In this section, considering measurement noise, incomplete recording data, and system damping ratio close to 0, the proposed method is verified in 179-bus system. The simulation model contains 179 buses, 29 generators, and 263 branches including transformers. The rotor motion of each generator is reflected by a classical second-order differential model. The damping parameters of all generators are initially set to 4 and all loads are modeled as a constant load. 28 natural oscillatory modes exist in this system, which range from 0.26~1.88 Hz [
29,
30]. The method has also proved to be effective with the actual event data happened in ISO New England and East China power system.
5.1. Sample Construction and Model Training
The Power System Analysis Toolbox (PSAT) is used to carry out batch simulation of natural oscillations and forced oscillations, and the simulation time is set to 18 s.
Natural oscillations samples are constructed by adjusting damping parameter of different generators and applying three-phase short-circuit faults at different locations.
Table 3 shows the detailed cases description of natural oscillations samples which are created in the modified WECC 179-bus power system. In each case, buses with generators whose damping parameter are modified, are shown in the second column, and the damping parameter of these generators are shown in the third column. ‘NO’ means natural oscillations. In each case of
Table 3, a three-phase short circuit that lasts 0.05 s is applied on fault bus, so samples of natural oscillations can be constructed. A series of samples in one case is obtained by increasing the load level from 95% to 105% rated load gradually, and the load changes 0.5% rated load in each step. For natural oscillations events, damping ratios of power system could be negative, close to zero or positive. The cases where damping ratios are close to zero are difficult to identify the type of LFO, because their waveforms are similar to forced oscillations waveforms. In order to improve identification ability of training model in these conditions, the samples in this special case, need to be included into natural oscillations samples. Based on this, NO8–NO15 are the cases with the damping ratio close to zero.
Forced oscillations samples are constructed by applying periodic disturbances to prime mover torques and excitation system inputs of 29 different generators in the system.
Table 4 shows the details of the disturbances applied to the generators. The amplitude is the ratio of disturbance to the initial output power of generators. For each generator, the disturbances in
Table 4 are applied to torques of prime movers and inputs of excitation systems, and disturbance amplitude step and frequency step are 0.05 and 0.02, respectively. Let the loads vary from 95% to 105% rated load, so the forced oscillations samples are generated by changing the load level when a disturbance is applied to the system.
In order to imitate the obtained PMU data in actual system, measurement noise of which the signal to noise ratio is 50 is applied to both the natural oscillations samples and the forced oscillations samples. Besides, the data sampling frequency is set to 30 Hz, which is widely adopted by the PMUs in actual system [
31,
32]. The apparent power base of the per unit (pu) is 100 MVA and the generator with the greatest active power fluctuation are selected to calculate the feature index sets, in which the sample entropy parameter
m is set to 2, and
r is set to 0.15 times the time series standard deviation. The nearest neighbor parameter
k of ReliefF algorithm is set to 10, and the number of features mRMR selected
q is 5. In order to demonstrate the advantages of ReliefF-mRMR, four methods are used for feature selection, which are ReliefF-mRMR, mRMR, ReilefF, and Pearson correlation coefficient, respectively.
Table 5 shows the features selected by the four methods and the identification accuracy of LFO type by training these features with SVM without parameter optimization. The penalty factor
ct of traditional SVM is set to 1 and the RBF kernel parameter
gt is set to 1.8, 7.3, 28, respectively [
33,
34]. Then the model with highest accuracy is selected. The reason why SVM without parameter optimization is used here is to highlight the advantages of ReliefF-mRMR, and the features selected by this method have better robustness. The number of selected features is set to 5 and 5-fold cross validation is used to verify the accuracy of four feature selection methods. As can be seen from
Table 5, ReliefF-mRMR has the highest accuracy among the four methods, so ReliefF-mRMR is chosen as the feature selection method in this paper. The selected feature subset with ReliefF-mRMR includes kurtosis index of time domain, waveform index of energy function, cross-correlation index, variance of frequency domain, and skewness of frequency domain.
In order to obtain higher accuracy identification model, GA-SVM is adopted to train the training group feature subset. The samples are divided into two groups, and proportions of the test group and training group to the total samples are 85% and 15%, respectively. Set maximum evolution generation to 100 and population to 20. The training model is utilized to identify the LFO type of test group. The accuracy of training model reaches 100%, and the optimized penalty factor
co of SVM is 75.1959 and the optimized RBF kernel parameter
go is 0.014305. The fitness curve is shown in
Figure 3.
5.2. Validation
In this section, the effectiveness of the method is verified for the case that recorded data is incomplete and natural oscillations damping ratio is close to zero.
(a) Recorded data is incomplete
In actual events, the initial period of oscillation may not be recorded which leads to the incompletion of recorded data. Therefore, both the initial period and steady period of LFO wave are tested and the accuracy of the training models are verified.
Batch simulation of two types of oscillations are carried out in the 179-bus system. Typical natural oscillations are shown in
Figure 4 and typical forced oscillations are shown in
Figure 5. The data of 0–8 s is taken as the initial period waveform and the data of 10–18 s is taken as steady period waveform. The oscillations of 0–8 s are termed as ‘initial oscillations’ and the oscillations of 10–18 s are termed as ‘steady oscillations’ in this paper. The reason for this is that the initial period of oscillations contains many components with small time constants, which will attenuate quickly. After these components attenuate, the remained components will sustain for longer time, which are hence considered as the steady oscillations. The training group are trained by SVM without parameter optimization and GA-SVM, respectively. The model accuracy of the LFO type identification models is shown in
Table 6. It can be seen that GA-SVM has a higher identification accuracy for the incomplete recording data.
(b) Damping ratio is close to zero
For the case where natural oscillations damping ratio is close to 0, the waveform (as shown in
Figure 6) is very similar to the forced oscillations. The feature subset of samples containing the natural oscillations which damping ratio is close to 0 is calculated, and then the training model is utilized to identify the oscillation type. By the test, the method successfully identifies that the oscillation in
Figure 6 is natural oscillations.
(c) ISO New England and East China Power Grid
Unlike in small system, the waveforms of LFOs happened in actual large interconnected power systems are often irregular due to the complexity of the power system and the diversity of disturbances. In order to verify the practicability of the proposed method in actual power system, the method is applied to the oscillation data of ISO New England and East China power grid. In addition, to further improve the accuracy of LFO type identification model applied to actual power systems, oscillation data of actual system is also added into the training group to improve the generalization ability of the model.
An actual LFOs event shown in
Figure 7 is used to validate the applicability of the method. The LFOs happened in New England on 17 June 2016 and its type is forced oscillations [
35]. It is a near-resonance condition with a system-wide natural oscillatory mode caused by a large generator. Its peak-to-peak magnitude reaches 27 MW and the frequency is 0.27 Hz.
Figure 7 shows that the waveform is relatively stable between 40 s and 80 s, so this period of oscillating data is chosen as an actual sample. The proposed method is applied to the data and the discriminant result is forced oscillations, which is consistent with the actual situation.
Test cases of natural oscillations and forced oscillations in East China power grid are used to verify the proposed method. A natural oscillations event in East China power grid is shown in
Figure 8, and it is the active power of ZTS generator in Zhejiang Province. These natural oscillation events are caused by a three-phase short circuit lasting 0.04 s at bus ZTS in Zhejiang Province. According to small signal stability analysis in East China power grid, ZTS mainly participates in an oscillation mode that the frequency is 1.55 Hz and the damping ratio is 0.001. Besides, the frequency of the oscillation curve in
Figure 8 at the steady oscillations state is 1.55 Hz by frequency domain analysis. Therefore, it can be considered that this LFO event is caused by the three-phase short circuit inducing the near-zero oscillation mode. After calculating the feature indexes of the waveform and inputting the feature indexes to the LFO identification model, the discriminant result also shows that this is a natural oscillation event, which is consistent with the actual situation.
Another forced oscillation event in East China power grid is adopted to verify the proposed method. The forced oscillation event is caused by a sinusoidal disturbance of 0.70 Hz at SHJ generator in Jiangsu Province, since there is an oscillation mode of 0.70 Hz between Jiangsu and Shanghai. Large oscillations of the HXB generator in Shanghai are induced and
Figure 9 shows the active power waveform of HXB generator. The maximum oscillation amplitude is about 0.18 pu and the frequency is 0.70 Hz. By applying the proposed method to the oscillations data, the LFO type is identified as forced oscillation, which is in accordance with the actual situation.