Nowadays, low frequency oscillation has become a major problem threatening the security of largescale interconnected power systems. According to generation mechanism, active power oscillation of electric power systems can be classified into two categories: free oscillation and forced oscillation. The former results from poor or negative damping ratio of power system and external periodic disturbance may lead to the latter. Thus control strategies to suppress the oscillations are totally different. Distinction from each other of those two different kinds of power oscillations becomes a precondition for suppressing the oscillations with proper measures. This paper proposes a practical approach for power oscillation classification by identifying realtime power oscillation curves. Hilbert transform is employed to obtain envelope curves of the power oscillation curves. Twenty sampling points of the envelope curve are selected as the feature matrices to train and test the supporting vector machine (SVM). The tests on the 16machine 68bus benchmark power system and a real power system in China indicate that the proposed oscillation classification method is of high precision.
Damping ratio is a key factor in electric power oscillations. With the interconnection of largescale power grids via high voltage long distance transmission lines, coupling between synchronous generators becomes weaker which leads to poor or negative damping ratio of power systems [
This paper focuses on the active power oscillation property classification problem. According to generation mechanism, active power oscillations of electric systems can be classified into two categories [
The other kind of active power oscillation is forced power oscillation, which is explained by the resonance mechanism [
Thus negative damping oscillation and forced oscillation have different generation mechanisms with different coping measures. It is extremely important and necessary to distinguish them from each other. However, both of them have similar oscillation forms with increasing amplitudes at initial stage and probably develop into a constant amplitude oscillation in the end. Correct and rapid identification of the oscillation property becomes a difficult problem to be solved. Nowadays, researches on power oscillation classification mostly concentrate on simulation after oscillation accidents. System response curves of simulation under negative damping oscillation condition and forced oscillation condition are compared with the actual oscilloscope records of power systems to judge the oscillation property of power oscillation accidents [
Statistical learning theory and support vector machine (SVM) have given a systemic theoretical explanation about pattern recognition under circumstances of finite samples. Many problems, like modelchoosing, overfitting, nonlinear, disaster of dimensionality, and local minimum, which have long hindered the development of machine learning are now solved to a great extent [
This paper proposes a practical approach for power oscillation classification by recognition of realtime power oscillation curves utilizing SVM. Hilbert transform is employed to obtain envelope curves of the power oscillation curves. Twenty sampling points on the envelope curve of power oscillation are selected for feature extraction. Then, forty power oscillation curves are employed as samples to train the supporting vector machine. At last, three tests on the 16machine 68bus benchmark system and a real power system in China indicate that the proposed oscillation classification method possesses good precision.
The rest of this paper is organized as follows. In Section
When a free oscillation happens in a power system, the rotor angle, rotation speed of synchronous generators, and relevant electric variables (such as the power flow of transmission lines and bus voltages) will oscillate accordingly, among which the power flow of transmission line
The oscillation curve of any free oscillation mode can be expressed as
Therefore, when any oscillation mode with
Power oscillation curve of tie line.
Negative damping oscillation
Forced oscillation
For any forced oscillation in the power system with an extreme disturbance like
Solving (
Under the circumstance of
From the analysis above, it can be concluded that the envelope curve of negative damping oscillation increases as
Hilbert transform (HT) [
Namely,
Therefore, the amplitude
The envelope curve of power oscillation will be obtained by HT after the power oscillation in power grid is detected by the wide area measurement system (WAMS). Then the envelope curve is normalized according to the steady value before oscillation happens. Finally, twenty evenly spaced points on the envelope curve are selected in every
Extraction of the elements in the feature matrices.
It is well known that the power oscillation in a power system generally combines various swing modes. If there is only one dominant oscillation mode, the oscillation amplitude of other oscillation modes is small compared with the dominant oscillation mode. The influence of other oscillation modes on dominant oscillation mode can be neglected. If there are two or more than two dominant oscillation modes, the dominant oscillation mode with positive damping ratio will decay after seconds or minutes. Then only the oscillation mode with negative damping ratio retains. Meanwhile, the data used for power oscillation feature extraction contains 40 cycles of the oscillation curve. After several cycles, only the oscillation mode with negative damping ratio will retain and be used for the oscillation property classification.
However, the power oscillation with two negative damping oscillation modes has similar expression with forced power oscillation. The beatfrequency oscillation will also be perceived in the power oscillation with two negative damping oscillation modes. It is hard to distinguish the forced power oscillation and the power oscillation with two negative damping oscillation modes. However, the power oscillation with two negative damping oscillation modes is very unusual in power system; thus the negative damping power oscillation in this paper is the power oscillation with only one negative damping oscillation mode. Under this premise, the feature matrices can represent the power oscillation property of the system.
Difference of adjacent points of the feature matrices denotes the change direction of the envelope curve and the secondorder difference denotes its change tendency. As for negative damping oscillation, the variation rate of the envelope curves is generally positive with oscillation amplitude growing more and more rapidly. This means that the firstorder and secondorder difference of adjacent points from the feature matrices should also be positive. However, for forced oscillations, the envelope curve has minimum and maximum points. This indicates that the firstorder or secondorder difference of adjacent points could be zero or negative. Therefore, the feature matrices obtained in this paper at least contain the oscillation characteristic of the power oscillation which could be utilized for power oscillation property classification. Besides, the feature matrices extraction of power oscillation curves will be the foundation of the following work.
SVMbased classification method is established on the basis of structural risk minimization principle and VC theory (Vapnik and Chervonenkis theory) [
A classification example in a twodimensional space based on SVM [
For the given linear and separable training patterns
If the vector
If the training data in the input space is nonlinear, in order to construct a hyper plane to classify the nonlinear samples, one first has to map the input vector
Consider the case when the training data cannot be classified without error. Penalty constant
The Lagrange function for this problem is
Using the conditions for the minimum of this function at the extreme point
From (
Thus the decision function in (
Substituting the expressions for
The original convex optimization problem is also transformed into a quadratic optimization problem:
Under this circumstance, the optimal Lagrange’s multiplicator
According to (
From (
The input parameters of the kernel function are the training data
linear function:
sigmoid function:
radial basis function:
When power oscillation happens, active power oscillations at substation, tie line, and generator terminal will be detected by WAMS. The oscillation property can be well classified by training historical data with SVM algorithm. Figure
Input historical data and oscillation future extraction. Collect the power oscillation data of the power oscillation incidence that has happened. And then extract the oscillation feature of the power oscillation data by the proposed method in Section
Parameter initialization for the SVM model: Lagrange multiplier
Obtain the optimal parameter of the SVM model. Based on training samples, the objective function of (
Power oscillation incidence detection: judge whether the power oscillation amplitude of the fifth cycle is larger than 50 MW or not for any 500 kV tie line and record the oscillation curve for the oscillation property classification.
Classify the oscillation properties of the power oscillation curves. Classify the property of the power oscillation curves recorded by the WAMS from different buses at the power grid using the trained SVM model in procedure (
Property classification of the oscillation incident: if the quantity of 1 is much more than −1, the oscillation incident is negative damping oscillation. Else if the quantity of −1 is much more than 1, the oscillation incident is forced oscillation.
Flow chart of the oscillation property classification.
The circuit diagram of IEEE16machine 68bus benchmark system is shown in Figure
Testing result of 16machine 68bus benchmark system.
Kernel function  Signal type  

No noise  5% noise  10% noise  
Polynomial kernel function  C1  C2  C1  C2  C1  C2  
C1  72  1  C1  70  3  C1  66  4  
C2  4  43  C2  6  41  C2  10  40  
Precision  95.80%  Precision  92.50%  Precision  88.30%  


RBF kernel function  C1  C2  C1  C2  C1  C2  
C1  74  2  C1  71  2  C1  66  4  
C2  2  42  C2  5  42  C2  10  40  
Precision  96.70%  Precision  94.20%  Precision  88.30%  


Sigmoid kernel function  C1  C2  C1  C2  C1  C2  
C1  75  1  C1  72  1  C1  68  3  
C2  1  43  C2  4  43  C2  8  41  
Precision  98.30%  Precision  95.80%  Precision  90.80% 
Simulation example of IEEE16machine 68bus benchmark system.
Since noise is omnipresent in electrical power system, Gaussian white noise is considered in the classification of power oscillations. Different levels of noises with the noise to signal ratio values ranging from 5% to 10% were considered. As the noise to signal ratio increases, the adaptability of SVM model decreases and the precision of the power oscillation property classification degrades. Table
In 2008, a thermal power plant was asynchronously connected to the Central China Power Grid through 110 kV transmission lines. Power oscillations were observed in Henan, Hunan, and Jiangxi power grids. The whole oscillation duration was about two minutes with 0.7 Hz oscillation frequency at initial stage and then the oscillatory power of the tie line increased gradually. When the oscillation stabilized, the oscillatory frequency of the power grid was 0.62 Hz and the oscillatory amplitude of the active power of tie line between Henan and Hubei was about 250 MW. Subsequently, the 110 kV transmission line in the fault region was cut off and the oscillation died down quickly. This power oscillation incident was classified as a typical forced power oscillation incident and the thermal power plant was the oscillation source [
Identification result of oscilloscope records of forced oscillation incidence.
Oscillation type  C1 
C2 
Identification result 

Number  10  1  C1 
The active power oscilloscope record of YaoShao tie line.
In 2005, a wide area power oscillation took place in Central China Power Grid and the whole oscillation lasted for about five minutes. The power oscillation frequency was about 0.77 Hz. Large power fluctuations were detected at the Three Gorges Hydroelectric Power Plant and its nearby power plants in Douli, Jianglin, Longquan, and Wanxian. Then the operator of the power grid increased the output reactive power of the Three Gorges Hydroelectric Power Plant and decreased the active power output of Huanglongtan Power Plant in northwest Hubei. Subsequently, the oscillation decayed gradually until it died out. The incident was a typical negative damping power oscillation [
Identification result of oscilloscope records of negative damping oscillation incidence.
Oscillation type  C1 
C2 
Identification result 

Number  2  18  C2 
The active power oscilloscope record of the second LongDou tie line.
Active power oscillation in power systems can be classified into two types: negative damping oscillation and forced oscillation. Although their oscillation curves are similar, the adopted suppressing control strategies are totally different. Thus the oscillation property classification is the premise for suppressing the power oscillation. To properly identify the oscillation property, the paper proposed an oscillation property classification method utilizing the SVM. Through the simulation analysis, it can be concluded that the envelope curves of the negative damping oscillation and forced oscillation are different and can be used as the feature for classification. As noise is omnipresent in electrical power system, Gaussian white noise is considered in the research of power oscillation classification. With the increase of the noise to signal ratio, the adaptability of SVM model decreases and the precision of the power oscillation property classification degrades. However, even with the noise to signal ratio reaching up 10%, the precision of the power oscillation property classification is still above 88%. Moreover, two real incidents in the real power systems are used to verify the proposed classification method. Results show that the identified results from the proposed method is the same with the postincident analytical identification result, while the postanalytical identification is an offline time consuming method only applied after the oscillation happens. The proposed method can be applied online and provides guidance for the dispatcher to select the correct suppressing control (the negative damping one or the forced oscillating one) during the oscillation period to stop the propagation of oscillations.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China (nos. 51177057 and 51228701).