturbance amplitude of 0.0648 p.u.Finally,an 18.43 Hz subsynchronous oscillation with a disturbance amplitude of 0.0628 p.u.was observed from 6 to 7 s.

Table 2 Parameters of PMSG

Fig.7 Topology of four-machine,14-node system

Fig.8 Timing diagram showing port active power of forced oscillation source

First,we verified the applicability of the proposed method to power systems.For a realistic evaluation,we added 20 dB Gaussian white noise to the measurement data to simulate actual engineering scenarios.The sampling frequency was set to 400 Hz.Prior to applying the enhanced STFT,we decentered the measurement data to accentuate their oscillatory characteristics.Using the oscillation source port as a reference,we extracted the instantaneous frequencies of the 14 components,as shown in Fig.9.Using these 14 components,we performed an SST.The subsequent time-frequency analysis results are presented in Fig.10 (f).A comparison with Fig.10 shows that our method reduces noise interference in the TFD,thus offering a significant frequency resolution advantage over the standard STFT and other methods.Table 3 further shows that the proposed technique has the lowest Rényi entropy and excellent time-frequency energy convergence.This implies its superior ability to depict the TFD.Consequently,using the enhanced STFT,we can generate the input image required for the CNN.

Table 3 Rényi entropy derived from various TFD methods

Fig.9 Extraction of instantaneous frequency of each component

Fig.10 Comparative analysis of different TFD methods

Fig.11 Accuracy curve with iteration

Fig.12 Loss curve with iteration

Generator units G1,G2,G3,and G4 were designated as the subsynchronous oscillation sources in succession.The samples were constructed from the port measurement data for each unit.The generator number corresponding to the subsynchronous oscillation source was used as a label.Table 4 presents the types of sample labels used in this study.For training and testing,labeled samples were randomly selected in an 8∶2 ratio.

Table 4 Reference for sample labels

4.1.2 CNN simulation analysis

Table 5 lists the structure and parameters of the CNN.In our study,we trained the CNN model using the adaptive dynamic estimation algorithm (Adam) and set the learning rate to 0.001.After 432 iterations,Figs.10 and 11 depict the accuracy curve of the test set and the loss value curve obtained during training.

Table 5 Structure and parameters of CNN

As shown in Figs.11 and 12,the accuracy of the test set surpassed 99% and the loss value diminished to 0.01 by the 241st iteration.Beyond this point,the model achieved full convergence.Both the model’s accuracy and loss value stabilized thereafter,with the accuracy eventually settling at 100% and the loss value approaching 0.These results validated the effectiveness of the proposed method for localizing forced oscillations.

The accuracy of the CNN-based subsynchronous oscillation localization model was validated using a test set.The confusion matrix illustrating the localization accuracy of the training model for all samples is presented in Fig.13.The matrix reveals that the model correctly identified G1 and G4 as subsynchronous oscillation sources with 100% accuracy.However,when G2 functioned as a subsynchronous oscillator,5.13% of the samples mistakenly identified G3 as the oscillator.Similarly,when G3 was the subsynchronous oscillation source,2.63% of the samples incorrectly recognized G4 as the source.Overall,the test set achieved an accuracy of 98.09%.These results confirm that the trained model can effectively and accurately localize forced oscillations in real time.

Fig.13 Confusion matrix for testing data

4.2 Natural oscillation

4.2.1 Generation of feature maps

For illustrative purposes,a three-machine,nine-node system was modeled on the PSCAD/EMTDC platform.The system topology,as depicted in Fig.14,incorporates a PMSG to replace one of the synchronous machines with equal capacity.The PMSG parameters are listed in Table 6.Consequently,the replaced unit was considered a subsynchronous oscillation source.Subsynchronous oscillations were induced in the system by connecting an appropriate reactance to the PMSG port at 10 s.Considering the stochastic volatility of wind farms and the effect of wind speed on the modes of subsynchronous oscillation,the wind-speed fluctuation was configured to span from 9 to 11 m/s in every simulation.The wind speed fluctuations within this range adhered to a uniform distribution,with each fluctuation persisting for 2 s,as shown in Fig.15.Fig.16 shows the timing diagram of the subsynchronous oscillating active power superimposed with 20 dB Gaussian white noise for each turbine port under altered wind speed conditions.Within the 0.5 s time window,spectral analysis reveals that the port active power of G3 oscillated at 11.97 Hz,with an amplitude of 0.107 p.u.from 10.70 to 11.20 s.Subsequently,it oscillated at 10.47 Hz with an amplitude of 0.098 p.u.from 13.00 to 13.50 s.

Table 6 Parameters of PMSG

Fig.14 Topology of three-machine,nine-node system

Fig.15 Wind speed of wind farms considering stochastic volatility

Fig.16 Timing diagram showing active power for each unit port

In this study,we set the data sampling frequency to 400 Hz and captured the active time-series data from each generation unit port within 5 s of the onset of subsynchronous oscillations.The initial steps included the decentering of meteorological data,followed by the application of the enhanced STFT.Using the unit port as a reference,we extracted the instantaneous frequencies of 20 components,as shown in Fig.17.Subsequently,we applied the STFT-based SST to obtain a high-resolution TFD image,as shown in Fig.18.Subsequently,the input image for the CNN was constructed using the high-resolution TFD image,as shown in (18).

Fig.17 Extraction of instantaneous frequency of each component

Fig.18 TFD obtained by enhanced STFT

By adopting the aforementioned procedure,we created samples using the port measurement data of each unit as well as utilizing G1,G2,and G3 generation units as subsynchronous oscillation sources.Subsequently,we utilized the numerical identifier assigned to the subsynchronous oscillation source generator unit for identification.The categorization of the sample labels is presented in Table 7.Training and testing sets were generated by randomly selecting from each labeled sample at an 8∶2 ratio.

Table 7 Reference for sample labels

4.2.2 CNN simulation analysis

Table 5 provides details regarding the structure and parameters of the CNN.In this study,we employed the Adam optimizer to train the CNN model under a learning rate of 0.001.After 432 iterations,the resultant-loss and accuracy curves for the training set obtained during training are as shown in Fig.19 and Fig.20 respectively.

Fig.19 Accuracy vs.iteration

Fig.20 Loss vs.iteration

Figures 19 and 20 show that the training set’s accuracy surpassed 99% with a corresponding decrease in the loss to 0.01 at 275 iterations.The model exhibited complete convergence at this point.Furthermore,both the model’s accuracy and loss value stabilized,with the accuracy stabilizing at 100% and the loss value approaching 0.This demonstrates the efficacy of the proposed method in achieving subsynchronous oscillation localization.

A testing set was employed to validate the accuracy of the CNN-based subsynchronous oscillation localization model.The confusion matrix showing the localization precision of the model for all samples is illustrated in Fig.21.The trained model exhibited 100% accuracy in identifying the units as subsynchronous oscillation sources when G1 and G2 were set as such.When G3 was set as a subsynchronous oscillation source,approximately 3.7% of the outputs indicated that G1 functioned as the subsynchronous oscillation source.Overall,the testing set accuracy was 98.78%,thus further emphasizing the model’s capability for achieving accurate online subsynchronous oscillation localization.

Fig.21 Confusion matrix for testing data

The proposed method was compared with a 1D-CNN and a backpropagation neural network (BPNN),both of which use 1D time-series signals as their model training input.Table 4 presents the comparison results.The CNN was superior to both the 1D-CNN and BPNN in terms of accuracy and offered substantial improvement in terms of training time compared with the BPNN.Although the 1D-CNN benefits from a simpler network structure and shorter training time than the CNN,its accuracy is lower than that of the method proposed herein.This is primarily owing to its 1D data input and limited convolution kernel size,which hinder it from fully utilizing the advantages of CNNs.

Table 8 shows a comparison of the proposed method to the 1D-CNN and BPNN,whose training models receive 1D time-series data as inputs.The results show that the CNN is superior to the 1D-CNN and BPNN in terms of accuracy and that its training time was significantly better than that of the BPNN.Although the 1D-CNN exhibits a simpler network structure that results in shorter training times than the CNN,its input is limited to 1D data.This limitation,coupled with the restricted size of the convolutional kernel,prevents the full exploitation of the CNN’s benefits.Consequently,the accuracy of the 1D-CNN is not comparable to that of the method proposed herein.

Table 8 Comparison of different machine-learning methods

5 Conclusion

Subsynchronous oscillations in wind farms pose significant challenges to the safe and reliable operation of power grids.Timely localization of subsynchronous generation units is crucial for maintaining the stability of power systems.In this study,we proposed a subsynchronous oscillation source-localization method that leverages high-resolution TFD images and a CNN.The primary conclusions of this study are as follows∶

(1) We proposed a method to obtain a high-resolution TFD image by employing an improved STFT.The proposed method can extract the multicomponent instantaneous frequency of the measurement data from a power system,thus accurately reflecting the TFD of the active power at the unit port.Compared with other methods,it demonstrates robust antinoise capabilities,thus rendering it suitable for the measurement data of actual power systems.

(2) The subsynchronous oscillation localization model was established using a CNN,where TFD images were used as inputs to enable the online localization of subsynchronous oscillations.Compared with the 1D-CNN and BPNN,the trained CNN model offers superior accuracy owing to its transformation of 1D data into images,which enables the better preservation of the features of subsynchronous oscillation.

(3) On the PSCAD/EMTDC platform,we constructed a four-machine,14-node forced oscillation scenario and a three-machine,nine-node natural oscillation scenario to obtain measurement data.The efficacy of subsynchronous oscillation source localization was subsequently validated.The online subsynchronous oscillation localization model considered the stochastic fluctuations of wind farms and the noise in practical measurement data.The model was not confined to a particular operating condition of the power system and relied solely on measurable electrical quantities in an actual power system.The proposed method delivered an accuracy exceeding 98% in localizing the source of subsynchronous oscillations in different scenarios,thus facilitating the analysis and suppression of such oscillations.

Acknowledgments

This work was supported by the Science and Technology Project of State Grid Corporation of China (5100-202199536A-0-5-ZN).

Declaration of competing interest

We declare that we have no conflict of interest.